FRAGSTATS HELP

FRAGSTATS HELP
FRAGSTATS HELP
21 April 2015
Kevin McGarigal,
Sole proprietor, LandEco Consulting
Professor, Department of Environmental Conservation
University of Massachusetts, Amherst
[email protected]
Table of Contents
WHAT’S NEW IN VERSION 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
BACKGROUND. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
What Is a Landscape?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Classes of Landscape Pattern.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Patch-Corridor-Matrix Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
The Importance of Scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Landscape Context.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Perspectives on Categorical Map Patterns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Scope of Analysis.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Levels of Heterogeneity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Patch-based Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Surface Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Structural Versus Functional Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Limitations in the Use and Interpretation of Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
USER GUIDELINES.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
What is FRAGSTATS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Scale Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Computer Requirements.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Data Formats. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Raster Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Vector to Raster Conversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Levels of Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Output Files. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Nodata, Backgrounds, Borders, and Boundaries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Installation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Running via the Graphical User Interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Step 1. Starting the FRAGSTATS GUI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Step 2. Creating a Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Step 3. Selecting Input Layers.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Step 4. Specifying Common Tables [optional]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Step 5. Setting Analysis Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Step 6. Selecting and Parameterizing Patch, Class, and Landscape Metrics. . . . . . . . . 71
Step 7. Executing FRAGSTATS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Step 8. Browsing and Saving the Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Step 9. Getting Help. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Running via the Command Line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
FRAGSTATS METRICS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
Patch Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Class Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Landscape Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
General Comments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Mean versus area-weighted mean. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Area and Edge Metrics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Shape Metrics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Core Area Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Contrast Metrics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Aggregation Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Diversity Metrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
LITERATURE CITED. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
WHAT’S NEW IN VERSION 4
The major changes in version 4 are as follows:
1. Version 4 is a major internal architectural revision to accommodate several new features,
including a wide variety of sampling methods to facilitate analyzing sub-landscapes (v4.2), cell
metrics (v4.3), and continuous surface metrics (i.e., landscape gradient model)(v4.4).
2. The graphical user interface is entirely new and is described in detail in the user guidelines, but
has the same functionality as version 3.
3. The ancillary tables used to specify the class properties (i.e., class descriptors, which specify a
character description for each numeric class value, whether to output the statistics for each class,
and whether to treat each class as background) and parameterize the functional metrics
associated with core area metrics, contrast metrics, and similarity index have a new table
structure (see user guidelines).
4. The batch file table used to import a batch file (i.e., multiple input landscapes) has a new
argument for the Nodata cell value, and thus the syntax has changed, starting with v4.2.
5. Supported image formats beginning with version 4.1 include: (1) ASCII grid, (2-4) 8-, 16- and
32-bit integer grids, (5) ESRI grid (or raster), (6) GeoTIFF grid, (7) VTP binary terrain format
grid, (8) ESRI header labelled grid, (9) ERDAS Imagine grid, (10) PCRaster grid, and (11) SAGA
GIS binary format grid. Support for the latter six image formats is via the GDAL library.ASCII
grid, 8-, 16- and 32-bit integer grids, ESRI grid (or raster), GeoTIFF grid, VTP binary terrain
format grid, ESRI header labelled grid, ERDAS Imagine grid, PCRaster grid, and SAGA GIS
binary format grid. Support for the latter six image formats is via the GDAL library.
6. The model file (i.e., full parameterization of FRAGSTATS) is saved with the filename extension
.fca instead of .frg. The .fca stands for “fragstats categorical model” and reflects the forthcoming
extensions in version 4.4 and higher to accommodate landscape gradients or continuous surface
patterns which will have a different model structure and be saved with a different extension
(.fco).
7. You can no longer input a unique patch ID grid. We realized too many conflicts with the
user-provided patch ID file not being consistent with the user-specified model; e.g., input
patches defined using a 4-neighbor rule but the model parameterized using an 8-neighbor rule.
For the time being, we removed the option of inputting a patch ID file, but maintained the
option of outputting a patch ID file.
BACKGROUND
Introduction
Landscape ecology, if not ecology in general, is largely founded on the notion that environmental
patterns strongly influence ecological processes (Turner 1989). The habitats in which organisms live,
for example, are spatially structured at a number of scales, and these patterns interact with organism
perception and behavior to drive the higher level processes of population dynamics and community
structure (Johnson et al. 1992). Anthropogenic activities (e.g. development, timber harvest) can
disrupt the structural integrity of landscapes and is expected to impede, or in some cases facilitate,
ecological flows (e.g., movement of organisms) across the landscape (Gardner et al. 1993). A
disruption in landscape patterns may therefore compromise its functional integrity by interfering
with critical ecological processes necessary for population persistence and the maintenance of
biodiversity and ecosystem health (With 2000). For these and other reasons, much emphasis has
been placed on developing methods to quantify landscape patterns, which is considered a
prerequisite to the study of pattern-process relationships (e.g., O'Neill et al. 1988, Turner 1990,
Turner and Gardner 1991, Baker and Cai 1992, McGarigal and Marks 1995). This has resulted in the
development of literally hundreds of indices of landscape patterns. This progress has been facilitated
by recent advances in computer processing and geographic information (GIS) technologies.
Unfortunately, according to Gustafson (1998), “the distinction between what can be mapped and
measured and the patterns that are ecologically relevant to the phenomenon under investigation or
management is sometimes blurred.”
What Is a Landscape?
Landscape ecology by definition deals with the ecology of landscapes. Surprisingly, there are many
different interpretations of the term “landscape.” The disparity in definitions makes it difficult to
communicate clearly, and even more difficult to establish consistent management policies.
Definitions of landscape invariably include an area of land containing a mosaic of patches or
landscape elements (see below). Forman and Godron (1986) defined landscape as a heterogeneous
land area composed of a cluster of interacting ecosystems that is repeated in similar form
throughout. The concept differs from the traditional ecosystem concept in focusing on groups of
ecosystems and the interactions among them. There are many variants of the definition depending
on the research or management context.
For example, from a wildlife perspective, we might define landscape as an area of land containing a
mosaic of habitat patches, often within which a particular "focal" or "target" habitat patch is
embedded (Dunning et al. 1992). Because habitat patches can only be defined relative to a particular
organism's perception and scaling of the environment (Wiens 1976), landscape size would differ
among organisms. However, landscapes generally occupy some spatial scale intermediate between an
organism's normal home range and its regional distribution. In-other-words, because each organism
scales the environment differently (i.e., a salamander and a hawk view their environment on
different scales), there is no absolute size for a landscape; from an organism-centered perspective,
the size of a landscape varies depending on what constitutes a mosaic of habitat or resource patches
meaningful to that particular organism.
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This definition most likely contrasts with the more anthropocentric definition that a landscape
corresponds to an area of land equal to or larger than, say, a large basin (e.g., several thousand
hectares). Indeed, Forman and Godron (1986) suggested a lower limit for landscapes at a "few
kilometers in diameter", although they recognized that most of the principles of landscape ecology
apply to ecological mosaics at any level of scale. While this may be a more pragmatic definition than
the organism-centered definition and perhaps corresponds to our human perception of the
environment, it has limited utility in managing wildlife populations if you accept the fact that each
organism scales the environment differently. From an organism-centered perspective, a landscape
could range in absolute scale from an area smaller than a single forest stand (e.g., a individual log) to
an entire ecoregion. If you accept this organism-centered definition of a landscape, a logical
consequence of this is a mandate to manage habitats across the full range of spatial scales; each
scale, whether it be the stand or watershed, or some other scale, will likely be important for a subset
of species, and each species will likely respond to more than one scale.
Ke y Po in t It is not our intent to argue for a single definition of landscape. Rather, we wish to point out that there
are many appropriate ways to define landscape depending on the phenomenon under consideration. The
important point is that a landscape is not necessarily defined by its size; rather, it is defined by an
interacting mosaic of patches relevant to the phenomenon under consideration (at any scale). It is
incumbent upon the investigator or manager to define landscape in an appropriate manner. The essential
first step in any landscape-level research or management endeavor is to define the landscape, and this is of
course prerequisite to quantifying landscape patterns.
Classes of Landscape Pattern
Real landscapes contain complex spatial patterns in the distribution of resources that vary over time;
quantifying these patterns and their dynamics is the purview of landscape pattern analysis.
Landscape patterns can be quantified in a variety of ways depending on the type of data collected,
the manner in which it is collected, and the objectives of the investigation. Broadly considered,
landscape pattern analysis involves four basic types of spatial data corresponding to different
representations of spatial heterogeneity (or models of landscape structure), although in practice
these fundamental conceptual models of landscape structure are sometimes combined in various
ways. These basic classes of landscape pattern look rather different numerically, but they share a
concern with the characterization of spatial heterogeneity:
(1) Spatial point patterns – Spatial point patterns represent collections of entities where the geographic
locations of the entities are of primary interest, rather than any quantitative or qualitative attribute of
the entity itself. A familiar example is a map of all trees in a forest stand, wherein the data consists of
a list of trees referenced by their geographic locations. Typically, the points would be labeled by
species, and perhaps further specified by their sizes (a marked point pattern). The goal of point
pattern analysis with such data is to determine whether the points are more or less clustered than
expected by chance and/or to find the spatial scale(s) at which the points tend to be more or less
clustered than expected by chance, and a variety of methods have been developed for this purpose
(Greig-Smith 1983, Dale 1999).
(2) Linear network patterns – Linear network patterns represent collections of linear landscape
elements that intersect to form a network. A familiar example is a map of shelterbelts in an
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agricultural landscape, wherein the data consists of nodes (intersections of the linear features) and
segments (linear features that connect nodes); the intervening area is considered the matrix and is
typically ignored (i.e., treated as ecologically neutral). Often, the nodes and segments are further
characterized by composition (e.g., vegetation type) and spatial character (e.g., width). As with point
patterns, it is the geographic location and arrangement of nodes and segments that is of primary
interest. The goal of linear network pattern analysis with such data is to characterize the physical
structure (e.g., network density, mesh size, network connectivity and circuitry) of the network, and a
variety of metrics have been developed for this purpose (Forman 1995).
(3) Surface patterns – Surface patterns represent quantitative measurements that vary continuously
across the landscape (i.e., there are no explicit boundaries between patches). Hence, this type of
spatial pattern is also referred to as a “landscape gradient”. Here, the data can be conceptualized as
representing a three-dimensional surface, where the measured value at each geographic location is
represented by the height of the surface. A familiar example is a digital elevation model, but any
quantitative measurement can be treated this way (e.g., plant biomass, leaf area index, soil nitrogen,
density of individuals). Analysis of the spatial dependencies (or autocorrelation) in the measured
characteristic is the purview of geostatistics, and a variety of techniques exist for measuring the
intensity and scale of this spatial autocorrelation (Legendre and Fortin 1989, Legendre and Legendre
1999). Techniques also exist that permit the kriging or modeling of these spatial patterns; that is, to
interpolate values for unsampled locations using the empirically estimated spatial autocorrelation
(Bailey and Gatrell 1995). These geostatistical techniques were developed to quantify spatial patterns
from sampled data (n). When the data is exhaustive (i.e., the whole population, N) over the study
landscape, like it is with the case of remotely sensed data, other techniques (e.g., quadrat variance
analysis, Dale 1999; spectral analysis, Ford and Renshaw 1984, Renshaw and Ford 1984, Legendre
and Fortin 1989; wavelet analysis, Bradshaw and Spies 1992, Dale and Mah 1998; or lacunarity
analysis, Plotnick et al. 1993 and 1996, Dale 2000) are more appropriate. All of these geostatistical
techniques share a goal of describing the intensity and scale of pattern in the quantitative variable of
interest. In all cases, while the location of the data points (or quadrats) is known and of interest, it is
the values of the measurement taken at each point that are of primary concern. Here, the basic
question is, "Are samples that are close together also similar with respect to the measured variable?”
Alternatively, “What is the distance(s) over which values tend to be similar?”, and “What is the
dominant scale(s) of variability in the measured variable?”
While the geostatistical properties of surface patterns has been the focus of nearly all surface pattern
analysis in landscape ecology, recently it was revealed that surface metrology (derived from the field
of structural and molecular physics) offers a variety of surface metrics for quantifying landscape
gradients akin to the more familiar patch metrics described below for categorical maps (McGarigal
and Cushman 2005). Like their analogous patch metrics, surface metrics describe both the
nonspatial and spatial character of the surface as a whole, including the variability in the overall
height distribution of the surface (nonspatial) and the arrangement, location or distribution of
surface peaks and valleys (spatial). Here, the goal of the analysis is to describe the spatial structure of
the entire surface in a single metric, and a variety of surface metrics have been developed for this
purpose (McGarigal et al. 2009).
(4) Categorical (or thematic; choropleth) map patterns – Categorical map patterns represent data in which
the system property of interest is represented as a mosaic of discrete patches. Hence, this type of
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spatial pattern is also referred to as a “patch mosaic”. From an ecological perspective, patches
represent relatively discrete areas of relatively homogeneous environmental conditions at a particular
scale. The patch boundaries are distinguished by abrupt discontinuities (boundaries) in
environmental character states from their surroundings of magnitudes that are relevant to the
ecological phenomenon under consideration (Wiens 1976, Kotliar and Wiens 1990). A familiar
example is a map of land cover types, wherein the data consists of polygons (vector format) or grid
cells (raster format) classified into discrete land cover classes. There are a multitude of methods for
deriving a categorical map (patch mosaic) which has important implications for the interpretation of
landscape pattern metrics (see below). Patches may be classified and delineated qualitatively through
visual interpretation of the data (e.g., delineating vegetation polygons through interpretation of aerial
photographs), as is typically the case with vector maps constructed from digitized lines.
Alternatively, with raster grids (constructed of grid cells), quantitative information at each location
may be used to classify cells into discrete classes and to delineate patches by outlining them, and
there are a variety of methods for doing this. The most common and straightforward method is
simply to aggregate all adjacent (touching) areas that have the same (or similar) value on the variable
of interest. An alternative approach is to define patches by outlining them: that is, by finding the
edges around patches (Fortin 1994, Fortin and Drapeau 1995, Fortin et al. 2000). An edge in this
case is an area where the measured value changes abruptly (i.e., high local variance or rate of
change). An alternative is to use a divisive approach, beginning with a single patch (the entire
landscape) and then successively partitioning this into regions that are statistically homogeneous
patches (Pielou 1984). A final method to create patches is to cluster them hierarchically, but with a
constraint of spatial adjacency (Legendre and Fortin 1989).
Regardless of data format (raster or vector) and method of classifying and delineating patches, the
goal of categorical map pattern analysis with such data is to characterize the composition and spatial
configuration of the patch mosaic, and a plethora of metrics has been developed for this purpose
(Forman and Godron 1986, O'Neill et al. 1988, Turner 1990, Musick and Grover 1991, Turner and
Gardner 1991, Baker and Cai 1992, Gustafson and Parker 1992, Li and Reynolds 1993, McGarigal
and Marks 1995, Jaeger 2000, McGarigal et al. 2002). While these patch metrics are quite familiar to
landscape ecologists, scaling techniques for categorical map data are less commonly employed in
landscape ecology. This is because in applications involving categorical map patterns, the relevant
scale of the mosaic is often defined a priori based on the phenomenon under consideration. In such
cases, it is usually assumed that it would be meaningless to determine the so-called characteristic
scale of the mosaic after its construction. However, there are many situations when the categorical
map is created through a purely objective classification procedure and the scaling properties of the
patch mosaic is of great interest. Lacunarity analysis is one technique borrowed from fractal
geometry by which class-specific aggregation can be characterized across a range of scales to
examine the scale(s) of clumpiness (Plotnick et al. 1993 and 1996, Dale 2000).
Ke y Po in t There are several major classes of landscape patterns that fall within the purview of landscape pattern
analysis. These classes of pattern are not intrinsic to the landscape under consideration, but rather reflect
a human construct pertaining to the spatial heterogeneity of interest to the investigator or manager. It is
incumbent upon the investigator or manager to choose the appropriate class of pattern for the question
under consideration. FRAGSTATS currently deals with categorical map patterns (v4.2 and earlier)
and surface patterns (scheduled for v4.4).
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Patch-Corridor-Matrix Model
Landscapes are composed of elements – the spatial components that make up the landscape. A
convenient and popular model for conceptualizing and representing the elements in a categorical
map pattern (or patch mosaic) is known as the patch-corridor-matrix model (Forman 1995). Under this
model, three major landscape elements are typically recognized, and the extent and configuration of
these elements defines the pattern of the landscape.
(1) Patch – Landscapes are composed of a mosaic of patches (Urban et al. 1987). Landscape
ecologists have used a variety of terms to refer to the basic elements or units that make up a
landscape, including ecotope, biotope, landscape component, landscape element, landscape unit,
landscape cell, geotope, facies, habitat, and site (Forman and Godron 1986). Any of these terms,
when defined, are satisfactory according to the preference of the investigator. Like the landscape,
patches comprising the landscape are not self-evident; patches must be defined relative to the
phenomenon under consideration. For example, from a timber management perspective a patch
may correspond to the forest stand. However, the stand may not function as a patch from a
particular organism's perspective. From an ecological perspective, patches represent relatively
discrete areas (spatial domain) or periods (temporal domain) of relatively homogeneous
environmental conditions where the patch boundaries are distinguished by discontinuities in
environmental character states from their surroundings of magnitudes that are perceived by or
relevant to the organism or ecological phenomenon under consideration (Wiens 1976). From a
strictly organism-centered view, patches may be defined as environmental units between which
fitness prospects, or "quality", differ; although, in practice, patches may be more appropriately
defined by nonrandom distribution of activity or resource utilization among environmental units, as
recognized in the concept of "Grain Response".
Patches are dynamic and occur on a variety of spatial and temporal scales that, from an organismcentered perspective, vary as a function of each animal's perceptions (Wiens 1976 and 1989, Wiens
and Milne 1989). A patch at any given scale has an internal structure that is a reflection of patchiness
at finer scales, and the mosaic containing that patch has a structure that is determined by patchiness
at broader scales (Kotliar and Wiens 1990). Thus, regardless of the basis for defining patches, a
landscape does not contain a single patch mosaic, but contains a hierarchy of patch mosaics across a
range of scales. For example, from an organism-centered perspective, the smallest scale at which an
organism perceives and responds to patch structure is its "grain" (Kotliar and Wiens 1990). This
lower threshold of heterogeneity is the level of resolution at which the patch size becomes so fine
that the individual or species stops responding to it, even though patch structure may actually exist
at a finer resolution (Kolasa and Rollo 1991). The lower limit to grain is set by the physiological and
perceptual abilities of the organism and therefore varies among species. Similarly, "extent" is the
coarsest scale of heterogeneity, or upper threshold of heterogeneity, to which an organism responds
(Kotliar and Wiens 1990, Kolasa and Rollo 1991). At the level of the individual, extent is
determined by the lifetime home range of the individual (Kotliar and Wiens 1990) and varies among
individuals and species. More generally, however, extent varies with the organizational level (e.g.,
individual, population, metapopulation) under consideration; for example the upper threshold of
patchiness for the population would probably greatly exceed that of the individual. Therefore, from
an organism-centered perspective, patches can be defined hierarchically in scales ranging between
the grain and extent for the individual, deme, population, or range of each species.
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Patch boundaries are artificially imposed and are in fact meaningful only when referenced to a
particular scale (i.e., grain size and extent). For example, even a relatively discrete patch boundary
between an aquatic surface (e.g., lake) and terrestrial surface becomes more and more like a
continuous gradient as one progresses to a finer and finer resolution. However, most environmental
dimensions possess one or more "domains of scale" (Wiens 1989) at which the individual spatial or
temporal patches can be treated as functionally homogeneous; at intermediate scales the
environmental dimensions appear more as gradients of continuous variation in character states.
Thus, as one moves from a finer resolution to coarser resolution, patches may be distinct at some
scales (i.e., domains of scale) but not at others.
Ke y Po in t It is not my intent to argue for a particular definition of patch. Rather, I wish to point out the following:
(1) that patch must be defined relative to the phenomenon under investigation or management; (2) that,
regardless of the phenomenon under consideration (e.g., a species, geomorphological disturbances, etc),
patches are dynamic and occur at multiple scales; and (3) that patch boundaries are only meaningful
when referenced to a particular scale. It is incumbent upon the investigator or manager to establish the
basis for delineating among patches and at a scale appropriate to the phenomenon under consideration.
(2) Corridor – Corridors are linear landscape elements that can be defined on the basis of structure or
function. Forman and Godron (1986) define corridors as “narrow strips of land which differ from
the matrix on either side. Corridors may be isolated strips, but are usually attached to a patch of
somewhat similar vegetation.” These authors focus on the structural aspects of the linear landscape
element. As a consequence of their form and context, structural corridors may function as habitat,
dispersal conduits, or barriers. Three different types of structural corridors exist: (1) line corridors, in
which the width of the corridor is too narrow to allow for interior environmental conditions to
develop; (2) strip corridors, in which the width of the corridor is wide enough to allow for interior
conditions to develop; and (3) stream corridors, which are a special category.
Corridors may also be defined on the basis of their function in the landscape. At least four major
corridor functions have been recognized, as follows:
1. Habitat Corridor – Linear landscape element that provides for survivorship, natality, and
movement (i.e., habitat), and may provide either temporary or permanent habitat. Habitat
corridors passively increase landscape connectivity for the focal organism(s).
2. Facilitated Movement Corridor – Linear landscape element that provides for survivorship
and movement, but not necessarily natality, between other habitat patches. Facilitated
movement corridors actively increase landscape connectivity for the focal organism(s).
3. Barrier or Filter Corridor – Linear landscape element that prohibits (i.e., barrier) or
differentially impedes (i.e., filter) the flow of energy, mineral nutrients, and/or species across
(i.e., flows perpendicular to the length of the corridor). Barrier or filter corridors actively
decrease matrix connectivity for the focal process.
4. Source of Abiotic and Biotic Effects on the Surrounding Matrix – Linear landscape element
that modifies the inputs of energy, mineral nutrients, and/or species to the surrounding
matrix and thereby effects the functioning of the surrounding matrix.
9
Most of the attention and debate has focused on facilitated movement corridors. It has been argued that
this corridor function can only be demonstrated when the immigration rate to the target patch is
increased over what it would be if the linear element was not present (Rosenberg et al. 1997).
Unfortunately, as Rosenberg et al. point out, there have been few attempts to experimentally
demonstrate this. In addition, just because a corridor can be distinguished on the basis of structure,
it does not mean that it assumes any of the above functions. Moreover, the function of the corridor
will vary among organisms due to the differences in how organisms perceive and scale the
environment.
Ke y Po in t Corridors are distinguished from patches by their linear nature and can be defined on the basis of either
structure or function or both. If a corridor is specified, it is incumbent upon the investigator or manager to
define the structure and implied function relative to the phenomena (e.g., species) under consideration.
(3) Matrix – A landscape is composed typically of several types of landscape elements (usually
patches). Of these, the matrix is the most extensive and most connected landscape element type, and
therefore plays the dominant role in the functioning of the landscape (Forman and Godron 1986).
For example, in a large contiguous area of mature forest embedded with numerous small
disturbance patches (e.g., timber harvest patches), the mature forest constitutes the matrix element
type because it is greatest in areal extent, is mostly connected, and exerts a dominant influence on
the area flora and fauna and ecological processes. In most landscapes, the matrix type is obvious to
the investigator or manager. However, in some landscapes, or at a certain point in time during the
trajectory of a landscape, the matrix element will not be obvious. Indeed, it may not be appropriate
to consider any element as the matrix. Moreover, the designation of a matrix element is largely
dependent upon the phenomenon under consideration. For example, in the study of
geomorphological processes, the geological substrate may serve to define the matrix and patches;
whereas, in the study of vertebrate populations, vegetation structure may serve to define the matrix
and patches. In addition, what constitutes the matrix is dependent on the scale of investigation or
management. For example, at a particular scale, mature forest may be the matrix with disturbance
patches embedded within; whereas, at a coarser scale, agricultural land may be the matrix with
mature forest patches embedded within.
It is important to understand how measures of landscape pattern are influenced by the designation
of a matrix element. If an element is designated as matrix and therefore presumed to function as
such (i.e., has a dominant influence on landscape dynamics), then it should not be included as
another "patch" type in any metric that simply averages some characteristic across all patches (e.g.,
mean patch size, mean patch shape). Otherwise, the matrix will dominate the metric and serve more
to characterize the matrix than the patches within the landscape, although this may itself be
meaningful in some applications. From a practical standpoint, it is important to recognize this
because in FRAGSTATS, the matrix can be excluded from calculations by designating its class value
as background. If the matrix is not excluded from the calculations, it may be more meaningful to use
the class-level statistics for each patch type and simply ignore the patch type designated as the
matrix. From a conceptual standpoint, it is important to recognize that the choice and interpretation
of landscape metrics must ultimately be evaluated in terms of their ecological meaningfulness, which
is dependent upon how the landscape is defined, including the choice of patch types and the
designation of a matrix.
10
Ke y Po in t It is incumbent upon the investigator or manager to determine whether a matrix element exists and
should be designated given the scale and phenomenon under consideration.
The Importance of Scale
The pattern detected in any ecological mosaic is a function of scale, and the ecological concept of
spatial scale encompasses both extent and grain (Forman and Godron 1986, Turner et al. 1989,
Wiens 1989). Extent is the overall area encompassed by an investigation or the area included within
the landscape boundary. From a statistical perspective, the spatial extent of an investigation is the
area defining the population we wish to sample. Grain is the size of the individual units of
observation. For example, a fine-grained map might structure information into 1-ha units, whereas a
map with an order of magnitude coarser resolution would have information structured into 10-ha
units (Turner et al. 1989). Extent and grain define the upper and lower limits of resolution of a study
and any inferences about scale-dependency in a system are constrained by the extent and grain of
investigation (Wiens 1989). From a statistical perspective, we cannot extrapolate beyond the
population sampled, nor can we infer differences among objects smaller than the experimental units.
Likewise, in the assessment of landscape pattern, we cannot detect pattern beyond the extent of the
landscape or below the resolution of the grain (Wiens 1989).
As with the concept of landscape and patch, it may be more ecologically meaningful to define scale
from the perspective of the organism or ecological phenomenon under consideration. For example,
from an organism-centered perspective, grain and extent may be defined as the degree of acuity of a
stationary organism with respect to short- and long-range perceptual ability (Kolasa and Rollo 1991).
Thus, grain is the finest component of the environment that can be differentiated up close by the
organism, and extent is the range at which a relevant object can be distinguished from a fixed
vantage point by the organism (Kolasa and Rollo 1991). Unfortunately, while this is ecologically an
ideal way to define scale, it is not very pragmatic. Indeed, in practice, extent and grain are often
dictated by the scale of the imagery (e.g., aerial photo scale) being used or the technical capabilities
of the computing environment.
It is critical that extent and grain be defined for a particular study and represent, to the greatest
possible degree, the ecological phenomenon or organism under study, otherwise the landscape
patterns detected will have little meaning and there is a good chance of reaching erroneous
conclusions. For example, it would be meaningless to define grain as 1-ha units if the organism
under consideration perceives and responds to habitat patches at a resolution of 1-m2. A strong
landscape pattern at the 1-ha resolution may have no significance to the organism under study.
Likewise, it would be unnecessary to define grain as 1-m2 units if the organism under consideration
perceives habitat patches at a resolution of 1-ha. Typically, however, we do not know what the
appropriate resolution should be. In this case, it is much safer to choose a finer grain than is believed
to be important Remember, the grain sets the minimum resolution of investigation. Once set, we
can always dissolve to a coarser grain. In addition, we can always specify a minimum mapping unit
that is coarser than the grain. That is, we can specify the minimum patch size to be represented in a
landscape, and this can easily be manipulated above the resolution of the data. It is important to
note that the technical capabilities of GIS with respect to image resolution may far exceed the
technical capabilities of the remote sensing equipment. Thus, it is possible to generate GIS images at
too fine a resolution for the spatial data being represented, resulting in a more complex
11
representation of the landscape than can truly be obtained from the data.
Information may be available at a variety of scales and it may be necessary to extrapolate
information from one scale to another. In addition, it may be necessary to integrate data represented
at different spatial scales. It has been suggested that information can be transferred across scales if
both grain and extent are specified (Allen et al. 1987), yet it is unclear how observed landscape
patterns vary in response to changes in grain and extent and whether landscape metrics obtained at
different scales can be compared. The limited work on this topic suggests that landscape metrics
vary in their sensitivity to changes in scale and that qualitative and quantitative changes in
measurements across spatial scales will differ depending on how scale is defined (Turner et al. 1989).
Therefore, in investigations of landscape pattern, until more is learned, it is critical that any attempts
to compare landscapes measured at different scales be done cautiously.
Ke y Po in t One of the most important considerations in any landscape ecological investigation or landscape structural
analysis is (1) to explicitly define the scale of the investigation or analysis, (2) to describe any observed
patterns or relationships relative to the scale of the investigation, and (3) to be especially cautious when
attempting to compare landscapes measured at different scales.
Landscape Context
Landscapes do not exist in isolation. Landscapes are nested within larger landscapes, that are nested
within larger landscapes, and so on. In other words, each landscape has a context or regional setting,
regardless of scale and how the landscape is defined. The landscape context may constrain processes
operating within the landscape. Landscapes are "open" systems; energy, materials, and organisms
move into and out of the landscape. This is especially true in practice, where landscapes are often
somewhat arbitrarily delineated. That broad-scale processes act to constrain or influence finer-scale
phenomena is one of the key principles of hierarchy theory (Allen and Star 1982) and 'supply-side'
ecology (Roughgarden et al. 1987). The importance of the landscape context is dependent on the
phenomenon of interest, but typically varies as a function of the "openness" of the landscape. The
"openness" of the landscape depends not only on the phenomenon under consideration, but on the
basis used for delineating the landscape boundary. For example, from a geomorphological or
hydrological perspective, the watershed forms a natural landscape, and a landscape defined in this
manner might be considered relatively "closed". Of course, energy and materials flow out of this
landscape and the landscape context influences the input of energy and materials by affecting
climate and so forth, but the system is nevertheless relatively closed. Conversely, from the
perspective of a bird population, topographic boundaries may have little ecological relevance, and
the landscape defined on the basis of watershed boundaries might be considered a relatively "open"
system. Local bird abundance patterns may be produced not only by local processes or events
operating within the designated landscape, but also by the dynamics of regional populations or
events elsewhere in the species' range (Wiens 1981, 1989b, Vaisanen et al. 1986, Haila et al. 1987,
Ricklefs 1987).
Landscape metrics quantify the pattern of the landscape within the designated landscape boundary
only. Consequently, the interpretation of these metrics and their ecological significance requires an
acute awareness of the landscape context and the openness of the landscape relative to the
phenomenon under consideration. These concerns are particularly important for nearest-neighbor
12
metrics. For example, nearest-neighbor distances are computed solely from patches contained within
the landscape boundary. If the landscape extent is small relative to the scale of the organism or
ecological processes under consideration and the landscape is an "open" system relative to that
organism or process, then nearest-neighbor results can be misleading. Consider a small
subpopulation of a species occupying a patch near the boundary of a somewhat arbitrarily defined
(from the organism's perspective) landscape. The nearest neighbor within the landscape boundary
might be quite far away, yet in reality the closest patch might be very close, but just outside the
landscape boundary. The magnitude of this problem is a function of scale. Increasing the size of the
landscape relative to the scale at which the organism under investigation perceives and responds to
the environment will generally decrease the severity of this problem. In general, the larger the ratio
of extent to grain (i.e., the larger the landscape relative to the average patch size), the less likely these
and other metrics will be dominated by boundary effects.
Ke y Po in t The important point is that a landscape should be defined relative to both the spatial pattern within the
landscape as well as the landscape context. Moreover, consideration should always be given to the
landscape context and the openness of the landscape relative to the phenomenon under consideration when
choosing and interpreting landscape metrics.
Perspectives on Categorical Map Patterns
There are at least two different perspectives on categorical map patterns (or patch mosaics) that
have profoundly influenced the development of landscape metrics and have important implications
for the choice and interpretation of individual landscape metrics.
(1) Island Biogeographic Model – In the island biogeographic model, the emphasis is on a single patch
type; disjunct patches (e.g., habitat fragments) are viewed as analogues of oceanic islands embedded
in an inhospitable or ecologically neutral background (matrix). This perspective emerged from the
theory of island biogeography (MacArthur and Wilson 1967) and subsequent interest in habitat
fragmentation (Saunders et al. 1991). Under this perspective, there is a binary patch structure in
which the focal patches (fragments) are embedded in a neutral matrix. Here, the emphasis is on the
extent, spatial character, and distribution of the focal patch type without explicitly considering the
role of the matrix. Under this perspective, for example, connectivity may be assessed by the spatial
aggregation of the focal patch type without consideration of how intervening patches affect the
functional connectedness among patches of the focal class. The island biogeography perspective has
been the dominant perspective since inception of the theory. The major advantage of the island
model is its simplicity. Given a focal patch type, it is quite simple to represent the structure of the
landscape in terms of focal patches contrasted sharply against a uniform matrix, and it is relatively
simple to devise metrics that quantify this structure. Moreover, by considering the matrix as
ecologically neutral, it invites ecologists to focus on those patch attributes, such as size and isolation,
that have the strongest effect on species persistence at the patch level. The major disadvantage of
the strict island model is that it assumes a uniform and neutral matrix, which in most real-world
cases is a drastic over-simplification of how organisms interact with landscape patterns.
(2) Landscape Mosaic Model – In the landscape mosaic model, landscapes are viewed as spatially
complex, heterogeneous assemblages of patch types, which can not be simply categorized into
discrete elements such as patches, matrix, and corridors (With 2000). Rather, the landscape is viewed
13
from the perspective of the organism or process of interest. Patches are bounded by patches of
other patch types that may be more or less similar to the focal patch type, as opposed to highly
contrasting and often hostile habitats, as in the case of the island model. Connectivity, for example,
may be assessed by the extent to which movement is facilitated or impeded through different patch
types across the landscape. The landscape mosaic perspective derives from landscape ecology itself
(Forman 1995) and has emerged as a viable alternative to the island biogeographic model. The major
advantage of the landscape mosaic model is its more realistic representation of how organisms
perceive and interact with landscape patterns. Few organisms, for example, exhibit a binary (all or
none) response to habitats (patch types), but rather use habitats proportionate to the fitness they
confer to the organism. Moreover, movement among suitable habitat patches usually is a function of
the character of the intervening habitats, which usually vary in the resistance they offer to
movement. The major disadvantage of the landscape mosaic model is that it requires detailed
understanding of how organisms interact with landscape pattern, and this has complicated the
development of additional metrics that adopt this perspective.
Ke y Po in t There are two major perspectives, or “models”, of categorical map patterns, or patch mosaics: 1) the
island biogeographic model, and 2) the landscape mosaic model. Both models fall within the purview of
categorical map patterns and neither are intrinsic to the landscape under consideration, but rather reflect
a human construct pertaining to the patch mosaic of interest to the investigator or manager. It is
incumbent upon the investigator or manager to choose the appropriate patch mosaic model for the question
under consideration and then choose landscape metrics that are relevant for this model.
Scope of Analysis
The scope of analysis pertains to the scale and or focus of the investigation. There are three levels of
analysis, at least for categorical map patterns (or patch mosaics), that represent fundamentally
different perspectives on landscape pattern analysis and that have important implications for the
choice and interpretation of individual landscape metrics and the form of the results.
(1) Focal Patch Analysis – Under the patch mosaic model of landscape structure the focus of the
investigation may be on individual patches (instead of the aggregate properties of patches);
specifically, the spatial character and/or context of individual focal patches. This is a ‘patch-centric’;
perspective on landscape patterns in which the scope of analysis is restricted to the characterization
of individual focal patches. In this case, each focal patch is characterized according to one or more
patch-level metrics (see below). The results of a focal patch analysis is typically given in the form of
a table, where each row represents a separate patch and each column represents a separate patch
metric.
(2) Local Neighborhood Structure – In many applications it may be appropriate to assume that organisms
experience landscape structure as local pattern gradients that vary through space according to the
perception and influence distance of the particular organism or process. Thus, instead of analyzing
global landscape patterns, e.g., as measured by conventional landscape metrics for the entire
landscape (see below), we would be better served by quantifying the local landscape pattern across
space as it may be experienced by the organism of interest, given their perceptual abilities. The local
landscape structure can be examined by passing a ‘moving window’; of fixed or variable size across
the landscape one cell at a time. The window size and form should be selected such that it reflects
14
the scale and manner in which the organism perceives or responds to pattern. If this is unknown,
the user can vary the size of the window over several runs and empirically determine which scale the
organism is most responsive to. The window moves over the landscape one cell at a time, calculating
the selected metric within the window and returning that value to the center cell. The result is a
continuous surface which reflects how an organism of that perceptual ability would perceive the
structure of the landscape as measured by that metric. The surface then would be available for
combination with other such surfaces in multivariate models to predict, for example, the distribution
and abundance of an organism continuously across the landscape.
(3) Global Landscape Structure – The traditional application of landscape metrics involves
characterizing the structure of the entire landscape with one or more landscape metrics. For
example, traditional landscape pattern analysis would measure the total contrast-weighted edge
density for the entire landscape. This would be a global measure of the average property of that
landscape. This is a ‘landscape-centric’; perspective on landscape patterns in which the scope of
analysis is restricted to the characterization of the entire patch mosaic in aggregate. In this case, the
landscape is characterized according to one or more landscape-level metrics (see below). The results
of a global landscape structure analysis is typically given in the form of a vector of measurements,
where each element represents a separate landscape metric.
Ke y Po in t There are three levels of analysis, at least for categorical map patterns (or patch mosaics), that represent
fundamentally different perspectives on landscape pattern analysis and that have important implications
for the choice and interpretation of individual landscape metrics and the form of the results: 1) focal patch
analysis, 2) local neighborhood structure analysis, and 3) global landscape structure analysis. It is
incumbent upon the investigator or manager to choose the appropriate scope of analysis for the question
under consideration and then choose appropriate landscape metrics that reflect this scope of analysis.
Levels of Heterogeneity
Patches form the basis (or building blocks) for categorical maps (or patch mosaics). Depending on
the method used to derive patches (and therefore the data available), they can be characterized
compositionally in terms of variables measured within them. This may include the mean (or mode,
median, or max) value and internal heterogeneity (variance, range). However, in most applications,
once patches have been established, the within-patch heterogeneity is ignored and the patches are
assigned a nominal class value to represent the composition of the patch. Landscape pattern metrics
focus on the spatial character and distribution of patches in the neighborhood of each cell or across
the landscape as a whole. While individual patches possess relatively few fundamental spatial
characteristics (e.g., size, perimeter, and shape), collections of patches may have a variety of
aggregate properties, depending on whether the aggregation is over a single class (patch type) or
multiple classes, and whether the aggregation is within a specified subregion of a landscape (e.g., the
neighborhood of each focal cell) or across the entire landscape. Consequently, landscape metrics can
be defined at four levels corresponding to a logical hierarchical organization of spatial heterogeneity
in patch mosaics.
(1) Cell-level metrics – Cell metrics provide the finest spatial unit of resolution for characterizing spatial
patterns in categorical maps (when defined as a raster image). They are defined for individual grid
cells, and characterize the spatial context (i.e., ecological neighborhood) of cells without explicit
15
regard to patch or class affiliation. In other words, cell metrics are not patch-centric, even though
the ecological neighborhood (defined by the user) is characterized by the structure of the patch
mosaic surrounding the cell. The result is a single value for each cell. For example, an individual
organism dispersing from its natal habitat interacts with the structure of the landscape in the
neighborhood surrounding that initial location. Thus, the ability to traverse across the landscape
from that location may be a function of the landscape character within some ecological
neighborhood defined by dispersal distance. Cell metrics may be computed for a targeted set of
focal cells representing specific locations of interest (e.g., nest sites, capture locations, etc.), in which
case the standard output would consist of a vector of cell-based measurements reported in tabular
form (i.e., one record for each focal cell). Cell metrics may also be computed exhaustively for every
cell in the landscape, in which case the standard output would consist of a continuous surface grid
or map.
(2) Patch-level metrics – Patch metrics are defined for individual patches, and characterize the spatial
character and context of patches. In most applications, patch metrics serve primarily as the
computational basis for several of the landscape metrics, for example by averaging patch attributes
across all patches in the class or landscape; the computed values for each individual patch may have
little interpretive value. However, sometimes patch indices can be important and informative in
landscape-level investigations. For example, many vertebrates require suitable habitat patches larger
than some minimum size (e.g., Robbins et al. 1989), so it would be useful to know the size of each
patch in the landscape. Similarly, some species are adversely affected by edges and are more closely
associated with patch interiors (e.g., Temple 1986), so it would be useful to know the size of the
core area for each patch in the landscape. The probability of occupancy and persistence of an
organism in a patch may be related to patch insularity (sensu Kareiva 1990), so it would be useful to
know the nearest neighbor of each patch and the degree of contrast between the patch and its
neighborhood. The utility of the patch characteristic information will ultimately depend on the
objectives of the investigation.
(3) Class-level metrics – Class metrics are integrated over all the patches of a given type (class). These
may be integrated by simple averaging, or through some sort of weighted-averaging scheme to bias
the estimate to reflect the greater contribution of large patches to the overall index. There are
additional aggregate properties at the class level that result from the unique configuration of patches
across the landscape. In many applications, the primary interest is in the amount and distribution of
a particular patch type. A good example is in the study of habitat fragmentation. Habitat
fragmentation is a landscape-level process in which contiguous habitat is progressively sub-divided
into smaller, geometrically more complex (initially, but not necessarily ultimately), and more isolated
habitat fragments as a result of both natural processes and human land use activities (McGarigal and
McComb 1999). This process involves changes in landscape composition, structure, and function
and occurs on a backdrop of a natural patch mosaic created by changing landforms and natural
disturbances. Habitat loss and fragmentation is the prevalent trajectory of landscape change in
several human-dominated regions of the world, and is increasingly becoming recognized as a major
cause of declining biodiversity (Burgess and Sharpe 1981, Whitcomb et al. 1981, Noss 1983, Harris
1984, Wilcox and Murphy 1985, Terborgh 1989, Noss and Cooperrider 1994). Class indices
separately quantify the amount and spatial configuration of each patch type and thus provide a
means to quantify the extent and fragmentation of each patch type in the landscape.
16
(4) Landscape-level metrics – Landscape metrics are integrated over all patch types or classes over the
full extent of the data (i.e., the entire landscape). Like class metrics, these may be integrated by a
simple or weighted averaging, or may reflect aggregate properties of the patch mosaic. In many
applications, the primary interest is in the pattern (i.e., composition and configuration) of the entire
landscape mosaic. A good example is in the study of wildlife communities. Aldo Leopold (1933)
noted that wildlife diversity was greater in more diverse and spatially heterogenous landscapes. Thus,
the quantification of landscape diversity and heterogeneity has assumed a preeminent role in
landscape ecology. Indeed, the major focus of landscape ecology is on quantifying the relationships
between landscape pattern and ecological processes. Consequently, much emphasis has been placed
on developing methods to quantify landscape pattern (e.g., O'Neill et al. 1988, Li 1990, Turner 1990,
Turner and Gardner 1991) and a great variety of landscape-level metrics have been developed for
this purpose.
It is important to note that while many metrics have counterparts at several levels, their
interpretations may be somewhat different. Cell metrics represent the spatial context of local
neighborhoods centered on each cell. Patch metrics represent the spatial character and context of
individual patches. Class metrics represent the amount and spatial distribution of a single patch type
and are interpreted as fragmentation indices. Landscape metrics represent the spatial pattern of the
entire landscape mosaic and generally interpreted more broadly as landscape heterogeneity indices
because they measure the overall landscape structure. Hence, it is important to interpret each metric
in a manner appropriate to its level (cell, patch, class, or landscape).
In addition, it is important to note that while most metrics at higher levels are derived from
patch-level attributes, not all metrics are defined at all levels. In particular, collections of patches at
the class and landscape level have aggregate properties that are undefined (or trivial) at lower levels.
The fact that most higher-level metrics are derived from the same patch-level attributes has the
further implication that many of the metrics are correlated. Thus, they provide similar and perhaps
redundant information (see below). Even though many of the class- and landscape-level metrics
represent the same fundamental information, naturally the algorithms differ slightly.
In addition, while many metrics have counterparts at all levels, their interpretations may be
somewhat different. Cell-level metrics represent the spatial context of individual cells. Patch-level
metrics represent the spatial character and context of individual patches. Class-level metrics
represent the amount and spatial distribution of a single patch type and may be interpreted as
fragmentation indices. Landscape-level metrics represent the spatial pattern of the entire landscape
mosaic and may be interpreted more broadly as landscape heterogeneity indices because they
measure the overall landscape structure. Hence, it is important to interpret each metric in a manner
appropriate to its level (cell, patch, class, or landscape).
Lastly, class and landscape metrics are typically computed for the entire extent of the landscape; i.e.,
they quantify the structure of the individual class or the entire mosaic over the full extent of the
data. This is referred to as “global landscape structure”, even though the focus may be on a single
class within the landscape. However, both class and landscape metrics can also be computed for
local windows (defined by the user) placed over each cell one at a time, via a moving window, where
the value of the class or landscape metric in each window is returned to the focal cell. The result is
new grid in which the cell value represents the “local neighborhood structure”. This is very similar
17
to the cell metrics described above, since both focus on the structure of a local neighborhood
around a focal cell; the main difference is that cell metrics employ unique algorithms that are defined
only at the cell level, whereas here the metrics are literally the same as the class and landscape
metrics only they are applied to local windows around each focal cell.
Ke y Po in t Landscape metrics for categorical map patterns can be defined at four levels corresponding to a logical
hierarchical organization of spatial heterogeneity in patch mosaics: 1) cell-level metrics, 2) patch-level
metrics, 3) class-level metrics, and 4) landscape-level metrics. Each level of the hierarchy reflects a
different focus on spatial heterogeneity. It is incumbent upon the investigator or manager to choose the
appropriate level of heterogeneity for the question under consideration and then choose appropriate
landscape metrics that reflect this level of heterogeneity.
Patch-based Metrics
The common usage of the term "landscape metrics" refers exclusively to numerical indices
developed to quantify categorical map patterns (or patch mosaics). Under the patch mosaic
perspective, landscape metrics are algorithms that quantify specific spatial characteristics of patches,
classes of patches, or entire landscape mosaics, or the spatial context of individual cells within a
patch mosaic, and a plethora of metrics have been developed for this purpose. An exhaustive review
of all published metrics, therefore, is beyond the scope of this document. These metrics fall into two
general categories: those that quantify the composition of the map without reference to spatial
attributes, and those that quantify the spatial configuration of the map, requiring spatial information for
their calculation (McGarigal and Marks 1995, Gustafson 1998).
(1) Composition – Composition is easily quantified and refers to features associated with the variety
and abundance of patch types within the landscape, but without considering the spatial character,
placement, or location of patches within the mosaic. Because composition requires integration over
all patch types, composition metrics are only applicable at the landscape-level. There are many
quantitative measures of landscape composition, including the proportion of the landscape in each
patch type, patch richness, patch evenness, and patch diversity. Indeed, because of the many ways in
which diversity can be measured, there are literally hundreds of possible ways to quantify landscape
composition. Unfortunately, because diversity indices are derived from the indices used to
summarize species diversity in community ecology, they suffer the same interpretative drawbacks. It
is incumbent upon the investigator or manager to choose the formulation that best represents their
concerns. The principle measures of composition are:
•
Proportional Abundance of each Class – One of the simplest and perhaps most useful pieces of
information that can be derived is the proportion of each class relative to the entire map.
•
Richness – Richness is simply the number of different patch types.
•
Evenness – Evenness is the relative abundance of different patch types, typically emphasizing
either relative dominance or its compliment, equitability. There are many possible evenness (or
dominance) measures corresponding to the many diversity measures. Evenness is usually
reported as a function of the maximum diversity possible for a given richness. That is, evenness
is given as 1 when the patch mosaic is perfectly diverse given the observed patch richness, and
18
approaches 0 as evenness decreases. Evenness is sometimes reported as its complement,
dominance, by subtracting the observed diversity from the maximum for a given richness. In
this case, dominance approaches 0 for maximum equitability and increases >0 for higher
dominance.
•
Diversity – Diversity is a composite measure of richness and evenness and can be computed in a
variety of forms (e.g., Shannon and Weaver 1949, Simpson 1949), depending on the relative
emphasis placed on these two components.
(2) Spatial configuration – Spatial configuration is much more difficult to quantify and refers to the
spatial character and arrangement, position, or orientation of patches within the class or landscape.
Some aspects of configuration, such as patch isolation or patch contagion, are measures of the
placement of patch types relative to other patches, other patch types, or other features of interest.
Other aspects of configuration, such as shape and core area, are measures of the spatial character of
the patches. There are many aspects of configuration and the literature is replete with methods and
indices developed for representing them (see previous references).
Configuration can be quantified in terms of the landscape unit itself (i.e., the patch). The spatial
pattern being represented is the spatial character of the individual patches, even though the
aggregation is across patches at the class or landscape level. The location of patches relative to each
other is not explicitly represented. Metrics quantified in terms of the individual patches (e.g., mean
patch size and shape) are spatially explicit at the level of the individual patch, not the class or
landscape. Such metrics represent a recognition that the ecological properties of a patch are
influenced by the surrounding neighborhood (e.g., edge effects) and that the magnitude of these
influences are affected by patch size and shape. These metrics simply quantify, for the class or
landscape as a whole, some attribute of the statistical distribution (e.g., mean, max, variance) of the
corresponding patch characteristic (e.g., size, shape). Indeed, any patch-level metric can be
summarized in this manner at the class and landscape levels. Configuration also can be quantified in
terms of the spatial relationship of patches and patch types (e.g., nearest neighbor, contagion). These
metrics are spatially explicit at the class or landscape level because the relative location of individual
patches within the patch mosaic is represented in some way. Such metrics represent a recognition
that ecological processes and organisms are affected by the overall configuration of patches and
patch types within the broader patch mosaic.
A number of configuration metrics can be formulated either in terms of the individual patches or in
terms of the whole class or landscape, depending on the emphasis sought. For example, perimeterarea fractal dimension is a measure of shape complexity (Mandelbrot 1982, Burrough 1986, Milne
1991) that can be computed for each patch and then averaged for the class or landscape, or it can be
computed from the class or landscape as a whole by regressing the logarithm of patch perimeter on
the logarithm of patch area. Similarly, core area can be computed for each patch and then
represented as mean patch core area for the class or landscape, or it can be computed simply as total
core area in the class or landscape. Obviously, one form can be derived from the other if the
number of patches is known and so they are largely redundant; the choice of formulations is
dependent upon user preference or the emphasis (patch or class/landscape) sought. The same is true
for a number of other common landscape metrics. Typically, these metrics are spatially explicit at
the patch level, not at the class or landscape level.
19
The principle aspects of configuration and a sample of representative metrics are:
•
Patch area and edge – The simplest measure of configuration is patch size, which represents a
fundamental attribute of the spatial character of a patch. Most landscape metrics either directly
incorporate patch size information or are affected by patch size. Patch size distribution can be
summarized at the class and landscape levels in a variety of ways (e.g., mean, median, max,
variance, etc.). Patch size is typically computed as the total area of the patch, regardless of its
spatial character. However, patch size can also be characterized by its spatial extent; i.e., how
far-reaching it is. This is known as the patch radius of gyration, which measures how far across
the landscape a patch extends its reach on average, given by the mean distance between cells in a
patch. The radius of gyration can be considered a measure of the average distance an organism
can move within a patch before encountering the patch boundary from a random starting point.
When summarized for the class or landscape as a whole using an area-weighted mean, this
metric is also known as correlation length and gives the distance that one might expect to
traverse the map while staying in a particular patch, from a random starting point and moving in
a random direction (Keitt et al. 1997). The boundaries between patches (or edges) represent
another fundamental spatial attribute of a patch mosaic. The length of edge can be summarized
at the patch level as the perimeter of the patch, and at the class and landscape levels as the total
length of edge involving the focal class or across the entire mosaic, respectively.
•
Patch shape complexity – Shape complexity refers to the geometry of patches--whether they tend to
be simple and compact, or irregular and convoluted. Shape is an extremely difficult spatial
attribute to capture in a metric because of the infinite number of possible patch shapes. Hence,
shape metrics generally index overall shape complexity rather than attempt to assign a value to
each unique shape or morphology. The most common measures of shape complexity are based
on the relative amount of perimeter per unit area, usually indexed in terms of a perimeter-to-area
ratio, or as a fractal dimension, and often standardized to a simple Euclidean shape (e.g., circle
or square). The interpretation varies among the various shape metrics, but in general, higher
values mean greater shape complexity or greater departure from simple Euclidean geometry.
Other measures emphasize particular aspects of patch shape, such as compaction/elongatedness
(contiguity index, LaGro 1991; linearity index, Gustafson and Parker 1992; and elongation and
deformity indices, Baskent and Jordan 1995), but these have not yet become widely used
(Gustafson 1998).
•
Core Area – Core area refers the interior area of patches after a user-specified edge buffer is
eliminated. The edge buffer represents the distance at which the “core” or interior of a patch is
unaffected by the edge of the patch. This “edge effect” distance is defined by the user to be
relevant to the phenomenon under consideration and can either be treated as fixed or adjusted
for each unique edge type. Core area integrates patch size, shape, and edge effect distance into a
single measure. All other things equal, smaller patches with greater shape complexity have less
core area. Most of the metrics associated with patch area (e.g., mean patch size and variability)
can be formulated in terms of core area.
•
Contrast – Contrast refers to the relative difference among patch types. For example, mature
forest next to young forest might have a lower-contrast edge than mature forest adjacent to
open field, depending on how the notion of contrast is defined. This can be computed as a
20
contrast-weighted edge density, where each type of edge (i.e., between each pair of patch types)
is assigned a contrast weight. Alternatively, this can be computed as a neighborhood contrast
index, where the mean contrast between the focal patch and all patches within a user-specified
neighborhood is computed based on assigned contrast weights. Note, contrast is an attribute of
the edge itself, whereas core area is an attribute of the patch interior after accounting for adverse
edge effects that penetrate into patches (and thus have a corresponding depth-of-edge effect).
•
Aggregation – Aggregation refers to the degree of aggregation or clumping of patch types. This
property is also often referred to as landscape texture. Aggregation is an umbrella term used to
describe several closely related concepts: 1) dispersion, 2) interspersion, 3) subdivision, and 4)
isolation. Each of these concepts relates to the broader concept of aggregation, but is distinct
from the others in subtle but important ways. Aggregation metrics deal variously with the spatial
properties of dispersion and interspersion. Dispersion refers to the spatial distribution of a patch
type (i.e., how spread out or disperse it is) without explicit reference to any other patch types.
Interspersion refers to the spatial intermixing of different patch types without explicit reference to
the dispersion of any patch type. In the real world, however, these properties are often
correlated. Not surprisingly, therefore, some aggregation metrics deal with dispersion solely,
others deal with interspersion solely, and others deal with both, and thus there are a bewildering
variety of metrics in this group. Many of the metrics in this group are derived from the cell
adjacency matrix, in which the adjacency of patch types is first summarized in an adjacency or
co-occurrence matrix, which shows the frequency with which different pairs of patch types
(including like adjacencies between the same patch type) appear side-by-side on the map.
•
Subdivision – Subdivision refers to the degree to which the landscape is broken up (i.e.,
subdivided) into separate patches (i.e., fragments), not the size (per se), shape, relative location,
or spatial arrangement of those patches. Note, subdivision and dispersion are closely related
concepts. Both refer generally to the aggregation of the landscape, but subdivision deals
explicitly with the degree to which the landscape is broken up into disjunct patches, whereas the
concept and measurement of dispersion does not honor patches per se (since it is based on cell
adjacencies). In the real world, these two aspects of landscape structure are often highly
correlated. Subdivision can be measured quite simply by the number or density of patches.
However, a suite of metrics derived from the cumulative distribution of patch sizes provide
alternative and more explicit measures of subdivision (Jaeger 2000). When applied at the class
level, these metrics can be used to measure the degree of fragmentation of the focal patch type.
•
Isolation – Isolation refers to the tendency for patches to be relatively isolated in space (i.e.,
distant) from other patches of the same or ecologically similar class. Isolation is closely related to
the concept of subdivision; both refer to the subdivision per se of patch types, but isolation
deals explicitly with the degree to which patches are spatially isolated from each other, whereas
subdivision doesn't address the distance between patches, only that they are disjunct. Because
the notion of “isolation” is vague, there are many possible measures depending on how distance
is defined and how patches of the same class and those of other classes are treated. If dij is the
nearest-neighbor distance from patch i to another patch j of the same type, then the average
isolation of patches can be summarized simply as the mean nearest-neighbor distance over all
patches. Isolation can also be formulated in terms of both the size and proximity of neighboring
patches within a local neighborhood around each patch using the isolation index of Whitcomb
21
et al. (1981) or proximity index of Gustafson and Parker (1992), where the neighborhood size is
specified by the user and presumably scaled to the ecological process under consideration. The
original proximity index was formulated to consider only patches of the same class within the
specified neighborhood. This binary representation of the landscape reflects an island
biogeographic perspective on landscape pattern. Alternatively, this metric can be formulated to
consider the contributions of all patch types to the isolation of the focal patch, reflecting a
landscape mosaic perspective on landscape patterns, as in the similarity index (McGarigal et al.
2002). Importantly, in all of these measures of isolation, distance need not be defined as
Euclidean (i.e., straight line) distance. Instead, the functional distance between patches might be
based on some nonlinear function of Euclidean distance that reflects the probability of
connection at a given distance, or a resistance-weighted distance function that reflects the cost
distance between patches on a resistant (cost) surface.
Ke y Po in t Patch-based metrics (i.e., for categorical map patterns or patch mosaics) fall into two general categories:
1) those that quantify the composition of the map without reference to spatial attributes, and 2) those
that quantify the spatial configuration of the map, requiring spatial information for their calculation.
Each category contains a variety of metrics for quantifying different aspects of pattern. It is incumbent
upon the investigator or manager to choose the appropriate metrics for the question under consideration.
Surface Metrics
While the term “landscape metrics”, in practice, typically refers to numerical indices developed to
quantify categorical map patterns (or patch mosaics), the term more generally refers to numerical
indices that quantity any spatial heterogeneity (or landscape patterns), which includes not only
categorical map patterns, but also surface patterns (or landscape gradients), linear networks and
spatial point patterns. A wide variety of methods have been developed for quantifying the intensity
and scale of pattern in regionalized quantitative variables; i.e., continuous variables that can be
represented as a continuous surface (or landscape gradient). Surface metrics fall into two general
categories: autocorrelation structure functions that quantify the spatial dependencies of the quantitative
attribute, and surface metrology metrics that quantify other aspects of the spatial structure of a surface
(McGarigal et al 2009).
(1) Autocorrelation Structure Functions – The most basic and common measures of pattern in
regionalized quantitative variables (i.e., landscape gradients) are based on autocorrelation structure
functions, including for example Moran's I autocorrelation coefficient and semivariance, which we
described previously as scaling techniques for continuous gradient data. Both measures are typically
used to describe the magnitude of autocorrelation as a function of distance between locations, as
expressed by the correlogram and variogram (or semi-variogram), respectively. There are many other
structure functions for analyzing the intensity and scale of pattern with continuous data, especially
when the data is collected along continuous transects or two-dimensional surfaces, including
quadrat-variance analysis, spectral analysis, wavelet analysis and lacunarity analysis. Like the
autocorrelation structure functions, these techniques are typically used to quantify spatial
dependencies in a quantitative variable in relation to scale (distance, in this case).
(2) Surface Metrology Metrics – The autocorrelation and other related structure functions described
above can provide useful indices to quantitatively compare the intensity and extent of
22
autocorrelation in quantitative variables among landscapes. However, while they can provide
information on the distance at which the measured variable becomes statistically independent, and
reveal the scales of repeated patterns in the variable, if they exist, they do little to describe other
interesting aspects of the surface. For example, the degree of relief, density of troughs or ridges, and
steepness of slopes are not measured. Fortunately, a number of gradient-based metrics that
summarize these and other interesting properties of continuous surfaces have been developed in the
physical sciences for analyzing three-dimensional surface structures (Barbato et al. 1996, Sout et al.
1994, Villarrubia 1997). In the past ten years, researchers involved in microscopy and molecular
physics have made tremendous progress in this area, creating the field of surface metrology (Barbato
et al. 1996).
In surface metrology, several families of surface pattern metrics have become widely utilized. One
so-called family of metrics quantify intuitive measures of surface amplitude in terms of its overall
roughness, skewness and kurtosis, and total and relative amplitude. Another family records attributes
of surfaces that combine amplitude and spatial characteristics such as the curvature of local peaks.
Together these metrics quantify important aspects of the texture and complexity of a surface. A
third family measures certain spatial attributes of the surface associated with the orientation of the
dominant texture. A final family of metrics is based on the surface bearing area ratio curve (or
Abbott curve). The Abbott curve is computed by inversion of the cumulative height distribution
histogram. The curve describes the distribution of mass in the surface across the height profile. A
number of indices have been developed from the proportions of this cumulative height-volume
curve which describe structural attributes of the surface.
Many of the patch-based metrics for analyzing categorical landscapes have analogs in surface
metrology. For example, compositional metrics such as patch density, percent of landscape and
largest patch index are matched with peak density, surface volume, and maximum peak height.
Configuration metrics such as edge density, nearest neighbor index and fractal dimension index are
matched with mean slope, mean nearest maximum index and surface fractal dimension. Many of the
surface metrology metrics, however, measure attributes that are conceptually quite foreign to
conventional landscape pattern analysis. Landscape ecologists have not yet explored the behavior
and meaning of these new metrics; it remains for them to demonstrate the utility of these metrics, or
develop new surface metrics better suited for landscape ecological questions.
McGarigal et al. (2009) examined landscapes in Turkey defined using both the landscape gradient
and patch mosaic models according to a variety of landscape definition schemes and conducted
multivariate statistical analyses to identify the universal, consistent and important components of
surface patterns and their relationship to patch-based metrics. They observed four relatively distinct
components of landscape structure based on empirical relationships among 17 surface metrics
across 18 landscape gradient models:
•
Surface roughness – The dominant structural component of the surfaces was actually a combination
of two distinct sub-components: (1) the overall variability in surface height and (2) the local
variability in slope. The first sub-component refers to the nonspatial (composition) aspect of the
vertical height profile; that is, the overall variation in the height of the surface without reference
to the horizontal variability in the surface, and is represented by three surface amplitude metrics:
average roughness (Sa), root mean square roughness (Sq), and ten-point height (S10z). These
metrics are analogous to the patch type diversity measures (e.g., Simpson's diversity index) in the
23
patch mosaic paradigm, whereby greater variation in surface height equates to greater landscape
diversity. Importantly, while these metrics reflect overall variability in surface height, they say
nothing about the spatial heterogeneity in the surface.
The second sub-component refers to the spatial (configuration) aspect of surface roughness with
respect to local variability in height (or steepness of slope), and includes two surface metrics:
surface area ratio (Sdr) and root mean square slope (Sdq). These metrics are analogous to the
edge density and contrast metrics (e.g., contrast-weighted edge density, total edge contrast index)
in the patch mosaic paradigm, whereby greater local slope variation equates to greater density
and contrast of edges. Interestingly, while these surface metrics reflect something akin to edge
contrast, they do so without the need to supply edge contrast weights because they are structural
metrics. These two metrics appear to have the greatest overall analogy to the patch-based
measures of spatial heterogeneity and overall patchiness. A fine-grained patch mosaic (as
represented by any number of common patch metrics, such as mean patch size or density) is
conceptually equivalent to a rough surface with high local variability.
On conceptual and theoretical grounds, these spatial and nonspatial aspects of surface roughness
are independent components of landscape structure; however, in the landscape gradients we
examined these two aspects were highly correlated empirically. This distinction between
conceptually and/or theoretically related metrics and groupings based on their empirical
behavior has also been demonstrated for patch metrics.
•
Shape of the surface height distribution – Another important nonspatial (composition) component of
the surfaces we examined was the shape of the surface height distribution. This component was
comprised of five metrics: skewness (Ssk), kurtosis (Sku), surface bearing index (Sbi), valley fluid
retention index (Svi), and core fluid retention index (Sci). All of these metrics measure departure
from a Gaussian distribution of surface heights, but emphasize different aspects of departure
from normality. Ssk and Sku measure the familiar skewness and kurtosis of the surface height
distribution, while the surface bearing metrics, Sbi, Sci and Svi, measure different aspects of the
surface height distribution in its cumulative form. This component was universally present
across landscape models, but the composition of metrics varied somewhat among models
reflecting the complexities inherent in measuring non-parametric shape distributions. There were
no strong patch mosaic analogs to these surface metrics; however, departure from a Gaussian
distribution of surface heights was weakly correlated with, and conceptually most closely related
to, patch-based measures of landscape dominance (or its compliment, evenness) such as
Simpson's evenness index (SIEI) and largest patch index (LPI). Importantly, these five surface
metrics measure the 'shape' of the surface height distribution and are not affected by the surface
roughness (as defined above) per se.
•
Angular texture – A third prominent component of the surfaces we examined was the angular
orientation (direction) of the surface texture and its magnitude. This component is inherently
spatial, since the arrangement of surface peaks and valleys determines whether the surface has a
particular orientation or not, and is represented by four spatial metrics: dominant texture
direction (Std), texture direction index (Stdi), and two texture aspect ratios (Str20 and Str37).
The computational methods behind these metrics are too complex to describe here, but are
based on common geostatistical methods (Fourier spectral analysis and autocorrelation
24
functions) that determine the degree of anisotropy (orientation) in the surface. Not surprisingly
given our knowledge of the study landscape, we did not observe sample landscapes with a strong
texture orientation. We did observe mild levels of texture orientation in some landscapes, but
many were without apparent orientation. Importantly, the measurement of texture direction has
no obvious analog in the patch mosaic paradigm; indeed, we observed no pairwise correlation
greater than ±0.22 between any of these four surface metrics and any of the 28 patch metrics.
•
Radial texture – The fourth prominent component of the surfaces we examined was the radial
texture of the surface and its magnitude. Radial texture refers to repeated patterns of variation in
surface height radiating outward in concentric circles from any location. Like angular texture,
this component is inherently spatial, since the arrangement of surface peaks and valleys
determines whether the surface has any radial texture or not, and is represent by three spatial
metrics: dominant radial wavelength (Srw), radial wave index (Srwi), and fractal dimension (Sfd).
Again, the computational methods behind these metrics are based on common geostatistical
methods. A limitation of these and other metrics based on Fourier spectral analysis and
autocorrelation functions is that they are only sensitive to repeated, regular patterns. We
observed that in the absence of a prominent radial texture, the dominant radial wavelength (Srw)
ends up being equal to the diameter of the sample landscape. As a result, in some of our
landscape gradient models we observed too little variation in this metric and were forced to drop
it from the final analyses. Despite these limitations, we observed sample landscapes with varying
degrees of radial texture based on the other two metrics. In contrast to angular texture, the
measurement of radial texture has at least one conceptual analog in the patch mosaic paradigm mean and variability in nearest neighbor distance. On conceptual grounds, Srw should equate to
mean nearest neighbor distance, and Srwi and Sfd should equate to the coefficient of variation in
nearest neighbor distance. However, in our study the corresponding pairwise correlations did
not exceed ±0.22, nor were there any pairwise correlations greater than ±0.40 between either of
these surface metrics and any of the 28 patch metrics.
Ke y Po in t Surface metrics (i.e., for continuous surface patterns or landscape gradients) fall into several categories,
loosely reflecting different aspects of the composition or spatial configuration of the map. Each category
contains a variety of metrics for quantifying different aspects of pattern. It is incumbent upon the
investigator or manager to choose the appropriate metrics for the question under consideration.
Structural Versus Functional Metrics
Landscape metrics can also be classified according to whether or not they measure landscape
patterns with explicit reference to a particular ecological process.
•
Structural metrics can be defined as those that measure the physical composition or configuration
of the patch mosaic without explicit reference to an ecological process. The functional relevance
of the computed value is left for interpretation during a subsequent step. Most landscape metrics
are of this type.
•
Functional metrics, on the other hand, can be defined as those that explicitly measure landscape
pattern in a manner that is functionally relevant to the organism or process under consideration.
Functional metrics require additional parameterization prior to their calculation, such that the
25
same metric can return multiple values depending on the user specifications.
The difference between structural and functional metrics is best illustrated with an example. As
conventionally computed, mean nearest neighbor distance is based on the distances between
neighboring patches of the same class. The mosaic is in essence treated as a binary landscape (i.e.,
patches of the focal class versus everything else). The composition and configuration of the
intervening matrix is ignored. Consequently, the same landscape can only return a single value for
this metric. Clearly, this is a structural metric because the functional meaning of any particular
computed value is left to subsequent interpretation. Conversely, connectivity metrics that consider
the permeability of various patch types to movement of the organism or process of interest are
functional metrics. Here, every patch in the mosaic contributes to the calculation of the metric.
Moreover, there are an infinite number of values that can be returned from the same landscape,
depending on the permeability coefficients assigned to each patch type. Given a particular
parameterization, the computed metric is in terms that are already deemed functionally relevant.
Ke y Po in t Landscape metrics can be classified as either “structural” metrics, that measure the physical composition
or configuration of the patch mosaic without explicit reference to an ecological process, or “functional”
metrics, that explicitly measure landscape pattern in a manner that is functionally relevant to the
organism or process under consideration and require additional parameterization prior to their
calculation. It is incumbent upon the investigator or manager to choose the appropriate metrics, structural
and/or functional, for the question under consideration.
Limitations in the Use and Interpretation of Metrics
The quantitative analysis of landscape patterns is fraught with numerous challenges. Four broad
issues that currently limit the effective use and interpretation of landscape metrics are considered
here:
(1) Defining a relevant landscape – All landscape metrics represent some aspect of landscape pattern.
However, the user must first define the landscape, including its thematic content and resolution,
spatial grain and extent, and boundary before any of these metrics can be computed. In addition, for
the functional metrics, the user must specify additional input parameters such as edge effect
distances, edge contrast weights, resistance coefficients, and search distance. Hence, the computed
value of any metric is merely a function of how the investigator chose to define and scale the
landscape and parameterize the metric, if appropriate. If the measured pattern of the landscape does
not correspond to a pattern that is functionally meaningful for the organism or process under
consideration, then the results will be meaningless. For example, the criteria for defining a patch
may vary depending on how much variation will be allowed within a patch, on the minimum size of
patches that will be mapped, and on the components of the system that are deemed ecologically
relevant to the phenomenon of interest (Gustafson 1998). Ultimately, patches occur on a variety of
scales, and a patch at any given scale has an internal structure that is a reflection of patchiness at
finer scales, and the mosaic containing that patch has a structure that is determined by patchiness at
broader scales (Kotliar and Wiens 1990). Thus, regardless of the basis for defining patches, a
landscape does not contain a single patch mosaic, but contains a hierarchy of patch mosaics across a
range of scales. Indeed, patch boundaries are artificially imposed and are in fact meaningful only
when referenced to a particular scale (i.e., grain size and extent). It is incumbent upon the
26
investigator to establish the basis for delineating among patches and at a scale appropriate to the
phenomenon under consideration. Extreme caution must be exercised in comparing the values of
metrics computed for landscapes that have been defined and scaled differently.
Given the subjectivity in defining patches, scaling techniques can provide an objective means to help
determine the scale of patchiness (Gustafson 1998). In many studies, the identification of patches
reflects a minimum mapping unit that is chosen for practical or technical reasons and not for
ecological reasons. Scaling techniques such as those described previously can provide insight into
the scale of patchiness and whether there are hierarchies of scale. This information can then provide
the empirical basis for choosing the scale for mapping patches, rather than relying on subjective and
somewhat arbitrary criteria. Better yet, given the myriad ways to the define the landscape for the
phenomenon under investigation, it may be may be desirable to evaluate alternative landscape
definitions against ecological data and empirically determine the best definition. Few studies have
adopted this approach, but see Thompson and McGarigal (2002) for an example.
The format (raster versus vector) and scale (grain and extent) of the data can have a profound
influence on the value of many metrics. Because vector and raster formats represent lines differently,
metrics involving edge or perimeter will be affected by the choice of formats. Edge lengths will be
biased upward in raster data because of the stair-step outline, and the magnitude of this bias will vary
in relation to the grain of the image. In addition, the grain-size of raster data can have a profound
influence on the value of certain metrics. Metrics involving edge or perimeter will be affected; edge
lengths will be biased upwards in proportion to the grain size - larger grains result in greater bias.
Metrics based on cell adjacency information such as most of the aggregation metrics will be affected
as well, because grain size effects the proportional distribution of adjacencies. For example, as
resolution is increased (grain size reduced), the proportional abundance of like adjacencies (cells of
the same class) increases, and the measured contagion increases. Finally, the boundary of the
landscape can have a profound influence on the value of certain metrics. Landscape metrics are
computed solely from patches contained within the landscape boundary. If the landscape extent is
small relative to the scale of the organism or ecological process under consideration and the
landscape is an "open" system relative to that organism or process, then any metric will have
questionable meaning. Metrics based on nearest neighbor distance or employing a search radius can
be particularly misleading. Consider, for example, a local population of a bird species occupying a
patch near the boundary of a somewhat arbitrarily defined landscape. The nearest neighbor within
the landscape boundary might be quite far away; yet, in reality, the closest patch might be very close
but just outside the designated landscape boundary. In addition, those metrics that employ a search
radius (e.g., proximity index) will be biased for patches near the landscape boundary because the
searchable area will be much less than a patch in the interior of the landscape. In general, boundary
effects will increase as the landscape extent decreases relative to the patchiness or heterogeneity of
the landscape.
(2) Gaining a theoretical and empirical understanding of metric behavior – In addition to these technical issues,
current use of landscape metrics is constrained by the lack of a proper theoretical understanding of
metric behavior. The interpretation of a landscape metric is contingent upon having an adequate
understanding of how it responds to variation in landscape patterns (e.g., Gustafson and Parker
1992, Hargis et al. 1998, Jaeger 2000). Failure to understand the theoretical behavior of the metric
can lead to erroneous interpretations (e.g., Jaeger 2000). Neutral models (Gardner et al. 1987,
27
Gardner and O'Neill 1991, With 1997) provide an excellent way to examine metric behavior under
controlled conditions because they control the process generating the pattern, allowing
unconfounded links between variation in pattern and the behavior of the index (Gustafson 1998,
Neel et al. 2004). Unfortunately, existing neutral models are extremely limited in the types of
patterns that can be generated, so developing a better theoretical understanding of metric behaviour
through the use of neutral models is somewhat limited at this time.
(3) Metric redundancy: In search of parsimony – Although the literature is replete with metrics now
available to describe landscape pattern, there are still only two major components--composition and
configuration, and only a few aspects of each of these. Metrics often measure multiple aspects of
this pattern. Thus, there is seldom a one-to-one relationship between metric values and pattern.
Most of the metrics are in fact correlated among themselves (i.e., they measure a similar or identical
aspect of landscape pattern) because there are only a few primary measurements that can be made
from patches (patch type, area, edge, and neighbor type), and most metrics are then derived from
these primary measures. Some metrics are inherently redundant because they are alternate ways of
representing the same basic information (e.g., mean patch size and patch density). In other cases,
metrics may be empirically redundant, not because they measure the same aspect of landscape
pattern, but because for the particular landscapes under investigation, different aspects of landscape
pattern are statistically correlated.
Several investigators have attempted to identify the major components of landscape pattern for the
purpose of identifying a parsimonious suite of independent metrics (e.g., Li and Reynolds 1995,
McGarigal and McComb 1995, Ritters et al. 1995, Cushman et al. 2008). Although these studies
suggest that patterns can be characterized by only a handful of components, consensus does not
exist on the choice of individual metrics. These studies were constrained by the pool of metrics
existing at the time of each investigation. Given the expanding development of functional metrics,
particularly those based on a landscape mosaic perspective, it seems unlikely that a single
parsimonious set exists. Ultimately, the choice of metrics should explicitly reflect some hypothesis
about the observed landscape pattern and what processes or constraints might be responsible for
that pattern.
(4) A reference framework for interpreting landscape metrics – In practice, the interpretation of landscape
metrics is plagued by the lack of a proper reference framework. Landscape metrics quantify the
pattern of a single landscape at a snapshot in time. Yet it is often difficult, if not impossible, to
determine the ecological significance of the computed value without understanding the range of
natural variation in landscape pattern in space and time. For example, in disturbance-dominated
landscapes, patterns may fluctuate widely over time in response to the interplay between disturbance
and succession processes (e.g., Wallin et al. 1996, He and Mladenoff 1999, Haydon et al. 2000,
Wimberly et a. 2000). It is logical, therefore, that landscape metrics should exhibit statistical
distributions that reflect the natural temporal dynamics of the landscape. By comparison to this
distribution, a more meaningful interpretation can be assigned to any computed value.
Unfortunately, despite widespread recognition that landscapes are dynamic, there is a dearth of
empirical work quantifying the range of natural variation in landscape metrics. In part, this stems
from the difficulty of defining a meaningful temporal reference, but more often it stems from the
lack of historical spatial data. In the absence of historical data, however, a spatial reference
framework may be a viable option in some cases, whereby the focal landscape is compared to other
28
landscapes within the broader regional context (e.g., Cardille et al. 2005). Establishing a reference
framework to aid in the interpretation of landscape metrics should be a priority in future landscape
pattern analyses.
In summary, the importance of fully understanding each landscape metric before it is selected for
interpretation cannot be stressed enough. Specifically, these questions should be asked of each
metric before it is selected for interpretation:
•
•
•
•
•
•
•
Does it represent landscape composition or configuration, or both?
What aspect of composition or configuration does it represent?
Is it spatially explicit, and, if so, at the patch-, class-, or landscape-level?
How is it effected by the designation of a matrix element?
Does it reflect an island biogeographic or landscape mosaic perspective of landscape pattern
How does it behave or respond to variation in landscape pattern?
What is the range of variation in the metric under an appropriate spatio-temporal reference
framework?
Based on the answers to these questions, does the metric represent landscape pattern in a manner
and at a scale ecologically meaningful to the phenomenon under consideration? Only after
answering these questions should one attempt to draw conclusions about the pattern of the
landscape.
Ke y Po in t There are numerous challenges to the use and proper interpretation of landscape metrics, including: 1)
defining a relevant landscape for the phenomenon or question under consideration, 2) gaining a proper
theoretical and empirical understanding of metric behavior to aid in the interpretation of each metric, 3)
understanding the theoretical and empirical redundancies among metrics to ensure their parsimonious use,
and 4) developing a proper reference framework for ecologically interpreting the computed value of each
metric. There is no cookbook approach to dealing with these challenges; in general, it must come from
experience. It is incumbent upon the investigator or manager to be aware of these limitations and
interpret and present the results of their analyses within these limits.
29
USER GUIDELINES
Overview
Wh at is FRAGST AT S
FRAGSTATS is a spatial pattern analysis program for quantifying the structure (i.e., composition
and configuration) of landscapes. The landscape subject to analysis is user-defined and can represent
any spatial phenomenon. FRAGSTATS simply quantifies the spatial heterogeneity of the landscape
as represented in either a categorical map (i.e., landscape mosaic) or continuous surface (i.e.,
landscape gradient, expected in version 4.4); it is incumbent upon the user to establish a sound basis
for defining and scaling the landscape in terms of thematic content and resolution and spatial grain
and grain. We strongly recommend that you read the FRAGSTATS Background section before
using this program. Importantly, the output from FRAGSTATS is meaningful only if the landscape
as defined is meaningful relative to the phenomenon under consideration.
Sc ale Co n s id e ratio n s
FRAGSTATS requires the spatial grain or resolution of the grid to be > 0.001 m, but it places no
limit on the spatial extent of the landscape per se, although there are memory limitations on the size
of the grid that can be loaded. However, the distance- and area-based metrics computed in
FRAGSTATS are reported in meters and hectares, respectively. Thus, landscapes of extreme extent
and/or resolution may result in rather cumbersome numbers and/or be subject to rounding errors.
However, FRAGSTATS outputs data files in ASCII format that can be manipulated using any
database management program to rescale metrics or to convert them to other units (e.g., converting
hectares to acres).
Co m p u te r Re q u ire m e n ts
FRAGSTATS is a stand-alone program written in Microsoft Visual C++ for use in the Windows
operating environment and is a 32-bit process (even if running on a 64-bit machine). FRAGSTATS
was developed and tested on the Windows 7 operating systems, although it should run under all
Windows operating systems. Note, FRAGSTATS is highly platform dependent, as it was developed
in the Microscroft environment, so portability to other platforms is not easily accomplished.
FRAGSTATS is a compute-intensive program; its performance is dependent on both processor
speed and computer memory (RAM). Ultimately, the ability to process an image is dependent on the
availability of sufficient memory, and the speed of processing that image is dependent on processor
speed.
Of particular note is the memory constraint. FRAGSTATS is a 32-bit process and, as such, can only
use up to 2GB of memory; although if properly configured Windows can allow a 32-bit machine to
see up to 3GB of memory (with the /3GB flag set in boot.ini) and a 64-bit machine to see up to 4
GB of memory (if it is available, although the operating system reserves at least 1GB to itself
because it is built with /LARGEADDRESSAWARE flag set). FRAGSTATS loads the input grid
into memory and then computes all requested calculations. Thus, you must have sufficient memory
30
to load the grid and then enough leftover for processing and other operating system needs. As a
guide to help you determine whether you have sufficient memory to process a particular grid, you
can use the following formula: #cells*4bytes. Thus, if you have a 256 rows by 256 columns grid, the
memory requirement is 256 kb (256*256*4/1024 bytes/kb) just to load the grid; you still need lots
more memory to process the grid and meet your other operating system needs. Unfortunately, it is
nearly impossible for us to determine the exact memory requirement beyond that needed to load the
grid, because it depends on many unknown factors such as how many patches there are. The
memory requirement is not particularly constraining in a standard analysis, unless you are working
with very large images and limited computer memory. One potential solution to this problem if it
arises – unfortunately – is to get more memory, but this still has limits as noted above. Another
solution is to resample the grid to a coarser resolution to effectively reduce the grid size, but this is
only viable if the coarser resolution is meaningful ecologically given the specific application. An
alternative solution is to break up the landscape into several smaller landscapes and analyze each
separately. Indeed, in most applications, landscapes that are too large to fit in memory are more than
likely too large to be meaningful landscapes for purposes of analyzing landscape patterns (see the
Background document for a discussion of defining meaningful landscapes).
The memory requirement is especially constraining in the moving window analysis because
FRAGSTATS requires enough memory for the input grid plus one output grid, plus enough leftover
for other processing needs and system needs. If the moving window analysis is selected,
FRAGSTATS checks to see if it can allocate enough memory for three grids (i.e., 1 input grid + 1
output grid + enough leftover to insure performance). In the above example, you would need at
least 768 kb of memory to conduct a moving window analysis. Not too terribly constraining for
most computers when analyzing relatively small landscapes. However, consider a 10,000x10,000
input grid; to conduct a moving window analysis you would need 1.14 Gb of RAM.
Data Fo rm ats
FRAGSTATS accepts raster images in a variety of formats (below). All input data formats have the
following common requirements:
# All input grids should be signed integer grids (i.e., each cell should be assigned an integer value
corresponding to its class membership or patch type). Note, assigning the zero value to a class
may cause problems when the landscape contains a border because zero cannot be negative and
all border cells must be negative. Note, unsigned integer grids are acceptable if you do not
have a "border" (with negative cell values).
# All input grids must consist of perfectly square cells with cell size specified in meters. For
certain input formats (ASCII and BINARY), this is not an issue because cells are assumed to be
square and you are required to enter the cell size (in meters) in the graphical user interface.
FRAGSTATS assumes all other grid formats include header information that defines cell size.
Consequently these grids must have a metric projection (e.g., UTM) to ensure that cell size is
given in metric units. With the exception of ESRI ArcGrids (see below), FRAGSTATS accepts
cells that exhibit differences between height and width less than 0.1%. This means that cells
need to be approximately square, usually out to several decimal places. With respect to ESRI
ArcGrids, FRAGSTATS cannot accept anything but perfectly square cells. Importantly, this is a
31
hidden problem with ESRI ArcGrids in some cases. Although the grid description will say the
cells are square, this can be an artifact of the rounding done for display purposes. Sometimes the
non-square problem is beyond the first 14 decimal places, and ESRI does not allow you to see
more precision, even though it exist internally. The problem is that the error happens inside a
FRAGSTATS call of an ESRI function, and there is nothing we can do except catch the
exception and log it. Unfortunately, re-sampling the grid with the same cell size does solve the
problem. However, re-sampling the grid with a different cell size does solve the problem. Note,
the functions we are using from the ESRI library are those that were published and partially
documented 10 years ago, because these are the only functions they will allow third party access
to. In the meantime, they have added many more functions that ArcGIS uses but nobody else
can access. There is simply no ESRI documentation for handling situations like the one we're
facing here. Thanks again ESRI.
# All input grids must have a cell size > 0.001 m.
# Input grids should not have a nodata value that is the same as the designated background
value (see below for discussion on nodata, backgrounds, borders, and boundaries). One of the
basic assumptions of FRAGSTATS is that the nodata and background are distinct values, even
though the nodata is re-classified into negative background before any processing takes place.
Importantly, it is possible for the model to run fine and give correct results even when this
assumption is broken, but only if there is no actual background in the landscape. If there is any
background, it will be confused with nodata and re-classified incorrectly. With the image
formats containing header information (i.e., all but raw ASCII and Binary), the value of nodata
will be read from the image header and cannot be changed in FRAGSTATS. It is incumbent on
the user to specify a different value for the background, recognizing that it will only matter if
the image contains true background. With the image formats that do not contain header
information (i.e., raw ASCII and Binary), the user is required to enter a nodata value and ensure
that it is different from the specified background value, again recognizing that it will only
matter if the image contains true background.
# If by chance you are working with the same grid in different image formats (see below), it is best
to store these grids in separate folders, because there are some peculiar conflicts that can arise
via the use of the GDAL library to read certain grid formats that can cause the program to crash.
# Lastly, the path (directory) name containing the input grid should not contain any symbols,
Greek characters or anything but English letters and/or numbers.
There are some additional special considerations for each input data format, as follows:
# ESRI ArcGrid – Note, FRAGSTATS does not accept ArcGIS vector coverages or shapefiles.
To use ESRI ArcGrids (referred to as a "Raster" data format in ArcGIS) you must have ArcGIS
10 (or earlier) with a license for Spatial Analyst or ArcView 3.3 Spatial Analyst installed on your
computer and FRAGSTATS must have access to the dll libraries found in the "Bin" directory
(for ArcGIS installation) or the "Bin32" directory (for ArcView 3.3 installation). Note, the paths
to the Bin or Bin32 may differ depending on your version and installation. The path to the
corresponding bin directory should be specified in the windows system environmental variable
32
PATH (or path). In Windows 7, the Environmental variables can be accessed and edited from
the Control Panel - System and Security - System - Advanced system settings under the
"Advanced" tab and by clicking on "Environment Variables". In the list of System variables,
select the “path” variable and select "edit" and add the path to the corresponding bin directory.
The path may look something like this (but check to make sure you use the correct path for your
system): “;c:\Program Files (x86)\ArcGIS\Desktop10.0\Bin”. Note, the semicolon in the path
is used to separate items in the path list.
Importantly, do NOT add any file name (e.g. aigridio.dll) to the end of the path; the path should
end with “Bin”. In addition, make sure that the path to the Bin directory is the FIRST path listed
that contain ArcGIS.
In addition, if you are using ArcGrids, you cannot have spaces in the path to the directory
containing the grids. Note, this pertains to the path to the grids, not the path to the Bin folder as
the example above illustrates. For example, the following path to your input grids is illegal:
"c:\Users\Smith\My Documents\Grids" because of the space between “My” and
“Documents”. Note, this limitation applies only to ArcGrids; all other image formats can
accommodate spaces in the path.
# Raw ASCII grid, no header – Each record should contain 1 image row. Cell values should be
separated by a comma or a space(s). Note, it will be necessary to strip (delete) the header
information from the image file if it exists, but be sure to keep it for later reference regarding
background cell value, # rows, # columns, cell size, and nodata value. The default file name
extension for a raw ascii grid is .asc for file navigation purposes, but any extension can be used.
# Raw 8-, 16-, or 32-bit (binary) integer grid, no header – The only limitation on 8- and 16-bit
binary files is that they are not suitable for moving window analysis, which requires the output
grids to be floating points (32 bit files). Note, it will be necessary to strip (delete) the header
information from the image file if it exists, but be sure to keep it for later reference regarding
background cell value, # rows, # columns, cell size, and nodata value. The default file name
extension for a raw binary grid is .raw for file navigation purposes, but any extension can be
used.
# GeoTIFF grid – The default file name extension for a GeoTIFF grid is .tif for file navigation
purposes, but any extension can be used.
# VTP binary terrain format grid – The default file name extension for a VTP binary terrain
format grid is .bt for file navigation purposes, but any extension can be used.
# ESRI header labelled grid – The default file name extension for an ESRI header labelled grid
is .bil for file navigation purposes, but any extension can be used.
# ERDAS Imagine grid – The default file name extension for an ERDAS Imagine grid is .img
for file navigation purposes, but any extension can be used.
# PCRaster grid – The default file name extension for a PCRaster grid is .map for file navigation
33
purposes, but any extension can be used.
# SAGA GIS binary format grid – The default file name extension for a SAGA GIS binary
format grid is .sdat for file navigation purposes, but any extension can be used.
Ras te r Co n s id e ratio n s
It is important to realize that the depiction of edges in raster images is fundamentally constrained by
the lattice grid structure. Consequently, raster images portray lines in stair-step fashion. The result is
an upward bias in the measurement of edge length; that is, the measured edge length is always more
than the true edge length. The magnitude of this bias depends on the grain or resolution of the
image (i.e., cell size), and the consequences of this bias with regards to the use and interpretation of
edge-based metrics must be weighed relative to the phenomenon under investigation.
Ve c to r to Ras te r Co n v e rs io n
In some investigations, it may be necessary to convert a vector image into a raster image in order to
run FRAGSTATS. It is critical that great care be taken during the rasterization process and that the
resulting raster image be carefully scrutinized for accurate representation of the original image. For
example, during the rasterization process, it is possible for disjunct patches to join and vice versa.
This problem can be quite severe (e.g., resulting in numerous 1-cell patches and disrupting the
continuity of linear landscape elements) if the cell size chosen for the rasterization is too large
relative to the minimum patch dimension in the vector image. In general, a cell size less than ½ the
narrowest dimension of the smallest patches is necessary to avoid these problems.
Le v e ls o f Me tric s
FRAGSTATS (v4.2 and earlier) computes 3 levels of metrics corresponding to: (1) each patch in the
mosaic; (2) each patch type (class) in the mosaic; and (3) the landscape mosaic as a whole. These
metrics are described in detail in the FRAGSTATS Metrics section. In addition, FRAGSTATS
computes the adjacency matrix (i.e., tally of the number of cell adjacencies between each pairwise
combination of patch types, including like-adjacencies between cells of the same class), which is
used in the computation of several class- and landscape-level aggregation metrics. Note, cell-level
metrics are scheduled to be included in version 4.3.
O u tp u t File s
Depending on which metrics are selected by the user, FRAGSTATS currently creates 4 output files
corresponding to the three levels of metrics and the adjacency matrix (cell-level metrics will be
included in v4.3). The user supplies a "basename" for the output files and FRAGSTATS appends
the extensions .patch, .class, .land, and .adj to the basename. All files created are comma-delimited
ASCII files and viewable. These files are formatted to facilitate input into spreadsheets and database
management programs:
# "basename".patch file.–Contains the patch metrics; the file contains 1 record (row) for each
34
patch in the landscape; columns represent the selected patch metrics. If a batch file is analyzed,
the file contains 1 record for each patch in each landscape specified in the batch file. The first
record is a column header consisting of the acronyms for all the metrics that follow. For a single
landscape, the patch output file would be structured as follows:
LID,
D:\testgrid,
D:\testgrid,
Etc.
PID,
9,
0,
TYPE,
forest,
shrub,
AREA,
1.0000,
4.0000,
PERIM, GYRATE, CORE
400.0000, 38.1195,
0.1600
800.0000, 76.4478,
1.9600
# "basename".class file.–Contains the class metrics; the file contains 1 record (row) for each
class in the landscape; columns represent the selected class metrics. If a batch file is analyzed, the
file contains 1 record for each class in each landscape specified in the batch file. The first record
is a column header consisting of the acronyms for all the metrics that follow. For a single
landscape, the class output file would be structured as follows:
LID,
D:\testgrid,
D:\testgrid,
Etc.
TYPE,
forest,
shrub,
CA,
8.0000,
21.0000,
PLAND,
22.5000,
26.2500,
NP,
4,
3,
PD,
5.0000,
3.7500,
LPI
15.0000
12.5000
# "basename".land file.–Contains the landscape metrics; the file contains 1 record (row) for the
landscape; columns represent the selected landscape metrics. If a batch file is analyzed, the file
contains 1 record for each landscape specified in the batch file. The first record is a column
header consisting of the acronyms for all the metrics that follow. For a single landscape, the
landscape output file would be structured as follows:
LID,
D:\testgrid,
TA,
80.0000,
NP,
12,
PD,
15.0000,
LPI,
15.0000,
TE,
ED
7800.0000, 97.5000
# “basename”.adj file.–Contains the class adjacency matrix; the file contains a simple header in
addition to 1 record (row) for each class in the landscape, and is given in the form of a 2-way
matrix. Specifically, first record contains the input file name, including the full path. The second
record and first column contain the class IDs (i.e., the grid integer values associated with each
class), and the elements of the matrix are the tallies of cell adjacencies for each pairwise
combination of classes. For a single landscape, the adjacency output file would be structured as
follows:
D:\testgrid
Class ID / ID, 2,
2,
6840,
3,
120,
4,
100,
5,
10,
3,
130,
7960,
140,
40,
4,
120,
160,
9880,
30,
5,
10,
40,
40,
3080,
Background
0
10
20
16
Note, the adjacency tallies are generated from the double-count method in which each cell side is
35
counted twice–at least for all positively-valued nonbackground cells–and only the 4 orthogonal
neighbors are considered. In addition, the matrix may not be symmetrical if a landscape border
is present because landscape boundary edges are only counted once. For example, a cell of
class 3 (inside the landscape) adjacent to a cell of class -5 (in the landscape border) results in
an adjacency for class 3; specifically, a 3 (row) -5 (column) adjacency. It does not result in an
adjacency for class 5 (row), because the border cells themselves are not evaluated. For this
reason, the adjacency matrix must be read as follows: each row represents the adjacency
tallies for cells of that class, and the sum of adjacencies across all columns represents the
total number of adjacencies for that class. These row totals should equal the number of
positively-valued cells (i.e., inside the landscape) of the corresponding class times 4 (i.e., 4
surfaces for each cell). These row totals are used in several of the aggregation metrics. Note
that the adjacency matrix includes a column for background adjacencies, which represent cell
surfaces of the corresponding class adjacent to designated background. If there is no
specified background in the input landscape and a landscape border is not present, then the
background adjacencies represent the cell surfaces along the landscape boundary–which are
treated as background in the absence of a border. If a border is provided and no background
is specified, then the background adjacencies will equal zero because every cell surface,
including those along the landscape boundary, will be adjacent to a real non-background
class. If a batch file is analyzed, the adjacency matrices corresponding to each landscape
specified in the batch file are appended to the same file.
No d ata, B ac kg ro u n d s , B o rd e rs , an d B o u n d arie s
FRAGSTATS accepts images in several forms, depending on whether the image contains nodata
and/or background, and whether the landscape contains a border outside the landscape boundary
(Fig. 1). The distinction among nodata, background, border, and boundary and how they affect the
landscape analysis and the calculations of various metrics is a source of great confusion and thus
great importance. Great care should be taken to fully understand these distinctions before trying to
run FRAGSTATS. We strongly suggest that you read through this section twice, once to familiarize
yourself with the terminology and a second time to understand the implications.
# Nodata – Some images will contain nodata cells – unclassified areas of the input grid. These
areas may be inside the landscape boundary (see below) or, more typically, outside the landscape
boundary. In either case, these are unclassified cells that are considered “external” to the
landscape of interest and are essentially ignored by FRAGSTATS. For example, a nonrectangular landscape will have nodata cells surrounding it in order to fill out a rectangular grid,
since all grids are at least internally stored as rectangular rasters. Often, the nodata cells are
invisible to the user, since most GIS programs don’t even display the nodata cells. Thus, it is
easy to forget about the nodata cells and ignore their treatment in FRAGSTATS. However, this
can be a mistake as it is important to distinguish between nodata cells, for which FRAGSTATS
will always consider them to be “external” to the landscape of interest, and background cells (see
below), which will be treated as “internal” to the landscape of interest if given positive cell
values and thus contribute to the total landscape area. It is critically important to ensure that the
nodata cell value is different than the user-specified background value – when background
exists.
36
Importantly, all nodata cells will be reassigned negative (user-specified) background cell values
by FRAGSTATS and treated as such. Therefore, all nodata cells will be considered “external” or
“outside” the landscape of interest, even if they are located within the landscape boundary.
37
Figure 1. Alternative image formats with regards to background (given a class value of 99
here) and border. The thick solid line represents the landscape boundary. Positive values
are ‘inside’ the landscape of interest and contribute to the computed total landscape area;
negative values are ‘outside’ the landscape of interest and are only utilized to determine
edge types for patches along the landscape boundary.
38
# Landscape boundary – Every image will include a landscape boundary that defines the
perimeter of the landscape and surrounds the patch mosaic of interest. The boundary is simply
an invisible line around the landscape of interest. It is not given explicitly in the image; rather, it
is defined by an imaginary line around the outermost cells of positively valued cells. The
landscape boundary distinguishes between cells inside the landscape of interest from those
outside, and thus ultimately determines the total landscape area. All positively valued cells are
assumed to be inside the landscape of interest and are thus included in the total area of the
landscape, regardless of whether they are classified as background (see below) or not. This is
important, because many metrics include total landscape area in their calculation. Note, in most
cases the landscape boundary will surround a single contiguous region of positively valued cells.
However, it is possible to have disjunct regions of positively valued cells. In this case, the
landscape boundary is not a single continuous line around the landscape of interest, but rather
separate boundaries around each disjunct region of interest. The important point is that
positively valued cells are inside the landscape of interest, while negatively valued cells are
outside, and the landscape boundary is the imaginary line(s) that separates inside from outside.
Hence, if the input image contains all positively valued cells, then the entire grid is assumed to
be inside the landscape of interest and the landscape boundary represents an imaginary line
around the entire grid. If the input image contains negatively valued cells, then those cells are
assumed to be outside the landscape of interest and thus outside the landscape boundary. In this
case, the edge between positively and negatively valued cells represents the landscape boundary.
The landscape boundary is important in the absence of a landscape border (see below) because
FRAGSTATS needs to know how to treat the edges along the boundary in all edge calculations.
In the absence of a border, the landscape boundary will be treated according to user
specifications (see below).
# Background – An image may include background – an undefined area either ‘inside’ or
‘outside’ the landscape of interest. Note that background can exist as ‘holes’ in the landscape
and/or can partially or completely surround the landscape of interest. The background value can
be any integer value. Positively valued cells of background are assumed to be ‘inside’ the
landscape of interest; negatively valued cells of background are assumed to be ‘outside’ the
landscape of interest. This distinction is important, as noted above, because positively valued
background (interior background) will be included in the total landscape area, and thus will
affect many metrics, even though it will not be treated as a patch per se (see below). Negatively
valued background (external background) will be treated the same as nodata and can have a
minor affect on the computed metrics if certain functional metrics requiring edge or patch
adjacency information are selected (see below). Further, via the graphical user interface (see
below), any class or combination of classes can be treated (i.e., reclassified) as background for a
particular analysis. There are several critical issues regarding how background is handled by
FRAGSTATS:
1. Interior background (i.e., positively valued background) is included in the total landscape
area and thus effects metrics that include total landscape area in their calculations. However,
and this is quite tricky, interior background is in essence excluded from the total landscape
area in a number of class and landscape metrics that involve summarizing patch or class
metrics. For example, mean patch area is based on the average size of patches at the class or
landscape level. If interior background is present, mean patch size as computed by
39
FRAGSTATS will not equal the total landscape area divided by the number of patches,
because the total landscape area includes background area not accounted for in any patch.
Similarly, the area-weighted mean of any patch metric (i.e., distribution statistics at the class
and landscape level; see FRAGSTATS Metrics documentation) weights each patch by its
proportional area representation. Here, the proportional area of each patch is not based on
the total landscape area, but rather the sum of all patch areas, which is equivalent to the total
landscape area minus interior background. Similarly, a number of landscape metrics are
computed from the proportion of the landscape in each class (e.g., Shannon’s and Simpson’s
diversity). Here, proportional area of each class is not based on total landscape area because
the proportions must sum to 1 across all classes. Instead, the proportions are based on the
sum of all class areas, which is equivalent to the total landscape area minus interior
background. Given the subtle differences in how interior background affects various metrics,
it behooves you to carefully read the FRAGSTATS Metrics documentation pertaining to
each metric you choose, assuming of course that interior background is an issue.
2. Exterior background (i.e., negatively valued background) can have a minor effect on the
analysis if functional metrics are selected. Note, all nodata cells are reclassified to exterior
background internally by FRAGSTATS. Exterior background is assumed to be ‘outside’ the
landscape of interest and thus has no effect on the area-based metrics; however, the border
between exterior background and interior cells can effect the edge-based metrics (e.g., core
area, edge contrast, and aggregation metrics). Thus, the “extent” of exterior background in
the input landscape has no effect, but the “length of edge” between exterior background and
interior landscape cells can have an effect.
3. Background (both interior and exterior) cells adjacent to non-background classes represent
edges that must be accounted for in all edge-related metrics. The user specifies how
background edge segments should be handled in all edge-related calculations (see below).
# Landscape border – An image also may include a landscape border; a strip of land surrounding
the landscape of interest (i.e., outside the landscape boundary) within which patches have been
delineated and classified. Patches in the border must be set to the negative of the appropriate
patch type code. For example, if a border patch is a patch type of code 34, then its cell value
must be -34 (negative 34). The border can be any width (as long as it is at least 1 cell wide) and
provides information on patch type adjacency for patches on the edge of the landscape (i.e.,
along the landscape boundary). Essentially, patches in the border provide information on patch
type adjacency for patches in the landscape of interest located along the landscape boundary; all
other attributes of the patches in the border are ignored because they are outside the landscape of
interest. Thus, the border affects only metrics where patch type adjacency is considered: core
area, edge contrast, and aggregation metrics.
Under most circumstances, it is probably not valid to assume that all edges function the same.
Indeed, there is good evidence that edges vary in their affects on ecological processes and
organisms depending on the nature of the edge (e.g., type of adjacent patches, degree of
structural contrast, orientation, etc.). Accordingly, the user can specify a file containing edge
contrast weights (described in more detail in the Contrast Metrics section of the FRAGSTATS
Metrics documentation) for each combination of patch types (classes), including adjacencies
40
involving background if it exists. Briefly, these weights represent the magnitude of edge contrast
between adjacent patch types and must range between 0 (no contrast) and 1 (maximum
contrast). Edge contrast weights are used to compute several edge-based metrics. If this weight
file is not provided, these edge contrast metrics are simply not computed. Generally, if a
landscape border is designated, a weight file will be specified as well, because one of the
principal reasons for specifying a border is when information on edge contrast is deemed
important. If a border is present, the edge contrast associated with all landscape boundary edge
segments is made explicit due to knowledge of the abutting patch types. If a border is absent,
then all edge segments along the landscape boundary are treated the same as background, as
specified in the user-provided edge contrast weight file. Note, however, that the presence of a
landscape border will have no affect on the edge contrast metrics if a contrast weight file is not
specified – because these metrics will not be computed.
Similarly, the user can specify a file containing edge depths (described in more detail in the Core
Area Metrics section of the FRAGSTATS Metrics documentation) for each combination of
patch types (classes), including adjacencies involving background if it exists. Briefly, edge depths
represent the distance at which edge effects penetrate into a patch and must be given in distance
units (meters); edge depths can be any number $ 0. However, when implementing edge depths
for the purpose of determining core areas, FRAGSTATS is constrained by the minimum
resolution established by the cell size. Thus, in effect, edge depths will be rounded to the nearest
distance in increments of the cell size. For example, if the cell size is 30 m, and you specify a 100
m edge depth, the edge mask used to mask cells along the edge of a patch (i.e., eliminate them
from the “core” of the patch) will be 3 cells wide (90 m), because it is not possible to use a mask
that is 3.3 cells wide. Similarly, a specified edge depth of 50 m will in effect be rounded up to 2
cells (60 m). Therefore, it is generally advisable to specify edge depths in increments equal to the
cell size. Edge depths are used to compute several core area-based metrics. If this edge depth file
is not provided, these core area metrics are simply not computed. Typically, if a landscape
border is designated, an edge depth file will be specified as well, because one of the principal
reasons for specifying a border is when information on edge effects is deemed important. If a
border is present, the edge depths associated with all landscape boundary edge segments is made
explicit due to knowledge of the abutting patch types. If a border is absent, then all edge
segments along the landscape boundary are treated the same as background, as specified in the
user-provided edge depth file. Note, however, that the presence of a landscape border will have
no affect on the core area metrics if an edge depth file is not specified – because these metrics
will not be computed.
A landscape border is also useful for determining patch type adjacency for many of the aggregation
metrics. These metrics (described in more detail in the Aggregation Metrics section of the
FRAGSTATS Metrics documentation) require information on cell adjacency; that is, the
abutting class values for the side of every cell. The proportional distribution of cell adjacencies is
used to compute a variety of landscape texture metrics. Although a landscape border is not often
designated for the primary purpose of computing these texture metrics, a border will inform the
calculation of these metrics. If a border is present, the adjacencies associated with all landscape
boundary edge segments is made explicit due to knowledge of the abutting patch types. If a
border is absent, then all edge segments along the landscape boundary are treated the same as
background and the corresponding cell adjacencies are ignored in the calculation of these
41
metrics.
Metrics based on edge length (e.g., total edge or edge density) are affected by these
considerations as well. If a landscape border is present, then edge segments along the boundary
are evaluated to determine which segments represent ‘true’ edge and which do not. For example,
an edge segment between cells with class value 5 (inside the landscape of interest) and cells with
class value -5 (outside the landscape of interest; i.e., in the border) does not represent a true
edge; in this case, the landscape boundary artificially bisects an otherwise contiguous patch and
the edge is not counted in the calculations of total edge length. Conversely, an edge segment
between class 5 and -3 represents a true edge and is counted. If a landscape border is absent,
then the entire boundary is treated as background and is treated according to a user-specified
proportion. For example, if the user specifies that 50% of the landscape boundary should be
treated as true edge, then 50% of the landscape boundary involving background will be
incorporated into the edge length metrics. In other words, regardless of whether a landscape
border is present or not, if a background class is specified, then a user-specified proportion of
edge bordering background is treated as true edge and the remainder is ignored.
We recommend including a landscape border, especially if edge contrast, core area, or patch type
adjacency is deemed important. In most cases, some portions of the landscape boundary will
constitute ‘true’ edge (i.e., an edge with a contrast weight > 0) and others will not, and it will be
difficult to estimate the proportion of the landscape boundary representing true edge. Moreover,
it will be difficult to estimate the average edge contrast weight or edge depth for the entire
landscape boundary. Thus, the decision on how to treat the landscape boundary will be
somewhat subjective and may not accurately represent the landscape. In the absence of a
landscape border, the affects of the decision regarding how to treat the landscape boundary on
the landscape metrics will depend on landscape extent and heterogeneity. Larger and more
heterogeneous landscapes will have a greater internal edge-to-boundary ratio and therefore the
boundary will have less influence on the landscape metrics. Of course, only those metrics based
on edge lengths and types are affected by the presence of a landscape border and the decision on
how to treat the landscape boundary. When edge-based metrics are of particular importance to
the investigation and the landscapes are small in extent and relatively homogeneous, the
inclusion of a landscape border and the decision regarding the landscape boundary should be
considered carefully.
So, let’s try to put all of this together. There are five types of metrics affected by landscape
boundary, background, and border designations: (1) total landscape area, (2) edge length metrics, (3)
core area metrics, (4) contrast metrics, and (5) aggregation metrics. Let’s consider several scenarios
involving various combinations of background and border, and how each of these types of metrics
will be treated under each scenario.
# Scenario 1 – Input landscape contains all positively valued cells of non-background classes (Fig.
1a). In this case, the entire grid is assumed to be in the landscape of interest and every cell
belongs to a non-background class. The landscape boundary surrounds the entire grid and there
is no border or background present (this is probably the most common scenario).
Total landscape area.–All cells are included in the total landscape area calculation.
42
Edge length metrics.–User must specify the proportion of the landscape boundary to include as
edge. All other edges are explicit.
Core area metrics.–The landscape boundary is treated like background; the user must specify
the edge depth for cells abutting background in the edge depth file, and this depth is applied
to the landscape boundary. All other edges are explicit; their edge depths are specified in the
edge depth file.
Contrast metrics.–The landscape boundary is treated like background; the user must specify the
edge contrast for cells abutting background in the edge contrast weight file, and this weight
is applied to the landscape boundary. All other edges are explicit; their edge contrast weights
are specified in the edge contrast weight file.
Aggregation metrics.–The landscape boundary is treated like background and is simply ignored
since there is no information available on patch type adjacency.
# Scenario 2 – Input landscape contains all positively valued cells, but includes a background class
(Fig. 1b). In this case, the entire grid is assumed to be in the landscape of interest , but some
cells belong to a background class. Here, the background is interior because it is positively valued
and thus inside the landscape of interest. The landscape boundary surrounds the entire grid and
there is no border present.
Total landscape area.–All cells are included in the total landscape area calculation.
Edge length metrics.–User must specify the proportion of the landscape boundary and
background edges to include as edge. All other edges are explicit.
Core area metrics.–The landscape boundary is treated like background; the user must specify
the edge depth for cells abutting background in the edge depth file, and this depth is applied
to both the landscape boundary and background edges. All other edges are explicit; their
edge depths are specified in the edge depth file.
Contrast metrics.–The landscape boundary is treated like background; the user must specify the
edge contrast for cells abutting background in the edge contrast weight file, and this weight
is applied to both the landscape boundary and background edges. All other edges are
explicit; their edge contrast weights are specified in the edge contrast weight file.
Aggregation metrics.–The landscape boundary and background are treated similarly; both are
simply ignored when evaluating adjacencies since there is no information available on patch
type adjacency in either case.
# Scenario 3 – Input landscape contains a mixture of positively valued cells and negatively valued
background cells (Fig. 1c). Note, it doesn’t matter whether the negatively valued background
cells are located entirely on the periphery of the positively valued cells (i.e., outside the landscape
of interest) or located as holes in the interior of the landscape, or a combination of the two. In
all cases, the positively valued cells are is assumed to be inside the landscape of interest, whereas
43
the negatively valued background cells are assumed to be outside the landscape of interest and
thus outside the landscape boundary. In figure 1c, the background is entirely exterior because it is
all negatively valued and thus outside the landscape of interest (even though some of the exterior
background patches are embedded as holes within the landscape). The landscape boundary
separates contiguous regions of positively valued cells from the negatively valued cells and there
is no border present. Alternatively, the exterior background could be considered border, but the
use of border is generally reserved for situations involving negatively valued non-background
cells.
Total landscape area.–All positively valued cells are included in the total landscape area
calculation; negatively valued cells (here, all background) are ignored.
Edge length metrics.–User must specify the proportion of the landscape boundary and
background edges (in this case, they are the same) to include as edge. All other edges are
explicit.
Core area metrics.–The landscape boundary is treated like background; in this case, the entire
landscape boundary is in fact also background. The user must specify the edge depth for
cells abutting background in the edge depth file, and this depth is applied to the background
edges (in this case, all on the landscape boundary). All other edges are explicit; their edge
depths are specified in the edge depth file.
Contrast metrics.–The landscape boundary is treated like background; in this case, the entire
landscape boundary is in fact also background. The user must specify the edge contrast for
cells abutting background in the edge contrast weight file, and this weight is applied to the
background edges (in this case, all on the landscape boundary). All other edges are explicit;
their edge contrast weights are specified in the edge contrast weight file.
Aggregation metrics.–The landscape boundary and background (in this case, they are the same)
are treated similarly; they are simply ignored when evaluating adjacencies since there is no
information available on patch type adjacency.
# Scenario 4 – Input landscape contains a mixture of positively valued cells, including some
positively valued background cells, and negatively valued background cells (Fig. 1d). Note, as in
scenario 3, it doesn’t matter whether the negatively valued background cells are located entirely
on the periphery of the positively valued cells (i.e., outside the landscape of interest) or located
as holes in the interior of the landscape, or a combination of the two. In all cases, the positively
valued cells are is assumed to be inside the landscape of interest , whereas the negatively valued
background cells are assumed to be outside the landscape of interest and thus outside the
landscape boundary. Here, the background is a combination of interior and exterior background.
The landscape boundary separates contiguous regions of positively valued cells from the
negatively valued cells and there is no border present. As noted in scenario 3, the exterior
background could be considered border, but the use of border is generally reserved for
situations involving negatively valued non-background cells.
Total landscape area.–All positively valued cells, including the ‘interior’ background, are
44
included in the total landscape area calculation; negatively valued cells (here, all background)
are ignored.
Edge length metrics.–User must specify the proportion of the landscape boundary (in this case,
all background) and interior background edges to include as edge. All other edges are
explicit.
Core area metrics.–The landscape boundary is treated like background; in this case, the entire
landscape boundary is in fact also background. The user must specify the edge depth for
cells abutting background in the edge depth file, and this depth is applied to all background
edges (in this case, both on the landscape boundary and interior). All other edges are explicit;
their edge depths are specified in the edge depth file.
Contrast metrics.–The landscape boundary is treated like background; in this case, the entire
landscape boundary is in fact also background. The user must specify the edge contrast for
cells abutting background in the edge contrast weight file, and this weight is applied to all
background edges (in this case, both on the landscape boundary and interior). All other
edges are explicit; their edge contrast weights are specified in the edge contrast weight file.
Aggregation metrics.–The landscape boundary (in this case, all background) and interior
background are treated similarly; both are simply ignored when evaluating adjacencies since
there is no information available on patch type adjacency in either case.
# Scenario 5 – Input landscape contains a mixture of positively valued non-background cells and
negatively valued non-background cells (i.e., a true border; Fig. 1e). In this case, the positively
valued cells are is assumed to be inside the landscape of interest , whereas the negatively valued
cells are assumed to be outside the landscape of interest and thus outside the landscape boundary.
The landscape boundary separates contiguous regions of positively valued cells from the
negatively valued cells; no background exists; and there is a true border present. This is
unquestionably the ideal scenario because every cell is classified into a real class (i.e., no
background) and a border is included to inform all edge, core, and adjacency calculations.
Total landscape area.–All positively valued cells are included in the total landscape area
calculation; negatively valued cells are ignored.
Edge length metrics.–Because a border is present and there is no background, all edges are
explicit; that is, the image provides explicit information on whether every edge segment
along the boundary is a true edge or not. In this case, the user does not need to specify the
proportion of the landscape boundary to include as edge. In fact, any user specification in
this regard via the user interface will be disregarded.
Core area metrics.–Because a border is present and there is no background, all edges are
explicit; that is, the image provides explicit information on the abutting patch types along the
boundary. In this case, all edge depths are specified in the edge depth file.
Contrast metrics.–Because a border is present and there is no background, all edges are explicit;
45
that is, the image provides explicit information on the abutting patch types along the
boundary. In this case, all edge contrast weights are specified in the edge contrast weight file.
Aggregation metrics.–Because a border is present and there is no background, all edges are
explicit; that is, the image provides explicit information on the abutting patch types along the
boundary. In this case, all boundary edge segments are included in the adjacency
calculations.
# Scenario 6 – Input landscape contains a mixture of positively valued cells, including both
background and non-background classes, and negatively valued cells, including both background
and non-background classes (Fig. 1f). This is the most complex scenario involving a complicated
mixture in interior and exterior background and a border. In this case, all positively valued cells
(including interior background) are is assumed to be inside the landscape of interest, whereas the
negatively valued cells are assumed to be outside the landscape of interest and thus outside the
landscape boundary. The landscape boundary separates contiguous regions of positively valued
cells from the negatively valued cells. A true border is present, but it includes some background
class. This is perhaps also an ideal scenario, like scenario 5, but contains a realistic, sometimes
unavoidable, situation in which some areas must be classified as background, either because
there is no information available from which to classify them, or because it is deemed desirable
ecologically to treat these areas as undefined background.
Total landscape area.–All positively valued cells, including the interior background, are included
in the total landscape area calculation; negatively valued cells are ignored.
Edge length metrics.–Because a border is present but contains some background and there is
interior background, only a portion of edges are explicit; that is, some edges abut
background (either interior or exterior) and it is not explicit whether they represent true edge
or not. In this case, the user must specify the proportion of edges involving background to
include as edge.
Core area metrics.–Because a border is present but contains some background and there is
interior background, only a portion of edges are explicit. Here, all boundary edges involving
background and interior background edges are treated the same. The user must specify the
edge depth for cells abutting background in the edge depth file, and this depth is applied to
all background edges (in this case, both on the landscape boundary and interior). All other
edges are explicit; their edge depths are specified in the edge depth file.
Contrast metrics.–Because a border is present but contains background, and there is interior
background, only a portion of edges are explicit. Here, all boundary edges involving
background and interior background edges are treated the same. The user must specify the
edge contrast weight for cells abutting background in the edge contrast weight file, and this
weight is applied to all background edges (both on the landscape boundary and interior). All
other edges are explicit; their contrast weights are specified in the edge contrast weight file.
Aggregation metrics.–Because a border is present but contains some background, and there is
interior background, only a portion of edges are explicit. In this case, edge segments
46
involving background (both on the landscape boundary and interior) are ignored in the
adjacency calculations.
Installation
FRAGSTATS installation is quick and easy (hopefully). After downloading the zip file, simply
extract the file to any folder, double click on the frg_setup_4.*.exe file and follow the
instructions. To complete the installation you may need to disable your virus protection software, or
at least disable the disk access protection. Note, to work with ArcGIS grids, see additional
instructions in the Overview--Data Formats section. Once installed, FRAGSTATS is run by double
clicking on the frg_gui.exe file or selecting it from the start menu or desktop.
Running via the Graphical User Interface
FRAGSTATS is run via a graphical user interface (GUI). This GUI is intended to facilitate the
parameterization process and to provide maximum flexibility in the analysis. What follows is a stepby-step description of how to parameterize and run FRAGSTATS using the GUI:
Step 1. Starting the FRAGSTATS GUI
Step 2. Creating a Model
Step 3. Selecting Inputs
Step 4. Specifying Common Tables
Step 5. Setting Analysis Parameters
Step 6. Selecting and Parameterizing Patch, Class, and Landscape Metrics
Step 7. Executing FRAGSTATS
Step 8. Browsing and Saving the Results
Step 9. Getting Help
Ste p 1. Startin g th e FRAGST AT S GUI
To start FRAGSTATS, simply double click on the frg_gui.exe file and (hopefully) the opening
window shown in figure 2 will display.
The anatomy of the opening window is quite simple and is similar to many windows-based
programs:
# Title bar – The title bar lists the name of the current or open model file. The model file
contains the current parameterization scheme (see below). When you first start FRAGSTATS, a
model file does not exist. Consequently, the title is listed as “Fragstats 4.?” until you either create
a New model or Open an existing (saved) model. After selecting a New model, the title bar lists
“Unnamed” until the model is saved and named. After opening an existing (saved) model the
title bar lists the name of the model file.
# Menu bar – The menu bar consists of a several items that are not particularly relevant until a
47
Figure 2. Anatomy of the FRAGSTATS opening user
interface.
model is created or opened in the next step; as such, these items are discussed below.
# Tool bar – The tool bar consists of several common tools that are also accessible from the
drop-down menus, as discussed below.
# Action bar – The action bar merely echos the action that will be taken by the menu option or
tool button selected by the mouse. Thus, placing the mouse over the New button on the tool
bar will echo “create a new file”, which is the action that will happen if the button is selected.
# Minimize – Minimize window.
# Resize – Resize window.
# Close Program – Close FRAGSTATS.
Ste p 2. Cre atin g a Mo d e l
The first time you run FRAGSTATS you must create a new model. A model is simply a
FRAGSTATS formatted file that contains the model parameterization. Once a model has been
created and saved, it can be opened and run, or modified before running. The following options are
available from the tool bar or from the File drop-down menu:
# New – Creates a new (or blank) model file and opens the dialog shown in figure 3.
# Open – Opens an existing (previously saved) model file and the dialog shown in figure 3, but
48
containing whatever parameters were previously saved.
Figure 3. Model dialog for paramterizing FRAGSTATS, shown here for a “new” model that has
yet to be parameterized, and with the “Input layers” tab in the left panel selected.
# Save – Saves the current model to a file with the extension .fca. Note, if you are saving a model
file for the first time, you will be prompted to specify a location and file name. If you are saving
model with the same name as one that already exists in the current directory, you will be asked
whether to replace the existing file. This model file contains all the parameter settings in the
dialog boxes (below) at the time the file was saved. This can be very useful if you are running
FRAGSTATS repeatedly with the same or similar parameterization schemes.
# Save as – Saves the current model to a location and file name (with extension .fca) that you
specify.
Ste p 3. Se le c tin g In p u t Lay e rs
Once a new model has been created (Fig. 3), the next step is to select input layers (i.e., input grids).
Note, if you opened a saved model, you can modify the input parameters as well.
In the left pane of the model dialog window make sure the Input layers tab is selected. The top
half of the left pane is labeled Batch management and this is where you select the input grids
either singly (Add layer) or as a previously defined batch file (Import batch), and/or edit or modify
the input layers (Edit layer info), as follows:
49
# Add layer – Click Add layer to add a grid to the model (to be analyzed). This will open the
dialog shown in figure 4.
Figure 4. Dialog for adding a grid to the model.
First, select a Data type by clicking on the corresponding line in the left pane. FRAGSTATS
accepts several types of input image data formats. See Overview –Data Formats section for
details. Briefly, all input images should be integer grids (i.e., each cell should be assigned an
integer value corresponding to its class membership or patch type). Note, assigning the value 0
to a class is problematic if that class exists in the landscape border, since negative zeros are not
allowed, and thus 0 should not be used as a class value. In addition, all input grids should consist
of square cells with the measurement units in meters. Choose one of the following:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Raw ASCII grid, ascii grid (without header)[.asc]
Raw 8-bit integer grid, binary grid (without header)[.raw]
Raw 16-bit integer grid, binary grid (without header)[.raw]
Raw 32-bit integer grid, binary grid (without header)[.raw]
ESRI grid, ArcGIS raster grid (contains header)
GeoTIFF grid (contains header)[.tif]
VTP binary terrain format grid (contains header)[.bt]
ESRI header labelled grid (contains header)[.bil]
ERDAS Imagine grid (contains header)[.img]
PCRaster grid (contains header)[.map]
SAGA GIS binary format grid (contains header)[.sdat]
Second, select a dataset by entering the full path and file name of the input grid in the Dataset
name box, or click the navigate to button (...) and navigate to and select the desired input grid
of the corresponding data type. Note, the navigation window is context sensitive, so that only
files with the appropriate extension will be displayed by default (see default extensions in square
brackets above). However, you can change the extension filter to “all types” in the navigation
dialog by clicking the drop-down arrow to the right of the file name. Importantly, see the
50
discussion on Data Formats above before trying to import data layers.
Lastly, depending on the Data type, you will need to enter some information about the grid.
Note, only the text boxes that are required for the corresponding Data type will be active; all
others will be grayed out. Fill in all text boxes that are active.
1. Ro w c o u n t (y ) – Enter the number of rows in the input image. This is only required if the
input Data type is ASCII or Binary; otherwise, the value is taken from the header of the
input grid and cannot be changed.
2. Co lu m n c o u n t (x) – Enter the number of columns in the input image. This is only required
if the input Data type is ASCII or Binary; otherwise, the value is taken from the header of
the input grid and cannot be changed.
3. B an d – Some of the data formats allow for images with multiple bands. Consequently, If
your image has multiple bands (i.e., layers), you must select the band that you want to
import. By default the first band will be imported.
4. B ac kg ro u n d v alu e –[Optional] Enter the value to be used for background cells.
Importantly, this value should not be equal to the nodata value if interior background exists,
and thus it is safer to simply choose a different value from nodata. This is only required if
there are cells interior or exterior to the landscape of interest that you want to treat as
background (see Overview). Note, it is possible to specify multiple class values as
background, but this must be done in the Class descriptors table (see below). When this is
done, the designated classes are reclassified to the background value specified here in the
grid attributes. Note, all background cells are assigned this cell value, and this can have
important implications if you select core area metrics, edge contrast metrics, or the similarity
metric. Specifically, if you wish to specify a non-zero edge depth or edge contrast weight to
background edges or a non-unity similarity weight, you must include this background class
value in the pairwise combination of classes given in the edge depth, edge contrast, and
similarity weight files (see below).
5. Ce ll s ize (in meters) – Enter the size of cells in meters in the input image. Cells must be
square. The length of 1 side of a cell should be input. This is only required if the input Data
type is ASCII or Binary; otherwise, the value is taken from the header of the input grid and
cannot be changed.
6. No d ata v alu e – Enter the value for nodata cells. Note, this only matters if the grid contains
nodata cells, which may or may not be the case depending on the shape of the landscape.
This is only required if the input Data type is ASCII or 8-, 16- or 32-bit integer; otherwise,
the value is taken from the header of the input grid and cannot be changed. It is important
to note the following regarding the nodata value:
•
Some input data formats (e.g., ESRI grid) include the nodata value in the file header and
it is generally “hidden” to the user, whereas in other input data formats (e.g., ASCII and
51
8-, 16- and 32-bit integer formats) you must specify it here since there is no header
information in the image. Note, FRAGSTATS has a default nodata value for these latter
input data formats (ASCII=9999, 8-bit integer=127, 16- and 32-bit integer=9999) and
you need to be sure to change this value from the default if your input landscape
contains a different nodata value, otherwise the nodata cells in the input landscape will
be treated as a real class.
•
In any case, the background value (see above) should not be the same as the nodata
value (although this will only matter if you have true background). If the background
value is the same as the nodata value and you have true background in the landscape,
FRAGSTATS will not be able to distinguish between nodata and true background. In
this case, both the nodata and positive background (i.e., inside the landscape) will be
converted to negative background prior to the analysis, thus converting any real internal
background (positively valued background) to external background (negatively valued
background), and this will affect many of the metrics.
•
The specific nodata value that FRAGSTATS lists in the grid attributes for an ESRI grid
(and other formats with header files) may not match what you might see, for example, in
ArcMAP. The difference is that we use the outsider's API and only get to load the grids
in 32-bit signed integer format for which the nodata value is -2147483647 (the minimum
value the format can hold), while ESRI has access to a more fine-grained API that allows
ArcMAP to see that the dataset is actually stored in 16-bit signed integer format, RLE
compressed, and the nodata value for it is -32768 (the minimum value the format can
hold).
# Edit layer info – Click Edit layer info to reopens the dialog shown in figure 4 and edit any of
the grid parameters.
# Remove layer – Click Remove layer to remove the selected grid from the batch manager.
# Remove all layers – Click Remove all layers to remove all the grids from the batch manager.
# Export batch – Click Export batch to export the loaded grids as a batch file (.fbt) in the
format described below.
# Import batch – Click Import batch to load a batch file that already contains a list of input
grids to be analyzed. The batch file option is convenient if you want to analyze many landscapes.
If you select this option, you must specify a properly formatted batch file by navigating to the
appropriate file. Note, FRAGSTATS uses the file extension .fbt for batch files and will look for
files with this extension by default when navigating. The .fbt extension is not mandatory, but
using it can help keep files organized.
The batch file must be a comma-delimited ASCII file. Each line should specify the input landscape
file name, cell size, background value, number of rows, number of columns, band number,
nodata value, and input data type, in that order. The syntax for this file is as follows:
52
InputFileName, CellSize, Background, Rows, Columns, Band, Nodata, InputDataType
G InputFileName – is the full path and file name of the input landscape.
G CellSize – is an integer value corresponding to the cell size (in meters).
G Background – is an integer value corresponding to the designated background value. Note,
any class designated as background in the Class descriptors file (see below) will be
reclassified to this class value and treated as background. In addition, any nodata cells
will be reclassified to negative background.
G Rows – is an integer value corresponding to the number of rows in the input image.
G Columns – is an integer value corresponding to the number of columns in the input
image.
G Band – is an integer value corresponding to the desired band number (i.e., layer) to
import from the input file.
G Nodata – is an integer value corresponding to the nodata value. Note, it doesn’t matter
whether you put a negative sign in front of the nodata value or not, regardless of
whether the true nodata value is negative number, because FRAGSTATS treats any cell
with the nodata value, positive or negative, as nodata and thus outside the landscape of
interest. In fact, internally, FRAGSTATS will convert all nodata cells to negative the
user-specified background value prior to the analysis.
G InputDataType – is a character string identifying the input data format, with the following
options corresponding to the various input data format types listed above:
#
#
#
#
#
#
#
#
#
#
#
IDF_ASCII
IDF_8BIT
IDF_16BIT
IDF_32BIT
IDF_ARCGRID
IDF_GeoTIFF
IDF_BT
IDF_EHDR
IDF_EIMG
IDF_SagaGIS
IDF_PCRaster
The batch file should contain a record for each input landscape, and all arguments should be
separated by a comma. The parameter values should reflect the input Data type for each input
landscape; if it is ASCII or 8-, 16- or 32-bit integer, then the record must contain all of the
parameters specified above. However, if it is any of the other formats, then the record need only
contain the input landscape file name, the background value, and the Band number; the
remaining parameters should be assigned “x”, as illustrated in the following example:
D:\Foo\Bar\ASCII_filename, 25, 999, 250, 300, 1, 9999, IDF_ASCII
D:\Foo\Bar\8BIT_filename, 25, 999, 250, 300, 1, 127, IDF_8BIT
D:\Foo\Bar\16BIT_filename, 25, -9999,999, 250, 300, 1, 9999, IDF_16BIT
D:\Foo\Bar\32BIT_filename, 25, -9999,999, 250, 300,1, 9999, IDF_32BIT
53
D:\Foo\Bar\ARCGRID_folder, x, 999, x, x, 1, x, IDF_ARCGRID
D:\Foo\Bar\GeoTIFF_filename, x, 999, x, x,1, x, IDF_GeoTIFF
D:\Foo\Bar\VTP_binary_terrain_format_filename, x, 999, x, x, 1, x, IDF_BT
D:\Foo\Bar\ESRI_header_labelled_filename, x, 999, x, x, 1, x, IDF_EHDR
D:\Foo\Bar\ERDAS_Imagine_filename, x, 999, x, x, 1, x, IDF_EIMG
D:\Foo\Bar\PCRaster_filename, x, 999, x, x, 1, x, IDF_PCRaster
D:\Foo\Bar\SAGA_GIS_binary_format_filename, x, 999, x, x, 1, x, IDF_SagaGIS
etc.
NOTE, since ArcGrid files are actually folders containing multiple files, not single image files,
the file naming convention is a bit different. In this case, the input file name should be given as
the path to the ArcGrid folder (i.e., the file is the folder). In addition, regardless of input data
type, the cell size, nodata value, background value, rows and columns, and band can be different
for each input landscape.
NOTE, running from a batch file does not eliminate the necessity of completing the
parameterization of FRAGSTATS; it only provides a mechanism for running FRAGSTATS on
more than one landscape without having to parameterize and run each landscape separately.
Specifically, you still must set analysis parameters and select and parameterize the individual
metrics, as described below. The batch file only specifies the file name, input data type, and grid
attributes for each input landscape; all other parameters must be specified according to the
directions below.
Ste p 4. Sp e c ify in g Co m m o n T ab le s [o p tio n al]
Once a new model has been created (Fig. 3) and the input grids have been added or imported from
a batch file, the next optional step is to specify common tables (in the bottom left pane of the model
dialog, figure 3) used to describe and attribute the classes (patch types) and assign edge depths, edge
contrasts, and similarity coefficients used in the corresponding functional metrics, as described
below:
# Class descriptors [Optional] – Click on the corresponding browse button and navigate to and
select the desired file. Note, FRAGSTATS uses the file extension .fcd for class descriptor files
and will look for files with this extension by default when navigating. The .fcd extension is not
mandatory, but using it can help keep files organized. Each record in the file should contain a
numeric class (patch type) value, the character descriptor for that patch type, a logical status
indicator, and a local background indicator. The syntax for this comma-delimited ASCII file is as
follows:
ID, Name, Enabled, IsBackground
G ID – is an integer value corresponding to a class value in the landscape.
G Name – is a descriptive name of the class; descriptive names can be any length and
contain any characters, including spaces, but cannot include commas. This descriptive
name is reported in all patch and class output files for the variable TYPE.
G Enabled – can take on the values: true, or t; and false, or f. (upper or lower case), and
determines whether the corresponding class should be processed and added to the
54
results or simply ignored in the output files. A “true” or “t” indicates that the class is
enabled and should be output in the patch and class output files. A “false” or “f” indicates
that the class is disabled and should not be output. Note, enabling or disabling a class
does not effect the computation of landscape metrics; disabled classes are still included,
as necessary, in the computation of landscape metrics. Although there is some savings of
computer processing by disabling a class, the primary effect is on the output. This
feature allows you to “turn off” classes that you are not interested in so that you don’t
have to view their statistics in the output files.
G IsBackground – can take on the values: true, or t; and false, or f (upper or lower case), and
determines whether the corresponding class should be reclassified and treated as
background (i.e., assigned the background value specified in the grid attributes). Note,
classifying a class as background will have an effect on many landscape metrics (see
Overview).
The class descriptors file should contain a record for each class in the input landscape, and
all arguments should be separated by a comma or space(s). For example:
ID, Name, Enabled, IsBackground
1,shrubs,true,false
2,conifers,true, false
3,deciduous,true,false
4,other,false,true
etc.
Note, the class descriptors file in FRAGSTATS must include the header line shown above
(this is a change from FRAGSTATS 3.x). In addition, the class descriptors file can contain
additional classes that do not exist in the input landscape, but all classes that exist should be
listed in this file.
In summary, the class descriptors file allows you to do three things: (1) specify character
descriptors for each class in order to facilitate interpretation of the output files, (2) limit the
output files to only the classes of interest, and (3) reclassify classes to background.
NOTE, if the class descriptors file is provided, the class names will be written to the output
files. Otherwise, the class IDs (numeric patch type codes) will be written to the output files.
# Edge depth [Optional] –The Edge depth table displays the “depth-of-edge” values to use in
determining what constitutes the core of a patch in the core area metrics and is only relevant if
one or more core area metrics are selected (see below). There are two options:
1. Fixe d e d g e d e p th –If you wish to treat all edges the same, then check the corresponding
check box (Use fixed depth), click the (...) button and enter a non-zero distance (in
meters). By default this box contains a zero, but you should enter a non-zero distance
because a zero depth-of-edge would result in the core area being equal to patch area, and
thus would be redundant.
55
2. Variab le e d g e d e p th s –Alternatively, you can specify separate edge depths for each edge
type (i.e., each pairwise combination of patch types). Click on the corresponding browse
button and navigate to and select the desired file. Note, FRAGSTATS uses the file extension
.fsq for edge depth files and will look for files with this extension by default when
navigating. The .fsq extension is not mandatory, but using it can help keep files organized.
The syntax for this comma-delimited ASCII file is as follows:
FSQ_TABLE
CLASS_LIST_LITERAL(1stClassName, 2ndClassName, etc.)
CLASS_LIST_NUMERIC(1stClassID, 2ndClassID, etc.)
EdgeDepth_1-1, EdgeDepth_1-2, etc.
EdgeDepth_2-1, EdgeDepth_2-2, etc.
etc.
<
<
<
<
<
<
Comment lines start with # and are allowed anywhere in the table.
FSQ_TABLE must be specified in the first line.
Two types of class lists are allowed CLASS_LIST_LITERAL() and
CLASS_LIST_NUMERIC(), but only the first one encountered is considered, so
you only need one of these lines.
Literal class names (1stClassName, 2ndClassName, etc.,) are character strings and
cannot contain spaces.
Class Ids (1stClassID, 2ndClassID, etc.) are integer values corresponding to class values
in the grid.
With regards to the edge depths, the order of rows and column is the one specified
in the CLASS_LIST_LITERAL() or CLASS_LIST_NUMERIC(), whichever comes
first. EdgeDepth_i-j is an integer value giving the depth-of-edge (in meters) for the
corresponding edge type (i.e., for the focal class designated by the ith ClassID and the
adjacent class designated by the jth ClassID). Note, it is advisable but not necessary to
provide edge depths in increments equal to the cell size, because FRAGSTATS will
always round up or down to the nearest cell when applying the edge mask (see
Overview).
The edge depth entries must be a square matrix (i.e., same number of rows and
columns), must have the same list and order of ClassIDs as given in the
CLASS_LIST_LITERAL or CLASS_LIST_NUMERIC, should contain a record for
each unique pairwise combination of patch types (classes) in the input landscape (any
missing class must be missing in both the rows and columns and will be assigned a zero
edge depth for all edges involving that class), and all arguments should be separated by a
comma. For example, given four classes, the following file would be suitable:
FSQ_TABLE
CLASS_LIST_NUMERIC(2, 3, 4, 5, 6)
0, 30, 30, 30, 30
70, 0, 40, 40, 40
30, 40, 0, 50, 50
30, 40, 50, 0, 60
56
30, 40, 50, 60, 0
NOTE, this table can be created and managed using any text editor and then simply
saved as a comma delimited file (.csv).
NOTE, the edge depth matrix can be asymmetrical; that is, upper right and lower left
triangles do not need to mirror each other. Accordingly, it is important to realize that the
rows represent the focal class and the columns represent the adjacent or abutting class.
Let’s consider the edge depths for focal class A (or ID=2) in the example above, given in
the first row of the edge depth matrix. An adjacent patch of class B (or ID=3) has an
edge depth of 30 m; i.e., has an edge effect that penetrates 30 m into the patch of class
A. Conversely, class A penetrates 70 m into class B (row 2, column 1). Thus, the edge
effect penetrates less into class A than into class B. This asymmetry may be important in
some applications; for example, when urban edge effects penetrate deeply into forest,
but forest edge effects penetrate very little, if at all, into urban areas.
NOTE, the diagonals are typically given a zero edge depth, but it is possible to specify a
non-zero diagonal. However, the only situation in which a patch can abut a patch of the
same class is along the landscape boundary when a landscape border is present (see
Overview). In this case, it is possible to specify a non-zero edge depth, although in most
cases it would not be logical to do so.
NOTE, if you have background in the image, you need to include the background class
value specified in the grid properties during data import, otherwise all background edges
will be given a zero edge depth.
# Edge contrast [Optional] – The Edge contrast table displays the “edge contrast” values to
use in determining the magnitude of contrast for each edge type (i.e., each pairwise combination
of patch types) and is only relevant if one or more edge contrast metrics are selected (see below).
Click on the corresponding browse button and navigate to and select the desired file. Note,
FRAGSTATS uses the file extension .fsq for edge contrast files and will look for files with this
extension by default when navigating. The .fsq extension is not mandatory, but using it can help
keep files organized. The syntax for this comma-delimited ASCII file is as follows:
FSQ_TABLE
CLASS_LIST_LITERAL(1stClassName, 2ndClassName, etc.)
CLASS_LIST_NUMERIC(1stClassID, 2ndClassID, etc.)
ContrastWeight_1-1, ContrastWeight_1-2, etc.
ContrastWeight_2-1, ContrastWeight_2-2, etc.
etc.
<
<
<
<
Comment lines start with # and are allowed anywhere in the table.
FSQ_TABLE must be specified in the first line.
Two types of class lists are allowed CLASS_LIST_LITERAL() and
CLASS_LIST_NUMERIC(), but only the first one encountered is considered.
Literal class names (1stClassName, 2ndClassName, etc.,) are character strings and cannot
57
<
<
<
contain spaces.
Class Ids (1stClassID, 2ndClassID, etc.) are integer values corresponding to class values in
the grid.
With regards to the contrast weights, the order of rows and column is the one specified
in the CLASS_LIST_LITERAL() or CLASS_LIST_NUMERIC(), whichever comes
first. ContrastWeight_i-j is an integer value giving the depth-of-edge (in meters) for the
corresponding edge type (i.e., for the focal class designated by the ith ClassID and the
adjacent class designated by the jth ClassID).
Contrast weights must range from 0 (no contrast) to 1 (maximum contrast).
The edge contrast entries must be a square matrix (i.e., same number of rows and columns),
must have the same list and order of ClassIDs as given in the CLASS_LIST_LITERAL or
CLASS_LIST_NUMERIC, should contain a record for each unique pairwise combination
of patch types (classes) in the input landscape (any missing class must be missing in both the
rows and columns and will be assigned an edge contrast weight of one (maximum)), and all
arguments should be separated by a comma. For example, given four classes the following
file would be suitable:
FSQ_TABLE
CLASS_LIST_NUMERIC(2, 3, 4, 5, 6)
0, 0.2, 0, 0.4, 0.6
0.2, 0, 0, 0.2, 0.4
0, 0, 0, 0, 0
0.4, 0.2, 0, 0, 0.2
0.6, 0.4, 0, 0.2, 0
NOTE, this table can be created and managed using any text editor and then simply saved as
a comma delimited file (.csv).
NOTE, this matrix must be symmetrical; that is, upper right and lower left triangles must be
mirror images, because edge contrast is a property of the edge itself.
NOTE, the diagonals are typically given a zero edge contrast since there is no contrast
between patches of the same type, although any value can be specified. However, the only
situation in which a patch can abut a patch of the same class is along the landscape boundary
when a landscape border is present (see Overview). In this case, it is possible to specify a
nonzero edge contrast, although in most cases it would not be logical to do so.
NOTE, if you have background in the image, you need to include the background class value
specified in the grid properties during data import, otherwise all background edges will be
given a zero edge contrast.
# Similarity [Optional] – The Similarity table displays the “similarity” values to use in
determining the similarity between each pairwise combination of patch types and is only
relevant if the similarity index is selected (see below). Click on the corresponding browse button
and navigate to and select the desired file. Note, FRAGSTATS uses the file extension .fsq for
58
Figure 5. Model dialog for paramterizing FRAGSTATS, shown here for a “new” model that
has yet to be parameterized, and with the “Analysis parameters” tab in the left panel selected.
Note, the bottom left window (sampling strategy) has been truncated in this image.
similarity weights files and will look for files with this extension by default when navigating. The
.fsq extension is not mandatory, but using it can help keep files organized. The syntax for this
comma-delimited ASCII file is as follows:
FSQ_TABLE
CLASS_LIST_LITERAL(1stClassName, 2ndClassName, etc.)
CLASS_LIST_NUMERIC(1stClassID, 2ndClassID, etc.)
SimilarityWeight_1-1, SimilarityWeight_1-2, etc.
SimilarityWeight_2-1, SimilarityWeight_2-2, etc.
etc.
<
<
<
<
<
<
Comment lines start with # and are allowed anywhere in the table.
FSQ_TABLE must be specified in the first line.
Two types of class lists are allowed CLASS_LIST_LITERAL() and
CLASS_LIST_NUMERIC(), but only the first one encountered is considered.
Literal class names (1stClassName, 2ndClassName, etc.,) are character strings and cannot
contain spaces.
Class Ids (1stClassID, 2ndClassID, etc.) are integer values corresponding to class values in
the grid.
With regards to the similarity weights, the order of rows and column is the one specified
in the CLASS_LIST_LITERAL() or CLASS_LIST_NUMERIC(), whichever comes
first. SimilarityWeight_i-j is an integer value giving the similarity weight for the for the
focal class designated by the ith ClassID and the adjacent class designated by the jth
59
Figure 6. Schematic diagram of alternative
landscape sampling strategies.
<
ClassID).
Similarity weights must range from 0 (minimum similarity) to 1 (maximum similarity).
The similarity entries must be a square matrix (i.e., same number of rows and columns),
must have the same list and order of ClassIDs as given in the CLASS_LIST_LITERAL or
CLASS_LIST_NUMERIC, should contain a record for each unique pairwise combination
of patch types (classes) in the input landscape (any missing class must be missing in both the
rows and columns and will be assigned a zero similarity (minimum) for all comparisons
involving that class), and all arguments should be separated by a comma. For example, given
four classes the following file would be suitable:
FSQ_TABLE
CLASS_LIST_NUMERIC(2, 3, 4, 5, 6)
1, 0.8, 0, 0.6, 0.4
0.2, 1, 0, 0.8, 0.6
60
0, 0, 1, 0, 0
0.6, 0.8, 0, 1, 0.8
0.4, 0.6, 0, 0.8, 1
NOTE, this table can be created and managed using any text editor and then simply saved as
a comma delimited file (.csv).
NOTE, the similarity matrix can be asymmetrical; that is, upper right and lower left triangles
do not need to mirror each other. Accordingly, it is important to realize that the rows
represent the focal class and the columns represent the adjacent or abutting class. Let’s
consider the similarity weights for focal class A (or ID=2) in the example above, given in the
first row of the similarity matrix. Given a focal patch of class A, a neighboring patch of type
B (or ID=3) has a similarity of 0.8. Conversely, given a focal patch of class B, a neighboring
patch of class A has a similarity of 0.2. In most cases, however, it is more logical to think of
similarity in terms of symmetrical weights.
NOTE, the diagonals are typically given a similarity weight of one, because the similarity of
two patches of the same class is generally assumed to be maximum, but it is possible to
specify a different value.
NOTE, if you have background in the image, you need to include the background class value
specified in the grid properties during data import, otherwise all background edges will be
given a zero weight.
Ste p 5. Se ttin g An aly s is Param e te rs
Once a dataset has been imported (step 3), and either before or after specifying any common tables
(step 4), the next step is to set some global analysis parameters. Note, if you opened a previously
saved model, you can modify the analysis parameters as well before executing the program.
In the left pane of the model dialog window make sure the Analysis parameters tab is selected, as
shown in figure 5.
# Neighbor rule – Chose between the 4-cell and 8-cell rule for delineating patches. The 4-cell rule
considers only the 4 adjacent cells that share a side with the focal cell (i.e., orthogonal neighbors)
for determining patch membership. The 8-cell rule considers all 8 adjacent cells, including the 4
orthogonal and 4 diagonal neighbors. Thus, if the 4-cell rule is selected, two cells of the same
class that are diagonally touching will be considered as part of separate patches; if the 8-cell rule
is selected, these will be considered part of the same patch. The choice of patch neighbor rule
will affect most of the configuration metrics, but will have no affect on the composition metrics.
The 8-cell rule is the default.
# Automatically save results – You can automatically save the results to output files after
execution by checking the Automatically save results check box. If you choose to
automatically save results, you must also specify a “basename” for the output files by clicking on
61
the browse button and navigating to the desired folder, and then entering a “basename” or
selecting an existing file name to overwrite. This basename will be given the extensions .patch,
.class, .land and .adj for the corresponding patch, class, and landscape metrics and adjacency
matrix, as selected.
<
<
<
<
Note, if you do NOT check the Automatically save results box, the results can always be
saved after the execution from the results dialog box (see below).
Note, if you check the Automatically save results box and fail to specify a basename file
for the output, FRAGSTATS will not run and you will get an error message to that effect in
the activity log.
Note, if you specify the basename of a file that already exists, FRAGSTATS will
automatically rename the extension of the existing files to *.bk1. The next time there is a
conflict, the files will be renamed *.bk2, and so on. Appending the results to an existing file
is not an option because there is no guarantee that the output file structure will be the same.
Note, if you specify the basename of a file name that already exists, you need only include
the basename of the file; i.e., the name up to the first period. You do not need to include the
file extension, as it will be ignored.
# Sampling Strategy – There are seven different sampling strategies to chose from that facilitate
analyzing sub-landscapes, as illustrated in figure 6. You must chose a strategy, and only one
strategy is allowed per run. Also, if you specify multiple input layers (i.e., a batch) in the Input
Layers tab, then ‘no sampling’ (see below) is the only option allowed. All other sampling
options are limited to a single input layer and an error will be sent to the activity log window
indicating as much if multiple input layers are listed and one of the sampling options is selected.
1. No s am p lin g – The default strategy is ‘no sampling’ – this is the conventional approach. In
this strategy, each input landscape is analyzed as a single landscape. You have the option of
computing metrics at the patch, class and landscape levels; you must select at least one level.
G Patc h m e tric s – If selected, patch metrics can be computed. However, this merely
enables (i.e., turns on) patch metrics; you still must select one or more individual patch
metrics (see below), otherwise no patch metrics will be calculated.
G Clas s m e tric s – If selected, class metrics can be computed. However, this merely
enables class metrics; you still must select one or more individual class metrics (see
below), otherwise no class metrics will be calculated.
G Lan d s c ap e m e tric s – If selected, landscape metrics can be computed. However, this
merely enables landscape metrics; you still must select one or more individual landscape
metrics (see below), otherwise no landscape metrics will be calculated.
G Ge n e rate p atc h ID file – You have the option of creating and outputting a Patch ID
image. If you select this option, a patch ID image will be created by FRAGSTATS and
output in the same data type format as the Input Data Type. The Patch ID image will
contain a unique ID for each patch in the landscape. All background cells will be
62
assigned a negative of the user-specified background value. This patch ID corresponds
to the patch ID in the "basename".patch output file. This image is needed if you wish to
associate the patch-level output with specific patches and view the results using a GIS.
Note, the patch ID file will be named using the following convention and output to the
same directory as the input image:
Input file name _4 or 8 (depending on neighbor rule) + ID
Thus, an input file named "test" analyzed with an 8-neighbor rule will be given the
following patch ID file name: “test_8id”. If you attempt to create and output an ID
image that already exists, e.g., from a previous run, FRAGSTATS will ask you whether
you want to overwrite the existing file. NOTE, if you are using ArcGrids and if you
attempt to create and output an ID image with the same name as a grid that is currently
open in another program, e.g., in ArcMap, the grid will be corrupted and an error
message will be written to the log window. In this case, the grid folder must be deleted,
even after closing ArcMap, before you can create and output an ID image with that
name.
2. Us e r-p ro v id e d tile s – The first option for exhaustive sampling of the landscape is ‘userprovided tiles’, in which the landscape is subdivided into user-provided tiles representing
sub-landscapes. If this option is selected, you must provide a tile grid that has the same input
data format and identical cell size and geographical alignment as the input landscape. In the
Tile grid box, click the navigate to button (...) and select the corresponding input data type
and navigate to and select the desired tile grid. In addition, as described above, you have the
option of computing metrics at the patch, class and/or landscape levels – you must select at
least one level, and the output will consist of separate results for each sub-landscape.
In addition, for each tile (or sub-landscape), FRAGSTATS will automatically add a one-cell
wide ‘border’ around the landscape. Recall from the background section that a border is a
strip of negatively-valued cells along the landscape boundary outside the landscape of
interest. Negative cell values in the border denote that they are ‘outside’ the landscape of
interest. The border provides information on cell adjacency for cells along the landscape
boundary and informs both core area and edge contrast metrics (see background section).
Note, any added border composed of ‘nodata’ will be assigned negative background class
values.
3. Un ifo rm tile s – The second option for exhaustive sampling of the landscape is ‘uniform tiles’,
in which FRAGSTATS uniformly subdivides the landscape into square tiles representing
sub-landscapes. If this option is selected, you must specify the size of the square tiles by
specifying the length of one side (in meters). The default is 100 m. To change the size, click
the (...) button and enter a new value. Note, the actual size of the tile created may not be
equal exactly to the specified side length, because it is constrained to be a multiple of the cell
size. Consequently, the actual side length of the tile will always be rounded down to the
nearest multiple of the cell size. For example, if the cell size is 30 m and you specify a side
length of 500 m, the actual window side length will be 480 m (16*30).
63
Figure 7. (A) Moving window applied to an input grid without a border
produces an output grid for each unique class-metric combination in which a
strip the width of the window around the periphery of the grid is given a
background value in the output grid. (B) A landscape border at least as wide as
the window allows all cells inside the landscape boundary (dark line) (i.e.,
positive values) to be given the computed focal cell value.
In addition, you also have the option of specifying a criterion for including tiles that contain
a maximum percentage of border or nodata cells. The default is 0%, which means that a tile
containing any border (negative cell values) or nodata cells will be ignored. If you specify,
e.g., 20%, then up to 20% of the tile area can be comprised of border or nodata and the
selected metrics will be calculated. Note, some metrics are sensitive to the absolute area of
the landscape and, more specifically, to the area ‘inside’ the landscape (i.e., positive cell
values), so modifying this value from the default of zero should be done cautiously and with
complete understanding of the implications given the selected metrics.
Lastly, as described above, a border will automatically be included around every tile and you
have the option of computing metrics at the patch, class and/or landscape levels – you must
select at least one level, and the output will consist of separate results for each sublandscape.
4. Mo v in g w in d o w – The third option for exhaustive sampling of the landscape is a ‘moving
64
window analysis’. Note, this is similar to the uniform tile strategy above, except that with the
uniform tile strategy the tiles are non-overlapping (i.e., mutually exclusive and all inclusive),
but with the moving window approach the tiles overlap. If you select the moving window
option, then you must specify the level of heterogeneity (class and/or landscape) and the
shape (round or square) and size (radius or length of side, in meters) of the window to be
used. In addition, as described above, a border will automatically be included around every
window and you also have the option of specifying the maximum percentage of the window
comprised of border or nodata cells (see below).
A window of the specified shape and size is passed over every positively valued cell in the
grid (i.e., all cells inside the landscape of interest). However, only cells in which the window
does not extend beyond the edge of the rectangular grid and meets the threshold for
maximum percentage of border/nodata (as described above) are evaluated (see below).
Within each window, each selected metric at the class or landscape level is computed and the
value returned to the focal (center) cell. Patch metrics are not allowed in the moving window
analysis. The moving window is passed over the grid until every positively valued cell
(including positively valued background cells) containing a valid window is assessed in this
manner. Note, internal background cells containing real positively-valued classes in the
window may receive a value in the output grid, despite the fact that the cell is background in
the input grid. Specifically, if the entire window is internal background, then the cell will
receive a minus background value in the output grid. There are several important
considerations when conducting a moving window analysis:
•
Win d o w s h ap e an d s ize – The user-specified window size refers to the radius (in
meters) of a near-circular window or the length of the side (in meters) of a square
window, depending on the shape chosen. It is important to note that the actual area of
the window as implemented algorithmically will vary slightly from the area calculated
mathematically based on the geometry of a circle or square for two reasons. First, the
radius is given as the distance from the focal cell to the edge of the window. For
example, given a cell size of 10 m and a circular window, a 40 m radius would be
implemented as a mask 4 cells wide. The diameter of the window would equal 90
m–twice the radius plus the size of the focal cell–as opposed to 80 m. The addition of
the focal cell to the diameter of the window is necessary to force the focal cell to always
be located at the exact center of the window. Second, the specified radius (in meters) is
always rounded to the nearest cell. Thus, if the radius is not perfectly divisible by the cell
size, the actual window will be somewhat smaller or larger. Essentially, the window will
always be rounded to the nearest odd number of cells so that the focal cell is always
located at the exact center of the window. In the case of a square window, for example, a
user-specified side length of 500 m and a cell size of 50 m would result in a radius of
500/2/50 = 5 cells. The window size in number of cells would be 2 times the radius plus
1 ((2*5)+1=11) cells on a side or an 11x11 window (550x550 m). Note, a user-specified
side length of 550 m would result in the same final window, since the radius is always
rounded down to the nearest integer.
•
B o u n d ary e ffe c ts – Cells located close to the edge of the landscape (i.e., near the
landscape boundary) are biased in moving window calculations if the window intersects
65
the landscape boundary. Consider a cell located on the landscape boundary. A normal
window placed on that cell would extend well outside the landscape boundary; in fact,
half the window would extend beyond the landscape where information on landscape
structure is absent. Any cell within the specified radius of a round window or ½ the
length of a side of a square window will be biased in this way. There are several
alternative ways of handling this bias – none of which are entirely acceptable.
FRAGSTATS lets you chose whether you want to include windows that contain border
or nodata. The default, and conservative approach, is to not compute the metrics for
focal cells containing a partial window (i.e., a window not fully contained within the
landscape proper). In this case, FRAGSTATS returns the user-specified exterior
(negative) background value for these cells. Thus, in practice, the output grid will contain
a peripheral buffer of negatively-valued background cells surrounding the core of the
landscape – only the core (cells containing a full window of positively-valued cells) will
contain metric values (Fig. 7a). However, FRAGSTATS also allows you to relax this
criterion and compute metrics for windows containing any percentage of border/nodata,
but this should be done with caution and a complete understanding of the implications
for the selected metrics. IMPORTANTLY, regardless of whether you change the
percentage of border/nodata to something greater than 0%, the full window still must lie
entirely within the input grid for the window to be considered valid. In other words, first
the window must lie entirely within the input grid (including whatever is input as nodata
cells, negatively-valued border cells and the positively-valued landscape cells). If the
window lies entirely within the input grid, then the window is evaluated as to whether it
meets the specified criterion for the minimum percentage of border/nodata cells. If that
criterion is met, the window is considered valid and the metrics are computed.
Clearly, as landscape extent increases relative to window size, the magnitude and spatial
extent of the boundary effect decreases. For this reason, care should be exercised in
selecting a window size that minimizes the loss of information due to the boundary
effect. An alternative approach for dealing with the boundary effect is to expand the
extent of the input landscape to include a suitably wide expansion strip of positively
valued, classified cells around the actual landscape of interest, where the width of this
extension is equal to the radius of the window (Fig. 7b). In this manner, the core of the
landscape in the output grid produced by the moving window analysis will align with the
original landscape boundary of interest. It is important to realize that including a suitably
wide landscape border (negatively valued, but classified cells) does not have the same effect.
Border, by definition, consists of negatively valued cells outside the landscape of interest,
and FRAGSTATS ignores all negatively valued cells when calculating metrics, except for
the information they provide on adjacency to positively valued cells.
•
In p u t d ata ty p e s – Moving window analysis is restricted to input data types that can
effectively handle floating point values. Thus, the 8- and 16-bit binary data formats are
not allowed in a moving window analysis. If these data type are included in a batch file
used in conjunction with a moving window analysis, the corresponding records will be
ignored.
•
Se le c tio n o f c las s e s an d m e tric s – For each selected metric and enabled class,
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FRAGSTATS outputs a separate grid (in the same format as the input grid). Thus, if the
input landscape contains 10 classes and all of them are enabled in the class descriptors file
(see above) and you select one class-level metric, then FRAGSTATS outputs 10 grids,
one for each class for the selected metric. In this case, each output grid represents a
separate class, and the cell values represent the computed values of the selected metric
for that class. Specifically, a window is placed over the first cell in the input landscape,
the selected metric is computed for the first class, and this value is output to the
corresponding cell in a new grid for that specific metric-class combination. The process
is repeated for the next class, and so on, until all classes have been assessed. Next, the
window is placed over the next cell and the process is repeated. The process is repeated
in this manner until all positively valued cells containing a full window in the input
landscape have been evaluated. The end result is a new grid for each class, in which the
cell values represent the values of the computed metric. Accordingly, if you select five
class-level metrics, then FRAGSTATS outputs 50 grids, one for each class-metric
combination. If, in addition to these class metrics, you also select three landscape
metrics, FRAGSTATS outputs an additional three grids, one for each landscape metric.
Clearly, the number of output grids can increase quickly with several classes and several
metrics. Thus, it is important to carefully select the most parsimonious set of classes and
metrics. Note, windows containing no cells of the corresponding class, or in some cases
just a single cell of the corresponding class, will be assigned a background value in the
output grid.
•
Co m p u te r p ro c e s s in g an d m e m o ry re q u ire m e n ts – The computer processing and
memory demands of the moving window analysis are phenomenal. Consider a relatively
small grid of 100 x 100 cells; i.e., 10,000 cells. The moving window analysis involves
placing a window over every cell and computing one or more metrics. This is equivalent
to doing 10,000 FRAGSTATS analyses. Now imagine that you have a larger grid of 1000
x 1000 cells; i.e., 1,000,000 cells. Clearly, the processing time quickly becomes
overwhelming. In addition, the memory demands increase as a function of the size the
input grid. FRAGSTATS must be able to allocate memory for at three grids, where each
grid requires four bytes for every cell. See Computer Requirements in the Overview
Section for a detailed description of the memory requirements. Clearly, given the limited
memory available in most personal computers, it is quite possible that you will not have
enough memory to do even a single unique class-metric combination, let alone the
dozens or hundreds that could easily result if you selected several classes and several
metrics. If more than one class-metric combinations are selected, FRAGSTATS will
determine how many can be done given the available memory and then parse the job
into separate passes. For example, if 20 class-metric combinations are selected, but
available memory is sufficient for only four at a time, then FRAGSTATS will conduct
five passes across the landscape, output four grids each pass. Given these considerations,
it behooves you to use this option sparingly and with great patience until computer
processing capabilities increase substantially. And don’t be too surprised if your
computer is simply unable to allocate sufficient memory to do any moving window
analysis.
•
O u tp u t g rid n am in g c o n v e n tio n – Given the number of possible output grids
67
Figure 8. Dialog for selecting and parameterizing metrics.
produced from a moving window analysis and limits on the file name length with some
data types (e.g., ArcGrids), the output file naming convention is somewhat cumbersome
and limiting. If a moving window analysis is selected, FRAGSTATS will create a new
subdirectory beneath the directory containing the input file by appending “_MW1" (for
moving window #1) to the name of the input file. Thus, a directory named “Test”
containing the input file named “TestGrid” will have a new subdirectory under the Test
directory named “TestGrid_MW1". This subdirectory will contain an output grid for
each class-metric combination and landscape metric selected. For landscape metrics, the
output grids are named using the metric acronym. For example, the landscape-level
Contagion index (CONTAG) would be given the grid name “contag”. For class metrics,
the metric acronym is combined with the class ID value (see Class descriptors) because
each class has a separate output grid. For example, the class-level Clumpiness index
(CLUMPY) for class ID #3 would be given the grid name: “clumpy_3". See the list of
metrics in the FRAGSTATS Metrics section for the metric acronyms. If a second
moving window analysis is conducted on the same input file (e.g., using a different
window size), a second directory is created by appending "_MW2" to the name of the
input file. And so on for each subsequent moving window analysis.
Importantly, for reasons unknown to us, ArcGrid names are limited to 13 characters.
The naming convention above for some class metrics with long names (e.g., gyrate_am)
is problematic at the class level if the numeric class value exceeds three digits. For
example, a class value of 3000 for gyrate_am would end up with the name
“gyrate_am_3000", which is one digit too long for ArcGIS. So, in a few cases the class
metric names have been shortened (just for the moving window output grids) to
accommodate up to a 4 digit class value, including the following metrics: “gyrate”
becomes “gyra”, “circle” becomes “circ”, and “contig” becomes “cont”. If the final grid
68
is still too long because the class value is more than four digits, an error will be logged
and you will need to shorten the numeric class values in your input grid.
5. Us e r-p ro v id e d p o in ts – The first option for partial sampling of the landscape is ‘userprovided points’, in which FRAGSTATS puts a window of specified size and shape around
each user-provided point (focal cell) as the basis for defining sub-landscapes. Note, the
actual window size may differ from the specified size for the reasons described above (see
moving window). If you select this option, then you must provide either a grid or table that
identifies the points (focal cells), and you must specify the level of heterogeneity (patch, class
and/or landscape) and the shape (round or square) and size (radius or length of side, in
meters) of the window to be used, and the output will consist of separate results for each
sub-landscape (point). In addition, as described above, a border will automatically be
included around every window and you also have the option of specifying the maximum
percentage of the window comprised of border or nodata cells. Lastly, as described above
for moving windows, any window that extends beyond the edge of the rectangular grid will
be ignored.
•
Po in ts g rid – If you select the points grid as the means of designating the focal cells,
then the points grid must have the same input data format and identical extent, cell size
and geographical alignment as the input landscape. In the Points grid box, click the
navigate to button (...) and select the corresponding input data type and navigate to and
select the desired points grid. Note, if you have point layer in vector format, you must
convert it to a raster grid to use this option. The grid should contain unique non-zero,
positive integer values for the points (focal cells) and all other cells should be assigned
nodata values.
•
Po in ts tab le – If you select the point table as the means of designating the focal cells,
then click on the corresponding browse to button (...) and navigate to and select the
desired file. Note, FRAGSTATS uses the file extension .fpt for points files and will look
for files with this extension by default when navigating. The .fpt extension is not
mandatory, but using it can help keep files organized. The syntax for this ASCII file is as
follows:
FPT_TABLE
[first point id#: first point row#: first point col#]
[second point id#: second point row#: second point col#]
etc.
<
<
<
<
<
Comment lines start with # and are allowed anywhere in the table.
FPT_TABLE must be specified in the first line.
Each bracketed item contains point coordinates of the following form: [id : row :
column] or [id:row:column].
Point id values must be unique integer values, duplicates will be ignored.
Row and column values must be integer values within the ranges specific to the
target dataset, and represent row and column numbers not geographic coordinates,
starting from the top left corner and including the nodata portion of the grid (i.e., the
69
topmost row is row #1, and the leftmost column is col #1); out-of-range and
duplicate coordinates will be ignored.
For example, for a table containing three focal points, the following file would be
suitable:
FPT_TABLE
[1:2819:17300]
[2:2752:17300]
[3:1880:17303]
NOTE, this table can be created and managed using any text editor and then simply
saved as an ASCII text file.
6. Ran d o m p o in ts w ith o u t o v e rlap – The second option for partial sampling of the landscape
is ‘random points without overlap’ in which FRAGSTATS will select a user-specified
number of focal cells at random and put a window of specified size and shape around each
point as the basis for defining sub-landscapes. If you select this option, then you must
specify the level of heterogeneity (patch, class and/or landscape), the shape (round or
square) and size (radius or length of side, in meters) of the window to be used, and the target
number of focal cells (to be selected randomly), and the output will consist of separate
results for each sub-landscape (point). Note, the actual window size may differ from the
specified size for the reasons described above (see moving window). In addition, as
described above, a border will automatically be included around every window and you also
have the option of specifying the maximum percentage of the window comprised of border
or nodata cells.
Importantly, this option prevents the windows around the selected focal cells to overlap;
thus, the sub-landscapes are non-overlapping. However, depending on the target number of
points specified and the size and shape of the window specified, it may not be possible to
meet the target number of windows. FRAGSTATS attempts to meet the target, but after a
threshold number of failed attempts due to overlapping existing windows, FRAGSTATS
terminates the process. Thus, in practice, you may not get the desired number of random
sub-landscapes.
7. Ran d o m p o in ts w ith o v e rlap – The second option for partial sampling of the landscape is
‘random points with overlap’ in which FRAGSTATS selects a user-specified number of
focal cells at random and puts a window of specified size and shape around each point as the
basis for defining sub-landscapes. If you select this option, then you must specify the level of
heterogeneity (patch, class and/or landscape), the shape (round or square) and size (radius or
length of side, in meters) of the window to be used, and the target number of focal cells (to
be selected randomly), and the output will consist of separate results for each sub-landscape
(point). Note, the actual window size may differ from the specified size for the reasons
described above (see moving window). In addition, as described above, a border will
automatically be included around every window and you also have the option of specifying
the maximum percentage of the window comprised of border or nodata cells.
70
Importantly, this option prevents the windows around the selected focal cells to overlap;
thus, the sub-landscapes are non-overlapping. However, depending on the target number of
points specified and the size and shape of the window specified, it may not be possible to
meet the target number of windows. FRAGSTATS attempts to meet the target, but after a
threshold number of failed attempts due to overlapping existing windows, FRAGSTATS
terminates the process. Thus, in practice, you may not get the desired number of random
sub-landscapes.
Ste p 6. Se le c tin g an d Param e te rizin g Patc h , Clas s , an d Lan d s c ap e Me tric s
The next step is to select and parameterize the patch, class, and landscape metrics. Note, these
options are only consequential if you select the respective levels in the Analysis Parameters dialog
box (Fig. 5). The metrics are selected and parameterized (as needed) in the right pane of the model
dialog (Fig. 8). Note, there is a separate set of tabbed dialogs for each level of metrics (patch, class,
and landscape). Each dialog box consists of a series of tabbed pages. Each tabbed page represents a
group of related metrics as discussed in the Background section, although the aggregation tab
includes all of the aggregation, subdivision and isolation groups of metrics.
The selection of metrics is relatively straightforward. On each tabbed page select the desired
individual metrics using the check boxes, or select all of the metrics using the Select All button.
You can also De-select All or Invert your selection using the corresponding buttons. Each metric
is discussed in detail in the FRAGSTATS Metrics section.
A number of metrics require you to provide additional parameters before they can be calculated. In
most cases, this involves entering a number in a text box, while in other cases, this involves
specifying a separate table. These special requirements are described below in association with the
corresponding tabbed page.
# Area-Edge – If you select Total Edge (TE) or Edge Density (ED) on the Area-Edge tab at either
the class or landscape level, you must also specify how you want to treat boundary and
background edges (Fig. 1); specifically, what percentage of the landscape boundary and
background class edges to treat as true edge and therefore included in the edge length
calculations? Note, if a border is present, then only background edges are affected by this
designation, since all other edges along the landscape boundary will be made explicit by the
information in the border. If a border is absent, then all boundary and background edges are
affected. See the Overview section for a more detailed discussion. There are three options to
choose from by clicking on the select button [...]:
" None – Do not count any boundary/background as edge (0%). This is the default.
" All – Count all boundary/background as edge (100%).
" Partial – Specify the percentage of boundary/background edge to treat as an edge (0-100%).
For example, if you specify 50%, then half the total length of edge of involving the
landscape boundary (if a border is absent) and any internal background will be included as
71
edge in the affected metrics.
# Core area – If you select any of the core area metrics on the Core area tab, you must also
either specify a fixed edge depth (in meters) or specify an edge depth table as described
previously (see Specifying Common Tables).
# Contrast – If you select any of the contrast metrics on the Contrast tab, you must also specify
an edge contrast table as described previously (see Specifying Common Tables).
# Aggregation – If you select Proximity index (PROX) or Similarity index (SIMI) on the
Aggregation tab at either the class or landscape level, you must also specify a search radius
(i.e., the distance [in meters] from a focal patch within which neighboring patches are evaluated).
There is no default value, so if you fail to enter a distance, an error message will be written to the
Activity log window upon execution and the run will fail. In addition, if you select the similarity
index, you must also specify a similarity weights table as described previously (see Specifying
Common Tables).
Likewise, if you select the Connectance index (CONNECT) at either the class or landscape level,
you must also specify a threshold distance (i.e., the distance [in meters] between patches
below which they are deemed connected). There is no default value, so if you fail to enter a
distance, an error message will be written to the Activity log window upon execution and the run
will fail.
# Diversity – If you select Relative patch richness (RPR) on the Diversity tab at the landscape level,
you must also specify the maximum number of classes. There is no default value, so if you
fail to enter a distance, an error message will be written to the Activity log window upon
execution and the run will fail.
Ste p 7. Exe c u tin g FRAGST AT S
Now you are finally ready to execute FRAGSTATS. Click on the Run button on the toolbar or
select Run from the Analysis drop-down menu. This will open up the Run dialog (Fig. 9) that will
list the analysis type (referring to the sampling method
selected), current file, number of metrics selected at
each level, and prompt you to click on Proceed to
execute or Cancel to cancel the run. The Current file
will be blank until clicking on Proceed, after which it
will list the current file being processed. Thus, if you
are running a batch file, then it will list each input file
in turn as it is being processed. After the run is
executed, the Activity log will report that the run has
ended. In addition, if you have automatically saved
Figure 9. Run dialog to execute
results, the Activity log will indicate that the results
FRAGSTATS.
were saved to the specified location. For long runs, a
72
progress indicator will display the progress of the run, and the activity log will report on various
stages of the run. For example, for batch processing the activity log will report on the stages of
processing each input layer.
Ste p 8. B ro w s in g an d Sav in g th e Re s u lts
The final step is to browse the output and, if desired, save it to a file (potentially several files). After
the run has ended (as indicated in the Activity log), click on the Results button in the right pane of
the model dialog (Fig. 10). In the corresponding dialog, the Run list includes a list of all the input
layers analyzed in each run. For example, if the batch manager included two input layers, then after
the execution the run list will include the results for the two input layers, and they will be listed with
the prefix R-001 to indicate Run number one (Fig. 10). A second execution will list the results for
each input layer, but with the prefix R-002, and so on for subsequent runs during the same session.
For each input layer, there is a separate set of tabbed dialogs for each level of metrics: patch, class,
and landscape. If you did not previously check the Automatically save results box and specify a
basename for the output files (see Setting Analysis Parameters) prior to executing the run, then you
can save the results to output files here.
Clicking on a particular input layer and a tab allows you to quickly view and evaluate the results of
an analysis before actually saving it to a file(s). This can save you the time of opening the results in a
separate text editor or importing the data to a spreadsheet before “seeing”’ the output. Note, the
tabs will only contain data if the corresponding metrics were selected for the analysis. In addition,
each time you execute a run within the same session, the results will be added to the results manager.
The results of your current session can be managed with the following options:
# Save ADJ file – If you check the Save ADJ file box in the Run list manager, the cell adjacency
file will be saved (basename.adj) when the corresponding run is saved (see Output files in the
Overview for information on the adjacency file).
# Save run as... – If you click the Save run as ... button, you will be prompted to navigate to a
destination folder and provide a basename for the output files (see Output files in the Overview
for information on the output files corresponding to the patch, class and landscape metrics)
associated with the corresponding run (i.e., the run associated with the highlighted input layer in
the Run list). Note, the “basename” will be combined with the .patch, .class, and .land
extensions for the corresponding output files, as well as the .adj extension for the adjacency
matrix if the save ADJ file box is checked. If you attempt to save to a file name that already
exists, you will be prompted as to whether you want to overwrite this file or not; appending the
results to an existing file is not an option because there is no guarantee that the output file
structure will be the same. If you wish to append the results of several runs with identical output
formats, you will have to do so manually at your own risk. Importantly, saving a run involves
saving the results for all of the input layers associated with the run of the highlighted layer to a
single output file(s). Thus, if run #1 consists of five input layers, and any of the input layers are
highlighted in the run list, then the results for each of the five input layers will be appended to a
single output file for each level of metrics selected. For example, the basename.land file will
contain the landscape-level metrics for all five input layers associated with run #1.
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Figure 10. Results dialog depicting the layers analyzed and the corresponding patch, class and/or
landscape metrics computed for each layer.
# Drop selected run – If you click the Drop selected run button, the results associated with the
run number highlighted in the Run list will be dropped from the results. Note, the results for all
of the layers associated with the run of the layer highlighted will be dropped, not just the results
of the layer highlighted.
# Drop all – If you click the Drop all button, then all the runs in the Run list will be dropped
from the results.
Ste p 9. Ge ttin g He lp
The Help drop-down menu provides you with online help.
# Help Content – Allows you to access a familiar windows-based help interface with the standard
content, index, and find options. The help files include information on “what’s new”,
background on landscape pattern analysis, user guidelines, and details on the metrics.
# About FRAGSTATS – Lists the authors and the software release version.
Running via the Command Line
FRAGSTATS can be executed via a command line to allow you to run FRAGSTATS from within
another program (e.g., R). The command line control is limited to specifying a FRAGSTATS model
file (.fca). In essence, you can call FRAGSTATS, specify an existing model, and execute the model
from a single command line. However, the model file must be created first via the Graphical User
74
Interface in the usual way–there are simply too many parameters to make full specification via the
command line a practical alternative at this time. The syntax for this command line call is as follows
(note, there is a required space before and after -m, -b and -o in the command line below):
frg -m model_name_here -b batch_file_name_here -o output_file_name_here
Here are some example valid command line calls:
frg -m test.fca
frg.exe -m test.fca
c:\foobar\frg -m test.fca
frg -m test.fca -b c:\foobar\batch_file.fbt
frg -m test.fca -o c:\foobar\basename
frg -m test.fca -b c:\foobar\batch_file.fbt -o c:\foobar\basename
There are several important considerations regarding the arguments in the command line:
# frg [required] – frg simply calls and executes the program. The .exe extension is optional (i.e.,
either frg or frg.exe will work) and it is NOT case sensitive. If the FRAGSTATS executable
(frg.exe) is NOT in the current folder OR is NOT specified in the system’s Path variable, then
the full path to the executable is required, as in the third example given.
# -m [required] – This is a required switch to name a FRAGSTATS model file (.fca). The model
file is a fully parameterized model created via the graphical user interface. This file specifies all
required and user-selected parameters of the analysis. It should be parameterized completely
according to the instructions given elsewhere for Running FRAGSTATS via the Graphical User
Interface. Note, FRAGSTATS parameterization files are assigned the .fca extension and this
should be included in the argument. If the model file does not exist or is improperly formatted,
the execution will fail.
# -b [optional] – This is an optional switch to name a FRAGSTATS batch file (.fbt). The batch
file lists the input layers and the corresponding grid attributes of each layer (see previous
discussion). If you specify the -b switch, then you must provide a batch file. The batch file
specified here will override whatever is specified in the model file. Thus, the model file can be
created without specifying any input layers, if you intend on specifying a batch file here. Note,
specifying a batch file here is identical to loading the same batch file in the model via the
graphical user interface and not specifying the -b switch here. Importantly, if you do NOT
specify the -b switch, then the input layers must be specified in the model file, or the execution
will fail.
# -o [optional] – This is an optional switch to name an output file name (i.e., basename). The
output file name is the basename for the output files corresponding to each level of metrics
selected (basename.patch, basename.class, basename.land, and basename.adj). If you specify the
-o switch, then you must provide an output file name with a complete path. Note, if you specify
the basename of a file that already exists, FRAGSTATS will automatically rename the extension
of the existing files to *.bk1. The next time there is a conflict, the files will be renamed *.bk2,
75
and so on. Appending the results to an existing file is not an option because there is no
guarantee that the output file structure will be the same. Importantly, if you do NOT specify the
-o switch, then the output file (basename) must be specified and the Automatically save
results... button checked in the model file, or the execution will fail.
76
FRAGSTATS METRICS
Overview
FRAGSTATS computes several statistics for each patch and class (patch type) in the landscape and
for the landscape as a whole. At the class and landscape level, some of the metrics quantify
landscape composition, while others quantify landscape configuration. Landscape composition and
configuration can affect ecological processes independently and interactively (see Background).
Thus, it is especially important to understand for each metric what aspect of landscape pattern is
being quantified. In addition, many of the metrics are partially or completely redundant; that is, they
quantify a similar or identical aspect of landscape pattern. In most cases, redundant metrics will be
very highly or even perfectly correlated. For example, at the landscape level, patch density (PD) and
mean patch size (MPS) will be perfectly correlated because they represent the same information. These
redundant metrics are alternative ways of representing the same information; they are included in
FRAGSTATS because the preferred form of representing a particular aspect of landscape pattern
will differ among applications and users. It behooves the user to understand these redundancies,
because in most applications only 1 of each set of redundant metrics should be employed. It is
important to note that in a particular application, some metrics may be empirically redundant as
well; not because they measure the same aspect of landscape pattern, but because for the particular
landscapes under investigation, different aspects of landscape pattern are statistically correlated. The
distinction between this form of redundancy and the former is important, because little can be
learned by interpreting metrics that are inherently redundant, but much can be learned about
landscapes by interpreting metrics that are empirically redundant.
Many of the patch indices have counterparts at the class and landscape levels. For example, many of
the class indices (e.g., mean shape index) represent the same basic information as the corresponding
patch indices (e.g., patch shape index), but instead of considering a single patch, they consider all
patches of a particular type simultaneously. Likewise, many of the landscape indices are derived
from patch or class characteristics. Consequently, many of the class and landscape indices are
computed from patch and class statistics by summing or averaging over all patches or classes. Even
though many of the class and landscape indices represent the same fundamental information,
naturally the algorithms differ slightly. Class indices represent the spatial distribution and pattern
within a landscape of a single patch type; whereas, landscape indices represent the spatial pattern of
the entire landscape mosaic, considering all patch types simultaneously. Thus, even though many of
the indices have counterparts at the class and landscape levels, their interpretations may be
somewhat different. Most of the class indices can be interpreted as fragmentation indices because
they measure the configuration of a particular patch type; whereas, most of the landscape indices
can be interpreted more broadly as landscape heterogeneity indices because they measure the overall
landscape pattern. Hence, it is important to interpret each index in a manner appropriate to its scale
(patch, class, or landscape).
In the sections that follow, each metric computed in FRAGSTATS is described in detail. Metrics are
grouped according to the aspect of landscape pattern measured (see Background), as follows:
•
Area and edge metrics
77
•
•
•
•
•
Shape metrics
Core area metrics
Contrast metrics
Aggregation metrics
Diversity metrics
Within each of these groups, metrics are further grouped into patch, class, and landscape metrics, as
described below.
Patc h Me tric s
Patch metrics are computed for every patch in the landscape; the resulting patch output file contains
a row (observation vector) for every patch, where the columns (fields) represent the individual
metrics. The first three columns include header information about the patch:
•
Landscape ID.--The first field in the patch output file is Landscape ID (LID). Landscape ID
is set to the name of the input image obtained from the input file (see Run Parameters).
•
Patch ID.--The second field in the patch output file is Patch ID (PID). If a Patch ID image
is specified that contains unique ID's for each patch, FRAGSTATS reads the patch ID from
the designated image. If an image is not specified, FRAGSTATS creates unique ID's for
each patch and optionally produces an image that contains patch ID's that correspond to the
FRAGSTATS output.
•
Patch Type.--The third field in the patch output file is Patch type (TYPE). FRAGSTATS
contains an option to name an ASCII file (class descriptors file) that contains character
descriptors for each patch type. If the class descriptors option is not used, FRAGSTATS will
write the numeric patch type codes to TYPE.
There are two basic types of metrics at the patch level: (1) indices of the spatial character and
context of individual patches, and (2) measures of the deviation from class and landscape norms;
that is, how much the computed value of each metric for a patch deviates from the class and
landscape means. The deviation statistics are useful in identifying patches with extreme values on
each metric. Because the deviation statistics are computed similarly for all patch metrics, they are
described in common below:
Patc h De v iatio n Statis tic s .--In addition to the standard patch metrics, FRAGSTATS computes
several deviation statistics for each patch that measures how much it deviates from the class or
landscape norm (i.e., how extreme an observation it is) for each metric. Specifically, for each patch
and each patch metric, FRAGSTATS computes the following four measures of deviation:
Standard Deviations from the Class Mean
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xij =
0i =
si =
value of a patch metric for patch ij.
mean value of the corresponding patch metric for patch type
(class) i.
standard deviation of the corresponding patch metric for patch
type (class) i.
Description
CSD equals the value of the metric (x) for the focal patch (ij) minus the mean of
the metric across all patches in the focal class, divided by the class standard
deviation (population formula).
Units
Same as the metric
Range
-4 < metric < +4
Although standard deviation has no theoretical limit, 66.5% of the observations
(assuming a normal distribution) will be within ±1 standard deviations of the
mean, 95% within ±2 standard deviations, and 99.7% within ±3 standard
deviations.
Comments
The number of standard deviations from the class mean is obtained from a zscore transformation of the observed value using the mean and standard
deviation derived from all patches in the focal class. This transformation results
in a standardized metric that has zero mean and unit variance for the class. Any
observation that is, say, more than 2.5 standard deviations from the class mean
can be considered an extreme observation. This is a quick and easy way to
identify patches with extreme values of a metric. However, it is necessary to
assume an underlying normal distribution in order for standard deviations to have
a direct interpretation regarding the percent of the distribution greater or smaller
than the observed value. CSD can be computed for each patch metric and is
reported in the patch output file as the metric name followed by _CSD. For
example, the class standard deviation metric for the shape index (SHAPE) would
be given the variable name: SHAPE_CSD.
Percentile of the Class Distribution
xij = value of a patch metric for patch ij.
ni = number of patches of the corresponding patch type
(class) i.
Description
CPS equals the percentile of the rank-ordered distribution of all patches in the
focal class for the corresponding metric (x); that is, the percent of observations in
rank order that are smaller than the observed value for the focal patch (ij).
Units
Percent
79
Range
0 # metric # 100
CPS = 0 if the observed patch metric is the lowest value for any patch in the
class. Conversely, CPS = 100 if the observed patch metric is the highest value for
any patch in the class.
Comments
The percentile of the class distribution is obtained by rank ordering observations
from lowest to highest and computing the percentage of observations smaller
than the observed value for the focal patch. In contrast to standard deviation, this
deviation statistic makes no assumption about the underlying distribution; it
simply quantifies the percent of the observed distribution that is smaller than the
observed value for the focal patch under consideration.
Standard Deviations from the Landscape Mean
xij =
0=
s=
value of a patch metric for patch ij.
mean value of the corresponding patch metric across all
patches in the landscape.
standard deviation of the corresponding patch metric for all
patches in the landscape.
Description
LSD equals the value of the metric (x) for the focal patch (ij) minus the mean of
the metric across all patches in the landscape divided by the landscape standard
deviation (population formula).
Units
Same as the metric
Range
-4 < metric < +4
Although standard deviation has no theoretical limit, 66.5% of the observations
(assuming a normal distribution) will be within ±1 standard deviations of the
mean, 95% within ±2 standard deviations, and 99.7% within ±3 standard
deviations.
80
Comments
The number of standard deviations from the landscape mean is obtained from a
z-score transformation of the observed value using the mean and standard
deviation derived from all patches in the landscape. This transformation results in
a standardized metric that has zero mean and unit variance for the entire
landscape. Any observation that is, say, more than 2.5 standard deviations from
the landscape mean can be considered an extreme observation. This is a quick
and easy way to identify patches with extreme values of a metric. However, it is
necessary to assume an underlying normal distribution in order for standard
deviations to have a direct interpretation regarding the percent of the distribution
greater or smaller than the observed value. LSD can be computed for each patch
metric and is reported in the patch output file as the metric name followed by a
_LSD. For example, the landscape standard deviation metric for the shape index
(SHAPE) would be given the variable name: SHAPE_LSD.
Percentile of the Landscape Distribution
xij = value of a patch metric for patch ij.
N = number of patches in the landscape.
Description
LPS equals the percentile of the rank ordered distribution of all patches in the
landscape for the corresponding metric (x); that is, the percent of observations in
rank order that are smaller than the observed value for the focal patch (ij).
Units
Percent
Range
0 # metric # 100
LPS = 0 if the observed patch metric is the lowest value for any patch in the
landscape. Conversely, LPS = 100 if the observed patch metric is the highest
value for any patch in the landscape.
Comments
The percentile of the landscape distribution is obtained by rank ordering
observations from lowest to highest and computing the percentage of
observations smaller than the observed value for the focal patch. In contrast to
standard deviation, this deviation statistic makes no assumption about the
underlying distribution; it simply quantifies the percent of the observed
distribution that is smaller than the observed value for the focal patch under
consideration.
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Clas s Me tric s
Class metrics are computed for every patch type or class in the landscape; the resulting class output
file contains a row (observation vector) for every class, where the columns (fields) represent the
individual metrics. The first two columns include header information about the class:
•
Landscape ID.--The first field in the class output file is Landscape ID (LID). Landscape ID
is set to the name of the input image obtained from the input layer.
•
Patch Type.--The second field in the class output file is Patch type (TYPE). FRAGSTATS
contains an option to name an ASCII file (class descriptors file) that contains character
descriptors for each patch type. If the class descriptor option is not used, FRAGSTATS will
write the numeric patch type codes to TYPE.
There are two basic types of metrics at the class level: (1) indices of the amount and spatial
configuration of the class, and (2) distribution statistics that provide first- and second-order
statistical summaries of the patch metrics for the focal class. The latter are used to summarize the
mean, area-weighted mean, median, range, standard deviation, and coefficient of variation in the
patch attributes across all patches in the focal class. Because the distribution statistics are computed
similarly for all class metrics, they are described in common below:
Clas s Dis trib u tio n Statis tic s .--Class metrics measure the aggregate properties of the patches
belonging to a single class or patch type. Some class metrics go about this by characterizing the
aggregate properties without distinction among the separate patches that comprise the class. These
metrics are defined elsewhere. Another way to quantify the configuration of patches at the class level
is to summarize the aggregate distribution of the patch metrics for all patches of the corresponding
patch type. In other words, since the class represents an aggregation of patches of the same type, we
can characterize the class by summarizing the patch metrics for the patches that comprise each class.
There are many possible first- and second-order statistics that can be used to summarize the patch
distribution. FRAGSTATS computes the following: (1) Mean (MN), (2) Area-weighted mean (AM), (3)
Median (MD), (4) Range (RA), (5) Standard deviation (SD), and (6) Coefficient of variation (CV).
FRAGSTATS computes these distribution statistics for all patch metrics at the class level. In the
class output file, these metrics are labeled by concatenating the metric acronym with an underscore
and the distribution statistic acronym. For example, Patch area (AREA) is summarized at the class
level by each of the distribution statistics and reported in the class output file as follows: Mean patch
area (AREA_MN), Area-weighted mean patch area (AREA_AM), Median patch area (AREA_MD), Range
in patch area (AREA_RA), Standard deviation in patch area (AREA_SD), and Coefficient of variation in patch
area (AREA_CV).
MN (Mean) equals the sum, across all patches of
the corresponding patch type, of the
corresponding patch metric values, divided by the
number of patches of the same type. MN is given
in the same units as the corresponding patch
metric.
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AM (area-weighted mean) equals the sum, across
all patches of the corresponding patch type, of the
corresponding patch metric value multiplied by
the proportional abundance of the patch [i.e.,
patch area (m2) divided by the sum of patch
areas].
MD (median) equals the value of the
corresponding patch metric for the patch
representing the midpoint of the rank order
distribution of patch metric values for patches of
the corresponding patch type.
RA (range) equals the value of the corresponding
patch metric for the largest observed value minus
the smallest observed value (i.e., the difference
between the maximum and minimum observed
values) for patches of the corresponding patch
type.
SD (standard deviation) equals the square root of
the sum of the squared deviations of each patch
metric value from the mean metric value of the
corresponding patch type, divided by the number
of patches of the same type; that is, the root mean
squared error (deviation from the mean) in the
corresponding patch metric. Note, this is the
population standard deviation, not the sample
standard deviation.
CV (coefficient of variation) equals the standard
deviation divided by the mean, multiplied by 100
to convert to a percentage, for the corresponding
patch metric.
83
Lan d s c ap e Me tric s
Landscape metrics are computed for entire patch mosaic; the resulting landscape output file contains
a single row (observation vector) for the landscape, where the columns (fields) represent the
individual metrics. The first column includes header information about the landscape:
(L1) Landscape ID.--The first field in the landscape output file is landscape ID (LID).
Landscape ID is set to the name of the input image obtained from the input file.
Like class metrics, there are two basic types of metrics at the landscape level: (1) indices of the
composition and spatial configuration of the landscape, and (2) distribution statistics that provide
first- and second-order statistical summaries of the patch metrics for the entire landscape. The latter
are used to summarize the mean, area-weighted mean, median, range, standard deviation, and
coefficient of variation in the patch attributes across all patches in the landscape. Because the
distribution statistics are computed similarly for all landscape metrics, they are described in common
below:
Lan d s c ap e Dis trib u tio n Statis tic s .--Landscape metrics measure the aggregate properties of the
entire patch mosaic. Some landscape metrics go about this by characterizing the aggregate properties
without distinction among the separate patches that comprise the mosaic. These metrics are defined
elsewhere. Another way to quantify the configuration of patches at the landscape level is to
summarize the aggregate distribution of the patch metrics for all patches in the landscape. In other
words, since the landscape represents an aggregation of patches, we can characterize the landscape
by summarizing the patch metrics. There are many possible first- and second-order statistics that can
be used to summarize the patch distribution. FRAGSTATS computes the following: (1) Mean (MN),
(2) Area-weighted mean (AM), (3) Median (MD), (4) Range (RA), (5) Standard deviation (SD), and (6)
Coefficient of variation (CV). FRAGSTATS computes these distribution statistics for all patch metrics at
the landscape level. In the class output file, these metrics are labeled by concatenating the metric
acronym with an underscore and the distribution statistic acronym. For example, Patch area (AREA)
is summarized at the landscape level by each of the distribution statistics and reported in the class
output file as follows: Mean patch area (AREA_MN), Area-weighted mean patch area (AREA_AM),
Median patch area (AREA_MD), Range in patch area (AREA_RA), Standard deviation in patch area
(AREA_SD), and Coefficient of variation in patch area (AREA_CV). Note, the acronyms for the
distribution statistics are the same at the class and landscape levels, so they can only be distinguished
by the output file they belong to (i.e., “.basename”.class or “basename”.land).
MN (Mean) equals the sum, across all patches in
the landscape, of the corresponding patch metric
values, divided by the total number of patches.
MN is given in the same units as the
corresponding patch metric.
84
AMN (area-weighted mean) equals the sum,
across all patches in the landscape, of the
corresponding patch metric value multiplied by
the proportional abundance of the patch [i.e.,
patch area (m2) divided by the sum of patch
areas]. Note, the proportional abundance of each
patch is determined from the sum of patch areas
rather than the total landscape area, because the
latter may include internal background area not
associated with any patch.
MD (median) equals the value of the
corresponding patch metric for the patch
representing the midpoint of the rank order
distribution of patch metric values based on all
patches in the landscape.
RA (range) equals the value of the corresponding
patch metric for the largest observed value minus
the smallest observed value (i.e., the difference
between the maximum and minimum observed
values) for all patches in the landscape.
SD (standard deviation) equals the square root of
the sum of the squared deviations of each patch
metric value from the mean metric value
computed for all patches in the landscape, divided
by the total number of patches; that is, the root
mean squared error (deviation from the mean) in
the corresponding patch metric. Note, this is the
population standard deviation, not the sample
standard deviation.
CV (coefficient of variation) equals the standard
deviation divided by the mean, multiplied by 100
to convert to a percentage, for the corresponding
patch metric.
85
Ge n e ral Co m m e n ts
Not all groups of metrics (see previous list) have metrics at all levels. For example, diversity metrics
only exist at the landscape level. Also note that the organizational hierarchy used here is opposite of
that used in the FRAGSTATS graphical user interface (GUI). In the GUI, metrics are first grouped
by level (patch, class, and landscape) and then further grouped by the aspect of landscape pattern
measured. The GUI organization strives to be consistent with the way most users conduct a
FRAGSTATS analysis. Often times, for example, users are only interested in class metrics. Here,
however, the discussion of the metrics is facilitated by reversing the hierarchy and first grouping
them according the aspect of pattern measured, then by the level of organization (patch, class, and
landscape). In this manner, issues common to all metrics that relate to the same aspect of landscape
pattern can be discussed once.
Following this convention, each metrics section begins with a brief introduction to the metrics in the
group, followed by an overview of the various metrics computed by FRAGSTATS and a discussion
of important limitations in their use and interpretation. Following this overview, each metric is
defined, including a mathematical definition, measurement units, theoretical range in values, and
any special considerations or limitations in the use of the metric. For each metric, the mathematical
formula is described in narrative terms to facilitate interpretation of the formula. The acronym for
the metric given on the left-hand side of the equation is the field name used in the ASCII output
files. To facilitate interpretation of the algorithm, we intentionally separate from each equation any
constants used to rescale the metric. For example, in many cases the right-hand side of the equation
is multiplied by 100 to convert a proportion to a percentage, or multiplied or divided by 10,000 to
convert m2 to hectares. These conversion factors are separated out by parentheses even though they
may be factored into the equation differently in the computational form of the algorithm.
Me an v e rs u s are a-w e ig h te d m e an
Metrics based on the mean patch characteristic, such as Mean patch size (AREA_MN) or Mean patch
shape index (SHAPE_MN), provide a measure of central tendency in the corresponding patch
characteristic across the entire landscape, but nevertheless describe the patch structure of the
landscape as that of the average patch characteristic. Thus, each patch regardless of its size is
considered equally (i.e., given equal weight) in describing the landscape structure. Consequently,
metrics based on the mean patch characteristic offer a fundamentally patch-centric perspective of the
landscape structure. They do not describe the conditions, for example, that an animal dropped at
random on the landscape would experience, because that depends on the probability of landing in a
particular patch, which is dependent on patch size.
Conversely, metrics based on the area-weighted mean patch characteristic, such as the Area-weighted
mean patch size (AREA_AM) and Area-weighted mean patch shape index (SHAPE_AM), while still derived
from patch characteristics, provide a landscape-centric perspective of landscape structure because they
reflect the average conditions of a pixel chosen at random or the conditions that an animal dropped
at random on the landscape would experience. This is in fact the basis for the subdivision metrics of
Jaeger (2000) described later.
86
All patch metrics can be summarized at the class or landscape level using the mean and the
area-weighted mean; the choice of formulation depends on the perspective sought: patch-centric or
landscape-centric. In most applications, the landscape-centric perspective is the one sought
and thus the area-weighted mean is the proper formulation. However, there are some special
cases involving the isolation metrics (Proximity index, Similarity index, and Euclidean nearest-neighbor
distance) where the area-weighted mean patch characteristic can provide misleading results. The
isolation metrics describe the spatial context of individual patches, and they can be summarized at
the class or landscape level to characterize the entire landscape. Consider the Proximity index
(PROX). The Proximity index operates at the patch level. For each patch, the size and distance to all
neighboring patches of the same type (within some specified search distance) are enumerated to
provide an index of patch isolation. A patch with lots of other large patches in close proximity will
have a large index value (i.e., low isolation). Both the Mean and Area-weighted mean proximity index can
be calculated at the class and landscape levels. A potential problem in interpretation lies in cases
involving widely varying patch sizes. Consider the special case involving 10 patches of the focal
class, in which 9 of the 10 patches are equal in size and quite small (say 1 ha each). The ninth patch,
however, is quite large (say 1,000 ha). Let's assume that all the small patches are close to the large
patch (within the search distance). The proximity index for each of the 9 small patches will be quite
large, because the single large patch will be enumerated in the index. The Proximity index for the
single large patch will be quite small, because the only neighboring patches are quite small (1 ha
each). Consequently, the Mean proximity index will be much larger than the Area-weighted mean proximity
index, connoting very different levels of patch isolation. Which is correct? It is difficult to say. From
a purely patch-based perspective, the mean would appear to capture the structure best, since the
average "patch" is not very isolated. However, the average "organism" would be found in the single
large patch, since it represents >99% of the focal habitat area, so it seems logical that the
area-weighted mean would provide a better measure. In this case, the Area-weighted mean proximity
index will be quite small, connoting high isolation, when in fact the single large patch represents the
matrix of the landscape. In this case, it is not clear whether either the Mean or Area-weighted mean
proximity index provides a useful measure of isolation. The important point here is that for some
metrics, namely the isolation metrics, under some conditions, namely extreme patch size
distributions, the mean and area-weighted mean can provide different and potentially misleading
results.
87
Area and Edge Metrics
Background.--This group of metrics represents a loose collection of metrics that deal with the size
of patches and the amount of edge created by these patches. Although these metrics could easily be
subdivided into separate groups or assigned to other already recognized groups, there is enough
similarity in the basic patterns assessed by these metrics to include them under one umbrella.
The area of each patch comprising a landscape mosaic is perhaps the single most important and
useful piece of information contained in the landscape. Not only is this information the basis for
many of the patch, class, and landscape indices, but patch area has a great deal of ecological utility in
its own right. For example, there is considerable evidence that bird species richness and the
occurrence and abundance of some species are strongly correlated with patch size (e.g., Robbins et
al. 1989). Most species have minimum area requirements: the minimum area needed to meet all life
history requirements. Some of these species require that their minimum area requirements be
fulfilled in contiguous habitat patches; in other words, the individual habitat patch must be larger
than the species minimum area requirement for them to occupy the patch. These species are
sometimes referred to as “area-sensitive” species. Thus, patch size information alone could be used
to model species richness, patch occupancy, and species distribution patterns in a landscape given
the appropriate empirical relationships derived from field studies.
Although patch area per se may be extremely important ecologically, the extent of patch (or patches
collectively) may be even more important. Connectivity is considered a “vital element of landscape
structure” (Taylor et al., 1993), but it has eluded precise definition and has been difficult to quantify
and implement in practice. In part, this is due to differences between the continuity or “structural
connectedness” of patch types (or habitat) and the connectivity or “functional connectedness” of the
landscape as perceived by an organism or ecological process. Continuity refers to the physical
continuity of a patch type (or a habitat) across the landscape. Contiguous habitat is physically
connected, but once subdivided, for example, as a result of habitat fragmentation, it becomes
physically disconnected. Continuity can be evaluated by a measure of habitat extensiveness; i.e., the
extent of the reach of a contiguous patch or collection of patches on average. The notion of
continuity adopts an island biogeographic perspective because the focus is on the physical continuity
of a single patch type. What constitutes connectivity or "functional connectedness" between
patches, on the other hand, clearly depends on the organism or process of interest; patches that are
connected for bird dispersal might not be connected for salamanders, seed dispersal, fire spread, or
hydrologic flow. As With (1999) notes, “what ultimately influences the connectivity of the landscape
from the organism’s perspective is the scale and pattern of movement (scale at which the organism
perceives the landscape) relative to the scale and pattern of patchiness (structure of the landscape);
...i.e., a species’ gap-crossing or dispersal ability relative to the gap-size distribution on the
landscape”(Dale et al. 1994, With and Crist 1995, Pearson et al. 1996, With et al. 1997). Functional
connectedness, therefore, relates to the interaction of ecological flows (including organisms) with
landscape pattern.
The amount of edge in a landscape is important to many ecological phenomena. In particular, a
great deal of attention has been given to wildlife-edge relationships (Thomas et al. 1978 and 1979,
Strelke and Dickson 1980, Morgan and Gates 1982, Logan et al. 1985). In landscape ecological
investigations, much of the presumed importance of spatial pattern is related to edge effects. The
88
forest edge effect, for example, results primarily from differences in wind and light intensity and
quality reaching a forest patch that alter microclimate and disturbance rates (e.g., Gratkowski 1956,
Ranney et al. 1981, Chen and Franklin 1990). These changes, in combination with changes in seed
dispersal and herbivory, can influence vegetation composition and structure (Ranney et al. 1981).
The proportion of a forest patch that is affected in this manner is dependent, therefore, upon patch
shape and orientation, and by adjacent land cover. A large but convoluted patch, for example, could
be entirely edge habitat. It is now widely accepted that edge effects must be viewed from an
organism-centered perspective because edge effects influence organisms differently; some species
have an affinity for edges, some are unaffected, and others are adversely affected.
Indeed, one of the most dramatic and well-studied consequences of habitat fragmentation is an
increase in the proportional abundance of edge-influenced habitat. Early wildlife management
efforts were focused on maximizing edge habitat because it was believed that most species favored
habitat conditions created by edges and that the juxtaposition of different habitats would increase
species diversity (Leopold 1933). Indeed this concept of edge as a positive influence guided land
management practices for most of the twentieth century. Recent studies, however, have suggested
that changes in microclimate, vegetation, invertebrate populations, predation, brood parasitism, and
competition along forest edges (i.e., edge effects) has resulted in the population declines of several
vertebrate species dependent upon forest interior conditions (e.g., Strelke and Dickson 1980,
Whitcomb et al. 1981, Kroodsma 1982, Brittingham and Temple 1983, Wilcove 1985, Temple 1986,
Noss 1988, Yahner and Scott 1988, Robbins et al. 1989). In fact, many of the adverse effects of
forest fragmentation on organisms seem to be directly or indirectly related to these so-called edge
effects. Forest interior species, therefore, may be sensitive to patch shape because for a given patch
size, the more complex the shape, the larger the edge-to-interior ratio. Total class edge in a
landscape, therefore, often is the most critical piece of information in the study of fragmentation,
and many of the class indices directly or indirectly reflect the amount of class edge. Similarly, the
total amount of edge in a landscape is directly related to the degree of spatial heterogeneity in that
landscape. Note, edges have myriad ecological effects, as noted above, and may be addressed by
simply quantifying the total length of edge (as in the edge metrics included here), or by quantifying
the core area remaining after accounting for adverse penetrating edge effects (see core area metrics),
or by quantifying the magnitude of contrast along edges due to differences between adjoining patch
types (see contrast metrics).
Overall, the size and extent of patches and the edges associated with patch boundaries comprising a
class or the entire landscape mosaic is one of the most basic aspects of landscape pattern that can
affect myriad processes. For example, although there are myriad effects of habitat fragmentation on
individual behavior, habitat use patterns, and intra- and inter-specific interactions, many of these
effects are caused by a reduction in habitat area and continuity and an increase in the proportion of
edge-influenced habitat. Briefly, as a species’ habitat is lost from the landscape (without being
fragmented), at some point there will be insufficient area of habitat to support a viable population,
and with continued loss eventually there will be insufficient area of habitat to support even a single
individual and the species will be extirpated from the landscape. This area relationship is expected to
vary among species depending on their minimum area requirements. Moreover, the area threshold
for occupancy may occur when total habitat area is still much greater than the individual’s minimum
area requirement. For example, an individual may not occupy available habitat unless there are other
individuals of the same species occupying the same or nearby patches of habitat, or an individual’s
89
occupancy may be influenced by what other species are occupying the patch. Similarly, as habitat is
lost and simultaneously fragmented into smaller and less extensive patches, at some point there will
be insufficient contiguous area of suitable habitat within a home range size area to support an
individual. Or the habitat may become too discontinuous, resulting in too much resistance to
movement through nonhabitat to accumulate enough suitable habitat. This is the ultimate
consequence of habitat loss and fragmentation–insufficient habitat quantity, quality and connectivity
to support individuals and viable populations.
FRAGSTATS Metrics.--FRAGSTATS computes several simple statistics representing area, extent
and perimeter (or edge) at the patch, class, and landscape levels. Area metrics quantify landscape
composition, not landscape configuration. As noted above, the area (AREA) of each patch
comprising a landscape mosaic is perhaps the single most important and useful piece of information
contained in the landscape. However, the size of a patch may not be as important as the
extensiveness of the patch for some organisms and processes. Radius of gyration (GYRATE) is a
measure of patch extent; that is, how far across the landscape a patch extends its reach. All other
things equal, the larger the patch, the larger the radius of gyration. Similarly, holding area constant,
the more extensive the patch (i.e., elongated and less compact), the greater the radius of gyration.
The radius of gyration can be considered a measure of the average distance an organism can move
within a patch before encountering the patch boundary from a random starting point.
Class area (CA) and percentage of landscape (PLAND) are fundamental measures of landscape
composition; specifically, how much of the landscape is comprised of a particular patch type. This is
an important characteristic in a number of ecological applications. For example, an important byproduct of habitat fragmentation is habitat loss. In the study of forest fragmentation, therefore, it is
important to know how much of the target patch type (habitat) exists within the landscape. In
addition, although many vertebrate species that specialize on a particular habitat have minimum area
requirements (e.g., Robbins et al. 1989), not all species require that suitable habitat to be present in a
single contiguous patch. For example, northern spotted owls have minimum area requirements for
late-seral forest that varies geographically; yet, individual spotted owls use late-seral forest that may
be distributed among many patches (Forsman et al. 1984). For this species, late-seral forest area
might be a good index of habitat suitability within landscapes the size of spotted owl home ranges
(Lehmkuhl and Raphael 1993). In addition to its direct interpretive value, class area (in absolute or
relative terms) is used in the computations for many of the class and landscape metrics.
In addition to these primary metrics, FRAGSTATS also summarizes the distribution of patch area
and extent (radius of gyration) across all patches at the class and landscape levels. For example, the
distribution of patch area (AREA) is summarized by its mean and variability. These summary
measures provide a way to characterize the distribution of area among patches at the class or
landscape level. For example, progressive reduction in the size of habitat fragments is a key
component of habitat fragmentation. Thus, a landscape with a smaller mean patch size for the target
patch type than another landscape might be considered more fragmented. Similarly, within a single
landscape, a patch type with a smaller mean patch size than another patch type might be considered
more fragmented. Thus, mean patch size can serve as a habitat fragmentation index, although the
limitations discussed below may reduce its utility in this respect. When aggregated at the class or
landscape level, the area-weighted mean patch radius of gyration (GYRATE_AM) provides a measure of
landscape continuity (also known as correlation length) that represents the average traversability of
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the landscape for an organism that is confined to remain within a single patch; specifically, it gives
the average distance one can move from an random starting point and traveling in a random
direction without leaving the patch.
Mean patch size (AREA_MN) at the class level is a function of the number of patches in the class and
total class area. Importantly, although mean patch size is derived from the number of patches, it
does not convey any information about how many patches are present. A mean patch size of 10 ha
could represent 1 or 100 patches and the difference could have profound ecological implications.
Furthermore, mean patch size represents the average condition. Variation in patch size may convey
more useful information. For example, a mean patch size of 10 ha could represent a class with 5 10ha patches or a class with 2-, 3-, 5-, 10-, and 30-ha patches, and this difference could be important
ecologically. For these reasons, mean patch size is probably best interpreted in conjunction with
total class area, patch density (or number of patches), and patch size variability. At the landscape
level, mean patch size and patch density are both a function of number of patches and total
landscape area. In contrast to the class level, these indices are completely redundant (assuming there
is no internal background). Although both indices may be useful for "describing" 1 or more
landscapes, they would never be used simultaneously in a statistical analysis of landscape structure.
In many ecological applications, second-order statistics, such as the variation in patch size, may
convey more useful information than first-order statistics, such as mean patch size. Variability in
patch size measures a key aspect of landscape heterogeneity that is not captured by mean patch size
and other first-order statistics. For example, consider 2 landscapes with the same patch density and
mean patch size, but with very different levels of variation in patch size. Greater variability indicates
less uniformity in pattern either at the class level or landscape level and may reflect differences in
underlying processes affecting the landscapes. Variability is a difficult thing to summarize in a single
metric. FRAGSTATS computes three of the simplest measures of variability–range, standard
deviation, and coefficient of variation.
Patch size standard deviation (AREA_SD) is a measure of absolute variation; it is a function of the
mean patch size and the difference in patch size among patches. Thus, although patch size standard
deviation conveys information about patch size variability, it is a difficult parameter to interpret
without doing so in conjunction with mean patch size because the absolute variation is dependent
on mean patch size. For example, two landscapes may have the same patch size standard deviation,
e.g., 10 ha; yet one landscape may have a mean patch size of 10 ha, while the other may have a mean
patch size of 100 ha. In this case, the interpretations of landscape pattern would be very different,
even though absolute variation is the same. Specifically, the former landscape has greatly varying and
smaller patch sizes, while the latter has more uniformly-sized and larger patches. For this reason,
patch size coefficient of variation (AREA_CV) is generally preferable to standard deviation for comparing
variability among landscapes. Patch size coefficient of variation measures relative variability about
the mean (i.e., variability as a percentage of the mean), not absolute variability. Thus, it is not
necessary to know mean patch size to interpret the coefficient of variation. Nevertheless, patch size
coefficient of variation also can be misleading with regards to landscape structure in the absence of
information on the number of patches or patch density and other structural characteristics. For
example, two landscapes may have the same patch size coefficient of variation, e.g., 100%; yet one
landscape may have 100 patches with a mean patch size of 10 ha, while the other may have 10
patches with a mean patch size of 100 ha. In this case, the interpretations of landscape structure
91
could be very different, even though the coefficient of variation is the same. Ultimately, the choice
of standard deviation or coefficient of variation will depend on whether absolute or relative variation
is more meaningful in a particular application. Because these measures are not wholly redundant, it
may be meaningful to interpret both measures in some applications.
It is important to keep in mind that both standard deviation and coefficient of variation assume a
normal distribution about the mean. In a real landscape, the distribution of patch sizes may be highly
irregular. It may be more informative to inspect the actual distribution itself, rather than relying on
summary statistics such as these that make assumptions about the distribution and therefore can be
misleading. Also, note that patch size standard deviation and coefficient of variation can equal 0
under 2 different conditions: (1) when there is only 1 patch in the landscape; and (2) when there is
more than 1 patch, but they are all the same size. In both cases, there is no variability in patch size,
yet the ecological interpretations could be different.
FRAGSTATS computes several statistics representing the amount of perimeter (or edge) at the
patch, class, and landscape levels. Edge metrics usually are best considered as representing landscape
configuration, even though they are not spatially explicit at all. At the patch level, edge is a function
of patch perimeter (PERIM). At the class and landscape levels, total edge (TE) is an absolute measure of
total edge length of a particular patch type (class level) or of all patch types (landscape level). In
applications that involve comparing landscapes of varying size, this index may not be useful. Edge
density (ED) standardizes edge to a per unit area basis that facilitates comparisons among landscapes
of varying size. However, when comparing landscapes of identical size, total edge and edge density
are completely redundant. Alternatively, the amount of edge present in a landscape can be compared
to that expected for a landscape of the same size but with a simple geometric shape (square) and no
internal edge. This is the basis for the landscape shape index (LSI) and its normalized version (nLSI)
that are described in Aggregation metrics section.
Limitations.--Area metrics have limitations imposed by the scale of investigation. Minimum patch
size and landscape extent set the lower and upper limits of these area metrics, respectively. These
are critical limits to recognize because they establish the lower and upper limits of resolution for the
analysis of landscape composition and configuration. Otherwise, area metrics have few limitations.
All edge indices are affected by the resolution of the image. Generally, the finer the resolution (i.e.,
the greater the detail with which edges are delineated), the greater the edge length. At coarse
resolutions, edges may appear as relatively straight lines; whereas, at finer resolutions, edges may
appear as highly convoluted lines. Thus, values calculated for edge metrics should not be compared
among images with different resolutions. In addition, patch perimeter and the length of edges will be
biased upward in raster images because of the stair-step patch outline, and this will affect all edge
indices. The magnitude of this bias will vary in relation to the grain or resolution of the image, and
the consequences of this bias with regards to the use and interpretation of these indices must be
weighed relative to the phenomenon under investigation.
Number
Metric (acronym)
Patch Metrics
P1
Patch Area (AREA)
92
P2
Patch Perimeter (PERIM)
P3
Radius of Gyration (GYRATE)
Class Metrics
C1
Total (Class) Area (CA)
C2
Percentage of Landscape (PLAND)
C3
Largest Patch Index (LPI)
C4
Total Edge (TE)
C5
Edge Density (ED)
C6-C11
Patch Area Distribution (AREA_MN, _AM, _MD, _RA, _SD, _CV)
C12-C17
Radius of Gyration Distribution (GYRATE_MN, _AM, _MD, _RA, _SD, _CV)
Landscape Metrics
L1
Total Area (TA)
L2
Largest Patch Index (LPI)
L3
Total Edge (TE)
L4
Edge Density (ED)
L5-L10
Patch Area Distribution (AREA_MN, _AM, _MD, _RA, _SD, _CV)
L11-L16
Radius of Gyration Distribution (GYRATE_MN, _AM, _MD, _RA, _SD, _CV)
(P1) Area
aij =
area (m2) of patch ij.
Description
AREA equals the area (m2) of the patch, divided by 10,000 (to convert to
hectares).
Units
Hectares
Range
AREA > 0, without limit.
The range in AREA is limited by the grain and extent of the image; in a particular
application, AREA may be further limited by the specification of a minimum
patch size that is larger than the grain.
93
Comments
The area of each patch comprising a landscape mosaic is perhaps the single most
important and useful piece of information contained in the landscape. Not only is
this information the basis for many of the patch, class, and landscape indices, but
patch area has a great deal of ecological utility in its own right. Note that the
choice of the 4-neighbor or 8-neighbor rule for delineating patches will have an
impact on this metric.
(P2) Perimeter
pij =
perimeter (m) of patch ij.
Description
PERIM equals the perimeter (m) of the patch, including any internal holes in the
patch, regardless of whether the perimeter represents ‘true’ edge or not (e.g., the
case when a patch is artificially bisected by the landscape boundary when a
landscape border is present).
Units
Meters
Range
PERIM > 0, without limit.
Comments
Patch perimeter is another fundamental piece of information available about a
landscape and is the basis for many class and landscape metrics. Specifically, the
perimeter of a patch is treated as an edge, and the intensity and distribution of
edges constitutes a major aspect of landscape pattern. In addition, the relationship
between patch perimeter and patch area is the basis for most shape indices.
(P3) Radius of Gyration
hijr =
z=
distance (m) between cell ijr [located within patch ij] and
the centroid of patch ij (the average location), based on
cell center-to-cell center distance.
number of cells in patch ij.
Description
GYRATE equals the mean distance (m) between each cell in the patch and the
patch centroid.
Units
Meters
Range
GYRATE $ 0, without limit.
GYRATE = 0 when the patch consists of a single cell and increases without limit
as the patch increases in extent. GYRATE achieves its maximum value when the
patch comprises the entire landscape.
94
Comments
Radius of gyration is a measure of patch extent; thus it is effected by both patch size
and patch compaction. Note that the choice of the 4-neighbor or 8-neighbor rule
for delineating patches will have an impact on this metric.
(C1) Total (Class) Area
aij =
area (m2) of patch ij.
Description
CA equals the sum of the areas (m2) of all patches of the corresponding patch
type, divided by 10,000 (to convert to hectares); that is, total class area.
Units
Hectares
Range
CA > 0, without limit.
CA approaches 0 as the patch type becomes increasing rare in the landscape. CA
= TA when the entire landscape consists of a single patch type; that is, when the
entire image is comprised of a single patch.
Comments
Class area is a measure of landscape composition; specifically, how much of the
landscape is comprised of a particular patch type. In addition to its direct
interpretive value, class area is used in the computations for many of the class and
landscape metrics.
(C2) Percentage of Landscape
Pi =
aij =
A=
proportion of the landscape occupied by patch
type (class) i.
area (m2) of patch ij.
total landscape area (m2).
Description
PLAND equals the sum of the areas (m2) of all patches of the corresponding
patch type, divided by total landscape area (m2), multiplied by 100 (to convert to a
percentage); in other words, PLAND equals the percentage the landscape
comprised of the corresponding patch type. Note, total landscape area (A)
includes any internal background present.
Units
Percent
95
Range
0 < PLAND # 100
PLAND approaches 0 when the corresponding patch type (class) becomes
increasingly rare in the landscape. PLAND = 100 when the entire landscape
consists of a single patch type; that is, when the entire image is comprised of a
single patch.
Comments
Percentage of landscape quantifies the proportional abundance of each patch type in
the landscape. Like total class area, it is a measure of landscape composition
important in many ecological applications. However, because PLAND is a relative
measure, it may be a more appropriate measure of landscape composition than
class area for comparing among landscapes of varying sizes.
(C3) Largest Patch Index
aij =
A=
area (m2) of patch ij.
total landscape area (m2).
Description
LPI equals the area (m2) of the largest patch of the corresponding patch type
divided by total landscape area (m2), multiplied by 100 (to convert to a
percentage); in other words, LPI equals the percentage of the landscape comprised
by the largest patch. Note, total landscape area (A) includes any internal
background present.
Units
Percent
Range
0 < LPI # 100
LPI approaches 0 when the largest patch of the corresponding patch type is
increasingly small. LPI = 100 when the entire landscape consists of a single patch
of the corresponding patch type; that is, when the largest patch comprises 100%
of the landscape.
Comments
Largest patch index at the class level quantifies the percentage of total landscape area
comprised by the largest patch. As such, it is a simple measure of dominance.
(C4) Total Edge
eik =
total length (m) of edge in landscape involving patch type
(class) i; includes landscape boundary and background
segments involving patch type i.
96
Description
TE equals the sum of the lengths (m) of all edge segments involving the
corresponding patch type. If a landscape border is present, TE includes landscape
boundary segments involving the corresponding patch type and representing ‘true’
edge only (i.e., abutting patches of different classes). If a landscape border is
absent, TE includes a user-specified proportion of landscape boundary segments
involving the corresponding patch type. Regardless of whether a landscape border
is present or not, TE includes a user-specified proportion of internal background
edge segments involving the corresponding patch type.
Units
Meters
Range
TE $ 0, without limit.
TE = 0 when there is no class edge in the landscape; that is, when the entire
landscape and landscape border, if present, consists of the corresponding patch
type and the user specifies that none of the landscape boundary and background
edge be treated as edge.
Comments
Total edge at the class level is an absolute measure of total edge length of a
particular patch type. In applications that involve comparing landscapes of varying
size, this index may not be as useful as edge density (see below). However, when
comparing landscapes of identical size, total edge and edge density are completely
redundant.
(C5) Edge Density
eik =
A=
total length (m) of edge in landscape involving patch
type (class) i; includes landscape boundary and
background segments involving patch type i.
total landscape area (m2).
Description
ED equals the sum of the lengths (m) of all edge segments involving the
corresponding patch type, divided by the total landscape area (m2), multiplied by
10,000 (to convert to hectares). If a landscape border is present, ED includes
landscape boundary segments involving the corresponding patch type and
representing ‘true’ edge only (i.e., abutting patches of different classes). If a
landscape border is absent, ED includes a user-specified proportion of landscape
boundary segments involving the corresponding patch type. Regardless of
whether a landscape border is present or not, ED includes a user-specified
proportion of internal background edge segments involving the corresponding
patch type. Note, total landscape area (A) includes any internal background
present.
Units
Meters per hectare
97
Range
ED $ 0, without limit.
ED = 0 when there is no class edge in the landscape; that is, when the entire
landscape and landscape border, if present, consists of the corresponding patch
type and the user specifies that none of the landscape boundary and background
edge be treated as edge.
Comments
Edge density at the class level has the same utility and limitations as Total Edge (see
Total Edge description), except that edge density reports edge length on a per unit
area basis that facilitates comparison among landscapes of varying size.
(L1) Total Area
A=
total landscape area (m2).
Description
TA equals the total area (m2) of the landscape, divided by 10,000 (to convert to
hectares). Note, total landscape area (A) includes any internal background present.
Units
Hectares
Range
TA > 0, without limit.
Comments
Total area (TA) often does not have a great deal of interpretive value with regards
to evaluating landscape pattern, but it is important because it defines the extent of
the landscape. Moreover, total landscape area is used in the computations for
many of the class and landscape metrics.
(L2) Largest Patch Index
aij =
A=
area (m2) of patch ij.
total landscape area (m2).
Description
LPI equals the area (m2) of the largest patch in the landscape divided by total
landscape area (m2), multiplied by 100 (to convert to a percentage); in other
words, LPI equals the percent of the landscape that the largest patch comprises.
Note, total landscape area (A) includes any internal background present.
Units
Percent
Range
0 < LPI # 100
LPI approaches 0 when the largest patch in the landscape is increasingly small.
LPI = 100 when the entire landscape consists of a single patch; that is, when the
largest patch comprises 100% of the landscape.
98
Comments
Largest patch index quantifies the percentage of total landscape area comprised by
the largest patch. As such, it is a simple measure of dominance.
(L3) Total Edge
E=
total length (m) of edge in landscape.
Description
TE equals the sum of the lengths (m) of all edge segments in the landscape. If a
landscape border is present, TE includes landscape boundary segments
representing ‘true’ edge only (i.e., abutting patches of different classes). If a
landscape border is absent, TE includes a user-specified proportion of the
landscape boundary. Regardless of whether a landscape border is present or not,
TE includes a user-specified proportion of internal background edge.
Units
Meters
Range
TE $ 0, without limit.
TE = 0 when there is no edge in the landscape; that is, when the entire landscape
and landscape border, if present, consists of a single patch and the user specifies
that none of the landscape boundary and background edge be treated as edge.
Comments
Total edge is an absolute measure of total edge length of a particular patch type. In
applications that involve comparing landscapes of varying size, this index may not
be as useful as edge density (see below). However, when comparing landscapes of
identical size, total edge and edge density are completely redundant.
(L4) Edge Density
E=
A=
total length (m) of edge in landscape.
total landscape area (m2).
Description
ED equals the sum of the lengths (m) of all edge segments in the landscape,
divided by the total landscape area (m2), multiplied by 10,000 (to convert to
hectares). If a landscape border is present, ED includes landscape boundary
segments representing ‘true’ edge only (i.e., abutting patches of different classes).
If a landscape border is absent, ED includes a user-specified proportion of the
landscape boundary. Regardless of whether a landscape border is present or not,
ED includes a user-specified proportion of internal background edge. Note, total
landscape area (A) includes any internal background present.
Units
Meters per hectare
99
Range
ED $ 0, without limit.
ED = 0 when there is no edge in the landscape; that is, when the entire landscape
and landscape border, if present, consists of a single patch and the user specifies
that none of the landscape boundary and background edge be treated as edge.
Comments
Edge density has the same utility and limitations as Total Edge (see Total Edge
description), except that edge density reports edge length on a per unit area basis
that facilitates comparison among landscapes of varying size.
100
Shape Metrics
Background.--The interaction of patch shape and size can influence a number of important
ecological processes. Patch shape has been shown to influence inter-patch processes such as small
mammal migration (Buechner 1989) and woody plant colonization (Hardt and Forman 1989), and
may influence animal foraging strategies (Forman and Godron 1986). However, the primary
significance of shape in determining the nature of patches in a landscape seems to be related to the
‘edge effect’ (see discussion of edge effects for Area and Edge Metrics).
Shape is a difficult parameter to quantify concisely in a metric for the reasons discussed below.
Generally speaking, the shape of a geometric object, such as a patch, is a function of its morphology.
Thus, one might expect shape metrics to discriminate among patch morphologies. While it is
possible to quantitatively distinguish morphological patterns, as is done in the field of computer
visions (e.g., face recognition), it is generally deemed unimportant to do so in landscape ecological
applications. Instead, the emphasis is on geometric complexity and distinguishing among patches
and landscapes on the basis of overall complexity rather than particular morphologies. Conseqently,
the shape metrics described below all deal with overall geometric complexity and do not distinguish
among distinct morphologies.
FRAGSTATS Metrics.--FRAGSTATS computes several metrics that quantify landscape
configuration in terms of the complexity of patch shape at the patch, class, and landscape levels.
Most of these shape metrics are based on perimeter-area relationships. Perhaps the simplest shape
index is a straightforward perimeter-area ratio (PARA). A problem with this metric as a shape index is
that it varies with the size of the patch. For example, holding shape constant, an increase in patch
size will cause a decrease in the perimeter-area ratio. Patton (1975) proposed a diversity index based
on shape for quantifying habitat edge for wildlife species and as a means for comparing alternative
habitat improvement efforts (e.g., wildlife clearings). This shape index (SHAPE) measures the
complexity of patch shape compared to a standard shape (square) of the same size, and therefore
alleviates the size dependency problem of PARA. This shape index is widely applicable in landscape
ecological research (Forman and Godron 1986).
Another other basic type of shape index based on perimeter-area relationships is the fractal dimension
index (FRAC). In landscape ecological research, patch shapes are frequently characterized via the
fractal dimension of the object (Krummel et al. 1987, Milne 1988, Turner and Ruscher 1988, Iverson
1989, Ripple et al. 1991). The appeal of fractal analysis is that it can be applied to spatial features
over a wide variety of scales. Mandelbrot (1977, 1982) introduced the concept of fractal, a geometric
form that exhibits structure at all spatial scales, and proposed a perimeter-area method to calculate
the fractal dimension of natural planar shapes. The perimeter-area method quantifies the degree of
complexity of the planar shapes. The degree of complexity of a polygon is characterized by the
fractal dimension (D), such that the perimeter (P) of a patch is related to the area (A) of the same
patch by P . /AD (i.e., log P . ½D log A). For simple Euclidean shapes (e.g., circles and
rectangles), P . /A and D = 1 (the dimension of a line). As the polygons become more complex,
the perimeter becomes increasingly plane-filling and P . A with D 6 2. Although fractal analysis
typically has not been used to characterize individual patches in landscape ecological research, we
use this relationship to calculate the fractal dimension of each patch separately. Note that the value
of the fractal dimension calculated in this manner is dependent upon patch size and/or the units
101
used (Rogers 1993). Thus, varying the cell size of the input image will affect the patch fractal
dimension. Therefore, caution should be exercised when using this fractal dimension index as a
measure of patch shape complexity.
Fractal analysis usually is applied to the entire landscape mosaic using the perimeter-area relationship
A = k P2/D, where k is a constant (Burrough 1986). If sufficient data are available, the slope of the
line obtained by regressing log(P) on log(A) is equal to 2/D (Burrough 1986). Note, fractal
dimension computed in this manner is equal to 2 divided by the slope; D is not equal to the slope
(Krummel et al. 1987) nor is it equal to 2 times the slope (e.g., O'Neill et al. 1988, Gustafson and
Parker 1992). We refer to this index as the perimeter-area fractal dimension (PAFRAC) in FRAGSTATS.
Because this index employs regression analysis, it is subject to spurious results when sample sizes are
small. In landscapes with only a few patches, it is not unusual to get values that greatly exceed the
theoretical limits of this index. Thus, this index is probably only useful if sample sizes are large (e.g.,
n > 20; although PAFRAC is computed in FRAGSTATS if n $ 10). If insufficient data are available,
an alternative to the regression approach is to calculate the mean patch fractal dimension (FRAC_MN)
based on the fractal dimension of each patch, or the area-weighted mean patch fractal dimension
(FRAC_AM) at the class and landscape levels by weighting patches according to their size, although
these metrics do not have the same interpretation or utility as PAFRAC. In contrast to the fractal
dimension of a single patch, which provides an index of shape complexity for that patch, the
perimeter-area fractal dimension of a patch mosaic provides an index of patch shape complexity
across a wide range of spatial scales (i.e., patch sizes). Specifically, it describes the power relationship
between patch area and perimeter, and thus describes how patch perimeter increases per unit
increase in patch area. If, for example, small and large patches alike have simple geometric shapes,
then PAFRAC will be relatively low, indicating that patch perimeter increases relatively slowly as
patch area increases. Conversely, if small and large patches have complex shapes, then PAFRAC will
be much higher, indicating that patch perimeter increases more rapidly as patch area
increases–reflecting a consistency of complex patch shapes across spatial scales. The fractal
dimension of patch shapes, therefore, is suggestive of a common ecological process or
anthropogenic influence affecting patches across a wide range of scales, and differences between
landscapes can suggest differences in the underlying pattern-generating process (e.g., Krummel
1987).
An alternative method of assessing shape is based on ratio of patch area to the area of the smallest
circumscribing circle, known as the related circumscribing circle (CIRCLE)(Baker and Cai 1992). The
circumscribing circle provides a measure of overall patch elongation. A highly convoluted but
narrow patch will have a low related circumscribing circle index due to the relative compactness of
the patch, yet a narrow and elongated patch will have a high related circumscribing square index.
This index may be particularly useful for distinguishing patches that are both linear (narrow) and
elongated.
A final method of assessing patch shape is based on the spatial connectedness, or contiguity, of cells
within a grid-cell patch to provide an index on patch boundary configuration and thus patch shape
(LaGro 1991). Contiguity index (CONTIG) is quantified by convolving a 3x3 pixel template with a
binary digital image in which the pixels within the patch of interest are assigned a value of 1 and the
background pixels (all other patch types) are given a value of zero. A template value of 2 is assigned
to quantify horizontal and vertical pixel relationships within the image and a value of 1 is assigned to
102
quantify diagonal relationships. This combination of integer values weights orthogonally contiguous
pixels more heavily than diagonally contiguous pixels, yet keeps computations relatively simple. The
center pixel in the template is assigned a value of 1 to ensure that a single-pixel patch in the output
image has a value of 1, rather than 0. The value of each pixel in the output image, computed when at
the center of the moving template, is a function of the number and location of pixels, of the same
class, within the nine cell image neighborhood. Specifically, the contiguity value for a pixel in the
output image is the sum of the products, of each template value and the corresponding input image
pixel value, within the nine cell neighborhood. Thus, large contiguous patches result in larger
contiguity index values.
Limitations.--All shape indices based on perimeter-area relationships have important limitations.
First, perimeter lengths are biased upward in raster images because of the stair-stepping pattern of
line segments, and the magnitude of this bias varies in relation to the grain or resolution of the
image. Thus, the computed perimeter-area ratio will be somewhat higher than it actually is in the
real-world. Second, as an index of "shape", the perimeter-to-area ratio method is relatively
insensitive to differences in patch morphology. Thus, although patches may possess very different
shapes, they may have identical areas and perimeters. For this reason, shape indices based on
perimeter-area ratios are not useful as measures of patch morphology; they are best considered as
measures of overall shape complexity. Alternative indices of shape that are not based on perimeterarea rations are less troubled by these limitations. But these too, generally do not distinguish patch
morphology, but instead emphasize one or more aspects of shape complexity (e.g., elongation).
Number
Metric (acronym)
Patch Metrics
P1
Perimeter-Area Ratio (PARA)
P2
Shape Index (SHAPE)
P3
Fractal Dimension Index (FRAC)
P4
Related Circumscribing Circle (CIRCLE)
P5
Contiguity Index (CONTIG)
Class Metrics
C1
Perimeter-Area Fractal Dimension (PAFRAC)
C2-C7
Perimeter-Area Ratio Distribution (PARA_MN, _AM, _MD, _RA, _SD, _CV)
C8-C13
Shape Index Distribution (SHAPE_MN, _AM, _MD, _RA, _SD, _CV)
C14-C19
Fractal Index Distribution (FRAC_MN, _AM, _MD, _RA, _SD, _CV)
C20-C25
Linearity Index Distribution (LINEAR_MN, _AM, _MD, _RA, _SD, _CV)
C26-C31
Related Circumscribing Square Distribution (SQUARE_MN, _AM, _MD, _RA, _SD, _CV)
C32-C37
Contiguity Index Distribution (CONTIG_MN, _AM, _MD, _RA, _SD, _CV)
103
Landscape Metrics
L1
Perimeter-Area Fractal Dimension (PAFRAC)
L2-L7
Perimeter-Area Ratio Distribution (PARA_MN, _AM, _MD, _RA, _SD, _CV)
L8-L13
Shape Index Distribution (SHAPE_MN, _AM _MD, _RA, _SD, _CV)
L14-L19
Fractal Index Distribution (FRAC_MN, _AM, _MD, _RA, _SD, _CV)
L20-L25
Linearity Index Distribution (LINEAR_MN, _AM, _MD, _RA, _SD, _CV)
L26-L31
Related Circumscribing Square Distribution (SQUARE_MN, _AM, _MD, _RA, _SD, _CV)
L32-L37
Contiguity Index Distribution (CONTIG_MN, _AM, _MD, _RA, _SD, _CV)
(P1) Perimeter-Area Ratio
pij =
aij =
perimeter (m) of patch ij.
area (m2) of patch ij.
Description
PARA equals the ratio of the patch perimeter (m) to area (m2).
Units
None
Range
PARA > 0, without limit.
Comments
Perimeter-area ratio is a simple measure of shape complexity, but without
standardization to a simple Euclidean shape (e.g., square). A problem with this
metric as a shape index is that it varies with the size of the patch. For example,
holding shape constant, an increase in patch size will cause a decrease in the
perimeter-area ratio.
(P2) Shape Index
pij =
aij =
perimeter (m) of patch ij.
area (m2) of patch ij.
Description
SHAPE equals patch perimeter (m) divided by the square root of patch area (m2),
adjusted by a constant to adjust for a square standard.
Units
None
Range
SHAPE $ 1, without limit.
SHAPE = 1 when the patch is square and increases without limit as patch shape
becomes more irregular.
104
Comments
Shape index corrects for the size problem of the perimeter-area ratio index (see
previous description) by adjusting for a square standard and, as a result, is the
simplest and perhaps most straightforward measure of shape complexity.
(P3) Fractal Dimension Index
pij =
aij =
perimeter (m) of patch ij.
area (m2) of patch ij.
Description
FRAC equals 2 times the logarithm of patch perimeter (m) divided by the
logarithm of patch area (m2); the perimeter is adjusted to correct for the raster bias
in perimeter.
Units
None
Range
1 # FRAC # 2
A fractal dimension greater than 1 for a 2-dimensional patch indicates a departure
from Euclidean geometry (i.e., an increase in shape complexity). FRAC
approaches 1 for shapes with very simple perimeters such as squares, and
approaches 2 for shapes with highly convoluted, plane-filling perimeters.
Comments
Fractal dimension index is appealing because it reflects shape complexity across a
range of spatial scales (patch sizes). Thus, like the shape index (SHAPE), it
overcomes one of the major limitations of the straight perimeter-area ratio as a
measure of shape complexity.
(P4) Related Circumscribing Circle
aij =
aijs =
area (m2) of patch ij.
area (m2) of smallest circumscribing circle around
patch ij.
Description
CIRCLE equals 1 minus patch area (m2) divided by the area (m2) of the smallest
circumscribing circle.
Units
None
Range
0 # CIRCLE < 1
CIRCLE = 0 for circular patches and approaches 1 for elongated, linear patches
one cell wide.
Comments
Related circumscribing circle derives from Baker and Cai (1992). Note, this index is not
influenced by patch size.
105
(P5) Contiguity Index
cijr =
v=
aij* =
contiguity value for pixel r in patch ij.
sum of the values in a 3-by-3 cell template (13 in
this case).
area of patch ij in terms of number of cells.
Description
CONTIG equals the average contiguity value (see discussion) for the cells in a
patch (i.e., sum of the cell values divided by the total number of pixels in the
patch) minus 1, divided by the sum of the template values (13 in this case) minus
1.
Units
None
Range
0 # CONTIG # 1
CONTIG equals 0 for a one-pixel patch and increases to a limit of 1 as patch
contiguity, or connectedness, increases. Note, 1 is subtracted from both the
numerator and denominator to confine the index to a range of 1.
Comments
Contiguity index assesses the spatial connectedness, or contiguity, of cells within a
grid-cell patch to provide an index on patch boundary configuration and thus
patch shape (LaGro 1991).
(C1) Perimeter-Area Fractal Dimension
aij =
pij =
ni =
area (m2) of patch ij.
perimeter (m) of patch ij.
number of patches in the
landscape of patch type (class) i.
Description
PAFRAC equals 2 divided by the slope of regression line obtained by regressing
the logarithm of patch area (m2) against the logarithm of patch perimeter (m).
That is, 2 divided by the coefficient b1 derived from a least squares regression fit
to the following equation: ln(area) = b0 + [email protected](perim). Note, PAFRAC excludes
any background patches.
Units
None
106
Range
1 # PAFRAC # 2
A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates
a departure from a Euclidean geometry (i.e., an increase in patch shape
complexity). PAFRAC approaches 1 for shapes with very simple perimeters such
as squares, and approaches 2 for shapes with highly convoluted, plane-filling
perimeters. PAFRAC employs regression techniques and is subject to small
sample problems. Specifically, PAFRAC may greatly exceed the theoretical range
in values when the number of patches is small (e.g., <10), and its use should be
avoided in such cases. In addition, PAFRAC requires patches to vary in size.
Thus, PAFRAC is undefined and reported as "N/A" in the "basename".class file
if all patches are the same size or there is < 10 patches.
Comments
Perimeter-area fractal dimension is appealing because it reflects shape complexity
across a range of spatial scales (patch sizes). However, like its patch-level
counterpart (FRACT), perimeter-area fractal dimension is only meaningful if the
log-log relationship between perimeter and area is linear over the full range of
patch sizes. If it is not (and this must be determined separately), then fractal
dimension should be computed separately for the range of patch sizes over which
it is constant. Note, because this index employs regression analysis, it is subject to
spurious results when sample sizes are small. In landscapes with only a few
patches, it is not unusual to get values that greatly exceed the theoretical limits of
this index. Thus, this index is probably most useful if sample sizes are large (e.g., n
$ 20), although FRAGSTATS computes the index for moderate sample sizes as
well (i.e., n $10). In addition, it is important to realize that the perimeter-area
fractal dimension computed in FRAGSTATS is based on the regression of log
area on log perimeter; that is, ln(area) = b0 + [email protected](perim). It is equally valid to
compute fractal dimension by regressing log perimeter on log area; that is,
ln(perim) = b0 + [email protected](area), in which case the fractal dimension (D) is equal to 2
times the slope (b1). These two approaches give slightly different answers and it is
not clear that one is superior to the other. Both approaches are used in practice, so
it behooves you to note the manner by which fractal dimension is computed when
comparing among studies.
(L1) Perimeter-Area Fractal Dimension
aij =
pij =
N=
107
area (m2) of
patch ij.
perimeter (m) of
patch ij.
total number of
patches in the
landscape.
Description
PAFRAC equals 2 divided by the slope of regression line obtained by regressing
the logarithm of patch area (m2) against the logarithm of patch perimeter (m).
That is, 2 divided by the coefficient b1 derived from a least squares regression fit
to the following equation: ln(area) = b0 + [email protected](perim). Note, PAFRAC excludes
any background patches.
Units
None
Range
1 # PAFRAC # 2
A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates
a departure from a Euclidean geometry (i.e., an increase in patch shape
complexity). PAFRAC approaches 1 for shapes with very simple perimeters such
as squares, and approaches 2 for shapes with highly convoluted, plane-filling
perimeters. PAFRAC employs regression techniques and is subject to small
sample problems. Specifically, PAFRAC may greatly exceed the theoretical range
in values when the number of patches is small (e.g., <10), and its use should be
avoided in such cases. In addition, PAFRAC requires patches to vary in size.
Thus, PAFRAC is undefined and reported as "N/A" in the "basename".land file if
all patches are the same size or there is only 1 patch.
Comments
Perimeter-area fractal dimension at the landscape level is identical to the class level (see
previous comments), except here all patches in the landscape are included in the
regression of patch area against patch perimeter.
108
Core Area Metrics
Background.– Core area is defined as the area within a patch beyond some specified depth-of-edge
influence (i.e., edge distance) or buffer width. Like patch shape, the primary significance of core area
in determining the character and function of patches in a landscape appears to be related to the
‘edge effect.’ As discussed elsewhere (see Area and Edge Metrics), edge effects result from a
combination of biotic and abiotic factors that alter environmental conditions along patch edges
compared to patch interiors. The nature of the edge effect differs among organisms and ecological
processes (Hansen and di Castri 1992). For example, some bird species are adversely affected by
predation, competition, brood parasitism, and perhaps other factors along forest edges. Core area
has been found to be a much better predictor of habitat quality than patch area for these forest
interior specialists (Temple 1986). Unlike patch area, core area is affected by patch shape. Thus,
while a patch may be large enough to support a given species, it still may not contain enough
suitable core area to support the species. In some cases, it seems likely that edge effects would vary
in relation to the type and nature of the edge (e.g., the degree of floristic and structural contrast and
orientation). Thus, FRAGSTATS allows the user to specified an edge depth file that contains edge
influence distances for every pairwise combination of patch types. In the absence of such
information, the user can specify a single edge depth for all edge types.
In raster images, there are different ways to determine core area. FRAGSTATS employs a method
involving the use of a variably-sized masked placed on cells on the perimeter of a patch, where the
mask size varies depending the specified edge depth associated with the corresponding combination
of patch types. Actually, the mask is placed over cells just outside the patch perimeter; referred to
here as ‘bounding’ cells. Briefly, a mask is placed over each bounding cell. The mask itself is near
circular in shape (as circular as you can get in the raster world) and sized according to the specified
edge depth, as follows.
First, the size of the user-specified edge-depth (D) radius is used to determine the size of a square
mask: 2 × R + 1, where R is equal to D rounded down to the nearest number of cell sizes. For
example, if cell size is 30 and D = 50, then R = 1 and mask size = 2 * 1 + 1 = 3x3 cells. Note, the
formula above ensures that each mask has a focal cell and is symmetrical in all directions so that it
can be centered on a bounding cell for processing. A 4x4 mask would have no center cell and could
no be superimposed centered on a bounding cell, making it useless. The effect is that all mask side
sizes are made up of an odd number of cells (3x3, 5x5, 7x7, 9x9, ..., 101x101, etc).
Next, after the square mask is built, the distance is measured between the center of the focal cell
(bounding cell) to the center of each of the others to determine if they are within the specified edge
depth. If the center is in, the whole cell is in (=1), otherwise the cell is rejected (=0). The result is a
final mask (cells = 1) that approximates a circular mask -- as well as can be done using rasters. The
smaller the edge depth, the choppier the resulting mask. Conversely, the larger the edge depth, the
better the circle will look.
Lastly, cells within the mask are eliminated from the ‘core’ of the patch. After all bounding cells are
treated in this manner, the remaining cells not masked constitute the ‘core’ of the patch.
FRAGSTATS Metics.--FRAGSTATS computes several metrics based on core area at the patch,
109
class, and landscape levels. Most of the indices dealing with number or density of patches, size of
patches, and variability in patch size have corresponding core area indices computed in the same
manner after eliminating the specified edge from all patches. For example, patch area, class area,
total landscape area, and the percentage of landscape in each patch type all have counterparts
computed after eliminating edge area defined by the specified edge depth; these are core area (CORE)
at the patch level, total core area (TCA) at the class and landscape levels, and core area percent of landscape
(CPLAND) at the class level. The latter index quantifies the core area in each patch type as a
percentage of total landscape area. For organisms strongly associated with patch interiors, this index
may provide a better measure of habitat availability than its counterpart, percentage of landscape
(PLAND). In contrast to their counterparts, these core area indices integrate into a single measure
the affects of patch area, patch shape, and edge effect distance. Therefore, although they quantify
landscape composition, they are affected by landscape configuration. For this reason, these metrics
at the class level may be very useful in the study of habitat loss and fragmentation.
From an organism-centered perspective, a single patch may actually contain several disjunct patches
of suitable interior habitat, and it may be more appropriate to consider disjunct core areas as
separate patches. For this reason, FRAGSTATS computes the number of core areas (NCORE) in each
patch, as well as the number in each class and the landscape as a whole (NDCA). If core area is
deemed more important than total area, then these indices may be more applicable than their
counterparts, but they are subject to the same limitations as their counterparts (number of patches)
because they are not standardized with respect to area. For this reason, number of core areas can be
reported on a per unit area basis (disjunct core area density, DCAD) that has the same ecological
applicability as its counterpart (patch density), except that all edge area is eliminated from
consideration. Conversely, this information can be represented as mean core area (CORE_MN).
Like their counterparts, note the difference between core area density and mean core area at the
class level. Specifically, core area density is based on total landscape area; whereas, mean core area is
based on total core area for the class. In contrast, at the landscape level, they are both based on total
landscape area and are therefore completely redundant (at least if the landscape contains no
background). Furthermore, mean core area can be defined in 2 ways. First, mean core area can be
defined as the mean core area per patch (CORE_MN). Thus, patches with no core area are included in
the average, and the total core area in a patch is considered together as 1 observation, regardless of
whether the core area is contiguous or divided into 2 or more disjunct areas within the patch.
Alternatively, mean core area can be defined as the mean area per disjunct core (DCORE_MN). The
distinction between these 2 ways of defining mean core area should be noted.
FRAGSTATS also computes an index that quantifies core area as a percentage of total area. The core
area index (CAI) at the patch level quantifies the percentage of the patch that is comprised of core
area. Similarly, at the class and landscape levels core area index area-weighted mean (CAI_AM) quantifies
core area for the entire class or landscape as a percentage of total class or landscape area,
respectively. Note, that this is equivalent to the total core area index reported in FRAGSTATS 2.0. The
core area index is basically an edge-to-interior ratio like many of the shape indices (see Shape
Metrics), the main difference being that the core area index treats edge as an area of varying width
and not as a line (perimeter) around each patch. In addition, the core area index is a relative
measure; it does not reflect patch size, class area, or total landscape area; it merely quantifies the
percentage of available area, regardless of whether it is 10 ha or 1,000 ha, comprised of core. This
index does not confound area and configuration like the previous core area indices; rather, it isolates
110
the configuration effect. For this reason, the core area index is probably best interpreted in
conjunction with total area at the corresponding scale. For example, in conjunction with total class
area, this index could serve as an effective fragmentation index for a particular class.
Limitations.--All core area indices are affected by the interaction of patch size, patch shape, and the
specified edge depths. In particular, increasing edge depths or shape complexity, or decreasing patch
size will decrease core area, and vice versa. On the one hand, this may be desirable as an integrative
measure that has explicit functional relevance to the organism or process under consideration. On
the other hand, there are potential pitfalls associated with integrative measures like core area. In
particular, the confounding of patch area and configuration effects can complicate interpretation.
For example, if the core area is small, it indicates that very little core area is available, but it does not
discriminate between a small patch (area effect) and a large patch with a complex shape
(configuration effect). In addition, core area is meaningful only if the specified depth-of-edge
distance is meaningful to the phenomenon under investigation. Unfortunately, in many cases there is
no empirical basis for specifying any particular depth-of-edge effect and so it must be chosen
somewhat arbitrarily. The usefulness of core area as a metric is directly related to the arbitrariness in
the specified edge depths, and this should be clearly understood when using these metrics.
Ultimately, the utility of core area metrics compared to their patch area counterparts depends on the
resolution, minimum patch dimensions, and edge influence distance(s) employed. For example,
given a landscape with a resolution of 1 m2 and minimum patch dimensions of 100 x 100 m, if an
edge influence distance of 1 m is specified, then core area and patch area will be nearly identical and
core area will be relatively insensitive to differences in patch size and shape. In this case, core area
offers little over its patch area counterpart.
Code
Metric (acronym)
Patch Metrics
P1
Core Area (CORE)
P2
Number of Core Areas (NCA)
P3
Core Area Index (CAI)
Class Metrics
C1
Total Core Area (TCA)
C2
Core Area Percentage of Landscape (CPLAND)
C3
Number of Disjunct Core Areas (NDCA)
C4
Disjunct Core Area Density (DCAD)
C5-C10
Core Area Distribution (CORE_MN, _AM, _MD, _RA, _SD, _CV)
C11-C16
Disjunct Core Area Distribution (DCORE_MN, _AM, _MD, _RA, _SD, _CV)
C17-C22
Core Area Index Distribution (CAI_MN, _AM, _MD, _RA, _SD, _CV)
111
Landscape Metrics
L1
Total Core Area (TCA)
L2
Number of Disjunct Core Areas (NDCA)
L3
Disjunct Core Area Density (DCAD)
L4-L9
Core Area Distribution (CORE_MN, _AM, _MD, _RA, _SD, _CV)
L10-L15
Disjunct Core Area Distribution (DCORE_MN, _AM, _MD, _RA, _SD, _CV)
L16-L21
Core Area Index Distribution (CAI_MN, _AM, _MD, _RA, _SD, _CV)
(P1) Core Area
aijc =
core area (m2) of patch ij based on specified edge
depths (m).
Description
CORE equals the area (m2) within the patch that is further than the specified
depth-of-edge distance from the patch perimeter, divided by 10,000 (to convert to
hectares). Edge segments along the landscape boundary are treated like
background (as specified in the edge depth file) unless a landscape border is
present, in which case the boundary edge types are made explicit by the
information in the border.
Units
Hectares
Range
CORE $ 0, without limit.
CORE = 0 when every location within the patch is within the specified depth-ofedge distance from the patch perimeter. CORE approaches AREA as the
specified depth-of-edge distance(s) decreases and as patch shape is simplified.
Comments
Core area represents the area in the patch greater than the specified depth-of-edge
distance from the perimeter. Note, that a single depth-of-edge distance can be
used for all edges or the user can specify a edge depth file that provides unique
distances for each pairwise combination of patch types.
(P2) Number of Core Areas
nijc =
Description
number of disjunct core areas in patch ij based on specified
edge depths (m).
NCORE equals the number of disjunct core areas contained within the patch
boundary.
112
Units
None
Range
NCORE $ 0, without limit.
NCORE = 0 when CORE = 0 (i.e., every location within the patch is within the
specified depth-of-edge distance from the patch perimeter). NCORE > 1 when,
because of shape, the patch contains disjunct core areas.
Comments
A disjunct core is a spatially contiguous (and therefore distinct) core area (see
Core Area description). Depending on the size and shape of the patch and the
specified depth-of-edge distance(s), a single patch may actually contain several
disjunct core areas. From an organism- or process-centered perspective, it may be
more appropriate to consider disjunct core areas as separate patches.
(P3) Core Area Index
aijc =
aij =
core area (m2) of patch ij based on specified edge depths
(m).
area (m2) of patch ij.
Description
CAI equals the patch core area (m2) divided by total patch area (m2), multiplied by
100 (to convert to a percentage); in other words, CAI equals the percentage of a
patch that is core area.
Units
Percent
Range
0 # CAI < 100
CAI = 0 when CORE = 0 (i.e., every location within the patch is within the
specified depth-of-edge distance(s) from the patch perimeter); that is, when the
patch contains no core area. CAI approaches 100 when the patch, because of size,
shape, and edge width, contains mostly core area.
Comments
Core area index is a relative index that quantifies core area as a percentage of patch
area (i.e., the percentage of the patch that is comprised of core area).
(C1) Total Core Area
aijc =
core area (m2) of patch ij based on specified edge
depths (m).
Description
TCA equals the sum of the core areas of each patch (m2) of the corresponding
patch type, divided by 10,000 (to convert to hectares).
Units
Hectares
113
Range
TCA $ 0, without limit.
TCA = 0 when every location within each patch of the corresponding patch type
is within the specified depth-of-edge distance(s) from the patch perimeters. TCA
approaches total class area (CA) as the specified depth-of-edge distance(s)
decreases and as patch shapes are simplified.
Comments
Total core area is defined the same as core area (CORE) at the patch level (see Core
Area), but here core area is aggregated (summed) over all patches of the
corresponding patch type.
(C2) Core Area Percentage of Landscape
aijc =
A=
core area (m2) of patch ij based on specified edge
depths (m).
total landscape area (m2).
Description
CPLAND equals the sum of the core areas of each patch (m2) of the
corresponding patch type, divided by total landscape area (m2), multiplied by 100
(to convert to a percentage); in other words, CPLAND equals the percentage the
landscape comprised of core area of the corresponding patch type. Note, total
landscape area (A) includes any internal background present.
Units
Percent
Range
0 # CPLAND < 100
CPLAND approaches 0 when core area of the corresponding patch type (class)
becomes increasingly rare in the landscape, because of increasing smaller patches
and/or more convoluted patch shapes. CPLAND approaches 100 when the entire
landscape consists of a single patch type (i.e., when the entire image is comprised
of a single patch) and the specified depth-of-edge distance(s) approaches zero.
Comments
Core area percentage of landscape is defined the same as core area (CORE) at the patch
level (see Core Area), but here core area is aggregated (summed) over all patches
of the corresponding patch type and computed as a percentage of the total
landscape area, which facilitates comparison among landscape of varying size.
(C3) Number of Disjunct Core Areas
nijc =
number of disjunct core areas in patch ij based on specified
edge depths (m).
114
Description
NDCA equals the sum of the number of disjunct core areas contained within each
patch of the corresponding patch type; that is, the number of disjunct core areas
contained within the landscape.
Units
None
Range
NDCA $ 0, without limit.
NDCA = 0 when TCA = 0 (i.e., every location within patches of the
corresponding patch type are within the specified depth-of-edge distance(s) from
the patch perimeters). NDCA > 1 when, due to patch shape complexity, a patch
contains more than 1 core area.
Comments
Number of disjunct core areas is defined the same at the patch level (see Number of
Core Areas), but here it is aggregated (summed) over all patches of the
corresponding patch type. Number of disjunct core areas is an alternative to the
number of patches when it makes sense to treat the core areas as functionally
distinct patches.
(C4) Disjunct Core Area Density
nijc =
A=
number of disjunct core areas in patch ij based
on specified edge depths (m).
total landscape area (m2).
Description
DCAD equals the sum of number of disjunct core areas contained within each
patch of the corresponding patch type, divided by total landscape area (m2),
multiplied by 10,000 and 100 (to convert to 100 hectares). Note, total landscape
area (A) includes any internal background present.
Units
Number per 100 hectares
Range
DCAD $ 0, without limit.
DCAD = 0 when TCA = 0 (i.e., every location within patches of the
corresponding patch type are within the specified depth-of-edge distance(s) from
the patch perimeters); in other words, when there are no core areas.
Comments
Disjunct core area density, like its counterpart, patch density (PD),expresses number
of disjunct core areas on a per unit area basis that facilitates comparisons among
landscapes of varying size. Of course, if total core area is held constant, then
disjunct core area density and number of disjunct core areas convey the same
information.
(L1) Total Core Area
115
aijc =
core area (m2) of patch ij based on specified edge
depths (m).
Description
TCA equals the sum of the core areas of each patch (m2), divided by 10,000 (to
convert to hectares).
Units
Hectares
Range
TCA $ 0, without limit.
TCA = 0 when every location within every patch is within the specified depth-ofedge distance(s) from the patch perimeters. TCA approaches total landscape area
as the specified depth-of-edge distance(s) decreases and as patch shapes are
simplified.
Comments
Total core area is defined the same as core area (CORE) at the patch level (see Core
Area), but here core area is aggregated (summed) over all patches.
(L2) Number of Disjunct Core Areas
nijc =
number of disjunct core areas in patch ij based on
specified edge depths (m).
Description
NDCA equals the sum of the number of disjunct core areas contained within each
patch in the landscape; that is, the number of disjunct core areas contained within
the landscape.
Units
None
Range
NDCA $ 0, without limit.
NCA = 0 when TCA = 0 (i.e., every location within every patch is within the
specified depth-of-edge distance(s) from the patch perimeters); in other words,
when there are no core areas. NDCA > 1 when, due to patch size and shape, at
least one core area exists.
Comments
Number of disjunct core areas is defined the same at the patch level (see Number of
Core Areas), but here it is aggregated (summed) over all patches. Number of
disjunct core areas is an alternative to the number of patches when it makes sense
to treat the core areas as functionally distinct patches.
(L3) Disjunct Core Area Density
116
nijc =
A=
number of disjunct core areas in patch ij
based on specified edge depths (m).
total landscape area (m2).
Description
DCAD equals the sum of number of disjunct core areas contained within each
patch, divided by total landscape area (m2), multiplied by 10,000 and 100 (to
convert to 100 hectares). Note, total landscape area (A) includes any internal
background present.
Units
Number per 100 hectares
Range
DCAD $ 0, without limit.
DCAD = 0 when TCA = 0 (i.e., every location within every patch is within the
specified depth-of-edge distance(s) from the patch perimeters); in other words,
when there are no core areas. DCAD > 1 when, due to patch size and shape, at
least one core area exists.
Comments
Disjunct core area density, like its counterpart, patch density (PD),expresses number
of disjunct core areas on a per unit area basis that facilitates comparisons among
landscapes of varying size. Of course, if total core area is held constant, then
disjunct core area density and number of disjunct core areas convey the same
information.
117
Contrast Metrics
Background.--Contrast refers to the magnitude of difference between adjacent patch types with
respect to one or more ecological attributes at a given scale that are relevant to the organism or
process under consideration. The contrast between a patch and its neighborhood can influence a
number of important ecological processes (Forman and Godron 1986). The ‘edge effects’ described
elsewhere (see Area and Edge Metrics), for example, are influenced by the degree of contrast
between patches. Microclimatic changes (e.g., wind, light intensity and quality, etc.) are likely to
extend farther into a patch along an edge with high structural contrast than along an edge with low
structural contrast (Ranney et al. 1981). Similarly, the adverse affects of brown-headed cowbird nest
parasitism on some forest-dwelling neotropical migratory bird species are likely to be greatest along
high-contrast forest edges (e.g., between mature forest patches and grassland), because cowbirds
prefer to forage in early-seral habitats and parasitize nests in late-seral habitats (Brittingham and
Temple 1983). In addition, patch isolation may be a function of the contrast between a patch and its
ecological neighborhood. In particular, the degree of contrast between a habitat patch and the
surrounding landscape may influence dispersal patterns and survival, and thus indirectly affect the
degree of patch isolation. Similarly, an organism's ability to use the resources in adjacent patches, as
in the process of landscape supplementation (Dunning et al. 1992), may depend on the nature of the
boundary between the patches. The boundary between patches can function as a barrier to
movement, a differentially-permeable membrane that facilitates some ecological flows but impedes
others, or as a semipermeable membrane that partially impairs flows (Wiens et al. 1985, Hansen and
di Castri 1992). The contrast along an edge may influence its function in this regard. For example,
high-contrast edges may prohibit or inhibit some organisms from seeking supplementary resources
in surrounding patches. Conversely, some species (e.g., great horned owl, Bubo virginianus) seem to
prefer the juxtaposition of patch types with high contrast, as in the process of landscape
complementation (Dunning et al. 1992).
Clearly, edge contrast can assume a variety of meanings for different ecological processes.
Therefore, contrast can be defined in a variety of ways, but it always reflects the magnitude of
difference between patches with respect to one or more ecological attributes at a given scale that are
important to the phenomenon under investigation (Kotliar and Wiens 1990, Wiens et al. 1985).
Similar to Romme (1982), FRAGSTATS employs weights to represent the magnitude of edge
contrast between adjacent patch types; weights must range between 0 (no contrast) and 1 (maximum
contrast). Under most circumstances, it is probably not valid to assume that all edges function
similarly. Often there will not be a strong empirical basis for establishing a weighting scheme, but a
reasoned guess based on a theoretical understanding of the phenomenon is probably better than
assuming all edges are alike. For example, from an avian habitat use standpoint, we might weight
edges somewhat subjectively according to the degree of structural and floristic contrast between
adjacent patches, because a number of studies have shown these features to be important to many
bird species (Thomas et al. 1978 and 1979, Logan et al. 1985).
FRAGSTATS Metrics.–FRAGSTATS computes several indices based on edge contrast at the
patch, class, and landscape levels. At the patch level, the edge contrast index (ECON) measures the
degree of contrast between a patch and its immediate neighborhood. Each segment of the patch
perimeter is weighted by the degree of contrast with the adjacent patch. Weights must range
between 0 (no contrast) and 1 (maximum contrast). Total patch perimeter is reduced proportionate
118
to the degree of contrast in the perimeter and reported as a percentage of the total perimeter. Thus,
a patch with a 10% edge contrast index has very little contrast with its neighborhood; it has the
equivalent of 10% of its perimeter in maximum-contrast edge. Conversely, a patch with a 90% edge
contrast index has high contrast with its neighborhood. Note that this index is a relative measure.
Given any amount of edge, it measures the degree of contrast in that edge. In other words, high
values of ECON mean that the edge present, regardless of whether it is 10 m or 1,000 m, is of high
contrast, and vice versa. At the class and landscape levels, FRAGSTATS computes a total edge contrast
index (TECI). Like its patch-level counterpart, this index quantifies edge contrast as a percentage of
maximum possible. However, this index ignores patch distinctions; it quantifies edge contrast for the
landscape as a whole. FRAGSTATS also computes distribution statistics for the edge contrast index
at the class and landscape levels. The mean edge contrast index (ECON_MN), for example, quantifies
the average edge contrast for patches of a particular patch type (class level) or for all patches in the
landscape.
These edge contrast indices are relative measures. Given any amount or density of edge, they
measure the degree of contrast in that edge. High values of these indices mean that the edge present,
regardless of whether it is 10 m or 1,000 m, is of high contrast, and vice versa. For this reason, these
indices are probably best interpreted in conjunction with total edge or edge density. Because of this,
FRAGSTATS also computes an index that incorporates both edge density and edge contrast in a
single index. Contrast-weighted edge density (CWED) standardizes edge to a per unit area basis that
facilitates comparison among landscapes of varying size. Unlike edge density, however, this index
reduces the length of each edge segment proportionate to the degree of contrast. Thus, 100 m/ha of
maximum-contrast edge (i.e., weight = 1) is unaffected; but 100 m/ha of edge with a contrast weight
of 0.2 is reduced by 80% to 20 m/ha of contrast-weighted edge. This index measures the equivalent
maximum-contrast edge density. For example, an edge density of 100 means that there are 100
meters of edge per hectare in the landscape. A contrast-weighted edge density of 80 for the same
landscape means that there are an equivalent of 80 meters of maximum-contrast edge per hectare in
the landscape. A landscape with 100 m/ha of edge and an average contrast weight of 0.8 would have
twice the contrast-weighted edge density (80 m/ha) as a landscape with only 50 m/ha of edge but
with the same average contrast weight (40 m/ha). Thus, both edge density and edge contrast are
reflected in this index. For many ecological phenomena, edge types function differently.
Consequently, comparing total edge density among landscapes may be misleading because of
differences in edge types. This contrast-weighted edge density index attempts to quantify edge from
the perspective of its functional significance. Thus, landscapes with the same contrast-weighted edge
density are presumed to have the same total magnitude of edge effects from a functional
perspective.
All edge contrast indices consider landscape boundary and background segments even if they have
an edge contrast weight of zero. In the absence of a landscape border, the landscape boundary is
assigned as background edge and treated according to the background contrast weight specified in
the contrast weight file. In the presence of a landscape border, all landscape boundary edges are
made explicit by the information present in the border and are assigned the appropriate contrast
weight given in the contrast weight file. Regardless of whether a border is present or not, all
background edges, both internal (positively valued) and external (negatively valued), are assigned the
background contrast weight specified in the contrast weight file. Assigning a meaningful contrast
weight to the boundary and background presents a special challenge because, in practice,
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background (and the boundary, in the absence of a border) often represents area for which nothing
is known. Thus, it can be difficult to assign a single contrast weight that applies equally well to all
background/boundary edges. A landscape border is often included to avoid this problem, because
all boundary edges are made explicit; however, even a border doesn’t eliminate the problem of
assigning a weight to background if it exists. The potential severity of the boundary/background
problem depends on the size and heterogeneity of the landscape and the extent of background edge.
Larger and more heterogeneous landscapes without little or no background will have
proportionately less total edge located along the boundary and/or background.
Limitations.–Edge contrast indices are limited by the considerations discussed elsewhere for
metrics based on total edge length (see Area and Edge Metrics). These indices are only calculated if
an edge contrast weight file is specified. More importantly, the usefulness of these indices is directly
related to the meaningfulness of the weighting scheme used to quantify edge contrast. Clearly, edge
contrast can assume a variety of meanings for different ecological processes. Therefore, contrast can
be defined in a variety of ways, but it always reflects the magnitude of difference between patches
with respect to one or more ecological attributes at a given scale that are important to the
phenomenon under investigation. Under most circumstances, it is probably not valid to assume that
all edges function similarly. Often there will not be a strong empirical basis for establishing a
weighting scheme, but a reasoned guess based on a theoretical understanding of the phenomenon is
probably better than assuming all edges are alike. For example, from an avian habitat use standpoint,
we might weight edges somewhat subjectively according to the degree of structural and floristic
contrast between adjacent patches, because a number of studies have shown these features to be
important to many bird species. Careful consideration should be given to devising weights that
reflect any empirical and theoretical knowledge and understanding of the phenomenon under
consideration. If the weighting scheme does not accurately represent the phenomenon under
investigation, then the results will be spurious.
Code
Metric (acronym)
Patch Metrics
P1
Edge Contrast Index (ECON)
Class Metrics
C1
Contrast-Weighted Edge Density (CWED)
C2
Total Edge Contrast Index (TECI)
C3-C8
Edge Contrast Index Distribution (ECON_MN, _AM, _MD, _RA, _SD, _CV)
Landscape Metrics
L1
Contrast-Weighted Edge Density (CWED)
L2
Total Edge Contrast Index (TECI)
L3-L8
Edge Contrast Index Distribution (ECON_MN, _AM, _MD, _RA, _SD, _CV)
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(P1) Edge Contrast Index
pijk =
dik =
pij =
length (m) of edge of patch ij adjacent to
patch type (class) k.
dissimilarity (edge contrast weight) between
patch types i and k.
length (m) of perimeter of patch ij.
Description
ECON equals the sum of the patch perimeter segment lengths (m) multiplied by
their corresponding contrast weights, divided by total patch perimeter (m),
multiplied by 100 (to convert to a percentage). Edge segments along the landscape
boundary are treated like background (as specified in the edge contrast weight file)
unless a landscape border is present, in which case the boundary edge types are
made explicit by the information in the border.
Units
Percent
Range
0 # ECON # 100
ECON = 0 if the landscape consists of only 1 patch and the landscape boundary
consists of all background (i.e., in the absence of a border) and is give a zerocontrast weight (d = 0). Also, ECON = 0 when all of the patch perimeter
segments involve patch type adjacencies that have been given a zero-contrast
weight in the edge contrast weight file. ECON = 100 when the entire patch
perimeter is maximum-contrast edge (d = 1). ECON < 100 when a portion of the
patch perimeter is less than maximum-contrast edge (d < 1).
Comments
Edge Contrast Index is founded on the notion that all edges are not created equal.
To account for this, the notion of edge “contrast” was created. This index is a
relative measure of the amount of contrast along the patch perimeter.
(C1) Contrast-Weighted Edge Density
eik =
dik =
A=
total length (m) of edge in landscape between
patch types (classes) i and k; includes landscape
boundary segments involving patch type i.
dissimilarity (edge contrast weight) between
patch types i and k.
total landscape area (m2).
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Description
CWED equals the sum of the lengths (m) of each edge segment involving the
corresponding patch type multiplied by the corresponding contrast weight,
divided by the total landscape area (m2), multiplied by 10,000 (to convert to
hectares). Edge segments along the landscape boundary are treated like
background (as specified in the edge contrast weight file) unless a landscape
border is present, in which case the boundary edge types are made explicit by the
information in the border. Note, total landscape area (A) includes any internal
background present.
Units
Meters per hectare
Range
CWED $ 0, without limit.
CWED = 0 when there is no class edge in the landscape; that is, when the entire
landscape and landscape border, if present, consists of the corresponding patch
type and the user specifies that background edge be given a zero-contrast weight
(d = 0). CWED increases as the amount of class edge in the landscape increases
and/or as the contrast in edges involving the corresponding patch type increase
(i.e., contrast weight approaches 1).
Description
Contrast-weighted edge density standardizes edge to a per unit area basis that facilitates
comparison among landscapes of varying size
(C2) Total Edge Contrast Index
eik =
total length (m) of edge in landscape between patch
types (classes) i and k; includes landscape boundary
segments involving patch type i.
*
e ik = total length (m) of edge in landscape between patch
types (classes) i and k; includes the entire landscape
boundary and all background edge segments,
regardless of whether they represent edge or not.
dik = dissimilarity (edge contrast weight) between patch
types i and k.
Description
TECI equals the sum of the lengths (m) of each edge segment involving the
corresponding patch type multiplied by the corresponding contrast weight,
divided by the sum of the lengths (m) of all edge segments involving the same
type, multiplied by 100 (to convert to a percentage). Edge segments along the
landscape boundary are treated like background (as specified in the edge contrast
weight file) unless a landscape border is present, in which case the boundary edge
types are made explicit by the information in the border.
Units
Percent
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Range
0 # TECI # 100
TECI = 0 when there is no class edge in the landscape; that is, when the entire
landscape and landscape border, if present, consists of the corresponding patch
type and the user specifies that background edge be given a zero-contrast weight
(d = 0). TECI approaches 0 as the contrast in edges involving the corresponding
patch type lesson (i.e., contrast weight approaches 0). TECI = 100 when all class
edge is maximum contrast (d = 1).
Description
Total edge contrast index is similar to the edge contrast index at the patch level, only
here it is applied to all edges of the corresponding patch type
(L1) Contrast-Weighted Edge Density
eik =
dik =
A=
total length (m) of edge in landscape
between patch types (classes) i and k;
includes landscape boundary segments
involving patch type i.
dissimilarity (edge contrast weight)
between patch types i and k.
total landscape area (m2).
Description
CWED equals the sum of the lengths (m) of each edge segment in the landscape
multiplied by the corresponding contrast weight, divided by the total landscape
area (m2), multiplied by 10,000 (to convert to hectares). Edge segments along the
landscape boundary are treated like background (as specified in the edge contrast
weight file) unless a landscape border is present, in which case the boundary edge
types are made explicit by the information in the border. Note, total landscape
area (A) includes any internal background present.
Units
Meters per hectare
Range
CWED $ 0, without limit.
CWED = 0 when there is no edge in the landscape; that is, when the entire
landscape and landscape border, if present, consists of the corresponding patch
type and the user specifies that background edge be given a zero-contrast weight
(d = 0). CWED increases as the amount of edge in the landscape increases and/or
as the contrast in edges increase (i.e., contrast weight approaches 1).
Description
Contrast-weighted edge density standardizes edge to a per unit area basis that facilitates
comparison among landscapes of varying size
(L2) Total Edge Contrast Index
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eik =
E* =
dik =
total length (m) of edge in landscape between
patch types (classes) i and k; includes landscape
boundary segments involving patch type i.
total length (m) of edge in landscape; includes
entire landscape boundary and background
edge segments regardless of whether they
represent edge or not.
dissimilarity (edge contrast weight) between
patch types i and k.
Description
TECI equals the sum of the lengths (m) of each edge segment in the landscape
multiplied by the corresponding contrast weight, divided by the total length (m) of
edge in the landscape, multiplied by 100 (to convert to a percentage). Edge
segments along the landscape boundary are treated like background (as specified
in the edge contrast weight file) unless a landscape border is present, in which case
the boundary edge types are made explicit by the information in the border.
Units
Percent
Range
0 # TECI # 100
TECI = 0 when there is no edge in the landscape; that is, when the entire
landscape and landscape border, if present, consists of a single patch or the user
specifies that all edge types be given a zero-contrast weight (d = 0). TECI
approaches 0 as the contrast in edges lesson (i.e., contrast weight approaches 0).
TECI = 100 when all edge is maximum contrast (d = 1).
Description
Total edge contrast index is similar to the edge contrast index at the patch level, only
here it is applied to all edges across the landscape.
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Aggregation Metrics
Background.–Aggregation refers to the tendency of patch types to be spatially aggregated; that is,
to occur in large, aggregated or “contagious” distributions. This property is also often referred to as
landscape texture. We use the term “aggregation” as an umbrella term to describe several closely
related concepts: 1) dispersion, 2) interspersion, 3) subdivision, and 4) isolation. Each of these
concepts relates to the broader concept of aggregation, but is distinct from the others in subtle but
important ways, as follows.
Dispersion and Interspersion.–Many of the aggregation metrics deal explicitly with the spatial properties
of dispersion and interspersion, and thus it is important to distinguish these two distinct
components. Dispersion refers to the spatial distribution of a patch type (class) without explicit
reference to any other patch types. Dispersion deals with how spread out or dispersed a patch type
is, whereby the greater the dispersion, the greater the disaggregation of the class or landscape.
Interspersion, on the other hand, refers to the spatial intermixing of different patch types (classes)
without explicit reference to the dispersion of any patch type. Interspersion deals solely with how
often each patch type is adjacent to each other patch type and not by the size, contiguity or
dispersion of patches. Dispersion and interspersion are both aspects of landscape texture; they both
deal with the adjacency of patch types, but do so in a different manner. Dispersion reflects the
spatial distribution of a particular patch type and is based on how often cells of a patch type are
adjacent to cells of the same patch type, whereas interspersion reflects the intermixing of patch types
and is based on how often cells along the perimeter of patches are adjacent to other patch types.
These two spatial properties are often highly confounded in real landscapes; as patch types become
more dispersed they also tend to be more well interspersed among other patch types. Thus, an
aggregated landscape tends to exhibit low dispersion and interspersion, whereas a disaggregated
landscape tends to exhibit high dispersion and interspersion. Nevertheless, these two components
can be measured independently or jointly, as described below.
Subdivision.–Subdivision is closely related to the concept of dispersion; both refer to the aggregation
of patch types, but subdivision deals explicitly with the degree to which patch types are broken up
(i.e., subdivided) into separate patches (i.e., fragments). Whereas dispersion deals with the
aggregation or disaggregation of cells of the same patch type and is based on cell adjacencies
independent of patch membership, subdivision deals explicitly with the subdivision of patch types
into disjunct patches. Thus, two distributions can have identical levels of dispersion (e.g., if there are
no like cell adjacencies, as in the case of a checkboard-like distribution), but they can have very
different levels of subdivision. Of course, these two components of aggregation are often highly
confounded in real landscapes; as patch types become more dispersed they also tend be more
subdivided.
The subdivision of a particular habitat type may affect a variety of ecological processes, depending
on the landscape context. For example, the number or density of patches may determine the
number of subpopulations in a spatially-dispersed population, or metapopulation, for species
exclusively associated with that habitat type. The number of subpopulations could influence the
dynamics and persistence of the metapopulation (Gilpin and Hanski 1991). The number or density
of patches also can alter the stability of species interactions and opportunities for coexistence in
both predator-prey and competitive systems (Kareiva 1990). The number or density of patches in a
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landscape mosaic (pooled across patch types) can have the same ecological applicability, but more
often serves as a general index of spatial heterogeneity of the entire landscape mosaic. A landscape
with a greater number or density of patches has a finer grain; that is, the spatial heterogeneity occurs
at a finer resolution. Although the number or density of patches in a class or in the landscape may
be fundamentally important to a number of ecological processes, often it does not have any
interpretive value by itself because it conveys no information about the area or distribution of
patches. Number or density of patches is probably most valuable, however, as the basis for
computing other, more interpretable, metrics, but is often use in combination with other metrics to
characterize subdivision.
Isolation.--Isolation is closely related to the concept of subdivision; both refer to the subdivision per
se of patch types, but isolation deals explicitly with the degree to which patches are spatially isolated
from each other, whereas subdivision doesn’t address the distance between patches, only that they
are disjunct. Thus, two distributions can have identical levels of subdivision (e.g., identical patch size
distributions), but they can have very different levels of isolation, for example if the patches are
farther apart in one landscape compared to the other. Of course, these two components of
aggregation are often highly confounded in real landscapes; as patch types become more subdivided
they also tend be more isolated, but this isn’t always the case. Consider the case when large
contiguous patches get subdivided by roads; the level of patch subdivision goes up but the patches
may or may not be more isolated from each other as a result.
The texture of a landscape is a fundamental aspect of landscape pattern and is important in many
ecological processes. Interspersion is presumed to affect the quality of habitat for many species that
require different patch types to meet different life history requisites, as in the process of landscape
complementation (Dunning et al. 1992). Indeed, the notion of habitat interspersion has had a
preeminent role in wildlife management during the past century. Wildlife management efforts are
often focused on maximizing habitat interspersion because it is believed that the juxtaposition of
different habitats will increase species diversity (Leopold 1933).
The disaggregation of a patch type of course plays a crucial role in the process of habitat loss and
fragmentation. Specifically, habitat loss and fragmentation generally involves the disaggregation of
contiguous habitat into more dispersed habitat and/or disjunct (i.e., subdivided) and more isolated
patches. As habitat loss and fragmentation proceeds, habitat becomes disaggregated and eventually
ecological function is impaired (Saunders et al.1991). Specifically, the subdivision and isolation of
populations caused by this habitat loss and fragmentation can lead to reduced dispersal success and
patch colonization rates which may result in a decline in the persistence of individual populations
and an enhanced probability of regional extinction for entire populations across the landscape (e.g.,
Lande 1987; With and King 1999a,b; With 1999). In addition, the disaggregation of patch types may
affect the propagation of disturbances across a landscape (Franklin and Forman 1987). Specifically, a
patch type that is highly disaggregated and/or subdivided may be more resistant to the propagation
of some disturbances (e.g., disease, fire, etc.), and thus more likely to persist in a landscape than a
patch type that is highly aggregated and/or contiguous. Conversely, highly disaggregated and/or
subdivided patch types may suffer higher rates of disturbance for some disturbance types (e.g.
windthrow) than more aggregated and/or contiguous distributions.
Isolation of habitat patches is a critical factor in the dynamics of spatially structured populations. For
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example, there has been a proliferation of mathematical models on population dynamics and species
interactions in spatially subdivided populations (Kareiva 1990), and results suggest that the dynamics
of local plant and animal populations in a patch are influenced by their proximity to other
subpopulations of the same or competing species. Patch isolation plays a critical role in island
biogeographic theory (MacArthur and Wilson 1967) and metapopulation theory (Levins 1970,
Gilpin and Hanski 1991). The role of patch isolation (e.g., as measured by interpatch distance) in
metapopulations has had a preeminent role in conservation efforts for endangered species (e.g.,
Lamberson et al. 1992, McKelvey et al. 1992).
Isolation is particularly important in the context of habitat loss and fragmentation. Several authors
have claimed, for example, that patch isolation explains why fragmented habitats often contain
fewer bird species than contiguous habitats (Moore and Hooper 1975, Forman et al. 1976, Helliwell
1976, Whitcomb et al. 1981, Hayden et al. 1985, Dickman 1987). Specifically, as habitat is lost and
fragmented, residual habitat patches become more isolated from each other in space and time. One
of the more immediate consequence of this is the disruption of movement patterns and the resulting
isolation of individuals and local populations. This has important metapopulation consequences. As
habitat is fragmented, it is broken up into remnants that are isolated to varying degrees. Because
remnant habitat patches are relatively small and therefore support fewer individuals, there will be
fewer local (within patch) opportunities for intra-specific interactions. This may not present a
problem for individuals (and the persistence of the population) if movement among patches is
largely unimpeded by intervening habitats in the matrix and connectivity across the landscape can be
maintained. However, if movement among habitat patches is significantly impeded or prevented,
then individuals (and local populations) in remnant habitat patches may become functionally
isolated. The degree of isolation for any fragmented habitat distribution will vary among species
depending on how they perceive and interact with landscape patterns (Dale et al. 1994, With and
Crist 1995, Pearson et al. 1996, With et al. 1997, With 1999); less vagile species with very restrictive
habitat requirements and limited gap-crossing ability will likely be most sensitive to isolation effects.
Habitat patches can become functionally isolated in several ways. First, the patch edge may act as a
filter or barrier that impedes or prevents movement, thereby disrupting emigration and dispersal
from the patch (Wiens et al. 1985). Some evidence for this exists for small mammals (e.g., Wegner
and Merriam 1979, Chasko and Gates 1982, Bendell and Gates 1987, Yahner 1986), but the data are
scarce for other vertebrates. Thus, subdivision per se can lead to increased isolation. Whether edges
themselves can limit movement presumably depends on what species are trying to cross the edge
and on the structure of the edge habitat (Kremsater and Bunnell 1999). Second, the distance from
remnant habitat patches to other neighboring habitat patches may influence the likelihood of
successful movement of individuals among habitat patches. Again, the distance at which movement
rates significantly decline will vary among species depending on how they scale the environment. In
general, larger organisms can travel longer distances. Therefore, a 100 m-wide agricultural field may
be a complete barrier to dispersal for small organisms such as invertebrates (e.g., Mader 1984), yet
be quite permeable for larger and more vagile organisms such as birds. Lastly, the composition and
structure of the intervening landscape mosaic may determine the permeability of the landscape to
movements. Note that under an island biogeographic perspective, habitat patches exist in a uniform
sea that is hostile to both survival and dispersal. In this case, the matrix is presumed to contain no
meaningful structure and isolation is influenced largely by the distance among favorable habitat
patches. However, under a landscape mosaic perspective, habitat patches are bounded by other
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patches that may be more or less similar (as opposed to highly contrasting and hostile) and
connectivity is assessed by the extent to which movement is facilitated or impeded through different
habitat types across the landscape. Each habitat may differ in its “viscosity” or resistance to
movement, facilitating movement through certain elements of the landscape and impeding it in
others. Again, the degree to which a given landscape structure facilitates or impedes movement will
vary among organisms. Regardless of how habitat patches become isolated, whether it be due to
properties of the edges themselves, the distance between patches, or properties of the intervening
matrix, the end result is the same–fewer individual movements among habitat patches.
FRAGSTATS Metrics.–There are several different approaches for measuring aggregation. One
popular index that subsumes both dispersion and interspersion is the contagion index (CONTAG)
based on the probability of finding a cell of type i next to a cell of type j. This index was proposed
first by O'Neill et al. (1988) and subsequently it has been widely used (Turner and Ruscher 1988,
Turner 1989, Turner et al. 1989, Turner 1990a and b, Graham et al. 1991, Gustafson and Parker
1992). Li and Reynolds (1993) showed that the original formula was incorrect; they introduced 2
forms of an alternative contagion index that corrects this error and has improved performance.
FRAGSTATS computes one of the contagion indices proposed by Li and Reynolds (1993). This
contagion index is based on raster “cell" adjacencies, not "patch" adjacencies, and consists of the
sum, over patch types, of the product of 2 probabilities: (1) the probability that a randomly chosen
cell belongs to patch type i (estimated by the proportional abundance of patch type i), and (2) the
conditional probability that given a cell is of patch type i, one of its neighboring cells belongs to
patch type j (estimated by the proportional abundance of patch type i adjacencies involving patch
type j). The product of these probabilities equals the probability that 2 randomly chosen adjacent
cells belong to patch type i and j. This contagion index is appealing because of the straightforward
and intuitive interpretation of this probability.
The contagion index has been widely used in landscape ecology because it seems to be an effective
summary of overall clumpiness on categorical maps (Turner 1989). In addition, in many landscapes,
it is highly correlated with indices of patch type diversity and dominance (Ritters et al. 1995) and
thus may be an effective surrogate for those important components of pattern (O’Neill et al. 1996).
Contagion measures both patch type interspersion (i.e., the intermixing of units of different patch
types) as well as patch dispersion (i.e., the spatial distribution of a patch type) at the landscape level.
All other things being equal, a landscape in which the patch types are well interspersed will have
lower contagion than a landscape in which patch types are poorly interspersed. Contagion measures
the extent to which patch types are aggregated or clumped (i.e., dispersion); higher values of
contagion may result from landscapes with a few large, contiguous patches, whereas lower values
generally characterize landscapes with many small and dispersed patches. Thus, holding
interspersion constant, a landscape in which the patch types are aggregated into larger, contiguous
patches will have greater contagion than a landscape in which the patch types are fragmented into
many small patches. Contagion measures dispersion in addition to patch type interspersion because
cells, not patches, are evaluated for adjacency. Landscapes consisting of large, contiguous patches
have a majority of internal cells with like adjacencies. In this case, contagion is high because the
proportion of total cell adjacencies comprised of like adjacencies is very large and the distribution of
adjacencies among edge types is very uneven.
Unfortunately, as alluded to above, there are alternative procedures for computing contagion, and
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this has contributed to some confusion over the interpretation of published contagion values (see
Ritters et al. 1996 for a discussion). Briefly, to calculate contagion, the adjacency of patch types is
first summarized in an adjacency or co-occurrence matrix, which shows the frequency with which
different pairs of patch types (including like adjacencies between the same patch type) appear sideby-side on the map (note, FRAGSTATS includes only the 4 orthogonal neighbors, not diagonal
neighbors, regardless of the choice of neighbor rules for defining patches). Although this would
seem to be a simple task, it is the source of differences among procedures for calculating contagion.
The difference arises out of the option to count each immediately-adjacent pixel pair once or twice.
In the single-count method, each pixel adjacency is counted once and the order of pixels is not
preserved; whereas, in the double-count method, each pixel adjacency is counted twice and the order
of pixels is preserved. Ritters et al. (1996) discuss the merits of both approaches. FRAGSTATS
adopts the double-count method in which pixel order is preserved, with two exceptions. If a landscape
border is present, the adjacencies along the landscape boundary (i.e., those between cells inside the
landscape and those in the border) are only counted once, and they are tallied for the cells inside the
landscape. For example, an adjacency on the landscape boundary between class 2 (inside the
landscape) and class -3 (in the landscape border) is recorded as a 2-3 adjacency in the adjacency
matrix, not a 3-2. Thus, if a landscape border is present, the adjacency matrix includes double-counts
for all internal cell adjacencies and single-counts for all adjacencies on the landscape boundary not
involving background. In effect, this gives double the weight to the internal adjacencies than those
on the boundary, although the effect will be trivial in most landscapes because the boundary edges
will represent a relative minor proportion of the total adjacencies. Similarly, all adjacencies involving
background (both internal, i.e., inside the landscape, and external, i.e., on the landscape boundary)
are counted only once, and they are tallied for the non-background cells. Essentially, each nonbackground cell inside the landscape (i.e., positively valued cell) is visited and the four cell sides are
evaluated and tallied in the adjacency matrix. Since background cells and all cells in the landscape
border, if present, are not visited per se, the edges involving these cells only get tallied once in
association with the non-background cell inside the landscape.
McGarigal and Marks (1995) introduced the interspersion and juxtaposition index (IJI) that isolates the
interspersion aspect of aggregation; it increases in value as patches tend to be more evenly
interspersed in a "salt and pepper" mixture. Unlike the previous contagion index that is based on
raster cell adjacencies, this index is based on patch adjacencies; only the patch perimeters are
considered in determining the total length of each unique edge type. Each patch is evaluated for
adjacency with all other patch types; like adjacencies are not possible because a patch can never be
adjacent to a patch of the same type. Because this index is a measure of patch adjacency and not cell
adjacency, the interpretation is somewhat different than the contagion index. The interspersion
index measures the extent to which patch types are interspersed (not necessarily dispersed); higher
values result from landscapes in which the patch types are well interspersed (i.e., equally adjacent to
each other), whereas lower values characterize landscapes in which the patch types are poorly
interspersed (i.e., disproportionate distribution of patch type adjacencies). The interspersion and
juxtaposition index is not directly affected by the number, size, contiguity, or dispersion of patches
per se, as is the contagion index. Consequently, a landscape containing 4 large patches, each a
different patch type, and a landscape of the same extent containing 100 small patches of 4 patch
types will have the same index value if the patch types are equally interspersed (or adjacent to each
other based on the proportion of total edge length in each edge type); whereas, the value of
contagion would be quite different. Like the contagion index, the interspersion and juxtaposition
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index is a relative index that represents the observed level of interspersion as a percentage of the
maximum possible given the total number of patch types.
It is important to note the differences between the contagion index and the interspersion and
juxtaposition index. Contagion is affected by both interspersion and dispersion. The interspersion
and juxtaposition index, in contrast, is affected only by patch type interspersion and not necessarily
by the size, contiguity, or dispersion of patches. Thus, although often indirectly affected by
dispersion, the interspersion and juxtaposition index directly measures patch type interspersion,
whereas contagion measures a combination of both patch type interspersion and dispersion. In
addition, contagion and interspersion are typically inversely related to each other. Higher contagion
generally corresponds to lower interspersion and vice versa. Finally, in contrast to the interspersion
and juxtaposition index, the contagion index is strongly affected by the grain size or resolution of
the image. Given a particular patch mosaic, a smaller grain size will result in greater contagion
because of the proportional increase in like adjacencies from internal cells. The interspersion and
juxtaposition index is not affected in this manner because it considers only patch edges. This scale
effect should be carefully considered when attempting to compare results from different studies.
FRAGSTATS computes a suite of metrics from the cell adjacency matrix that isolate the dispersion
aspect of aggregation. FRAGSTATS computes the percentage of like adjacencies (PLADJ), which is
computed as the sum of the diagonal elements (i.e., like adjacencies) of the adjacency matrix divided
by the total number of adjacencies. A landscape containing greater aggregation of patch types (e.g.,
larger patches with compact shapes) will contain a higher proportion of like adjacencies than a
landscape containing disaggregated patch types (e.g., smaller patches and more complex shapes). In
contrast to the contagion index, this metric measures only patch type dispersion, not interspersion,
and is unaffected by the method used to summarize adjacencies. At the class level, this metric is
computed as the percentage of like adjacencies of the focal class. A highly contagious (aggregated)
patch type will contain a higher percentage of like adjacencies. Conversely, a highly fragmented
(disaggregated) patch type will contain proportionately fewer like adjacencies. As such, this index
provides an effective measure of class-specific aggregation that isolates the dispersion (as opposed to
interspersion) component of aggregation. However, this index requires careful interpretation
because it varies in relation to the proportion of the landscape comprised of the focal class (Pi). It
has been shown that PLADJ for class i will equal Pi for a completely random map (Gardner and
O’Neill 1991). If the focal class is more dispersed than is expected of a random distribution (i.e.,
overdispersed), then PLADJ < Pi. If the focal class is more contagiously distributed, then PLADJ >
Pi. Thus, although PLADJ provides an absolute measure of aggregation of the focal class, it is
difficult to interpret as a measure of contagion without adjusting for Pi.
FRAGSTATS computes two indices based on PLADJ that adjust for Pi in different ways. The
aggregation index (AI) is computed as a percentage based on the ratio of the observed number of like
adjacencies (ei,i), based on the single-count method, to the maximum possible number of like
adjacencies (max_ei,i) given Pi (He et al. 2000). Note, the single-count method of tallying adjacencies
is employed to be consistent with the published algorithm. The maximum number of like
adjacencies is achieved when the class is clumped into a single compact patch, which does not have
to be a square. The trick here is in determining the maximum value of ei,i for any Pi,. He et al. (2000)
provide the formula for computing max_ei,i. The index ranges from 0 when there is no like
adjacencies (i.e., when the class is maximally dissagregated) to 1 when ei,i reaches the maximum (i.e.,
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when the class is maximally aggregated). However, AI is partially confounded with Pi because the
minimum value of the index varies with Pi when Pi > 0.5; specifically, the minimum value > 0 when
Pi > 0.5 and asymptotically approaches 1 as Pi 61. Thus, AI does not account for the expected value
under a spatially random distribution when Pi > 0.5; e.g., AI could equal 0.8 and yet the distribution
could be more disaggregated than expected under a random distribution if Pi > 0.8. Thus, caution
must be exercised in interpreting this metric. The clumpiness index (CLUMPY) is a class-level only
metric computed such that it ranges from -1 when the patch type is maximally disaggregated to 1
when the patch type is maximally clumped. It returns a value of zero for a random distribution,
regardless of Pi. Values less than zero indicate greater dispersion (or disaggregation) than expected
under a spatially random distribution, and values greater than zero indicate greater contagion.
Hence, this index provides a measure of class-specific aggregation that effectively isolates the
configuration component from the area component and, as such, provides an effective index of
fragmentation of the focal class that is not confounded by changes in class area.
FRAGSTATS computes a few metrics based on the number of unlike cell adjacencies (i.e., edges or
patch perimeters). As the proportion of like cell adjacencies increases, the number of unlike cell
adjacencies decreases. Unlike cell adjacencies represent the edges between patch types. Thus, there is
an inverse relationship between the proportion of like cell adjacencies (the basis for PLADJ, AI and
CLUMPY) and the length of edge. The Landscape shape index (LSI) index measures the perimeter-toarea ratio for the landscape as a whole. This index is identical to the habitat diversity index proposed
by Patton (1975), except that we apply the index at the class level as well. LSI is identical to the
shape index at the patch level (SHAPE), except that it treats the entire landscape as if it were one
patch and any patch edges (or class edges) as though they belong to the perimeter. Like the shape
index, it can be interpreted as a measure of the overall geometric complexity of the landscape or of a
focal class; however, it can also be interpreted as a measure of landscape disaggregation – the greater
the value of LSI, the more dispersed are the patch types. The landscape boundary must be included
as edge in the calculation in order to use a square standard for comparison. Unfortunately, this may
not be meaningful in cases where the landscape boundary does not represent true edge and/or the
actual shape of the landscape is of no particular interest. In this case, the total amount of true edge,
or some other index based on edge, would probably be more meaningful. If the landscape boundary
represents true edge or the shape of the landscape is particularly important, then LSI can be a useful
index, especially when comparing among landscapes of varying sizes. At the class level, the
landscape shape index suffers from confounding with the extent of the class, similar to PLADJ and
AI, but the confounding is nonlinear making interpretation even more difficult. Part of the difficulty
lies in the fact that the minimum and maximum length of edge varies with the proportion of the
landscape comprised of the focal patch, Pi. The normalized Landscape shape index (nLSI) isolates the
aggregation effect from the landscape composition effect by attempting to scale the index between
the theoretical minimum and maximum values for any given level of Pi, but it can be biased when Pi
is quite large (e.g., Pi >> .5) and when the landscape shape is not rectangular. Nevertheless, nLSI,
like CLUMPY, provides a more useful index of dispersion that isolates the configuration component
from the composition component. FRAGSTATS also computes the patch cohesion index
(COHESION) proposed by Schumaker (1996) to quantify the connectivity of habitat as perceived
by organisms dispersing in binary landscapes. COHESION is computed from the information
contained in patch area and perimeter; briefly, it is proportional to the area-weighted mean
perimeter-area ratio divided by the area-weighted mean patch shape index (i.e., standardized
perimeter-area ratio). COHESION is similar to the perimeter-to-area ratio metric (PARA, see Shape
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metrics) and thus is also confounded with Pi, like PLADJ, AI, and LSI, but it is invariant to changes
in the cell size and is bounded 0-1, which makes it easier to interpret and robust to changes in the
grain. It is well known that, on random binary maps, patches gradually coalesce as the proportion of
habitat cells increases, forming a large, highly connected patch (termed a percolating cluster) that
spans that lattice at a critical proportion (pc) that varies with the neighbor rule used to delineate
patches (Staufer 1985, Gardner et al. 1987). Patch cohesion has the interesting property of increasing
monotonically until an asymptote is reached near the critical proportion.
FRAGSTATS computes a suite of metrics that focus on the subdivision aspect of aggregation. The
simplest measure of subdivision is the number of patches (NP) or patch density (PD). However, these
simple measures of subdivision and other measures of aggregation have been criticized for their
insensitivity and inconsistent behavior across a wide range of subdivision patterns. Jaeger (2000)
discussed the limitations of these metrics for evaluating habitat fragmentation and concluded that
most of these metrics do not behave in a consistent and logical manner across all phases of the
fragmentation process. He introduced a suite of metrics derived from the cumulative distribution of
patch sizes that provide alternative and more explicit measures of subdivision. When applied at the
class level, these metrics can be used to measure the degree of fragmentation of the focal patch type.
Applied at the landscape level, these metrics measure the graininess of the landscape; i.e., the
tendency of the landscape to exhibit a fine- versus coarse-grain texture. FRAGSTATS computes
three of the subdivision metrics proposed by Jaeger (2000). All of these metrics are based on the
notion that two animals, placed randomly in different areas somewhere in a region, will have a
certain likelihood of being in the same undissected area (i.e., the same patch), which is a function of
the degree of subdivision of the landscape. The landscape division index (DIVISION) is based on the
degree of coherence (C), which is defined as the probability that two animals placed in different
areas somewhere in the region of investigation might find each other. Degree of coherence is based
on the cumulative patch area distribution and is represented graphically as the area above the
cumulative area distribution curve. Degree of coherence represents the probability that two animals,
which have been able to move throughout the whole region before the landscape was subdivided,
will be found in the same patch after the subdivision is in place. The degree of landscape division is
simply the complement of coherence and is defined as the probability that two randomly chosen
places in the landscape are not situated in the same undissected patch. Graphically, the degree of
landscape division is equal to the area below the cumulative area distribution curve.
The splitting index (SPLIT) is defined as the number of patches one gets when dividing the total
landscape into patches of equal size in such a way that this new configuration leads to the same
degree of landscape division as obtained for the observed cumulative area distribution. The splitting
index can be interpreted to be the “effective mesh number” of a patch mosaic with a constant patch
size dividing the landscape into S patches, where S is the splitting index. The effective mesh size
(MESH) simply denotes the size of the patches when the landscape is divided into S areas (each of
the same size) with the same degree of landscape division as obtained for the observed cumulative
area distribution. Thus, all three subdivision metrics are easily computed from the cumulative patch
area distribution. These measures have the particular advantage over other conventional measures of
subdivision (e.g., mean patch size, patch density) in that they are insensitive to the omission or
addition of very small patches. In practice, this makes the results more reproducible as investigators
do not always use the same lower limit of patch size. Jaeger (2000) argues that the most important
and advantageous feature of these new measures is that effective mesh size is ‘area-proportionately
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additive’; that is, it characterizes the subdivision of a landscape independently of its size. In fact,
these three measures are closely related to the area-weighted mean patch size (AREA_AM)
discussed previously, and under certain circumstances are perfectly redundant. The distinctions are
discussed below for each metric.
FRAGSTATS computes several metrics that focus on the isolation aspect of aggregation.
Unfortunately, because of the many factors that influence the functional isolation of a patch, it is a
difficult thing to capture in a single measure. In the context of habitat fragmentation, for example,
isolation can be measured as the time since the habitat was physically subdivided, but this is fraught
with practical difficulties, because rarely do we have accurate historical data from which to
determine when each patch was isolated. Moreover, given that fragmentation is an ongoing process,
it can be difficult to objectively determine at what point the habitat becomes subdivided, since this is
largely a function of scale. Isolation can be measured in the spatial dimension in several ways,
depending on how one views the concept of isolation. The simplest measures discussed below are
based on Euclidean distance between nearest neighbors (McGarigal and Marks 1995) or the
cumulative area of neighboring habitat patches weighted by nearest neighbor distance within some
ecological neighborhood (Gustafson and Parker 1992). These measures adopt an island
biogeographic perspective, as they treat the landscape as a binary mosaic consisting of habitat
patches and uniform matrix. Thus, the context of a patch is defined by the proximity and area of
neighboring habitat patches; the role of the matrix is ignored. However, these measures can be
modified to take into account other habitat types in the so-called matrix and their affects on the
insularity of the focal habitat. For example, simple Euclidean distance can be modified to account
for functional differences among organisms. The functional distance between patches clearly
depends on how each organism scales and interacts with landscape patterns (With 1999); in other
words, the same gap between patches may not be perceived as a relevant disconnection for some
organisms, but may be an impassable barrier for others.
FRAGSTATS computes three isolation metrics that adopt an island biogeographic perspective on
patch isolation. Euclidean nearest neighbor distance (ENN) is perhaps the simplest measure of patch
isolation. Here, nearest neighbor distance is defined using simple Euclidean geometry as the shortest
straight-line distance between the focal patch and its nearest neighbor of the same class, based on
the distance between the cell centers of the two closest cells from the respective patches. At the
class and landscape levels, FRAGSTATS computes the mean in ENN (ENN_MN). At the class
level, ENN_MN can only be computed if there are at least two patches of the corresponding type.
At the landscape level, ENN_MN considers only patches that have neighbors. Thus, there could be
10 patches in the landscape, but eight of them might belong to separate patch types and therefore
have no neighbor within the landscape. In this case, ENN_MN would be based on the distance
between the two patches of the same type. These two patches could be close together or far apart.
In either case, the mean nearest-neighbor distance for this landscape may not characterize the entire
landscape very well. For this reason, these metrics should be interpreted carefully when landscapes
contain rare patch types. In addition to these first-order statistics, the variability in ENN provides a
measure patch dispersion. Specifically, a small standard deviation (SD)in ENN (ENN_SD) relative
to the mean implies a fairly uniform or regular distribution of patches across landscapes, whereas a
large SD relative to the mean implies a more irregular or uneven distribution of patches. The
distribution of patches may reflect underlying natural processes or human-caused disturbance
patterns. In absolute terms, the magnitude of ENN_SD is a function of the mean nearest-neighbor
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distance and variation in nearest-neighbor distance among patches. Thus, while SD does convey
information about nearest neighbor variability, it is a difficult parameter to interpret without doing
so in conjunction with the mean nearest-neighbor distance. For example, two landscapes may have
the same ENN_SD, e.g., 100 m; yet one landscape may have a mean nearest-neighbor distance of
100 m, while the other may have a mean nearest-neighbor distance of 1,000 m. In this case, the
interpretations of landscape pattern would be very different, even though the absolute variation is
the same. Specifically, the former landscape has a more irregular but concentrated pattern of
patches, while the latter has a more regular but dispersed pattern of patches. For these reasons,
coefficient of variation (CV) often is preferable to SD for comparing variability among landscapes.
Coefficient of variation measures relative variability about the mean (i.e., variability as a percentage
of the mean), not absolute variability, and is akin to the familiar indices of dispersion in point
patterns based on the variance to mean ratio in nearest neighbor distance (e.g., Clark and Evans
1954). Thus, it is not necessary to know the mean nearest-neighbor distance to interpret this metric.
Even so, ENN_CV can be misleading with regards to landscape structure without also knowing the
number of patches or patch density and other structural characteristics. For example, two landscapes
may have the same ENN_CV, e.g., 100%; yet one landscape may have 100 patches with a mean
nearest-neighbor distance of 100 m, while the other may have 10 patches with a mean
nearest-neighbor distance of 1,000 m. In this case, the interpretations of overall landscape pattern
could be very different, even though ENN_CV is the same; although the identical CV's indicate that
both landscapes have the same regularity or uniformity in patch distribution. Finally, both SD and
CV assume a normal distribution about the mean. In a real landscape, nearest-neighbor distribution
may be highly irregular. In this case, it may be more informative to inspect the actual distribution
itself (e.g., plot a histogram of the nearest neighbor distances for the corresponding patches), rather
than relying on summary statistics such as SD and CV that make assumptions about the distribution
and therefore can be misleading.
FRAGSTATS also computes the connectance index (CONNECT) as the proportion of functional
joinings among all patches, where each pair of patches is either connected or not based on some
criterion. FRAGSTATS computes connectance using a threshold distance specified by the user and
reports it as a percentage of the maximum possible connectance given the number of patches. The
threshold distance in FRAGSTATS is based on Euclidean distance, but it could be based on some
other measure of functional distance, such as the least cost path distance.
Even though nearest-neighbor distance is often used to evaluate patch isolation, it is important to
recognize that the single nearest patch may not fully represent the ecological neighborhood of the
focal patch. For example, a neighboring patch 100 m away that is 1 ha is size may not be as
important to the effective isolation of the focal patch as a neighboring patch 200 m away, but 1000
ha in size. To overcome this limitation, the proximity index (PROX) was developed by Gustafson and
Parker (1992)[see also Gustafson and Parker 1994, Gustafson et al. 1994, Whitcomb et al. 1981].
This index considers the size and proximity of all patches whose edges are within a specified search
radius of the focal patch. The index is computed as the sum, over all patches of the corresponding
patch type whose edges are within the search radius of the focal patch, of each patch size divided by
the square of its distance from the focal patch. Note that FRAGSTATS uses the distance between
the focal patch and each of the other patches within the search radius, similar to the isolation index
of Whitcomb et al. (1981), rather than the nearest-neighbor distance of each patch within the search
radius (which could be to a patch other than the focal patch), as in Gustafson and Parker (1992).
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The proximity index quantifies the spatial context of a (habitat) patch in relation to its neighbors of
the same class; specifically, the index distinguishes sparse distributions of small habitat patches from
configurations where the habitat forms a complex cluster of larger patches. All other things being
equal, a patch located in a neighborhood (defined by the search radius) containing more of the
corresponding patch type than another patch will have a larger index value. Similarly, all other things
being equal, a patch located in a neighborhood in which the corresponding patch type is distributed
in larger, more contiguous, and/or closer patches than another patch will have a larger index value.
Thus, the proximity index measures both the degree of patch isolation and the degree of
fragmentation of the corresponding patch type within the specified neighborhood of the focal patch.
FRAGSTATS computes a single isolation metric that adopts a landscape mosaic perspective on
patch isolation. The similarity index (SIMI) is a modification of the proximity index, the difference
being that similarity considers the size and proximity of all patches, regardless of class, whose edges
are within a specified search radius of the focal patch. SIMI quantifies the spatial context of a
(habitat) patch in relation to its neighbors of the same or similar class; specifically, the index
distinguishes sparse distributions of small and insular habitat patches from configurations where the
habitat forms a complex cluster of larger, hospitable (i.e., similar) patches. All other things being
equal, a patch located in a neighborhood (defined by the search radius) deemed more similar (i.e.,
containing greater area in patches with high similarity) than another patch will have a larger index
value. Similarly, all other things being equal, a patch located in a neighborhood in which the similar
patches are distributed in larger, more contiguous, and/or closer patches than another patch will
have a larger index value. Essentially, the similarity index performs much the same way as the
proximity index, but instead of focusing on only a single patch type (i.e., island biogeographic
perspective), it considers all patch types in the mosaic (i.e., landscape mosaic perspective). Thus, the
similarity index is a more comprehensive measure of patch isolation than the proximity index for
organisms and processes that perceive and respond to patch types differentially.
Limitations.–All measures based on the adjacency matrix (i.e., the number of adjacencies between
each pair of patch types) that include like-adjacencies (i.e., PLADJ, AI, CLUMPY, and CONTAG)
are strongly affected by the grain size or resolution of the image. Given a particular patch mosaic, a
smaller grain size will result in a proportional increase in like adjacencies. Given this scale
dependency, these metrics are best used if the scale is held constant. Note, IJI, LSI, nLSI, and
COHESION are not affected by resolution directly because only patch edges are considered. In
addition, there are alternative ways to consider cell adjacencies. Adjacencies may include only the 4
cells sharing a side with the focal cell, or they may include the diagonal neighbors as well.
FRAGSTATS uses the 4-neighbor approach for the purpose of calculating these metrics. Further,
there are at least two basic approaches for counting cell adjacencies, referred to as the single count
and double count methods. As noted above, FRAGSTATS adopts the double count method in which
pixel order is preserved. In this method, all non-background cells inside the landscape (i.e.,
positively-valued cells) are visited and the four sides of each cell are tallied in the adjacency matrix.
As a result, all cell sides involving non-background classes inside the landscape are tallied twice
(hence the term double count), but all cell sides involving background or landscape border (i.e.,
negatively-valued cells) are only counted once, as those cells are themselves not visited.
There are significant limitations associated with the use of isolation metrics that must be understood
before they are used. The most important limitation of these particular metrics is that
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nearest-neighbor distances are computed solely from patches contained within the landscape
boundary. If the landscape extent is small relative to the scale of the organism or ecological
processes under consideration and the landscape is an "open" system relative to that organism or
process, then nearest-neighbor results can be misleading. For example, consider a small
subpopulation of a bird species occupying a patch near the boundary of a somewhat arbitrarily
defined (from a bird's perspective) landscape. The nearest neighbor within the landscape boundary
might be quite far away, yet in reality the closest patch might be very close, but just outside the
designated landscape boundary. The magnitude of this problem is a function of scale. Increasing the
size of the landscape relative to the scale at which the organism under investigation perceives and
responds to the environment will decrease the severity of this problem.
Similarly, the proximity and similarity indices involve a search window around the focal patch. Thus,
these metrics may be biased low for patches located within the search radius distance from the
landscape boundary because a portion of the search area will be outside the area under
consideration. The magnitude is of this problem is also a function of scale. Increasing the size of the
landscape relative to the average patch size and/or decreasing the search radius will decrease the
severity of this problem at the class and landscape levels. However, at the patch level, regardless of
scale, individual patches located within the search radius of the boundary will have biased indices. In
addition, these indices evaluate the landscape context of patches at a specific scale of analysis
defined by the size of the search radius. Therefore, these indices are only meaningful if the specified
search radius has some ecological relevance to the phenomenon under consideration. Otherwise, the
results will be arbitrary and therefore meaningless.
Lastly, the similarity index is a functional metric in that it requires additional parameterization, in this
case, similarity coefficients that are unique to the ecological phenomenon under consideration.
Consequently, as with any functional metric, its meaning depends entirely on the meaningfulness of
the similarity coefficients applied. If these are arbitrary assignments or based on weak observational
data, results will be arbitrary and therefore meaningless.
Code
Metric (acronym)
Patch Metrics
P1
Euclidean Nearest Neighbor Distance (ENN)
P2
Proximity Index (PROX)
P3
Similarity Index (SIMI)
Class Metrics
C1
Interspersion & Juxtaposition Index (IJI)
C2
Percentage of Like Adjacencies (PLADJ)
C3
Aggregation Index (AI)
C4
Clumpiness Index (CLUMPY)
C5
Landscape Shape Index (LSI)
136
C6
Normalized Landscape Shape Index (nLSI)
C7
Patch Cohesion Index (COHESION)
C8
Number of Patches (NP)
C9
Patch Density (PD)
C10
Landscape Division Index (DIVISION)
C11
Splitting Index (SPLIT)
C12
Effective Mesh Size (MESH)
C13-18
Euclidean Nearest Neighbor Distance Distribution (ENN_MN, _AM, _MD, _RA, _SD, _CV)
C19-24
Proximity Index Distribution (PROX_MN, _AM, _MD, _RA, _SD, _CV)
C25-30
Similarity Index Distribution (SIMI_MN, _AM, _MD, _RA, _SD, _CV)
C31
Connectance (CONNECT)
Landscape Metrics
L1
Contagion (CONTAG)
L2
Interspersion & Juxtaposition Index (IJI)
L3
Percentage of Like Adjacencies (PLADJ)
L4
Aggregation Index (AI)
L5
Landscape Shape Index (LSI)
L6
Patch Cohesion Index (COHESION)
L7
Number of Patches (NP)
L8
Patch Density (PD)
L9
Landscape Division Index (DIVISION)
L10
Splitting Index (SPLIT)
L11
Effective Mesh Size (MESH)
L12-17
Euclidean Nearest Neighbor Distance Distribution (ENN_MN, _AM, _MD, _RA, _SD, _CV)
L18-23
Proximity Index Distribution (PROX_MN, _AM, _MD, _RA, _SD, _CV)
L24-29
Similarity Index Distribution (SIMI_MN, _AM, _MD, _RA, _SD, _CV)
L30
Connectance (CONNECT)
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(P1) Euclidean Nearest-Neighbor Distance
hij =
distance (m) from patch ij to nearest neighboring patch of the
same type (class), based on patch edge-to-edge distance,
computed from cell center to cell center.
Description
ENN equals the distance (m) to the nearest neighboring patch of the same type,
based on shortest edge-to-edge distance. Note that the edge-to-edge distances are
from cell center to cell center.
Units
Meters
Range
ENN > 0, without limit.
ENN approaches 0 as the distance to the nearest neighbor decreases. The
minimum ENN is constrained by the cell size, and is equal to twice the cell size
when the 8-neighbor patch rule is used or the distance between diagonal
neighbors when the 4-neighbor rule is used. The upper limit is constrained by the
extent of the landscape. ENN is undefined and reported as "N/A" in the
“basename”.patch file if the patch has no neighbors (i.e., no other patches of the
same class).
Comments
Euclidean nearest-neighbor distance is perhaps the simplest measure of patch context
and has been used extensively to quantify patch isolation. Here, nearest neighbor
distance is defined using simple Euclidean geometry as the shortest straight-line
distance between the focal patch and its nearest neighbor of the same class.
(P2) Proximity Index
aijs =
hijs =
area (m2) of patch ijs within specified neighborhood (m)
of patch ij.
distance (m) between patch ijs and patch ijs, based on
patch edge-to-edge distance, computed from cell center
to cell center.
Description
PROX equals the sum of patch area (m2) divided by the nearest edge-to-edge
distance squared (m2) between the patch and the focal patch of all patches of the
corresponding patch type whose edges are within a specified distance (m) of the
focal patch. Note, when the search buffer extends beyond the landscape
boundary, only patches contained within the landscape are considered in the
computations. In addition, note that the edge-to-edge distances are from cell
center to cell center.
Units
None
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Range
PROX $ 0.
PROX = 0 if a patch has no neighbors of the same patch type within the specified
search radius. PROX increases as the neighborhood (defined by the specified
search radius) is increasingly occupied by patches of the same type and as those
patches become closer and more contiguous (or less fragmented) in distribution.
The upper limit of PROX is affected by the search radius and the minimum
distance between patches.
Comments
Proximity index was developed by Gustafson and Parker (1992) and considers the
size and proximity of all patches whose edges are within a specified search radius
of the focal patch. Note that FRAGSTATS uses the distance between the focal
patch and each of the other patches within the search radius, similar to the
isolation index of Whitcomb et al. (1981), rather than the nearest-neighbor
distance of each patch within the search radius (which could be to a patch other
than the focal patch), as in Gustafson and Parker (1992). The index is
dimensionless (i.e., has no units) and therefore the absolute value of the index has
little interpretive value; instead it is used as a comparative index.
(P3) Similarity Index
aijs =
dik =
hijs =
area (m2) of patch ijs within specified neighborhood
(m) of patch ij.
similarity between patch types i and k.
distance (m) between patch ijs and patch ijs, based
on patch edge-to-edge distance, computed from cell
center to cell center.
Description
SIMI equals the sum, over all neighboring patches with edges within a specified
distance (m) of the focal patch, of neighboring patch area (m2) times a similarity
coefficient between the focal patch type and the class of the neighboring patch (01), divided by the nearest edge-to-edge distance squared (m2) between the focal
patch and the neighboring patch. Note, when the search buffer extends beyond
the landscape boundary, only patches contained within the landscape are
considered in the computations. In addition, note that the edge-to-edge distances
are from cell center to cell center.
Units
None
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Range
SIMI $ 0
SIMI = 0 if all the patches within the specified neighborhood have a zero
similarity coefficient. SIMI increases as the neighborhood (defined by the
specified search radius) is increasingly occupied by patches with greater similarity
coefficients and as those similar patches become closer and more contiguous and
less fragmented in distribution. The upper limit of SIMI is affected by the search
radius and minimum distance between patches.
Comments
Similarity index is a modification of the proximity index (see Proximity Index
description), the difference being that similarity considers the size and proximity
of all patches, regardless of class, whose edges are within a specified search radius
of the focal patch. Like the proximity index, this index is dimensionless (i.e., has
no units) and therefore the absolute value of the index has little interpretive value;
instead it is used as a comparative index.
(C1) Interspersion and Juxtaposition Index
eik =
m=
total length (m) of edge in landscape
between patch types (classes) i and k.
number of patch types (classes)
present in the landscape, including
the landscape border, if present.
Description
IJI equals minus the sum of the length (m) of each unique edge type involving the
corresponding patch type divided by the total length (m) of edge (m) involving the
same type, multiplied by the logarithm of the same quantity, summed over each
unique edge type; divided by the logarithm of the number of patch types minus 1;
multiplied by 100 (to convert to a percentage). In other words, the observed
interspersion over the maximum possible interspersion for the given number of
patch types. Note, IJI considers all patch types present on an image, including any
present in the landscape border, if present. All background edge segments are
ignored, as are landscape boundary segments if a border is not provided, because
adjacency information for these edge segments is not available and the intermixing
of the focal class with background is assumed to be irrelevant.
Units
Percent
140
Range
0 < IJI # 100
IJI approaches 0 when the corresponding patch type is adjacent to only 1 other
patch type and the number of patch types increases. IJI = 100 when the
corresponding patch type is equally adjacent to all other patch types (i.e.,
maximally interspersed and juxtaposed to other patch types). IJI is undefined and
reported as “N/A" in the "basename".class file if the number of patch types is less
than 3.
Comments
Interspersion and juxtaposition index is based on patch adjacencies, not cell adjacencies
like the contagion index. As such, it does not provide a measure of class
aggregation like the contagion index, but rather isolates the interspersion or
intermixing of patch types.
(C2) Percentage of Like Adjacencies
gii =
gik =
number of like adjacencies (joins) between pixels of
patch type (class) i based on the double-count method.
number of adjacencies (joins) between pixels of
patch types (classes) i and k based on the double-count
method.
Description
PLADJ equals the number of like adjacencies involving the focal class, divided by
the total number of cell adjacencies involving the focal class; multiplied by 100 (to
convert to a percentage). In other words, the percentage of cell adjacencies
involving the corresponding patch type that are like adjacencies. All background
edge segments are included in the sum of all adjacencies involving the focal class,
including landscape boundary segments if a border is not provided. Cell
adjacencies are tallied using the double-count method in which pixel order is
preserved, at least for all internal adjacencies (i.e., involving cells on the inside of
the landscape). If a landscape border is present, adjacencies on the landscape
boundary are counted only once, as are all adjacencies with background.
Units
Percent
141
Range
0 # PLADJ # 100
PLADJ equals 0 when the corresponding patch type is maximally disaggregated
(i.e., every cell is a different patch) and there are no like adjacencies. This occurs
when the class is subdivided into one cell patches. Note, this condition can only
be achieved when the proportion of the landscape comprised of the focal class (Pi)
is # 0.5. When Pi = 0.5, this occurs only when the class is distributed as a perfect
checkerboard. When Pi > 0.5, the checkerboard begins to fill in and there will
exist like adjacencies. PLADJ increases as the corresponding patch type becomes
increasingly aggregated such that the proportion of like adjacencies increases.
PLADJ = 100 when the landscape consists of single patch and all adjacencies are
between the same class, and the landscape contains a border comprised entirely of
the same class. If the landscape consists of single patch but does not contain a
border, PLADJ will be less than 100 due to the background edge segments in the
tally of adjacencies involving the focal class. Finally, PLADJ is undefined and
reported as “N/A” in the “basename”.class file if the class consists of a single cell.
Comments
Percentage of like adjacencies is calculated from the adjacency matrix, which shows the
frequency with which different pairs of patch types (including like adjacencies
between the same patch type) appear side-by-side on the map. PLADJ measures
the degree of aggregation of the focal patch type. Thus, it is a measure of classspecific contagion. Regardless of how much of the landscape is comprised of the
focal class (Pi), this index will be minimum if the patch type is maximally dispersed
(or disaggregated), and it will be maximum if the patch type is maximally
contagious. However, this index does not account for the fact that the percentage
of like adjacencies for a random distribution equals Pi. If the percentage of like
adjacencies is less than Pi, then the patch type is more dispersed than expected of a
random landscape. Conversely, if the percentage of like adjacencies is greater than
Pi, then the patch type is contagiously distributed. Note, this metric measures only
dispersion and not interspersion, and thus may be a useful index of fragmentation
of the focal class when interpreted in conjunction with Pi.
(C3) Aggregation Index
gii =
number of like adjacencies (joins) between
pixels of patch type (class) i based on the singlecount method.
max-gii = maximum number of like adjacencies (joins)
between pixels of patch type (class) i (see below)
based on the single-count method.
142
Description
AI equals the number of like adjacencies involving the corresponding class,
divided by the maximum possible number of like adjacencies involving the
corresponding class, which is achieved when the class is maximally clumped into a
single, compact patch; multiplied by 100 (to convert to a percentage). If Ai is the
area of class i (in terms of number of cells) and n is the side of a largest integer
square smaller than Ai, and m = Ai - n2, then the largest number of shared edges
for class i, max-gii will take one of the three forms:
max-gii = 2n(n-1) , when m = 0, or
max-gii = 2n(n-1) + 2m -1, when m # n, or
max-gii = 2n(n-1) + 2m -2, when m > n.
Note, because of the design of the metric, like adjacencies are tallied using the
single-count method, and all landscape boundary edge segments are ignored, even if
a border is provided.
Units
Percent
Range
0 # AI # 100
Given any Pi , AI equals 0 when the focal patch type is maximally disaggregated
(i.e., when there are no like adjacencies); AI increases as the focal patch type is
increasingly aggregated and equals 100 when the patch type is maximally
aggregated into a single, compact patch. AI is undefined and reported as “N/A"
in the "basename".class file if the class consists of a single cell.
Comments
Aggregation index is calculated from an adjacency matrix, which shows the
frequency with which different pairs of patch types (including like adjacencies
between the same patch type) appear side-by-side on the map. Aggregation index
takes into account only the like adjacencies involving the focal class, not
adjacencies with other patch types. In addition, in contrast to all of the other
metrics based on adjacencies, the aggregation index is based on like adjacencies
tallied using the single-count method, in which each cell side is counted only once.
Consequently, the tallies given in the “basename”.adj output file are not correct
for this metric. Further, because of the design of the metric, landscape boundary
edge segments are ignored, even if a border is provided FRAGSTATS handles
this case by distinguishing between internal like adjacencies (i.e., like adjacencies
involving cells inside the landscape) and external like adjacencies (i.e., like
adjacencies between cells inside the landscape and those in the border). Only
internal like adjacencies are used in the calculation of this metric; a landscape
border has no affect on this metric. The aggregation index is scaled to account for
the maximum possible number of like adjacencies given any Pi. The maximum
aggregation is achieved when the patch type consists of a single, compact patch,
which is not necessarily a square patch.
143
(C4) Clumpiness Index
gii =
gik =
Pi =
number of like adjacencies
(joins) between pixels of
patch type (class) i based on
the double-count method.
number of adjacencies
(joins) between pixels of
patch types (classes) i and k
based on the double-count
method.
proportion of the landscape
occupied by patch type
(class) i.
Description
CLUMPY equals the proportional deviation of the proportion of like adjacencies
involving the corresponding class from that expected under a spatially random
distribution. If the proportion of like adjacencies (Gi) is greater than or equal to
the proportion of the landscape comprised of the focal class (Pi), then CLUMPY
equals Gi minus Pi, divided by 1 minus Pi. Likewise, if Gi < Pi, and Pi $0.5, then
CLUMPY equals Gi minus Pi, divided by 1 minus Pi. However, if Gi < Pi, and Pi <
0.5, then CLUMPY equals Pi minus Gi, divided by negative Pi. Note, all
background edge segments are included in the sum of all adjacencies involving the
focal class, including landscape boundary segments if a border is not provided.
Cell adjacencies are tallied using the double-count method in which pixel order is
preserved, at least for all internal adjacencies (i.e., involving cells on the inside of
the landscape). If a landscape border is present, adjacencies on the landscape
boundary are counted only once, as are all adjacencies with background. Note, Pi
is based on the total landscape area (A) including any internal background present.
Units
Percent
Range
-1 # CLUMPY # 1
Given any Pi , CLUMPY equals -1 when the focal patch type is maximally
disaggregated; CLUMPY equals 0 when the focal patch type is distributed
randomly, and approaches 1 when the patch type is maximally aggregated. Note,
CLUMPY equals 1 only when the landscape consists of a single patch and
includes a border comprised of the focal class.
144
Comments
Clumpiness index is calculated from the adjacency matrix, which shows the
frequency with which different pairs of patch types (including like adjacencies
between the same patch type) appear side-by-side on the map. Clumpiness is
scaled to account for the fact that the proportion of like adjacencies (Gi) will equal
Pi for a completely random distribution (see previous discussion). The formula is
contingent upon Gi and Pi because the minimum value of Gi has two forms which
depend on Pi. Specifically, when Pi # 0.5, Gi = 0 when the class is maximally
disaggregated (i.e., subdivided into one cell patches) and approaches 1 when the
class is maximally clumped. However, when Pi $ 0.5, Gi = 2Pi -1 when the class is
maximally disaggregated and approaches 1 when the class is maximally clumped.
Note, when Gi > Pi, the formula given above assumes a maximum value of Gi = 1
(i.e., maximum clumping). This is not strictly true. In fact, the maximum value of
Gi asymptotically approaches 1 as Pi increases to 1. At very small Pi, the maximum
value of Gi is somewhat less. However, the bias is only nontrivial when the focal
class consists of only a few cells. As the number of cells increases, the bias rapidly
decreases and becomes trivial. Hence, when Gi > Pi CLUMPY is slightly biased
low. That is, the computed degree of clumping is slightly less than the actual
degree of clumping, but again, the difference is trivial under most conditions. This
approach of assuming that a maximum value of Gi = 1 is necessary because it is
impossible to calculate the true maximum value of Gi, taking into account
potential like adjacencies of perimeter cell surfaces of the focal class when
maximally clumped into a single compact patch. Recall that FRAGSTATS allows
for the existence of a landscape border, which may consist of cells of the same
class as the neighboring patches inside the landscape proper (a situation virtually
guaranteed to occur in a moving window analysis). Unfortunately, there is no way
to calculate the expected number of perimeter cell surfaces adjacent to the
landscape boundary given any Pi–this depends on the exact configuration and
positioning of the focal class when maximally clumped. Note, the maximum like
adjacencies computed for the aggregation index does not include perimeter cell
surfaces. Thus, calculating maximum Gi based on this approach will always
underestimate the true value. The use of 1 as the maximum Gi guarantees a
theoretical maximum (upper limit) value of 1 for CLUMPY.
(C5) Landscape Shape Index
e*ik = total length (m) of edge in landscape between patch types
(classes) i and k; includes the entire landscape boundary and
some or all background edge segments involving class i.
A = total landscape area (m2).
145
Description
LSI equals .25 (adjustment for raster format) times the sum of the entire landscape
boundary (regardless of whether it represents ‘true’ edge or not, or how the user
specifies how to handle boundary/background) and all edge segments (m) within
the landscape boundary involving the corresponding patch type, including some
or all of those bordering background (based on user specifications), divided by the
square root of the total landscape area (m2). Note, total landscape area (A)
includes any internal background present.
Units
None
Range
LSI $ 1, without limit.
LSI = 1 when the landscape consists of a single square patch of the corresponding
type; LSI increases without limit as landscape shape becomes more irregular
and/or as the length of edge within the landscape of the corresponding patch type
increases.
Comments
Landscape shape index provides a standardized measure of total edge or edge density
that adjusts for the size of the landscape. Because it is standardized, it has a direct
interpretation, in contrast to total edge, for example, that is only meaningful
relative to the size of the landscape.
(C6) normalized Landscape Shape Index
ei =
total length of edge (or perimeter) of class i in terms
of number of cell surfaces; includes all landscape
boundary and background edge segments involving
class i.
min ei = minimum total length of edge (or perimeter) of
class i in terms of number of cell surfaces (see
below).
max ei = maximum total length of edge (or perimeter) of
class i in terms of number of cell surfaces (see
below).
146
Description
nLSI equals the total length of edge (or perimeter) involving the corresponding
class, given in number of cell surfaces, minus the minimum length of class edge
(or perimeter) possible for a maximally aggregated class, also given in number of
cell surfaces, which is achieved when the class is maximally clumped into a single,
compact patch, divided by the maximum minus the minimum length of class edge.
If ai is the area of class i (in terms of number of cells)[note, this is equivalent to the
sum of patch areas across all patches of class i] and n is the side of the largest
integer square smaller than ai (denoted ) and m = ai - n2, then the minimum edge
or perimeter of class i, min-ei, will take one of the three forms (Milne 1991,
Bogaert et al. 2000):
min-ei = 4n, when m = 0, or
min-ei = 4n + 2, when n2 < ai # n(1+n), or
min-ei = 4n + 4, when ai > n(1+n).
If A is the landscape area, including all internal background (in terms of number
of cells), B = number of cells on the boundary (perimeter) of the landscape, Z =
total length of landscape boundary (perimeter) given in number of cell surfaces,
and Pi = proportion of the landscape comprised of the corresponding class, then
the maximum edge or perimeter of class i, max-ei, will take one of the three forms:
max-ei = 4ai, when Pi # 0.5, or
max-ei = 3A - 2ai, when A is even; 0.5 < Pi # (0.5A + 0.5B)/A, or
max-ei = 3A - 2ai + 3, when A is odd; 0.5 < Pi # (0.5A + 0.5B)/A, or
max-ei = Z + 4(A - ai), when Pi > (0.5A + 0.5B)/A
Note, the formula for max-ei recognizes the fact that as Pi increases beyond 0.5,
the maximum total length of edge is achieved when the cells of the focal class fill
in first along the boundary of the landscape. Unfortunately, the formulas given
above for Pi > 0.5 are only an approximation for this effect. An analytical solution
is not possible given the infinite number of landscape shapes possible. In addition,
the formula for min-ei assumes that the maximally aggregated class is a single
square or almost square patch. However, if the landscape shape is highly irregular,
then as the proportional class area Pi approaches 1, the shape of the landscape will
constrain the minimum class edge possible (i.e., the actual min-ei << the
theoretical min-ei) and nLSI will biased high (i.e., the class will appear to be
relatively less aggregated than it actually is). However, for square or rectangular
landscapes, or classes with Pi << 1, there is either no bias or it is trivial.
Units
None
147
Range
0 # nLSI # 1
nLSI = 0 when the landscape consists of a single square or maximally compact
(i.e., almost square) patch of the corresponding type; LSI increases as the patch
type becomes increasingly disaggregated and is 1 when the patch type is maximally
disaggregated (i.e., a checkerboard when Pi # 0.5). Note, nLSI is undefined and
reported as N/A in the output files whenever max-ei = min-ei, which exists when
the class consists either of a single cell, comprises all but 1 cell, or comprises the
entire landscape, because it is impossible to distinguish between clumped, random
and dispersed distributions in these cases.
Comments
Normalized Landscape shape index is the normalized version of the landscape shape
index (LSI) and, as such, provides a simple measure of class aggregation or
clumpiness. The normalization essentially rescales LSI to the minimum and
maximum values possible for any class area. When the patch type is relatively rare
(say Pi < 0.1) or relative dominant (say Pi > 0.5), the range between the minimum
and maximum total edge (or perimeter) is relatively small; whereas when the patch
type is intermediate in abundance (say Pi = 0.5), the range is quite large. nLSI
essentially measures the degree of aggregation given this variable range. Note, just
as LSI and the Aggregation Index (AI) are closely related, the normalized versions
of these metrics are related, in fact perfectly so. For this reason, the normalized
version of AI is not computed since it is completely redundant with nLSI. In
addition, given the considerations given above regarding the computational
method that assumes a square or almost square shape for a maximally compact
class and the bias this creates if the landscape is highly irregular and the percentage
of the landscape comprised of the focal class is high, it is advisable to avoid using
this metric under these conditions of bias. Also, for these reasons, this metric is
not available in the Moving Window analysis mode when a circular window shape
is selected.
(C7) Patch Cohesion Index
pij* =
aij* =
Z=
Description
perimeter of patch ij in
terms of number of cell
surfaces.
area of patch ij in terms of
number of cells.
total number of cells in the
landscape.
COHESION equals 1 minus the sum of patch perimeter (in terms of number of
cell surfaces) divided by the sum of patch perimeter times the square root of patch
area (in terms of number of cells) for patches of the corresponding patch type,
divided by 1 minus 1 over the square root of the total number of cells in the
landscape, multiplied by 100 to convert to a percentage. Note, total landscape area
(Z) excludes any internal background present.
148
Units
None
Range
0 < COHESION < 100
COHESION approaches 0 as the proportion of the landscape comprised of the
focal class decreases and becomes increasingly subdivided and less physically
connected. COHESION increases monotonically as the proportion of the
landscape comprised of the focal class increases until an asymptote is reached near
the percolation threshold (see background discussion). COHESION is given as 0
if the landscape consists of a single non-background cell.
Comments
Patch cohesion index measures the physical connectedness of the corresponding
patch type. Below the percolation threshold, patch cohesion is sensitive to the
aggregation of the focal class. Patch cohesion increases as the patch type becomes
more clumped or aggregated in its distribution; hence, more physically connected.
Above the percolation threshold, patch cohesion does not appear to be sensitive
to patch configuration (Gustafson 1998).
(C8) Number of Patches
ni =
number of patches in the landscape of patch type (class) i.
Description
NP equals the number of patches of the corresponding patch type (class).
Units
None
Range
NP $ 1, without limit.
NP = 1 when the landscape contains only 1 patch of the corresponding patch
type; that is, when the class consists of a single patch.
Comments
Number of patches of a particular patch type is a simple measure of the extent of
subdivision or fragmentation of the patch type. Although the number of patches
in a class may be fundamentally important to a number of ecological processes,
often it has limited interpretive value by itself because it conveys no information
about area, distribution, or density of patches. Of course, if total landscape area
and class area are held constant, then number of patches conveys the same
information as patch density or mean patch size and may be a useful index to
interpret. Number of patches is probably most valuable, however, as the basis for
computing other, more interpretable, metrics. Note that the choice of the 4neighbor or 8-neighbor rule for delineating patches will have an impact on this
metric.
(C9) Patch Density
149
ni =
A=
number of patches in the landscape of patch type
(class) i.
total landscape area (m2).
Description
PD equals the number of patches of the corresponding patch type divided by total
landscape area (m2), multiplied by 10,000 and 100 (to convert to 100 hectares).
Note, total landscape area (A) includes any internal background present.
Units
Number per 100 hectares
Range
PD > 0, constrained by cell size.
PD is ultimately constrained by the grain size of the raster image, because the
maximum PD is attained when every cell is a separate patch. Therefore, ultimately
cell size will determine the maximum number of patches per unit area. However,
the maximum density of patches of a single class is attained when every other cell
is of that focal class (i.e., in a checker board manner; because adjacent cells of the
same class would be in the same patch).
Comments
Patch density is a limited, but fundamental, aspect of landscape pattern. Patch
density has the same basic utility as number of patches as an index, except that it
expresses number of patches on a per unit area basis that facilitates comparisons
among landscapes of varying size. Of course, if total landscape area is held
constant, then patch density and number of patches convey the same information.
Like number of patches, patch density often has limited interpretive value by itself
because it conveys no information about the sizes and spatial distribution of
patches. Note that the choice of the 4-neighbor or 8-neighbor rule for delineating
patches will have an impact on this metric.
(C10) Landscape Division Index
aij =
A=
area (m2) of patch ij.
total landscape area (m2).
Description
DIVISION equals 1 minus the sum of patch area (m2) divided by total landscape
area (m2), quantity squared, summed across all patches of the corresponding patch
type. Note, total landscape area (A) includes any internal background present.
Units
Proportion
150
Range
0 # DIVISION < 1
DIVISION = 0 when the landscape consists of single patch. DIVISION
approaches 1 when the focal patch type consists of single, small patch one cell in
area. As the proportion of the landscape comprised of the focal patch type
decreases and as those patches decrease in size, DIVISION approaches 1.
Comments
Division is based on the cumulative patch area distribution and is interpreted as the
probability that two randomly chosen pixels in the landscape are not situated in
the same patch of the corresponding patch type. Note, the similarity with
Simpson’s diversity index, only here the sum is across the proportional area of
each patch in the focal class, rather than the proportional area of each patch ‘type’
in the landscape. Note, DIVISION is redundant with effective mesh size (MESH)
below, i.e., they are perfectly, but inversely, correlated, but both metrics are
included because of differences in units and interpretation. DIVISION is
interpreted as a probability, whereas MESH is given as an area.
(C11) Splitting Index
aij =
A=
area (m2) of patch ij.
total landscape area (m2).
Description
SPLIT equals the total landscape area (m2) squared divided by the sum of patch
area (m2) squared, summed across all patches of the corresponding patch type.
Note, total landscape area (A) includes any internal background present.
Units
None
Range
1 # SPLIT # number of cells in the landscape area squared
SPLIT = 1 when the landscape consists of single patch. SPLIT increases as the
focal patch type is increasingly reduced in area and subdivided into smaller
patches. The upper limit of SPLIT is constrained by the ratio of landscape area to
cell size and is achieved when the corresponding patch type consists of a single
one pixel patch.
Comments
Split is based on the cumulative patch area distribution and is interpreted as the
effective mesh number, or number of patches with a constant patch size when the
corresponding patch type is subdivided into S patches, where S is the value of the
splitting index.
(C12) Effective Mesh Size
151
aij =
A=
area (m2) of patch ij.
total landscape area (m2).
Description
MESH equals the sum of patch area squared, summed across all patches of the
corresponding patch type, divided by the total landscape area (m2), divided by
10,000 (to convert to hectares). Note, total landscape area (A) includes any
internal background present.
Units
Hectares
Range
ratio of cell size to landscape area # MESH # total landscape area (A)
The lower limit of MESH is constrained by the ratio of cell size to landscape area
and is achieved when the corresponding patch type consists of a single one pixel
patch. MESH is maximum when the landscape consists of a single patch.
Comments
Mesh is based on the cumulative patch area distribution and is interpreted as the
size of the patches when the corresponding patch type is subdivided into S
patches, where S is the value of the splitting index. Note, MESH is redundant with
DIVISION above, i.e., they are perfectly, but inversely, correlated, but both
metrics are included because of differences in units and interpretation. DIVISION
is interpreted as a probability, whereas MESH is given as an area. In addition, note
the similarity between MESH and area-weight mean patch size (AREA_AM).
Conceptually, these two metrics are closely related, but computationally they are
quite different at the class level. Specifically, AREA_AM gives the area-weight
mean patch size of patches of the corresponding class, where the proportional
area of each patch is based on total class area (i.e., the total area of patches of the
corresponding patch type). MESH, on the other hand, also gives the areaweighted mean patch size of patches of the corresponding patch size, but the
proportional area of each patch is based on the total landscape area, not the class
area. In this way, MESH takes into account the patch size distribution of the
corresponding class as well as the total landscape area comprised of that class.
Thus, holding the patch size distribution (of the corresponding class) constant, as
the landscape extent increases (and the percent of the landscape comprised of this
class decreases), MESH for the corresponding class will decrease. Hence,
AREA_AM provides an absolute measure of patch structure, whereas MESH
provides a relative measure of patch structure.
(C31) Connectance Index
152
cijk =
ni =
joining between patch j and k (0 = unjoined,
1 = joined) of the corresponding patch type
(i), based on a user specified threshold
distance.
number of patches in the landscape of the
corresponding patch type (class).
Description
CONNECT equals the number of functional joinings between all patches of the
corresponding patch type (sum of cijk where cijk = 0 if patch j and k are not within
the specified distance of each other and cijk = 1 if patch j and k are within the
specified distance), divided by the total number of possible joinings between all
patches of the corresponding patch type, multiplied by 100 to convert to a
percentage.
Units
Percent
Range
0 # CONNECT # 100
CONNECT = 0 when either the focal class consists of a single patch or none of
the patches of the focal class are "connected" (i.e., within the user-specified
threshold distance of another patch of the same type). CONNECT = 100 when
every patch of the focal class is "connected."
Comments
Connectance is defined on the number of functional joinings between patches of the
corresponding patch type, where each pair of patches is either connected or not
based on a user-specified distance criterion. Connectance is reported as a
percentage of the maximum possible connectance given the number of patches.
Note, connectance can be based on either Euclidean distance or functional
distance, as described elsewhere (see Isolation/Proximity Metrics).
(L1) Contagion Index
Pi =
gik =
m=
proportion of the landscape occupied by patch type (class) i.
number of adjacencies (joins) between pixels of patch types (classes) i and k based on the
double-count method.
number of patch types (classes) present in the landscape, including the landscape border if
present.
153
Description
CONTAG equals minus the sum of the proportional abundance of each patch
type multiplied by the proportion of adjacencies between cells of that patch type
and another patch type, multiplied by the logarithm of the same quantity, summed
over each unique adjacency type and each patch type; divided by 2 times the
logarithm of the number of patch types; multiplied by 100 (to convert to a
percentage). In other words, the observed contagion over the maximum possible
contagion for the given number of patch types. Note, CONTAG considers all
patch types present on an image, including any present in the landscape border, if
present, and considers like adjacencies (i.e., cells of a patch type adjacent to cells
of the same type). All background edge segments are ignored, as are landscape
boundary segments if a border is not provided, because adjacency information for
these edge segments is not available and the intermixing of the classes with
background is assumed to be irrelevant. Cell adjacencies are tallied using the
double-count method in which pixel order is preserved, at least for all internal
adjacencies (i.e., involving cells on the inside of the landscape). If a landscape
border is present, adjacencies on the landscape boundary are counted only once as
are all adjacencies with background. Note, Pi is based on the total landscape area
(A) excluding any internal background present.
Units
Percent
Range
0 < CONTAG # 100
CONTAG approaches 0 when the patch types are maximally disaggregated (i.e.,
every cell is a different patch type) and interspersed (equal proportions of all
pairwise adjacencies). CONTAG = 100 when all patch types are maximally
aggregated. CONTAG is undefined and reported as “N/A” in the
“basename”.land file if the number of patch types is less than 2, or all classes
consist of one cell patches adjacent to only background.
Comments
Contagion is inversely related to edge density. When edge density is very low, for
example, when a single class occupies a very large percentage of the landscape,
contagion is high, and vice versa. In addition, note that contagion is affected by
both the dispersion and interspersion of patch types. Low levels of patch type
dispersion (i.e., high proportion of like adjacencies) and low levels of patch type
interspersion (i.e., inequitable distribution of pairwise adjacencies results in high
contagion, and vice versa.
(L2) Interspersion and Juxtaposition Index
154
eik =
E=
m=
total length (m) of edge in landscape
between patch types (classes) i and k.
total length (m) of edge in landscape,
excluding background.
number of patch types (classes) present in
the landscape, including the landscape
border, if present.
Description
IJI equals minus the sum of the length (m) of each unique edge type divided by
the total landscape edge (m), multiplied by the logarithm of the same quantity,
summed over each unique edge type; divided by the logarithm of the number of
patch types times the number of patch types minus 1 divided by 2; multiplied by
100 (to convert to a percentage). In other words, the observed interspersion over
the maximum possible interspersion for the given number of patch types. Note,
IJI considers all patch types present on an image, including any present in the
landscape border, if present. All background edge segments are ignored, as are
landscape boundary segments if a border is not provided, because adjacency
information for these edge segments is not available and the intermixing of classes
with background is assumed to be irrelevant.
Units
Percent
Range
0 < IJI # 100
IJI approaches 0 when the distribution of adjacencies among unique patch types
becomes increasingly uneven. IJI = 100 when all patch types are equally adjacent
to all other patch types (i.e., maximum interspersion and juxtaposition). IJI is
undefined and reported as "N/A" in the "basename".land file if the number of
patch types is less than 3.
Comments
Interspersion and juxtaposition index is based on patch adjacencies, not cell adjacencies
like the contagion index. As such, it does not provide a measure of class
aggregation like the contagion index, but rather isolates the interspersion or
intermixing of patch types.
(L3) Percentage of Like Adjacencies
gii =
gik =
number of like adjacencies (joins) between
pixels of patch type (class) i based on the doublecount method .
number of adjacencies (joins) between pixels of
patch types (classes) i and k based on the doublecount method.
155
Description
PLADJ equals sum of the number of like adjacencies for each patch type, divided
by the total number of cell adjacencies in the landscape; multiplied by 100 (to
convert to a percentage). In other words, the proportion of cell adjacencies
involving the same class. PLADJ considers all patch types present on an image,
including any present in the landscape border, if present. All background edge
segments are included in the denominator, including landscape boundary
segments if a border is not provided. Cell adjacencies are tallied using the doublecount method in which pixel order is preserved, at least for all internal adjacencies
(i.e., involving cells on the inside of the landscape). If a landscape border is
present, adjacencies on the landscape boundary are counted only once, as are all
adjacencies with background.
Units
Percent
Range
0 # PLADJ # 100
PLADJ equals 0 when the patch types are maximally disaggregated (i.e., every cell
is a different patch type) and there are no like adjacencies. PLADJ = 100 when all
patch types are maximally aggregated ( i.e., when the landscape consists of single
patch and all adjacencies are between the same class), and the landscape contains a
border comprised entirely of the same class. If the landscape consists of single
patch but does not contain a border, PLADJ will be less than 100 due to the
background edge segments along the boundary included in the tally of all
adjacencies. PLADJ is undefined and reported as “N/A” in the “basename”.land
file if the landscape consists of a single non-background cell.
Comments
Percentage of like adjacencies is calculated from the adjacency matrix, which shows the
frequency with which different pairs of patch types (including like adjacencies
between the same patch type) appear side-by-side on the map. PLADJ measures
the degree of aggregation of patch types. Thus, a landscape containing larger
patches with simple shapes will contain a higher percentage of like adjacencies
than a landscape with smaller patches and more complex shapes. In contrast to
the contagion index at the landscape level, this metric measures only dispersion
and not interspersion. Note, regardless of how much of the landscape is
comprised of each class, this index will be minimum if all patch types are
maximally dispersed (or disaggregated), and it will be maximum if all patch types
are maximally contagious.
(L4) Aggregation Index
156
gii =
number of like adjacencies (joins)
between pixels of patch type (class) i
based on the single-count method.
max-gii = maximum number of like
adjacencies (joins) between pixels of
patch type (class) i (see below) based
on the single-count method.
Pi =
proportion of landscape comprised
of patch type (class) i.
Description
AI equals the number of like adjacencies involving the corresponding class,
divided by the maximum possible number of like adjacencies involving the
corresponding class, which is achieved when the class is maximally clumped into a
single, compact patch, multiplied the proportion of the landscape comprised of
the corresponding class, summed over all classes and multiplied by 100 (to convert
to a percentage). If Ai is the area of class i (in terms of number of cells) and n is
the side of a largest integer square smaller than Ai, and m = Ai - n2, then the
largest number of shared edges for class i, max-gii will take one of the three forms:
max-gii = 2n(n-1), when m = 0,
max-gii = 2n(n-1) + 2m -1, when m # n, or
max-gii = 2n(n-1) + 2m -2, when m > n.
Note, because of the design of the metric, like adjacencies are tallied using the
single-count method, and all landscape boundary edge segments are ignored, even if
a border is provided. Also, Pi is based on the total landscape area (A) excluding
any background present.
Units
Percent
Range
0 # AI # 100
Given any Pi , AI equals 0 when the patch types are maximally disaggregated (i.e.,
when there are no like adjacencies); AI increases as the landscape is increasingly
aggregated and equals 100 when the landscape consists of a single patch. AI is
undefined and reported as “N/A" in the "basename".land file if each class consists
of a single cell (and hence is undefined).
Comments
Aggregation index is calculated from an adjacency matrix at the class level (see classlevel AI comments). At landscape level, the index is computed simply as an areaweighted mean class aggregation index, where each class is weighted by its
proportional area in the landscape. The index is scaled to account for the
maximum possible number of like adjacencies given any landscape composition.
157
(L5) Landscape Shape Index
E* =
A=
total length (m) of edge in landscape; includes the entire
landscape boundary and some or all background edge segments.
total landscape area (m2).
Description
LSI equals .25 (adjustment for raster format) times the sum of the entire landscape
boundary (regardless of whether it represents ‘true’ edge or not, or how the user
specifies how to handle boundary/background) and all edge segments (m) within
the landscape boundary, including some or all of those bordering background
(based on user specifications), divided by the square root of the total landscape
area (m2). Note, total landscape area (A) includes any internal background present.
Units
None
Range
LSI $ 1, without limit.
LSI = 1 when the landscape consists of a single square patch; LSI increases
without limit as landscape shape becomes more irregular and/or as the length of
edge within the landscape increases.
Comments
Landscape shape index provides a standardized measure of total edge or edge density
that adjusts for the size of the landscape. Because it is standardized, it has a direct
interpretation, in contrast to total edge, for example, that is only meaningful
relative to the size of the landscape.
(L6) Patch Cohesion Index
pij* =
aij* =
Z=
perimeter of patch ij in
terms of number of
cell surfaces.
area of patch ij in
terms of number of
cells.
total number of cells in
the landscape.
Description
COHESION equals 1 minus the sum of patch perimeter (in terms of number of
cells) divided by the sum of patch perimeter times the square root of patch area
(in terms of number of cells) for all patches in the landscape, divided by 1 minus 1
over the square root of the total number of cells in the landscape, multiplied by
100 to convert to a percentage. Note, total landscape area (Z) excludes any
internal background present.
Units
None
Range
The behavior of this metric at the landscape level has not yet been evaluated.
158
Comments
Patch cohesion index at the class level measures the physical connectedness of the
corresponding patch type. However, at the landscape level, the behavior of this
metric has not yet been evaluated.
(L7) Number of Patches
N=
total number of patches in the landscape.
Description
NP equals the number of patches in the landscape. Note, NP does not include any
internal background patches (i.e., within the landscape boundary) or any patches at
all in the landscape border, if present.
Units
None
Range
NP $ 1, without limit.
NP = 1 when the landscape contains only 1 patch.
Comments
Number of patches often has limited interpretive value by itself because it conveys no
information about area, distribution, or density of patches. Of course, if total
landscape area is held constant, then number of patches conveys the same
information as patch density or mean patch size and may be a useful index to
interpret. Number of patches is probably most valuable, however, as the basis for
computing other, more interpretable, metrics. Note that the choice of the 4neighbor or 8-neighbor rule for delineating patches will have an impact on this
metric.
(L8) Patch Density
N=
A=
total number of patches in the landscape.
total landscape area (m2).
Description
PD equals the number of patches in the landscape, divided by total landscape area
(m2), multiplied by 10,000 and 100 (to convert to 100 hectares). Note, PD does
not include background patches or patches in the landscape border, if present.
However, total landscape area (A) includes any internal background present.
Units
Number per 100 hectares
Range
PD > 0, constrained by cell size.
PD is ultimately constrained by the grain size of the raster image, because the
maximum PD is attained when every cell is a separate patch.
159
Comments
Patch density is a limited, but fundamental, aspect of landscape pattern. Patch
density has the same basic utility as number of patches as an index, except that it
expresses number of patches on a per unit area basis that facilitates comparisons
among landscapes of varying size. Of course, if total landscape area is held
constant, then patch density and number of patches convey the same information.
Like number of patches, patch density often has limited interpretive value by itself
because it conveys no information about the sizes and spatial distribution of
patches. Note that the choice of the 4-neighbor or 8-neighbor rule for delineating
patches will have an impact on this metric.
(L9) Landscape Division Index
aij =
A=
area (m2) of patch ij.
total landscape area (m2).
Description
DIVISION equals 1 minus the sum of patch area (m2) divided by total landscape
area (m2), quantity squared, summed across all patches in the landscape. Note,
total landscape area (A) includes any internal background present.
Units
Proportion
Range
0 # DIVISION < 1
DIVISION = 0 when the landscape consists of single patch. DIVISION is
achieves its maximum value when the landscape is maximally subdivided; that is,
when every cell is a separate patch.
Comments
Division is based on the cumulative patch area distribution and is interpreted as the
probability that two randomly chosen pixels in the landscape are not situated in
the same patch. Note, the similarity with Simpson’s diversity index, only here the
sum is across the proportional area of each patch, rather than the proportional
area of each patch type in the landscape. Note, DIVISION is redundant with
effective mesh size (MESH) below, i.e., they are perfectly, but inversely,
correlated, but both metrics are included because of differences in units and
interpretation. DIVISION is interpreted as a probability, whereas MESH is given
as an area. In addition, as described below (see MESH), DIVISION is perfectly
redundant with area-weighted mean patch size (AREA_AM) when there is no
background.
(L10) Splitting Index
160
aij =
A=
area (m2) of patch ij.
total landscape area (m2).
Description
SPLIT equals the total landscape area (m2) squared divided by the sum of patch
area (m2) squared, summed across all patches in the landscape. Note, total
landscape area (A) includes any internal background present.
Units
None
Range
1 # SPLIT # number of cells in the landscape squared
SPLIT = 1 when the landscape consists of single patch. SPLIT increases as the
landscape is increasingly subdivided into smaller patches and achieves its
maximum value when the landscape is maximally subdivided; that is, when every
cell is a separate patch.
Comments
Split is based on the cumulative patch area distribution and is interpreted as the
effective mesh number, or number of patches with a constant patch size when the
landscape is subdivided into S patches, where S is the value of the splitting index.
(L11) Effective Mesh Size
aij =
A=
area (m2) of patch ij.
total landscape area (m2).
Description
MESH equals 1 divided by the total landscape area (m2) multiplied by the sum of
patch area (m2) squared, summed across all patches in the landscape. Note, total
landscape area (A) includes any internal background present.
Units
Hectares
Range
cell size # MESH # total landscape area (A)
The lower limit of MESH is constrained by the cell size and is achieved when the
landscape is maximally subdivided; that is, when every cell is a separate patch.
MESH is maximum when the landscape consists of a single patch.
161
Comments
Mesh is based on the cumulative patch area distribution and is interpreted as the
size of the patches when the landscape is subdivided into S patches, where S is the
value of the splitting index. Note, MESH is redundant with DIVISION above,
i.e., they are perfectly, but inversely, correlated, but both metrics are included
because of differences in units and interpretation. DIVISION is interpreted as a
probability, whereas MESH is given as an area. In addition, note the similarity
between MESH and area-weight mean patch size (AREA_AM). Conceptually and
computationally, these two metrics are almost identical at the landscape level, and
under most circumstances will return identical values. Specifically, AREA_AM
gives the area-weight mean patch size, where the proportional area of each patch
is based on total landscape area excluding any background (i.e., background is
excluded from the total landscape area). MESH also gives the area-weighted mean
patch size, but the proportional area of each patch is based on the total landscape
area including any background. Background is included in the so-called ‘pedestal’ of
Jaeger (2000). Thus, if there is no internal background, these metrics will return
identical values. If there is internal background, these metrics will return different
values, and the magnitude of the difference will depend on the proportional extent
of background. In the latter case, the choice of metrics depends on how you want
to consider background.
(L30) Connectance Index
cijk =
ni =
joining between patch j and k (0 =
unjoined, 1 = joined) of the same
patch type, based on a user-specified
threshold distance.
number of patches in the landscape
of each patch type (i).
Description
CONNECT equals the number of functional joinings between all patches of the
same patch type (sum of cijk where cijk = 0 if patch j and k are not within the
specified distance of each other and cijk = 1 if patch j and k are within the
specified distance), divided by the total number of possible joinings between all
patches of the same type, multiplied by 100 to convert to a percentage.
Units
Percent
Range
0 # CONNECT # 100
CONNECT = 0 when either the landscape consists of a single patch, or all classes
consist of a single patch, or none of the patches in the landscape are "connected"
(i.e., within the user-specified threshold distance of another patch of the same
type). CONNECT = 100 when every patch in the landscape is "connected."
162
Comments
Connectance is defined on the number of functional joinings between patches of the
same type, where each pair of patches is either connected or not based on a userspecified distance criterion. Connectance is reported as a percentage of the
maximum possible connectance given the number of patches. Note, connectance
can be based on either Euclidean distance or functional distance.
163
Diversity Metrics
Background.–Diversity measures have been used extensively in a variety of ecological applications.
They originally gained popularity as measures of plant and animal species diversity. There has been
a proliferation of diversity indices and we will make no attempt to review them here. FRAGSTATS
computes 3 diversity indices. These diversity measures are influenced by 2 components--richness
and evenness. Richness refers to the number of patch types present; evenness refers to the
distribution of area among different types. Richness and evenness are generally referred to as the
compositional and structural components of diversity, respectively. Some indices (e.g., Shannon's
diversity index) are more sensitive to richness than evenness. Thus, rare patch types have a
disproportionately large influence on the magnitude of the index. Other indices (e.g., Simpson's
diversity index) are relatively less sensitive to richness and thus place more weight on the common
patch types. These diversity indices have been applied by landscape ecologists to measure one aspect
of landscape structure--landscape composition (e.g., Romme 1982, O'Neill et al. 1988, Turner
1990a).
FRAGSTATS Metrics.–FRAGSTATS computes several statistics that quantify diversity at the
landscape level. These metrics quantify landscape composition at the landscape level; they are not
affected by the spatial configuration of patches. The most popular diversity index is Shannon's diversity
index (SHDI) based on information theory (Shannon and Weaver 1949). The value of this index
represents the amount of "information" per individual (or patch, in this case). Information is a
somewhat abstract mathematical concept that we will not attempt to define. The absolute magnitude
of Shannon's diversity index is not particularly meaningful; therefore, it is used as a relative index for
comparing different landscapes or the same landscape at different times. Simpson's diversity index
(SIDI) is another popular diversity measure that is not based on information theory (Simpson 1949).
Simpson's index is less sensitive to the presence of rare types and has an interpretation that is much
more intuitive than Shannon's index. Specifically, the value of Simpson's index represents the
probability that any two cells selected at random would be different patch types. Thus, the higher
the value the greater the likelihood that any 2 randomly drawn cells would be different patch types.
Because Simpson's index is a probability, it can be interpreted in both absolute and relative terms.
FRAGSTATS also computes a modified Simpson's diversity index (MSIDI) based on Pielou's (1975)
modification of Simpson's diversity index; this index was used by Romme (1982). The modification
eliminates the intuitive interpretation of Simpson's index as a probability, but transforms the index
into one that belongs to a general class of diversity indices to which Shannon's diversity index
belongs (Pielou 1975). Thus, the modified Simpson's and Shannon's diversity indices are similar in
many respects and have the same applicability.
Patch richness (PR) measures the number of patch types present; it is not affected by the relative
abundance of each patch type or the spatial arrangement of patches. Therefore, two landscapes may
have very different structure yet have the same richness. For example, one landscape may be
comprised of 96% patch type A and 1% each of patch types B-E, whereas another landscape may be
comprised of 20% each of patch types A-E. Although patch richness would be the same, the
functioning of these landscapes and the structure of the animal and plant communities would likely
be greatly different. Because richness does not account for the relative abundance of each patch
type, rare patch types and common patch types contribute equally to richness. Nevertheless, patch
richness is a key element of landscape structure because the variety of landscape elements present in
164
a landscape can have an important influence on a variety of ecological processes. Because many
organisms are associated with a single patch type, patch richness often correlates well with species
richness.
Richness is partially a function of scale. Larger areas are generally richer because there is generally
greater heterogeneity over larger areas than over comparable smaller areas. This contributes to the
species-area relationship predicted by island biogeographic theory (MacArthur and Wilson 1967).
Therefore, comparing richness among landscapes that vary in size can be problematic. Patch richness
density (PRD) standardizes richness to a per area basis that facilitates comparison among landscapes,
although it does not correct for this interaction with scale. FRAGSTATS also computes a relative
richness index. Relative patch richness (RPR) is similar to patch richness, but it represents richness as a
percentage of the maximum potential richness as specified by the user (Romme 1982). This form
may have more interpretive value than absolute richness or richness density in some applications.
Note that relative patch richness and patch richness are completely redundant and would not be
used simultaneously in any subsequent statistical analysis.
Evenness measures the other aspect of landscape diversity--the distribution of area among patch
types. There are numerous ways to quantify evenness and most diversity indices have a
corresponding evenness index derived from them. In addition, evenness can be expressed as its
compliment--dominance (i.e., evenness = 1 - dominance). Indeed, dominance has often been the
chosen form in landscape ecological investigations (e.g., O'Neill et al. 1988, Turner et al. 1989,
Turner 1990a), although we prefer evenness because larger values imply greater landscape diversity.
FRAGSTATS computes three evenness indices (Shannon's evenness index, SHEI; Simpson's evenness
index, SIEI; modified Simpson's evenness index, MSIEI), corresponding to the three diversity indices.
Each evenness index isolates the evenness component of diversity by controlling for the
contribution of richness to the diversity index. Evenness is expressed as the observed level of
diversity divided by the maximum possible diversity for a given patch richness. Maximum diversity
for any level of richness is achieved when there is an equal distribution of area among patch types.
Therefore, the observed diversity divided by the maximum diversity (i.e., equal distribution) for a
given number of patch types represents the proportional reduction in the diversity index attributed
to lack of perfect evenness. As the evenness index approaches 1, the observed diversity approaches
perfect evenness. Because evenness is represented as a proportion of maximum evenness, Shannon's
evenness index does not suffer from the limitation of Shannon's diversity index with respect to
interpretability.
Limitations.–The use of diversity measures in community ecology has been heavily criticized
because diversity conveys no information on the actual species composition of a community.
Species diversity is a community summary measure that does not take into account the uniqueness
or potential ecological, social, or economical importance of individual species. A community may
have high species diversity yet be comprised largely of common or undesirable species. Conversely,
a community may have low species diversity yet be comprised of especially unique, rare, or highly
desired species. Although these criticisms have not been discussed explicitly with regards to the
landscape ecological application of diversity measures, these criticisms are equally valid when
diversity measures are applied to patch types instead of species. In addition, diversity indices like
Shannon’s index and Simpson’s index combine richness and evenness components into a single
measure, even though it is usually more informative to evaluate richness and evenness
165
independently.
Code
Metric (acronym)
Landscape Metrics
L1
Patch Richness (PR)
L2
Patch Richness Density (PRD)
L3
Relative Patch Richness (RPR)
L4
Shannon’s Diversity Index (SHDI)
L5
Simpson’s Diversity Index (SIDI)
L6
Modified Simpson’s Diversity Index (MSIDI)
L7
Shannon’s Evenness Index (SHEI)
L8
Simpson’s Evenness Index (SIEI)
L9
Modified Simpson’s Evenness Index (MSIEI)
(L1) Patch Richness
m=
number of patch types (classes) present in the landscape,
excluding the landscape border if present.
Description
PR equals the number of different patch types present within the landscape
boundary.
Units
None
Range
PR $ 1, without limit
Comments
Patch richness is perhaps the simplest measure of landscape composition, but note
that it does not reflect the relative abundances of patch types. Note, this metric is
redundant with both patch richness density and relative patch richness.
(L2) Patch Richness Density
m=
A=
Description
number of patch types (classes) present in the
landscape, excluding the landscape border if
present.
total landscape area (m2).
PR equals the number of different patch types present within the landscape
boundary divided by total landscape area (m2), multiplied by 10,000 and 100 (to
convert to 100 hectares). Note, total landscape area (A) includes any internal
background present.
166
Units
Number per 100 hectares
Range
PRD > 0, without limit
Comments
Patch richness density standardizes richness to a per area basis that facilitates
comparison among landscapes. Note, this metric is redundant with both patch
richness and relative patch richness.
(L3) Relative Patch Richness
m=
number of patch types (classes) present in the
landscape, excluding the landscape border if present.
Description
RPR equals the number of different patch types present within the landscape
boundary divided by the maximum potential number of patch types specified by
the user, based on the particular patch type classification scheme, multiplied by
100 (to convert to percent).
Units
Percent
Range
0 < RPR # 100
RPR approaches 0 when the landscape contains a single patch type, yet the
number of potential patch types is very large. RPR = 100 when all possible patch
types are represented in the landscape.
Comments
Relative patch richness is similar to patch richness, but it represents richness as a
percentage of the maximum potential richness as specified by the user. Note, this
metric is redundant with both patch richness and patch richness density.
(L4) Shannon's Diversity Index
Pi =
proportion of the landscape occupied by patch
type (class) i.
Description
SHDI equals minus the sum, across all patch types, of the proportional abundance
of each patch type multiplied by that proportion. Note, Pi is based on total
landscape area (A) excluding any internal background present.
Units
Information
167
Range
SHDI $ 0, without limit
SHDI = 0 when the landscape contains only 1 patch (i.e., no diversity). SHDI
increases as the number of different patch types (i.e., patch richness, PR) increases
and/or the proportional distribution of area among patch types becomes more
equitable.
Comments
Shannon’s diversity index is a popular measure of diversity in community ecology,
applied here to landscapes. Shannon’s index is somewhat more sensitive to rare
patch types than Simpson’s diversity index.
(L5) Simpson's Diversity Index
Pi =
proportion of the landscape occupied by patch type
(class) i.
Description
SIDI equals 1 minus the sum, across all patch types, of the proportional
abundance of each patch type squared. Note, Pi is based on total landscape area
(A) excluding any internal background present.
Units
None
Range
0 # SIDI < 1
SIDI = 0 when the landscape contains only 1 patch (i.e., no diversity). SIDI
approaches 1 as the number of different patch types (i.e., patch richness, PR)
increases and the proportional distribution of area among patch types becomes
more equitable.
Comments
Simpson’s diversity index is another popular diversity measure borrowed from
community ecology. Simpson's index is less sensitive to the presence of rare types
and has an interpretation that is much more intuitive than Shannon's index.
Specifically, the value of Simpson's index represents the probability that any 2
pixels selected at random would be different patch types.
(L6) Modified Simpson's Diversity Index
Pi =
Description
proportion of the landscape occupied by patch type
(class) i.
MSIDI equals minus the logarithm of the sum, across all patch types, of the
proportional abundance of each patch type squared. Note, Pi is based on total
landscape area (A) excluding any internal background present.
168
Units
None
Range
MSIDI $ 0, without limit
MSIDI = 0 when the landscape contains only 1 patch (i.e., no diversity). MSIDI
increases as the number of different patch types (i.e., patch richness, PR) increases
and the proportional distribution of area among patch types becomes more
equitable.
Comments
Modified Simpson's diversity index eliminates the intuitive interpretation of Simpson's
index as a probability, but transforms the index into one that belongs to a general
class of diversity indices to which Shannon's diversity index belongs.
(L7) Shannon's Evenness Index
Pi =
m=
proportion of the landscape occupied by patch type
(class) i.
number of patch types (classes) present in the
landscape, excluding the landscape border if present.
Description
SHEI equals minus the sum, across all patch types, of the proportional abundance
of each patch type multiplied by that proportion, divided by the logarithm of the
number of patch types. In other words, the observed Shannon's Diversity Index
divided by the maximum Shannon's Diversity Index for that number of patch
types. Note, Pi is based on total landscape area (A) excluding any internal
background present.
Units
None
Range
0 # SHEI # 1
SHDI = 0 when the landscape contains only 1 patch (i.e., no diversity) and
approaches 0 as the distribution of area among the different patch types becomes
increasingly uneven (i.e., dominated by 1 type). SHDI = 1 when distribution of
area among patch types is perfectly even (i.e., proportional abundances are the
same).
Comments
Shannon’s evenness index is expressed such that an even distribution of area among
patch types results in maximum evenness. As such, evenness is the complement of
dominance.
(L8) Simpson's Evenness Index
169
Pi =
m=
proportion of the landscape occupied by patch type
(class) i.
number of patch types (classes) present in the
landscape, excluding the landscape border if present.
Description
SIEI equals 1 minus the sum, across all patch types, of the proportional
abundance of each patch type squared, divided by 1 minus 1 divided by the
number of patch types. In other words, the observed Simpson's Diversity Index
divided by the maximum Simpson's Diversity Index for that number of patch
types. Note, Pi is based on total landscape area (A) excluding any internal
background present.
Units
None
Range
0 # SIEI # 1
SIDI = 0 when the landscape contains only 1 patch (i.e., no diversity) and
approaches 0 as the distribution of area among the different patch types becomes
increasingly uneven (i.e., dominated by 1 type). SIDI = 1 when distribution of area
among patch types is perfectly even (i.e., proportional abundances are the same).
Comments
Simpson’s evenness index is expressed such that an even distribution of area among
patch types results in maximum evenness. As such, evenness is the complement of
dominance.
(L9) Modified Simpson's Evenness Index
Pi =
m=
proportion of the landscape occupied by patch type
(class) i.
number of patch types (classes) present in the
landscape, excluding the landscape border if present.
Description
MSIEI equals minus the logarithm of the sum, across all patch types, of the
proportional abundance of each patch type squared, divided by the logarithm of
the number of patch types. In other words, the observed modified Simpson's
diversity index divided by the maximum modified Simpson's diversity index for
that number of patch types. Note, Pi is based on total landscape area (A) excluding
any internal background present.
Units
None
170
Range
0 # MSIEI # 1
MSIDI = 0 when the landscape contains only 1 patch (i.e., no diversity) and
approaches 0 as the distribution of area among the different patch types becomes
increasingly uneven (i.e., dominated by 1 type). MSIDI = 1 when distribution of
area among patch types is perfectly even (i.e., proportional abundances are the
same).
Comments
Modified Simpson’s evenness index is expressed such that an even distribution of area
among patch types results in maximum evenness. As such, evenness is the
complement of dominance.
171
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