FRAGSTATS SPATIAL PATTERN ANALYSIS PROGRAM FOR QUANTIFYING LANDSCAPE STRUCTURE

FRAGSTATS SPATIAL PATTERN ANALYSIS PROGRAM FOR QUANTIFYING LANDSCAPE STRUCTURE
FRAGSTATS
________________________________
SPATIAL PATTERN ANALYSIS PROGRAM
FOR
QUANTIFYING LANDSCAPE STRUCTURE
________________________________
Version 2.0
by
KEVIN MCGARIGAL1
Forest Science Department, Oregon State University, Corvallis, OR 97331
(303) 882-2114
BARBARA J. MARKS
Forest Science Department, Oregon State University, Corvallis, OR 97331
(503) 750-7287
March, 1994
1
Present address:
[(303) 882-2114]
P.O. Box 606, Dolores, Colorado 81323-9998
PREFACE and 2.0 UPGRADE INFORMATION
As the authors of FRAGSTATS, we are VERY concerned about the potential for misuse of
this program. Like most tools, FRAGSTATS is only as "good" as the user. FRAGSTATS
crunches out a lot of numbers about the input landscape. These numbers can easily become
"golden" in the hands of uninformed users. Unfortunately, the "garbage in-garbage out" axiom
applies here. We have done our best in the documentation to stress the importance of defining
landscape, patch, matrix, and landscape context at a scale and in a manner that is relevant and
meaningful to the phenomenon under consideration. Moreover, we have stressed the importance
of understanding the exact meaning of each metric before it is used. These and other important
considerations in any landscape structural analysis are discussed in the documentation. We
strongly urge you to read the entire documentation, especially the section on Key Concepts and
Terminology, before ever running FRAGSTATS.
We wish to remind users that we are not in the commercial software marketing business. We
are scientists who recognized the need for a tool like FRAGSTATS to assist us in our research on
landscape ecological issues. Therefore, we do not wish to spend a great deal of time consulting
on trivial matters concerning the use of FRAGSTATS. However, we do recognize an obligation
to provide some level of information support. Of course, we welcome and encourage your
criticisms and suggestions about the program at all times. We will welcome questions about how
to run FRAGSTATS or interpret the output only after the user has read the entire documentation.
This is only fair and will eliminate many trivial questions. Finally, we are always interested in
learning about how others have applied FRAGSTATS in ecological investigations and
management applications. Therefore, we encourage you to contact us and describe your
application after using FRAGSTATS.
This release of FRAGSTATS (version 2.0) differs from the previous version in only minor
ways. Several "bugs" have been corrected. The most important change is the added option to
treat a specified proportion of the landscape boundary and background edge (instead of just all or
none) as true edge in the edge metrics (bound_wght option). This fraction also is used as the
edge contrast weight for landscape boundary and background edge segments in the calculation of
edge contrast metrics. In addition, the convention for naming the output file containing patch
ID's in the raster version has been modified to comply with DOS requirements on a PC
(id_image option). Similarly, the output file name extensions in the PC raster version have been
shortened and renamed to comply with DOS requirements and to avoid conflicts with ERDAS
conventions (out_file). The Nearest-neighbor algorithm has been modified slightly to compute
actual edge-to-edge distance (previous version used cell midpoints rather than edge).
We hope that FRAGSTATS is of great assistance in your work and we look forward to
hearing about your applications.
ABSTRACT
Landscape ecology involves the study of landscape patterns, the interactions among patches
within a landscape mosaic, and how these patterns and interactions change over time. In
addition, landscape ecology involves the application of these principles in the formulation and
solving of real-world problems. Landscape ecology is largely founded on the notion that the
patterning of landscape elements (patches) strongly influences ecological characteristics,
including vertebrate populations. The ability to quantify landscape structure is prerequisite to the
study of landscape function and change. For this reason, much emphasis has been placed on
developing methods to quantify landscape structure. Most of the efforts to date have been
tailored to meet the needs of specific research objectives and have employed user-generated
computer programs to perform the analyses. Such user-generated programs allow for the
inclusion of customized analytical methods and easy linkages to other programs such as spatial
simulation models, yet generally lack the advanced graphics capabilities of commercially
available GIS. Most of these user-generated programs are limited to a particular hardware
environment, are embedded within a larger software package designed to accomplish a specific
research objective, do not offer a broad array of landscape metrics, and are designed to analyze
raster images only.
This report describes a program called FRAGSTATS that we developed to quantify
landscape structure. FRAGSTATS offers a comprehensive choice of landscape metrics and was
designed to be as versatile as possible. Moreover, the program is almost completely automated
and thus requires little technical training. Two separate versions of FRAGSTATS exist; one for
vector images and one for raster images. The vector version is an Arc/Info AML that accepts
Arc/Info polygon coverages. The raster version is a C program that accepts ASCII image files, 8
or 16 bit binary image files, Arc/Info SVF files, Erdas image files, and IDRISI image files. Both
versions of FRAGSTATS generate the same array of metrics, including a variety of area metrics,
patch density, size and variability metrics, edge metrics, shape metrics, core area metrics,
diversity metrics, and contagion and interspersion metrics. The raster version also computes
several nearest-neighbor metrics.
In this report, each metric calculated by FRAGSTATS is described in terms of its ecological
application and limitations. Example landscapes are included and a discussion is provided of
each metric as it relates to the sample landscapes. In addition, several important concepts and
definitions critical to the assessment of landscape structure are discussed. The appendices
include a complete list of algorithms, the units and ranges of each metric, examples of the
FRAGSTATS output files, and a users guide that describes in detail how to install and run
FRAGSTATS.
ACKNOWLEDGEMENTS and DISCLAIMER
Many individuals provided valuable feedback during the development and many revisions of
the software, including Steve Garman, Eric Gustafson, Jeff Nighbert, Tom Moore, Catherine
Rogers, and David Wallin. We are especially grateful to Catherine Rogers and Eric Gustafson
for their comprehensive and detailed testing of the program and their many useful suggestions.
We thank Jim Kiser for conducting the photogrammetry and digitization work on the landscapes
used in the documentation examples. Initial funding for this project was provided through the
Coastal Oregon Productivity Enhancement (COPE) program; COPE is a cooperative research
and technology transfer effort among Oregon State University, USDA Forest Service, USDI
Bureau of Land Management, other state and federal agencies, forest industry, county
governments, and resource protection organizations. Subsequent funding for the completion of
this documentation was provided by the USDI Bureau of Land Management Cooperative
Research Unit and the USDA Forest Service, Pacific Northwest Research Station, Corvallis,
Oregon.
This software is in the public domain, and the recipient may not assert any proprietary rights
thereto nor represent it to anyone as other than an Oregon State University-produced program.
FRAGSTATS is provided "as-is" without warranty of any kind, including, but not limited to, the
implied warranties of merchantability and fitness for a particular purpose. The user assumes all
responsibility for the accuracy and suitability of this program for a specific application. In no
event will the authors or Oregon State University be liable for any damages, including lost
profits, lost savings, or other incidental or consequential damages arising from the use of or the
inability to use this program.
TABLE OF CONTENTS
Page
INTRODUCTION
1
CONCEPTS AND DEFINITIONS
3
FRAGSTATS OVERVIEW
12
FRAGSTATS METRICS
21
General Considerations
Area Metrics
Patch Density, Size and Variability Metrics
Edge Metrics
Shape Metrics
Core Area Metrics
Nearest-Neighbor Metrics
Diversity Metrics
Contagion and Interspersion Metrics
21
23
27
31
36
39
45
49
51
LITERATURE CITED
54
APPENDICES
61
Appendix A. Example of the FRAGSTATS output file formatted exclusively for display
purposes (i.e., "basename".full). Each run of FRAGSTATS on a landscape produces an
output file like this one. The results reported here correspond to the landscape displayed
in figure 6 (landscape B). The results obtained using the vector and raster versions of
FRAGSTATS are included separately; note the differences in indices involving edge
lengths and patch perimeters.
Appendix B. FRAGSTATS user guidelines.
Appendix C. Definition and description of FRAGSTATS metrics.
LIST OF FIGURES
Figure
Page
1. Multi-scale view of "landscape" from an organism-centered perspective. Because the eagle,
cardinal, and butterfly perceive their environments differently and at different scales, what
constitutes a single habitat patch for the eagle may constitute an entire landscape or patchmosaic for the cardinal, and a single habitat patch for the cardinal may comprise an entire
landscape for the butterfly that perceives patches on an even finer scale.
4
2. Alternative image formats accepted in the vector version of FRAGSTATS. Landscape
boundary, background, and border are defined in the text.
15
3. Alternative image formats accepted in the raster version of FRAGSTATS. Landscape
boundary, background, and border are defined in the text.
16
4. Example of FRAGSTATS patch indices for 3 sample patches drawn from a sample
landscape. See text and Appendix C for a description and definition of each metric.
Indices with a '*' were computed using the raster version of FRAGSTATS.
19
5. Example of FRAGSTATS class indices for the mixed, large sawtimber (MLS) patch type
in 3 sample landscapes. See text and Appendix C for a description and definition of each
metric. Indices with a '*' were computed using the raster version of FRAGSTATS.
20
6. Example of FRAGSTATS landscape indices for 3 sample landscapes. See text and
Appendix C for a description and definition of each metric. Indices with a '*' were
computed using the raster version of FRAGSTATS.
21
LIST OF TABLES
Table
1. Metrics computed in FRAGSTATS, grouped by subject area. See Appendix C for a
mathematical definition of each metric.
Page
24
INTRODUCTION
Growing concerns over the loss of biodiversity has spurred land managers to seek better ways
of managing landscapes at a variety of spatial and temporal scales. A number of developments
have made possible the ability to analyze and manage entire landscapes to meet multi-resource
objectives. The developing field of landscape ecology has provided a strong conceptual and
theoretical basis for understanding landscape structure, function, and change (Forman and
Godron 1986, Urban et al. 1987, Turner 1989). Growing evidence that habitat fragmentation is
detrimental to many species and may contribute substantially to the loss of regional and global
biodiversity (Saunders et al. 1991, Harris 1984) has provided empirical justification for the need
to manage entire landscapes, not just the components. The development of GIS technology, in
particular, has made a variety of analytical tools available for analyzing and managing
landscapes. In response to this growing theoretical and empirical support and technical
capabilities, public land management agencies have begun to recognize the need to manage
natural resources at the landscape scale.
A good example of these changes is in the field of wildlife science. Wildlife ecologists often
have assumed that the most important ecological processes affecting wildlife populations and
communities operate at local spatial scales (Dunning et al. 1992). Vertebrate species richness
and abundance, for example, often are considered to be functions of variation in local resource
availability, vegetation composition and structure, and the size of the habitat patch (MacArthur
and MacArthur 1961, Willson 1974, Cody 1985). Correspondingly, most wildlife research and
management activities have focussed on the within-patch scale, typically small plots or forest
stands. Wildlife ecologists have become increasingly aware, however, that habitat variation and
its affects on ecological processes and vertebrate populations occurs at a wide range of spatial
scales (Wiens 1989a,b). In particular, there has been increasing awareness of the potential
importance of coarse-scale habitat patterns to wildlife populations, and there has been a
corresponding surge in landscape ecological investigations that examine vertebrate distributions
and population dynamics over broader spatial scales (e.g., McGarigal and McComb 1994). The
recent attention on metapopulation theory (Gilpin and Hanski 1991) and the proliferation of
mathematical models on dispersal and spatially distributed populations (Kareiva 1990) are
testimony to these changes. Moreover, recent conservation efforts for the northern spotted owl
(Strix occidentalis caurina) demonstrate the willingness and ability of public land management
agencies to analyze and manage wildlife populations at the landscape scale (Lamberson et al.
1992, Murphy and Noon 1992, Thomas et al. 1990).
The emergence of landscape ecology to the forefront of ecology is testimony to the growing
recognition that ecological processes affect and are affected by the dynamic interaction among
ecosystems. This surge in interest in landscape ecology also has become manifest in a wave of
recent efforts to incorporate a landscape perspective into policies and guidelines for managing
public lands. Landscape ecology embodies a way of thinking that many see as very useful for
organizing land management approaches. Specifically, landscape ecology focusses on 3
characteristics of the landscape (Forman and Godron, 1986):
"(1) Structure, the spatial relationships among the distinctive ecosystems or "elements"
present--more specifically, the distribution of energy, materials, and species in relation to
2
the sizes, shapes, numbers, kinds, and configurations of the ecosystems.
(2) Function, the interactions among the spatial elements, that is, the flows of energy,
materials, and species among the component ecosystems.
(3) Change, the alteration in the structure and function of the ecological mosaic over
time."
Thus, landscape ecology involves the study of landscape patterns, the interactions among patches
within a landscape mosaic, and how these patterns and interactions change over time. In
addition, landscape ecology involves the application of these principles in the formulation and
solving of real-world problems. Landscape ecology considers the development and dynamics of
spatial heterogeneity and its affects on ecological processes, and the management of spatial
heterogeneity (Risser et al. 1984).
Landscape ecology is largely founded on the notion that the patterning of landscape elements
(patches) strongly influences ecological characteristics, including vertebrate populations. The
ability to quantify landscape structure is prerequisite to the study of landscape function and
change. For this reason, much emphasis has been placed on developing methods to quantify
landscape structure (e.g., O'Neill et al. 1988, Li 1990, Turner 1990a, Turner and Gardner 1991).
Most of the efforts to date have been tailored to meet the needs of specific research objectives
and have employed user-generated computer programs to perform the analyses. Such usergenerated programs allow for the inclusion of customized analytical methods and easy linkages
to other programs such as spatial simulation models, yet generally lack the advanced graphics
capabilities of commercially available GIS (Turner 1990a). Most of these user-generated
programs are limited to a particular hardware environment or are embedded within a larger
software package designed to accomplish a specific research objective (e.g., to model fire
disturbance regimes). Of the available software programs that we are aware of, none offer a
broad array of landscape metrics and all are designed to analyze raster images only.
This report describes a program called FRAGSTATS that we developed to quantify
landscape structure. FRAGSTATS offers a comprehensive choice of landscape metrics and was
designed to be as versatile as possible. Moreover, the program is almost completely automated
and thus requires little technical training. Two separate versions of FRAGSTATS exist; one for
vector images and one for raster images. The vector version is an Arc/Info AML that accepts
Arc/Info polygon coverages. The raster version is a C program that accepts ASCII image files, 8
or 16 bit binary image files, Arc/Info SVF files, Erdas image files, and IDRISI image files. Both
versions of FRAGSTATS generate the same array of metrics, although a few additional metrics
are computed in the raster version.
In this report, each metric calculated by FRAGSTATS is described in terms of its ecological
application and limitations. Example landscapes are included and a discussion is provided of
each metric as it relates to the sample landscapes. In addition, several important concepts and
definitions critical to the assessment of landscape structure are discussed. The appendices
3
include a complete list of algorithms, the units and ranges of each metric, examples of the
FRAGSTATS output files, and a users guide that describes in detail how to install and run
FRAGSTATS.
CONCEPTS AND DEFINITIONS
It is beyond the scope and purpose of this document to provide a glossary of terms and a
comprehensive discussion of the many concepts embodied in landscape ecology. Instead, a few
key terms and concepts essential to the use of FRAGSTATS and the measurement of spatial
heterogeneity are defined and discussed; a thorough understanding of these concepts is
prerequisite to the effective use of FRAGSTATS.
Landscape.--What is a "landscape"? Surprisingly, there are many different interpretations of
this well-used term. 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. 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 of the environment (Wiens 1976)(i.e., each organism defines
habitat patches differently and at different scales), 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 (Fig. 1).
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 organismcentered 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 wildlife habitats
4
Figure 1. Multiscale view of “landscape” from an organism-centered perspective. Because the
eagle, cardinal, and butterfly perceive their environments differently and at different scales, what
constitutes a single habitat patch for the eagle may constitute an entire landscape or patch-mosaic
for the cardinal, and a single habitat patch for the cardinal may comprise an entire landscape for
the butterfly that perceives patches on an even finer scale.
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 1 scale.
KEY
POINT
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 landscape.
Patch.--What makes up a landscape? 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
5
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). We prefer the term patch, but 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" (Wiens 1976).
Patches are dynamic and occur on a variety of spatial and temporal scales that, from an
organism-centered perspective, vary as a function of each animal's perceptions (Wiens 1976 and
1989a, 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.
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 1 or more "domains of scale" (Wiens 1989a) at which the
6
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.
KEY
POINT
It is not our intent to argue for a particular definition of patch. Rather,
we 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 (i.e., patch type classification system) and at a scale appropriate to
the phenomenon under consideration.
Matrix.--A landscape is composed typically of several types of landscape elements (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.
KEY
POINT
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. This should be done prior to the analysis of landscape
structure since this decision will influence the choice and interpretation of
landscape metrics.
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
7
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
structure, 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 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
8
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 structure, until
more is learned, it is critical that any attempts to compare landscapes measured at different scales
be done cautiously.
KEY
POINT
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 structure 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
9
important for nearest-neighbor metrics. 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.
KEY
POINT
The important point is that a landscape should be defined relative to
both the patch mosaic 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.
Landscape Structure.--Landscapes are distinguished by spatial relationships among
component parts. A landscape can be characterized by both its composition and configuration
(sometimes referred to as landscape physiognomy or landscape pattern)[Dunning et al. 1992,
Turner 1989], and these 2 aspects of a landscape can independently or in combination affect
ecological processes and organisms. The difference between landscape composition and
configuration is analogous to the difference between floristics (e.g., the types of plant species
present) and vegetation structure (e.g., foliage height diversity) so commonly considered in
wildlife-habitat studies at the within-patch scale.
Landscape composition refers to features associated with the presence and amount of each
patch type within the landscape, but without being spatially explicit. In other words, landscape
composition encompasses the variety and abundance of patch types within a landscape, but not
the placement or location of patches within the landscape mosaic. Landscape composition is
important to many ecological processes and organisms. For example, many vertebrate species
require specific habitat types, and the total amount of suitable habitat (a function of landscape
composition) likely influences the occurrence and abundance of these vertebrate species. There
have been many attempts to model animal populations within landscapes based on landscape
composition alone; such models have been referred to as "island models" by Kareiva (1990).
Island models do represent the discrete patchwork mosaic of the landscape; the key feature of
these models is population subdivision. Yet these models do not specify the relative distances
among patches or their positions relative to each other. Thus, although these models provide
strong analytical solutions, they may be overly simplified for most natural populations. It is
important to note, however, that we have learned much about population dynamics in spatially
10
complex environments based on models of landscape composition alone (Kareiva 1990).
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. It is incumbent upon the investigator or
manager to choose the formulation that best represents their concerns.
Landscape configuration refers to the physical distribution or spatial character of patches
within the landscape. Some aspects of configuration, such as patch isolation or patch contagion,
are measures of the placement of patch types relative to other patch types, the landscape
boundary, 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 have been many attempts to
explicitly incorporate landscape configuration into models of ecological processes and
population dynamics within heterogeneous landscapes; such models have been referred to as
"stepping-stone models" by Kareiva (1990). In contrast to island models, stepping-stone models
have an explicit spatial dimension and can account for dispersal distances and environmental
variability with a spatial structure. Recently, there have been dramatic increases in the level of
sophistication in stepping-stone models and some results have had profound effects on the design
of managed landscapes (e.g., Lamberson et al. 1992, McKelvey et al. 1992).
There are many aspects of landscape configuration and the literature is replete with methods
and indices developed for representing them. Landscape configuration can be quantified using
statistics in terms of the landscape unit itself (i.e., the patch). The spatial pattern being
represented is the spatial character of the individual patches. The location of patches relative to
each other in the landscape (i.e., the configuration of patches within the landscape), is not
explicitly represented. Landscape metrics quantified in terms of the individual patches (e.g.,
mean patch core area, mean patch shape) are spatially explicit at the level of the individual patch.
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 landscape as a whole,
the average patch characteristics or some measure of variability in patch characteristics.
Although these metrics are not spatially explicit at the landscape level, they have clear ecological
relevance when considered from a patch dynamics standpoint (Pickett and White 1985). For
example, a number of bird species have been shown to be sensitive to patch core area (a function
of patch size and shape) because of negative intrusions from the surrounding landscape (e.g.,
Temple 1986, Robbins et al. 1989). Quantifying mean patch core area across the landscape
could provide a good index to landscape suitability for such species.
Landscape metrics quantified in terms of the spatial relationship of patches and matrix
comprising the landscape (e.g., nearest neighbor, contagion) are spatially explicit at the
landscape level because the relative location of individual patches within the landscape is
represented in some way. Such metrics represent a recognition that ecological processes and
organisms are affected by the interspersion and juxtaposition of patch types within the landscape.
11
For example, the population dynamics of species with limited dispersal ability are likely affected
by the distribution of suitable habitat patches. Both the distance between suitable patches and
the spatial arrangement of suitable patches can influence population dynamics (e.g., sensu
Kareiva 1990, Lamberson et al. 1992, McKelvey et al. 1992). Likewise, patch juxtaposition is
especially important to organisms that require $ 2 habitat types because the close proximity of
resources provided by different patch types is critical for their survival and reproduction. Patch
juxtaposition is also important for species adversely affected by edges because the types of
patches juxtaposed along an edge will influence the character of that edge.
A number of landscape configuration metrics can be formulated either in terms of the
individual patches or in terms of the whole landscape, depending on the emphasis sought. For
example, fractal dimension is a measure of shape complexity (Mandelbrot 1982, Burrough 1986,
Milne 1988) that can be computed for each patch and then averaged for the landscape, or it can
be computed from the landscape as a whole (e.g., using the box-count method, Morse et al.
1985). Similarly, core area can be computed for each patch and then represented as mean patch
core area for the landscape, or it can be computed simply as total core area in the 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 landscape) sought. The same is true for a number of other common landscape
metrics. Typically, these metrics are spatially explicit at the patch level but not at the landscape
level.
Not all landscape metrics can easily be classified as representing landscape composition or
landscape configuration. For example, landscape metrics such as mean patch size and patch
density are not really spatially explicit at either the patch or landscape level because they do not
depend explicitly on the spatial character of the patches or their relative location. Moreover,
mean patch size and patch density of a particular patch type reflect both the amount of a patch
type present (composition) and its spatial distribution (configuration). Because mean patch size
and patch density vary as a function of the spatial pattern complexity of the landscape, it is often
more appropriate to consider these indices of landscape configuration. In addition, there are
some landscape metrics that clearly represent pattern complexity but are not spatially explicit at
all. These metrics vary as a function of the heterogeneity of the landscape, but do not depend
explicitly on the relative location of patches within the landscape or their individual spatial
character. For example, total edge or edge density is a function of the amount of border between
patches. For a given edge density there could be 2 patches or 10 patches, they could be clustered
or maximally dispersed, or they could be skewed to one side of the landscape or in the middle. It
is not important that all metrics be classified according to the simple composition versus
configuration dichotomy. What is important, however, is that the investigator or manager
recognize that landscape structure consists of both composition and configuration and that
various metrics have been developed to represent these aspects of landscape structure separately
or in combination.
Finally, it is important to understand how measures of landscape structure are influenced by
the designation of a matrix element. If an element is designated as matrix and therefore
12
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.
KEY
POINT
The importance of fully understanding each landscape metric before it is
used cannot be emphasized enough. Specifically, these questions should be asked
of each metric before it is used: does it represent landscape composition,
configuration, or both; what aspect of configuration does it represent; what scale,
if any, is spatially explicit; how is it affected by the designation of a matrix
element? Based on answers to these questions, does the metric represent landscape
structure in a manner ecologically meaningful to the phenomenon under
consideration? Only after answering these questions should one attempt to draw
conclusions about the structure of the landscape analyzed.
FRAGSTATS OVERVIEW
FRAGSTATS is a spatial pattern analysis program for quantifying landscape structure. The
landscape subject to analysis is user-defined and can represent any spatial phenomenon.
FRAGSTATS quantifies the areal extent and spatial distribution of patches (i.e., polygons on a
map coverage) within a landscape; it is incumbent upon the user to establish a sound basis for
defining and scaling the landscape (including the extent and grain of the landscape) and the
scheme upon which patches within the landscape are classified and delineated (we strongly
recommend that you read the preceding section on Concepts and Definitions). The output from
FRAGSTATS is meaningful only if the landscape mosaic is meaningful relative to the
phenomenon under consideration.
FRAGSTATS does not limit the scale (extent or grain) of the landscape subject to analysis.
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).
There are 2 versions of FRAGSTATS; one that accepts Arc/Info polygon coverages (vector),
13
and one that accepts a raster image in a variety of formats. The vector version of FRAGSTATS
is an Arc/Info AML developed on a SUN workstation using Arc/Info version 6.1; it will not run
with earlier versions of Arc/Info. Because of limitations in Arc/Info, the AML calls several C
programs that were developed in a Unix environment and compiled with the GNU C compiler
(note, they may not compile with other compilers). The raster version of FRAGSTATS also was
developed on a SUN workstation in the Unix operating environment. It is written in C and also
compiled with the GNU C compiler. Both versions of FRAGSTATS respond to command line
input or allow the user to answer a series of prompts. Both versions of FRAGSTATS generate
the same array of metrics (see Table 1), although a few additional metrics (i.e., nearest-neighbor
metrics and contagion) are computed in the raster version, and the format of the output files is
exactly the same. The raster version of FRAGSTATS also has been compiled to run in the DOS
environment on a personal computer (PC). The directions for running the DOS version on a PC
are exactly the same as the Unix version.
It is important to realize that vector and raster images depict edges differently. Vector
images portray a line in the form it is digitized. Raster images, however, portray lines in stairstep fashion. Consequently, the measurement of edge length is biased upward in raster images;
that is, 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. As a result of this bias, the vector and raster versions of
FRAGSTATS will not produce identical results for a landscape.
In some investigations, it may be desirable or necessary to create a raster image from the
initial vector image and run the raster version of 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. 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) if the cell size chosen for the rasterization is too large relative to the
minimum patch dimension in the vector image.
FRAGSTATS accepts images in several forms, depending on whether the image contains
background and whether the landscape contains a border (Figs. 2 and 3). Every image will
include a landscape boundary that defines the perimeter of the landscape and surrounds the patch
mosaic of interest. An image may include background (also referred to as "mask"); an undefined
area either interior or exterior to 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 non-patch code, although it typically is set to a negative
integer. The background class is ignored in all metrics but those involving edge. The user
specifies how boundary and background edge segments should be handled (see below). 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 label must be -34. The border can
14
be any width and provides information on patch type adjacency for patches on the edge of the
landscape. It is ignored in all but the edge contrast, interspersion, and contagion 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.)[Hansen and di Castri 1992]. Accordingly, the user can
specify a file containing edge contrast weights for each combination of patch types (classes).
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 (see Edge Metrics below). If this weight file is not
provided, these edge contrast metrics are not computed and are reported as "NA" or "." in the
output files (see below). Generally, if a landscape border is designated, a weight file will be
specified also, because the main reason for specifying a border is when information on edge
contrast is deemed important. However, a border is also useful for determining patch type
adjacency for the interspersion and contagion indices. Any scheme can be used to establish
weights as long as it is meaningful with respect to the phenomenon under investigation.
Regardless of the image format (Figs. 2 and 3), the user must specify how the landscape
boundary and any edge segments bordering a specified background class should be treated with
regards to the edge metrics. This has various effects depending on whether a contrast weight file
is specified, whether a landscape border is present, and whether a background class is designated.
If a contrast weight file is specified, then all patch edges are evaluated for edge contrast based on
the weight file and the edge contrast metrics (see Edge Metrics below) are computed. In this
landscape border is present, then edge segments along the landscape boundary are evaluated for
edge contrast based on the weight file. Conversely, if a landscape border is absent, then edge
segments along the landscape boundary are treated as either maximum-contrast edge (weight =
1), no-contrast edge (weight = 0), or some intermediate, average-contrast edge (weight = user
specified), depending on how the user decides to handle boundary and background edge.
Regardless of whether a landscape border is present or not, if a background class is specified,
then edge segments bordering the background class are treated according to the user-specified
edge contrast. In other words, it is possible for a landscape border to be present and still have a
background class designated. The background may occur as "holes" in the landscape or along
the landscape boundary. In either case, edge segments bordering background are treated
according to the decision regarding boundary and background edge. Note, however, that the
presence of a landscape border and a background class and the decision on how to treat these
edges will have no affect on the edge contrast metrics if a contrast weight file is not specified-because these metrics will not be computed.
Regardless of whether an edge contrast weight file is specified, the presence of a landscape
border, the specification of a background class, and the decision regarding how to treat the
boundary and background edge will affect metrics based on patch type adjacency as well as those
based on edge length. Metrics based on patch type adjacency (e.g., interspersion and contagion
15
Figure 2. Alternative image formats accepted in the vector version of FRAGSTAST. Landscape
boundary, background, and border are defined in the text.
indices) consider only edge segments with adjacent patch information. Therefore, if a landscape
border is present, then edge segments along the border are considered in these calculations.
Conversely, if a landscape border is absent, then the entire landscape boundary is ignored in
these calculations. Similarly, if a background class is specified, then edge segments bordering
background are ignored in these calculations. 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 border are evaluated to determine which segments represent true edge
and which do not. Conversely, if a landscape border is absent, then a user-specified proportion
of the landscape boundary is treated as true edge and the remainder is ignored. For example, if
the user specifies that 50% of the landscape boundary/background should be treated as true edge,
then 50% of the landscape boundary will be incorporated into the edge length metrics.
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.
16
Figure 3. Alternative image formats accepted in the raster version of FRAGSTATS. Landscape
boundary, background, and border are defined in the text.
We recommend including a landscape border, especially if edge contrast 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 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 of how to treat the landscape boundary.
When edge-based metrics are of particular importance to the investigation and the landscapes are
17
small in extent and relatively homogeneous, the inclusion of a landscape border and the decision
regarding the landscape boundary should be considered carefully.
FRAGSTATS computes 3 groups of metrics. For a given landscape mosaic, FRAGSTATS
computes several statistics for (1) each patch in the mosaic (Fig. 4); (2) each patch type (class) in
the mosaic (Fig. 5); and (3) the landscape mosaic as a whole (Fig. 6)[see Table 1 for a
description of the acronyms for each metric]. In the assessment of landscape structure, patch
indices serve primarily as the computational basis for several of the landscape metrics; the
individual patch indices 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.
In many landscape ecological applications, the primary interest is in the amount and
distribution of a particular patch type (class). A good example is in the study of forest
fragmentation. Forest fragmentation is a landscape-level process in which forest tracts are
progressively sub-divided into smaller, geometrically more complex (initially but not necessarily
ultimately), and more isolated forest fragments as a result of both natural processes and human
land use activities (Harris 1984). 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. Forest fragmentation is the prevalent trajectory of landscape
change in several human-dominated forest regions of the world, and is increasingly becoming
recognized as a major cause of declining biodiversity (Whitcomb et al. 1981, Terborgh 1989).
Class indices separately quantify the amount and distribution of each patch type in the landscape
and thus can be considered indices of fragmentation for each patch type.
In many landscape ecological applications, the primary interest is in the structure (i.e.,
composition and pattern) of the entire landscape(s). A good example is in the study of landscape
diversity. Aldo Leopold (1933) noted that wildlife diversity was greater in more diverse
landscapes. Thus, the quantification of landscape diversity has assumed a preeminent role in
landscape ecology. A major focus of landscape ecology is on quantifying the relationships
between landscape structure and ecological processes. Consequently, much emphasis has been
placed on developing methods to quantify landscape structure (e.g., O'Neill et al. 1988, Li 1990,
Turner 1990a, Turner and Gardner 1991) and a great variety of landscape structural indices have
been developed for this purpose. Many of these published indices have been incorporated into
FRAGSTATS, although sometimes in modified form.
18
Figure 4. Example of FRAGSTATS patch indices for three sample patches drawn from a sample landscape. See
text and Appendix 3 for descriptions and definitions of the metrics. Indices with an asterisk were computed from
the raster version of FRAGSTATS.
19
Figure 5. Example of FRAGSTATS class indices for the mixed, large sawtimber (MLS) patch type in three sample
landscapes. See text and Appendix 3 for descriptions and definitions of the metrics. Indices with an asterisk were computed
from the raster version of FRAGSTATS.
20
Figure 6. Example of FRAGSTATS landscape indices for three sample landscapes. See text and Appendix 3 for descriptions
and definitions of the metrics. Indices with an asterisk were computed from the raster version of FRAGSTATS.
21
By default FRAGSTATS creates 4 output files. The user supplies a "basename" for the output
files and FRAGSTATS appends the extensions .full, .patch, .class, and .land to the basename.
All files created are ASCII and viewable. However, only the "basename".full file is in a format
intended for displaying results. The "basename".full file contains all the patch, class, and
landscape metrics calculated for an input landscape (see Appendix A for an example of the
"basename".full file). The name of each metric is spelled out along with its value and units.
This file's main utility is for viewing results; its format is not intended for input to other data
management or analysis programs.
The other 3 files are formatted to facilitate input into database management programs. The
"basename".patch file contains the patch metrics for a landscape; the file contains 1 record for
each patch in the landscape. Similarly, the "basename".class file contains the class metrics; the
file contains 1 record for each class in the landscape. Finally, the "basename".land file contains
the landscape metrics; the file contains 1 record for the landscape. The first record in all of these
files is a header consisting of the acronyms for all the metrics that follow. The user has the
option of suppressing the output of the patch and/or class metrics. If these metrics are
suppressed, the corresponding "basename" ASCII file is not created and the metrics are not
included in the "basename".full file.
FRAGSTATS METRICS
This section provides a general overview and discussion of the various metrics computed in
FRAGSTATS; detailed mathematical definitions and descriptions of each metric, including the
units and range in values, are provided in Appendix C. Metrics are grouped in logical fashion
according to the aspect of landscape structure measured. For example, the core area metrics (i.e.,
those based on core area measurements) computed at the patch, class, and landscape levels are
discussed together. For each group, the general applicability of the metrics to landscape
ecological investigations and some of their limitations are discussed. In addition, the results
presented in Figures 4-6 are discussed relative to each group of metrics at the end of each section
(in reduced font size on a shaded background).
General Considerations
Metrics involving standard deviation employ the population standard deviation formula, not
the sample formula, because all patches in the landscape (or class) are included in the
calculations. In other words, the landscape is considered a population of patches and every patch
is counted; FRAGSTATS does not sample patches from the landscape, it censuses the entire
landscape. Even if each landscape represents a sample from a larger region, it is still more
appropriate to compute the standard deviation for each landscape using the population formula.
In this case it would be appropriate to use the sample formula when calculating the variation
among landscapes using the FRAGSTATS output for each landscape. The difference between
the population and sample formulas is insignificant when sample sizes (i.e., number of patches)
22
are large (e.g., > 20). However, when quantifying landscapes with a small number of patches the
differences can be significant.
FRAGSTATS computes several statistics for each patch and class 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. As previously discussed,
composition and configuration can affect ecological processes independently and interactively.
Thus, it is especially important to understand for each metric what aspect of landscape structure
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 structure. 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 structure 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; not because they measure the same aspect of
landscape structure, but because for the particular landscapes under investigation, different
aspects of landscape structure 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 (see Appendix C). 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
fragmentation 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 structure. Hence, it is important to interpret each index in a manner appropriate to its
scale (patch, class, or landscape).
23
Area Metrics
FRAGSTATS computes several simple statistics representing area at the patch, class, and
landscape levels (Table 1). Area metrics quantify landscape composition, not landscape
configuration. 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. 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). 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.
Class area (CA) is a measure of landscape composition; specifically, how much of the
landscape is comprised of a particular patch type. This is an important measure in a number of
ecological applications. For example, an important by-product of habitat fragmentation is
quantitative 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 1
contiguous patch. For example, northern spotted owls have minimum area requirements for lateseral 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 is
used in the computations for many of the class and landscape metrics.
Total landscape area (TA) often does not have a great deal of interpretive value with regards
to evaluating landscape structure, 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. Total landscape area is included as both a class and landscape index (and
included in the corresponding output files) because it is important regardless of whether the
primary interest is in class or landscape indices.
24
Table 1. Metrics computed in FRAGSTATS, grouped by subject area. See Appendix C for a
mathematical definition of each metric.
__________________________________________________________________________________________
Scale
Acronym
Metric (units)
__________________________________________________________________________________________
Area metrics
Patch
Patch
Class
Class
Class/landscape
Class/landscape
AREA
LSIM
CA
%LAND
TA
LPI
Area (ha)
Landscape similarity index (%)
Class area (ha)
Percent of landscape (%)
Total landscape area (ha)
Largest patch index (%)
Patch density, patch size and variability metrics
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
NP
PD
MPS
PSSD
PSCV
Number of patches (#)
Patch density (#/100 ha)
Mean patch size (ha)
Patch size standard deviation (ha)
Patch size coefficient of variation (%)
PERIM
EDCON
TE
ED
CWED
TECI
MECI
AWM ECI
Perimeter (m)
Edge contrast index (%)
Total edge (m)
Edge density (m/ha)
Contrast-weighted edge density (m/ha)
Total edge contrast index (%)
Mean edge contrast index (%)
Area-weighted mean edge contrast index (%)
SHAPE
FRACT
LSI
MSI
AWM SI
DLFD
MPFD
AWM PFD
Shape index
Fractal dimension
Landscape shape index
Mean shape index
Area-weighted mean shape index
Double log fractal dimension
Mean patch fractal dimension
Area-weighted mean patch fractal dimension
CORE
NCORE
Core area (ha)
Number of core areas (#)
Edge m etrics
Patch
Patch
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Shape metrics
Patch
Patch
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Core area metrics
Patch
Patch
25
Table 1. Continued.
__________________________________________________________________________________________
Scale
Acronym
Metric (units)
__________________________________________________________________________________________
Core area metrics--continued.
Patch
Class
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
Class/landscape
CAI
C%LAND
TCA
NCA
CAD
MCA1
CASD1
CACV1
MCA2
CASD2
CACV2
TCAI
MCAI
Core area index (%)
Core area percent of landscape (%)
Total core area (ha)
Number of core areas (#)
Core area density (#/100 ha)
Mean core area per patch (ha)
Patch core area standard deviation (ha)
Patch core area coefficient of variation (%)
Mean area per disjunct core (ha)
Disjunct core area standard deviation (ha)
Disjunct core area coefficient of variation (%)
Total core area index (%)
Mean core area index (%)
Nearest-neighbor metrics
Patch
Patch
Class/landscape
Class/landscape
Class/landscape
Class/landscape
NEAR
PRO XIM
MNN
NNSD
NNCV
MPI
Nearest-neighbor distance (m)
Proximity index
Mean nearest-neighbor distance(m)
Nearest-neighbor standard deviation (m)
Nearest-neighbor coefficient of variation (%)
Mean proxim ity index
SHDI
SIDI
MSIDI
PR
PRD
RPR
SHEI
SIEI
MSIEI
Shannon's diversity index
Simpson's diversity index
Mod ified Simpson's diversity index
Patch richness (#)
Patch richness density (#/100 ha)
Relative patch richness (%)
Shannon's evenness index
Simpson's evenness index
Mod ified Simpson's evenness index
Diversity metrics
Landscape
Landscape
Landscape
Landscape
Landscape
Landscape
Landscape
Landscape
Landscape
Contagion and interspersion metrics
Class/landscape IJI
Interspersion and Juxtaposition index (%)
Landscape
CONTAG
Contagion index (%)
__________________________________________________________________________________________
26
These metrics quantify area in absolute terms (hectares). It is often desirable to quantify area
in relative terms as a percentage of total landscape area. Therefore, at the class level,
FRAGSTATS computes the percent of landscape (%LAND) occupied by each patch type. At
the patch level, the landscape similarity index (LSIM) equals the percent of the landscape
occupied by the same patch type as the patch (and is equivalent to %LAND). It is included as a
patch characteristic because some ecological properties of a patch can be influenced by the
abundance of similar patches in the surrounding landscape. For example, island biogeographic
theory predicts that the probability of patch occupancy for some species or species richness is a
function of both patch size and isolation (MacArthur and Wilson 1967). One aspect of isolation
is the amount of similar habitat within a specified distance. Thus, the dynamics of a local
population contained within a patch are likely to be influenced by the size of the metapopulation
occupying the entire landscape. Indeed, there is some evidence that regional habitat availability
has a strong influence on local bird populations at the patch level (e.g., Askins and Philbrick
1987). Finally, FRAGSTATS computes a largest patch index (LPI) at the class and landscape
levels that quantifies the percentage of total landscape area comprised by the largest patch.
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 pattern. Otherwise, these area metrics have few
limitations.
Patch -Level E xam ple.--Figure 4 depicts 3 patches extracted from a sample landscape that vary in size and
landscape similarity. Roughly 50% of the landscape is similar to patch A (%LAND ) and thus comprised of mixed,
large sawtimber (MLS). In contrast, patches B and C represent relatively rare patch types because only 8% of the
landscape is comprised of the respective patch types. Thus, patch A is less insular than patches B and C. The
dynamics of some ecological processes are likely to be different among patches A, B, and C. For example, an
organism inhabiting patch A and dependent on mixed, large sawtimber is likely to experience a different population
dynamic than a similar organism occupying either patch B or C because of the larger regional population size and
probab le incre ased interac tion amo ng in divid uals inhab iting the land scape. On the other h and , beca use o f their
rarity, patches B and C would probably contribute more to faunal species richness than patch A.
Class-Lev el Ex am ple.--Figure 5 depicts 3 sample landscapes that vary in the amount and pattern of mixed,
large sawtimber habitat. According to class area (CA), landscapes B and C have more than 10 times as much
mix ed, larg e saw timb er than landscape A . Rou ghly 50% of landscapes B and C are mix ed, larg e saw timb er, in
contrast to only 5% of landscape A, according to the percent of landscape (%LA ND) m easure. Thus, the dynamics
of some ecological processes are likely to be quite different in landscape A than in either B or C. For example,
populations of organisms associated with mixed, large sawtimber habitat are likely to be much smaller in landscape
A and perhaps subject to a
27
high er pro bab ility of local ex tinction than in either B or C. O n the other han d, the mix ed, larg e saw timb er habitat in
landscape A p robably con tributes proportionately more to landscape diversity and species richness than in either B
or C.
In addition, although class area and percent of landscape indicate that landscapes B and C are sim ilar in
com position w ith resp ect to m ixed, large sa wtim ber h abitat, other indices sugg est that they vary g reatly in
configuration. For example, the largest patch index (LPI) rep resents the 3 lan dscapes along a continu um from mo st
to least fragmented, and clearly distinguishes between landscapes B and C in terms of landscape configuration. The
largest patch in landscape B comprises only 17% of the landscape, whereas in landscape C it comprises 47% of the
landscape. Thus, although m ixed, large sawtimber is equally abundant in both landscapes, the largest patch index
indicates that it is fragmented into smaller patches in landscape B than in landscape C.
Lan dscape-L evel Exa mp le.--Figure 6 depicts 3 sample landscapes that vary in composition and pattern. The
largest patch index (LPI) indicates that almost half of landscape C, the least heterogeneous landscape, is comprised
of a single p atch. Ho wev er, the largest patch in landscape A com prises much m ore of the landscap e than the largest
patch in landscape B, even though landscape A is considerably more heterogeneous than B. If a single large patch
com prising > 25 % is im portant for the presen ce of a particular sp ecies, then lan dscape A could include suitable
habitat but landscape B would not. This illustrates both the potential usefulness of this index in particular
applications and the limitations of this index as a measure of overall heterogeneity.
Patch Density, Size and Variability Metrics
FRAGSTATS computes several simple statistics representing the number or density of
patches, the average size of patches, and the variation in patch size at the class and landscape
levels (Table 1). These metrics usually are best considered as representing landscape
configuration, even though they are not spatially explicit measures. Number of patches (NP) of a
particular habitat type may affect a variety of ecological processes, depending on the landscape
context. For example, the number 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 of patches also can alter the stability of
species interactions and opportunities for coexistence in both predator-prey and competitive
systems (Kareiva 1990). In addition, habitat subdivision, as indexed by the number of patches,
may affect the propagation of disturbances across a landscape (Franklin and Forman 1987).
Specifically, a patch type that is highly subdivided may be more resistent 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 contiguous. Conversely, habitat fragments may suffer higher rates of
disturbance for some disturbance types (e.g. windthrow) than contiguous habitats. The number
of patches in a landscape mosaic (pooled across patch types) can have the same ecological
applicability, but more often serves as a index of spatial heterogeneity of the entire landscape
mosaic. A landscape with a greater number of patches has a finer grain; that is, the spatial
heterogeneity occurs at a finer resolution. Although the number 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 area, distribution,
28
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 it could
be a useful index to interpret. Number of patches is probably most valuable, however, as the
basis for computing other, more interpretable, metrics.
Patch density (PD) is a limited, but fundamental, aspect of landscape structure. 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. If numbers of patches, not their area or distribution, is particularly
meaningful, then patch density for a particular patch type could serve as a good fragmentation
index. Holding class area constant, a landscape with a greater density of patches of a target patch
type would be considered more fragmented than a landscape with a lower density of patches of
that patch type. Similarly, the density of patches in the entire landscape mosaic could serve as a
good heterogeneity index because a landscape with greater patch density would have more
spatial heterogeneity.
Another class and landscape index based on the number of patches is mean patch size (MPS).
As discussed previously, the area of each patch comprising a landscape mosaic is perhaps the
single most important and useful piece of information contained in the landscape. The area
comprised by each patch type (class) is equally important. 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.
Like patch area, the range in mean patch size is ultimately constrained by the grain and extent
of the image and minimum patch size; relationships cannot be detected beyond these lower and
upper limits of resolution. Mean patch size at the class level is a function of the number of
patches in the class and total class area. In contrast, patch density is a function of total landscape
area. Therefore, at the class level, these 2 indices represent slightly different aspects of class
structure. For example, 2 landscapes could have the same number and size distribution of
patches for a given class and thus have the same mean patch size; yet, if total landscape area
differed, patch density could be very different between landscapes. Alternatively, 2 landscapes
could have the same number of patches and total landscape area and thus have the same patch
density; yet, if class area differed, mean patch size could be very different between landscapes.
These differences should be kept in mind when selecting class metrics for a particular
application. In addition, 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
29
with 5 10-ha 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. 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. Including
both of these indices in a discriminant analysis, for example, would cause a singularity in the
correlation matrix and inhibit the eigenanalysis.
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 2 of the simplest
measures of variability--standard deviation and coefficient of variation.
Patch size standard deviation (PSSD) 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, 2 landscapes may have the same patch size
standard deviation, e.g., 10 ha; yet 1 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
structure 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 (PSCV) 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, 2
landscapes may have the same patch size coefficient of variation, e.g., 100%; yet 1 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 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.
30
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.
Class-Lev el Ex am ple.--Figure 5 depicts 3 sample landscapes that vary in the amount and pattern of mixed,
large sawtimber habitat. Because total landscape area (TA ) is similar am ong the lan dscapes, number of patches
(NP) and patch density (PD ) con vey the sam e info rmation. Altho ugh the 3 landscapes vary co nside rably in bo th
am oun t and distribu tion o f mixed, large sa wtim ber, number of patches and patch density alone d o not capture these
landscape structural differen ces very w ell. For e xam ple, lan dscapes A and B differ dra ma tically in am oun ts of this
patch type, yet have about the same num ber and density of patches. The num ber and density of patches do indicate,
however, that the mixed, large sawtimber is more subdivided in landscape B than landscape C, and because class
area (CA) is similar among landscapes, landscape B can be considered more fragmented than landscape C.
In co ntrast to the previo us ind ices, mea n patch size (M PS) d oes a goo d job of ran king the 3 landscapes with
respe ct to m ixed, large sa wtim ber fragm entatio n (A being m ost frag me nted, C being least). How ever, mean patch
size is most informative when interpreted in conjunction with class area, patch density, and patch size va riability.
Patch size standard deviation (PSSD) measures absolute variation in patch size and is affected by the average patch
size. Patch size standard deviation in landscape A is several times smaller than in landscape B, reflecting the
smaller patch sizes in landscape A. However, according to patch size coefficient of variation (PSCV), these 2
landscapes have similar variability in patch sizes relative to their respective mean patch sizes (i.e., standard
deviation roughly eq uivalent to the mean in both landscap es). The greater patch size coefficient of variation in
landscape C compared to the other landscapes indicates a much larger relative variation in patch size.
According to these area metrics, it is apparent that landscape A contains several small and similar-sized mixed,
large sawtimber patches. Landscape B also contains several similar-sized mixed, large sawtimber patches, but the
patches are muc h larger. Thus, the mixed, large sawtimb er in landscapes A and B is fragmented to a similar a
degree, but landscape A has lost more of this habitat than has landscape B. Overall, landscape A is much farther
along in the fragmentation process than landscape B. Similarly, landscape B and C contain the same amount of
mixed, large sawtimber, but the habitat is fragmented into a greater number of smaller fragments in landscape B
because of pa st timb er m anagem ent ac tivities. Th us, the mix ed, larg e saw timb er habitat is m ore fragm ented in
landscape B than in landscape C, although they have both undergone the same degree of habitat loss. Finally,
landscapes A and B have been subject to greater human disturbance in the form of timber m anagement activities
than landscape C. D ifferences in patch size variability suggest that the huma n-altered landscapes contain more
uniformity in patch size than the unaltered landscape.
Lan dscape-L evel Exa mp le.--Figure 6 depicts 3 sam ple lan dscapes that vary in com position an d pattern.
Because total landscape area (TA ) is similar am ong the lan dscapes, number of patches (NP ), patch density (PD),
and mea n patch size (MPS) all convey the same information. All 3 metrics do a good job of representing the strong
landscape diversity or heterogeneity gradient among landscapes. Although these metrics indicate that the habitat
patterns in landscape A are much finer grained than those in B and C, they do not indicate anything about the
num ber of different patch types present or their relative abundance and spatial distribution. Thus, these metrics are
mo re me aningful wh en con sidered in conjun ction w ith other indices.
According to patch size standard deviation (PSSD ), in absolute term s, patch size in land scape A is much less
31
variable than in landscape C. Sixty-five percent of the patches in landscape A are w ithin 20 ha difference in size (±
1 standard deviation); whereas 65% of the patches in landscape C are within 100 ha difference in size. Therefore,
based on standard d eviation, the variation in patch size is much greater in Landscap e C than landscape A . Howev er,
according to patch size coefficient of variation (PSCV ), relative to mean p atch size, the patches in landscape A are
actua lly m uch mo re variable in size than in landscape C. H ence, dep end ing o n w hether yo u view v ariation in
abso lute (PSSD ) or relative (P SCV) terms, you can reach very different co nclusions regarding these land scapes.
Ultim ately, the cho ice be tween m easures w ill depe nd o n the application, but in mo st cases coefficient o f variation is
mo re m eaningful.
Edge Metrics
FRAGSTATS computes several statistics representing the amount of edge or degree of edge
contrast at the patch, class, and landscape levels (Table 1). Edge metrics usually are best
considered as representing landscape configuration, even though they are not spatially explicit at
all. Total 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 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.
Early wildlife management efforts were focussed 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 has guided land management practices until recently. Recent
studies, however, have suggested that changes in vegetation, invertebrate populations, predation,
brood parasitism, and competition along forest edges has resulted in the population declines of
several vertebrate species dependent upon forest interior conditions (e.g., Strelke and Dickson
1980, Kroodsma 1982, Brittingham and Temple 1983, Wilcove 1985, Temple 1986, Noss 1988,
Yahner and Scott 1988, Robbins et al. 1989). 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-tointerior ratio. Most of the adverse effects of forest fragmentation on organisms seem to be
directly or indirectly related to edge effects. 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.
32
At the patch level, edge is a function of patch perimeter (PERIM). The edge effect on a
patch can be indexed using the perimeter-to-area ratio employed in the shape indices discussed
below. At the class and landscape levels, edge can be quantified in other ways. 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.
These 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, vector and
raster images portray lines differently. 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.
The contrast between a patch and its neighborhood can influence a number of important
ecological processes (Forman and Godron 1986). The "edge effects" described previously are
influenced by the degree of contrast between patches. For example, 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). Because of
edge effects, the interface between some patch types can have sufficiently distinctive
characteristics to be considered a separate type of habitat (Reese and Ratti 1988).
Patch insularity is a function of many things, including distance between the patch and its
nearest neighbor, age of the patch or its duration of isolation, connectivity of the patch with
neighbors (e.g., through corridors), and the character of the intervening landscape. The
permeability of a landscape for some organisms may depend on the character of the intervening
landscape. The degree of contrast between the focal 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), depends 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). For example, high-contrast edges may prohibit or inhibit some
33
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 1 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 computes several indices based on edge contrast at the patch, class, and
landscape levels (Table 1). At the patch level, the edge contrast index (EDGECON) 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. Total patch
perimeter is reduced proportionate 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 maximumcontrast edge. Conversely, a patch with a 90% edge contrast index has high contrast with its
neighborhood. 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, thereby focussing on the landscape condition, not the
average patch condition, as does the mean edge contrast index (MECI). This latter index
quantifies the average edge contrast for patches of a particular patch type (class level) or for all
patches in the landscape. FRAGSTATS also computes an area-weighted mean edge contrast
index (AWMECI) by weighting patches according to their size. Larger patches are weighted
more heavily than smaller patches in calculating the average patch edge contrast for the class or
landscape. This area-weighted index may be more appropriate than the unweighted mean index
in cases where larger patches play a dominant role in the landscape dynamics relative to the
phenomenon under consideration. In such cases, it may make sense to weight larger patches
more heavily when characterizing landscape structure. Otherwise, small patches will have an
equal affect on the average edge contrast index, when in fact they play a disproportionately small
role in the overall landscape function.
These edge contrast indices are relative measures. Given any amount or density of edge, they
measure the degree of contrast in that edge. For this reason, these indices are probably best
34
interpreted in conjunction with total edge or edge density. 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. Note that these indices consider landscape boundary segments even if they have a contrast
of zero (i.e., the patch extends beyond the landscape boundary). These zero-contrast boundary
segments are included in the calculation of these indices because we believe that boundary
segments should be treated equal to internal edge segments in determining the degree of contrast
in the patch, class, or landscape. Similarly, background edges are included in the calculation of
these indices as well. Therefore, if a landscape border is absent, the choice of how to treat the
landscape boundary and background edge (i.e., user-specified average edge contrast) could have
significant affects on these indices, depending on the size and heterogeneity of the landscape. If
a landscape border is present, this decision can still have significant affects on these indices if
there is a large amount of background edge.
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 the 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.
Edge contrast indices are limited by the considerations discussed above for metrics based on
total edge length. These indices are only calculated and reported in the output files if an edge
contrast weight file is specified. The usefulness of these indices is directly related to the
meaningfulness of the weighting scheme used to quantify edge contrast. 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.
Patch -Level E xam ple.--Figure 4 depicts 3 patche s extracted from a sam ple lan dscape that vary in edge contrast.
According to the edge contrast index (EDG ECO N), patch A h as the least contrast with its neighborho od, where
contrast represents the degree difference in floristic and vegetation structure among patches. This is because patch
A is a m ixed, large sawtim ber patch surrou nded largely by conifer an d hard wood, large sawtim ber patches. Thus,
the differences in vegetation composition and structure along the patch perimeter is relatively subtle. Moreover, the
35
ecotones between patch A and these other large sawtimber patches are probably gradual. Consequently, although
there are im portant differences b etween these adjace nt patche s that warran t their discrimina tion, the con trast
between them is very low. An animal dispersing from patch A, for example, might not be impeded at all by the
low-contrast boundary of patch A. In contrast, patch C is a mixed, grass/forb (MGF) patch surrounded mostly by
large sawtimber patches. Hen ce, the degree of structural contrast between pa tch C and its neighborho od is very
high. The edge contrast index indicates that the pe rimeter of patch C has the equ ivalen t of 80 % o f its perim eter in
ma xim um -con trast edge, w hereas the p erim eter of patch A has the equ ivalen t of on ly 17 % o f its perim eter in
maximum -contrast edge. The edge contrast index seem s to do a good jo b of quantifyin g differences in in sularity
among these patch es.
Class-Lev el Ex am ple.--Figure 5 depicts 3 sample landscapes that vary in the amount and pattern of mixed,
large sawtimb er habitat. Be cause these land scapes are similar in size, total edge (TE) and edg e den sity (ED) are
largely redundant. Both indices are highest for landscape B and lowest for landscape A. Depending on the
application, the interpretation of these differences may vary. For example, the process of habitat fragmentation
involves both habitat loss and changes in habitat pattern. Over the course of fragmentation, the proportion of the
landscape composed of the target habitat type would go from 100% to 0%. The total amount of class edge would be
expected to peak at a landscape similarity index (LSIM) of approximately 50%, depending on the pattern of habitat
loss (Frank lin and Fo rman (1 987 ). Thus, from a fragm entation perspec tive, total edge and edg e den sity are best
interpreted in conjunction with the landscape similarity index. In this case, although landscapes B and C have
und ergo ne the sam e am oun t of m ixed, large sa wtim ber lo ss (i.e., similar LS IM values), total edge and edge den sity
indicate that this habitat in landscape B is m ore highly fragm ented than in landscape C. A lternatively, consider a
species that requires m ixed, large sa wtim ber edge habitat. Total edge or edge den sity might be used to model
habitat suitability. In this case, landscape A would be least suitable and landscape B most suitable.
If edge contrast is deemed important, then the edge contrast indices may lead to a slightly different
interp retation of the mix ed, larg e saw timb er habitat co ntext in these landscapes. Contrast-weig hted edge den sity
(CW ED ) indicates that althou gh landscape C h as rou ghly 33 m eters of mixed, large sa wtim ber edge per h ectare, it
has the equivalent of less than 2 meters of maximum -contrast edge per hectare. Thus, mixed, large sawtimber
hab itat in La ndscape C is not very insular; it is surrounde d by patch es very sim ilar in structure, and any edge effects
on th is habitat (or organ isms inhabiting it) are likely to be relatively w eak. Contrast-weig hted edge den sity indicates
that landscape C has the least equivalent maximu m-con trast edge density. This differs from the results of total edge
and edg e den sity, which both indicate that landscape A has the least edge. If the contrast weighting scheme used
here is particularly meaningful, then con trast-weighted ed ge density ma y be a more in sightfu l index of edge effects
than either total edge or edg e den sity.
Edge contrast can also be measured in relative terms using the total edge contrast index (TE CI), mean edge
contrast index (MECI), and area-weighted mean edge contrast index (AW MEC I). These 3 indices are largely
redundant in the sample landscapes and therefore lead to the same conclusions. The total edge contrast index
indicates that the mixed, large sawtimber edge present in landscape C has very low contrast; specifically, every 100
meters of edge has a maximum-contrast equivalent of only 4 meters. In contrast, the mixed, large sawtimber edge
in landscape A has much higher contrast; every 100 meters of edge has a maximum-contrast equivalent of 40
me ters. Althou gh landscape A has the low est total edge and edg e den sity, all 3 relative contrast indices indicate that
its edge contrast is the greatest. Similarly, although landscape B has the greatest amount of mixed, large sawtimber
edge, the contrast is moderate relative to landscapes A and C.
Lan dscape-L evel Exa mp le.--Figure 6 depicts 3 sam ple lan dscapes that vary in com position an d pattern.
Because these landscapes are similar in size, total edge (TE) and edg e den sity (ED ) are largely redu nda nt. Bo th
indices are highest for landscape A and lowest for landscape C, corresponding to the overall magnitude of spatial
heterogeneity in these landscapes. Conclusions regarding the overall ranking of landscapes based on con trastweig hted edge den sity (CWED ) are similar; although, it is apparent that landscape C contains low-contrast edges
amounting to an equivalent of only 3.7 m/ha of maximum -contrast edge. Landscape B has roughly twice as much
36
total edge as landscape C, but roughly 6 times more equivalent maximum-contrast edge. Likewise, the conclusions
based on the total edge contrast index (TE CI), mean edge contrast index (MECI), and area-weighted mean edge
contrast index (AW MECI) are similar, althou gh ed ge con trast is reported in relative term s.
Shape Metrics
FRAGSTATS computes several statistics that quantify landscape configuration in terms of
the complexity of patch shape at the patch, class, and landscape levels (Table 1). 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 edge metrics).
Shape is a difficult parameter to quantify concisely in a metric. FRAGSTATS computes 2
types of shape indices; both are based on perimeter-area relationships. 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. In the vector
version of FRAGSTATS, patch shape is evaluated with a circular standard; shape index is
minimum for circular patches and increases as patches become increasingly noncircular.
Similarly, in the raster version of FRAGSTATS, patch shape is evaluated with a square standard.
While there are other means of quantifying patch shape (e.g., Lee and Sallee 1970), this shape
index is widely applicable and used in landscape ecological research (Forman and Godron 1986).
This shape index can be applied at the class and landscape levels as well. Mean shape index
(MSI) measures the average patch shape, or the average perimeter-to-area ratio, for a particular
patch type (class) or for all patches in the landscape. FRAGSTATS also computes an areaweighted mean shape index (AWMSI) of patches at the class and landscape levels by weighting
patches according to their size. Specifically, larger patches are weighted more heavily than
smaller patches in calculating the average patch shape for the class or landscape. This index may
be more appropriate than the unweighted mean shape index in cases where larger patches play a
dominant role in the landscape function relative to the phenomenon under consideration. The
difference between the unweighted and weighted mean shape indices can be particularly
noticeable when sample sizes are small (i.e., only a few patches).
An alternative to these patch shape indices based on the "average" patch characteristics at the
class and landscape levels is the landscape shape index (LSI). This index measures the
perimeter-to-area 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. This index quantifies the amount of edge present in a landscape relative to what would be
present in a landscape of the same size but with a simple geometric shape (circle in vector,
square in raster) and no internal edge (i.e., landscape comprised of a single circular or square
37
patch). Landscape shape index is identical to the shape index at the patch level (SHAPE), except
that it treats the entire landscape as if it were 1 patch and any patch edges (or class edges) as
though they belong to the perimeter. The landscape boundary must be included as edge in the
calculation in order to use a circle or 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 the
landscape shape index can be a useful index, especially when comparing among landscapes of
varying sizes.
These shape indices have important limitations. First, vector and raster images use different
shapes as standards. Thus, the absolute value of these indices differs between vector and raster
images. The implications of this difference should be considered relative to the phenomenon
under investigation. Second, these shape indices are limited in the same manner as the edge
indices discussed above with regards to the differences between how lines are portrayed in vector
and raster images. Perimeter length will be biased upward in raster images because of the stairstepping pattern of line segments, and the magnitude of this bias will vary in relation to the grain
or resolution of the image. Third, 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 and shape indexes. For this
reason, these shape indices are not useful as measures of patch morphology; they are best
considered as measures of overall shape complexity. Finally, the mean shape index and areaweighted mean shape index are subject to the limitations of first-order statistics (e.g., the average
patch shape for a class or the landscape may not be very meaningful if the distribution of patch
shapes is complex).
The other basic type of shape index computed by FRAGSTATS is the fractal dimension. In
landscape ecological research, patch shapes are frequently characterized via the fractal dimension
(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 (FRACT) 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 used (Rogers 1993). Therefore, caution should be
exercised when using this fractal dimension index as a measure of patch shape complexity.
38
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 using this perimeter-area method 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) as reported by some authors. We refer to this index as the
double log fractal dimension (DLFD) 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). If insufficient
data are available, an alternative to the regression approach is to calculate the mean patch fractal
dimension (MPFD) based on the fractal dimension of each patch. FRAGSTATS also computes
an area-weighted mean patch fractal dimension (AWMPFD) at the class and landscape levels by
weighting patches according to their size, similar to the area-weighted mean shape index. These
latter 2 indices may be particularly meaningful if the focus of the analysis is on patch
characteristics; that is, when patch-level phenomena are deemed most important and patch shape
is particularly meaningful.
Because the method used to calculate these fractal indices involves perimeter-area
calculations, these fractal indices are subject to some of the same limitations as the shape indices
discussed above. Perhaps the greatest limitation of the fractal indices is the difficulty in
conceptualizing fractal dimension. Even though fractal dimension is increasingly being used in
landscape ecological research, it remains an abstract concept to many and it may easily be used
inappropriately.
Patch -Level E xam ple.--Figure 4 depicts 3 patches extracted from a sam ple landscape that vary in shape. In
particular, patch A has a much more com plex shape than either patch B or C. Accordingly, the shape index
(SHAPE ) for patch A is almost twice as large as that for the other 2 patches. The fractal dimension (FRACT)
results are consistent with the shape index; however, the magnitude of differences among patches in fractal
dimension is notably less than shape index values. In addition, the subtle difference in shape complexity between
patch B and C is reflected in a rather small difference in their shape indices. Overall, these shape indices do a good
job o f quantify ing o bvio us differen ces in shap e com plexity am ong these p atche s, but fractal dimension appears to
be less sensitive to differences than the shape index.
Class-Lev el Ex am ple.--Figure 5 depicts 3 sample landscapes that vary in the amount and pattern of mixed,
large sawtimb er habitat. In th is case, the land scape bound ary d oes n ot all rep resen t mix ed, larg e saw timb er edge.
Therefore, the landscape shape index (LSI) is not particularly meaningful because it treats the entire landscape
boundary as edge. The mean shape index (MSI) values for all 3 landscapes are greater than 1, indicating that the
averag e patch sh ape in all 3 landscapes is noncircular. The mixed, large saw timber patches in landscap e A (m ost
fragme nted) are lea st irregu lar in shape, whereas the patche s in landscape C (least fragm ented ) are m ost irreg ular.
The area-weighted mean shape index (AWM SI) supports these conclusions. In addition, the area-weighted values
for all 3 landscapes are greater than the unweighted values, indicating that the larger patches in each landscape are
mo re irregular in sh ape than the average. Th ese results indicate tha t hum an-induced fragm entation in lan dscapes A
and B caused a simplification in patch shapes compared to the geometrically complex patch shapes found in the
natural, unaltered landscape (C).
Because of the small sam ple sizes, double log fractal dimension (DLFD) is probably not a reliable index for
39
these 3 landscapes. Mean patch fractal dimension (MPFD) values do agree in rank order with mean shape index
values. According to the latter index, landscape A contains the simplest average patch shape, but according to mean
patch fractal dimension, the opposite is true. The reason for the discrepancy between these indices is not clear;
however, the mean shape index is more consistent with the results of other indices and is therefore probably m ore
reliable in this case.
Lan dscape-L evel Exa mp le.--Figure 6 depicts 3 sam ple lan dscapes that vary in com position an d pattern. In this
case, even though the landscape boundary does not all represent true edge, the landscape shape index (LSI) still
ranks the landscapes along an intuitive gradient from least to most heterogeneous. The mean shape index (MSI)
values for all 3 landscapes are gre ater tha n 1, indicatin g that the av erage patch sha pe in all 3 landscapes is
non circular. The patche s in landscap e A are least irregular in shap e, whe reas the patches in land scape C are m ost
irregular in shape. The area-weighted mean shape index (AWM SI) supports these conclusions. In addition, the
area-weighted values for all 3 landscapes are greater than the unweighted values, indicating that the larger patches
in each landscape are more irregular in shape than the average. These results reflect the simple shapes of
management units in landscape A compared to the natural shapes of patches in the undisturbed landscape C.
Because of the small sam ple size in land scape C, double log fractal dimension (DL FD ) is probab ly no t a
reliable index for this landscape. However, the index compares nicely with the mean shape index and areaweighted mean shape index for landscapes A and B. As in the class-level exam ple, the rank order of mean patch
fractal dimension (MPFD ) values do not agree with the other shape indices. The reason for the discrepancy
betw een these in dices is not clear; ho wever, b ecau se all oth er shape indices are co nsisten t with each other, mean
patch fractal dimension is probably less reliable in this case.
Core Area Metrics
FRAGSTATS computes several statistics based on core area at the patch, class, and
landscape levels (Table 1). Core area is defined as the area within a patch beyond some specified
edge distance or buffer width. Core area metrics reflect both landscape composition and
landscape configuration. 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 edge or buffer from all patches. Like patch shape, the primary
significance of core area in determining the nature of patches in a landscape appears to be related
to the "edge effect." As discussed previously, 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 (see
discussion of edge metrics for citations). 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.
For ecological processes or organisms adversely affected by edge, it seems likely that core
area would better characterize a patch than total area. In addition, 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). Unfortunately, in most cases, there is insufficient empirical
40
support (or none) for designating separate edge widths for each unique edge type. Accordingly,
in FRAGSTATS the user must specify a single edge width for all edge types.
In raster images, there are different ways to determine core area. FRAGSTATS employs a
method in which a cell's 4 parallel neighbors are evaluated for similarity; diagonal neighbors are
ignored. This method tends to slightly over-estimate the true core area. Other methods can
seriously under-estimate core area. For more details on the algorithm see the "patch.c" routine in
the source files.
Patch area, class area, total landscape area, and the percent of landscape in each patch type all
have counterparts computed after eliminating edge area defined by the specified edge width;
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 (C%LAND) 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. 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 useful in the study of habitat fragmentation,
because fragmentation affects both habitat area and configuration. On the other hand, these
indices confound the effects of habitat area and configuration. For example, if the core area
percent of a landscape is small, it indicates that very little core area is available, but it does not
discriminate between a small amount of the patch type (area effect) and a large amount of the
patch type in a highly fragmented configuration. Thus, like many indices that summarize more
than 1 feature (e.g., diversity indices), these indices are best interpreted in conjunction with other
indices to provide a more complete description of landscape structure.
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 (disjunct)
in each patch (NCORE), as well as the number in each class and the landscape as a whole
(NCA). 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.
Although these metrics are not particularly useful in most cases, they are used to compute other
landscape metrics based on core area.
Number of core areas can be reported on a per unit area basis (core area density, CAD) 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. 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. Furthermore, mean
41
core area can be defined in 2 ways. First, mean core area can be defined as the mean core area
per patch (MCA1). 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 (MCA2). The distinction between these 2
ways of defining mean core area should be noted.
FRAGSTATS also computes several relative core area indices that quantify 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, the total core area index (TCAI) at the
class and landscape levels quantifies core area for the entire class or landscape as a percentage of
total class or landscape area, respectively. At the class and landscape levels, FRAGSTATS also
computes the mean core area index (MCAI) of patches comprising the class or landscape. Note
that the total core area index is equivalent to an area-weighted mean core area index; thus, the
latter is not computed.
These core area indices are basically edge-to-interior ratios like the shape indices discussed
previously, the main difference being that the core area indices treat edge as an area of varying
width and not as a line (perimeter) around each patch. In addition, these core area indices are
relative measures. They do not reflect patch size, class area, or total landscape area; they
quantify the percentage of available area, regardless of whether it is 10 ha or 1,000 ha, comprised
of core. These indices do not confound area and configuration like the previous core area
indices; rather, they isolate the configuration effect. For this reason, these core area indices are
probably best interpreted in conjunction with total area at the corresponding scale. For example,
in conjunction with total class area, these indices could serve as effective fragmentation indices
for a particular class.
Variation in core area size may convey more useful information than mean core area. Like
variation in patch size, FRAGSTATS computes corresponding measures of variability among
patches in core area size. Core area standard deviation and core area coefficient of variation have
the same ecological applicability as patch size standard deviation and patch size coefficient of
variation, except that all edge area is eliminated from consideration. FRAGSTATS computes
both the patch core area standard deviation (CASD1) and patch core area coefficient of
variation (CACV1), which represent the variation in core area per patch (associated with
MCA1), as well as the disjunct core area standard deviation (CASD2) and disjunct core area
coefficient of variation (CACV2), which represent the variation in the size of disjunct core areas
(associated with MCA2). In contrast to their counterparts, these core area metrics reflect the
interaction of patch size and shape and edge width, and therefore may serve as better
heterogeneity indices when edge width can be meaningfully specified and edge effects are of
particular interest. Standard deviation can be difficult to interpret without doing so in
conjunction with other statistics (e.g., mean patch size or mean core area). For this reason, core
area coefficient of variation usually is preferable to core area standard deviation. Also, note that
core area standard deviation and coefficient of variation can equal 0 under 3 conditions: (1)
when there is only 1 core area in the landscape; (2) when there is more than 1 core area greater
42
than 0 in size, but they are all the same size; and (3) when there is more than 1 patch, but none
have any core area (CORE = 0). In all 3 cases, there is no variability in core area size, yet the
ecological implications could be quite different.
All of the core area indices are affected by the interaction of patch size, patch shape, and the
specified edge width. In particular, increasing edge width will decrease core area, and vice versa.
Therefore, these indices are meaningful only if the specified edge width is relevant and
meaningful to the phenomenon under investigation. Unfortunately, in many cases there is no
empirical basis for specifying any particular edge width and so it must be chosen somewhat
arbitrarily. The usefulness of these metrics is directly related to the arbitrariness in the specified
edge width and this should be clearly understood when using these metrics. Moreover, the utility
of core area indices compared to their area-based counterparts depends on the resolution,
minimum patch dimensions, and edge widths employed. For example, given a landscape with a
resolution of 1 m2 and minimum patch dimensions of 100 x 100 m, if an edge width of 1 m is
specified, then the core area indices and their counterparts will be nearly identical and the core
area indices will be relatively insensitive to differences in patch size and shape. In this case, core
area indices will offer little over their counterparts in terms of unique characterization of
landscape structure.
Patch -Level E xam ple.--Figure 4 depicts 3 patches extracted from a sample landscape that vary in core area
based on a 100 m edge w idth for all edg e types. A lthough patch A is alm ost 3 times larg er than p atch C, it has less
than twice the core area (CORE). This is because patch A has a more complex shape than patch C and therefore a
greater edge-to-interior ratio. Note also that although patch B and C are almost equal in size, patch B has half the
core area of patch C. This is a result of the interaction among patch size, patch shape, and edge width. With a 100
m edge width, the subtle difference in shape between patch B and C results in a large difference in core area. A
much larger edge width (e.g., 200 m) would result in both patches having 0 core area because of their small size,
and a much sm aller edge width (e.g., 10 m) would result in both patches having similar core areas. Thus, the affect
of patch shape on core area is dependent on both patch size and edge width.
According to the number of core areas (NC OR E), patche s B an d C both contain 1 core area b ecau se of th eir
simple shapes. Patch A, however, contains 2 core areas because it is narrower than 200 m in the middle and then
widens o n bo th sides. Thus, un der certain conditions it may be mo re m eaningful to treat patch A as 2 separate
patches. For ex am ple, if an organism avoid s ed ge habitat up to a distance of 100 m, the n from the organism's
perspective, patch A may actually contain 2 separate suitable habitat patches. However, like core area, number of
core areas is affected by the interaction of patch size, patch shape, and edge width. W ith a m uch larger edg e width
(e.g., 200 m) or much sm aller edge width (e.g., 10 m), patch A wou ld contain only 1 core area.
Although patch A is almost 3 times larger than patch B and has a more complex shape, it has roughly the same
core area index (CAI) as patch B. Thus, these 2 patches have about the same proportion of core area, even though
they differ markedly in absolute size and shape. In contrast, the core area index of patch B is about half that of
patch C, even though they are similar in size. Because of the interaction of patch size, patch shape, and edge width,
the slightly more com plex shape of patch B results in disproportionately less core area and therefore a much smaller
core area index than patch C. Again, note the affect of the interaction among patch size, patch shape, and edge
width on this index.
Class-Lev el Ex am ple.--Figure 5 depicts 3 sample landscapes that vary in the amount and pattern of mixed,
large sawtimber habitat based on a 100 m edge w idth for all edge types. According to the percent of landscape
(%LAND ) in this patch type, roughly 50% of landscapes B and C are mixed, large sawtimber. According to the
43
core area percent of landscape (C%LA ND), however, only 10% of this habitat type in landscape B is core area,
whereas 23% of this habitat type in landscape C is core area. Thus, the core area percent of landscape clearly
indicates that landscape B is fragmented to a much greater degree than landscape C. Note, however, that inspection
of this in dex alone does no t indica te wh ether differences in the am oun t of core area are b ecau se of d ifferen ces in
total habitat area, habitat configuration, or both. Nevertheless, for an organism specialized on interior mixed, large
sawtimber habitat, the core area percent of landscape suggests that landscape C contains twice the suitable habitat
as land scape B. T his w ould not n ecessarily be true if landscapes B and C were gre atly differen t in size becau se this
index is a relative measure. Note that all core area indices are affected by the interaction of patch size, patch shape,
and edge width. For exam ple, with a much larger edg e width (e.g., 200 m) o r much smaller edge width (e.g., 10 m ),
the index values would change dramatically, especially in landscapes A and B, because of the size and shapes of the
mixed, large saw timber patches in these landscapes.
Total core area (TCA) indicates that although landscape A contains 4 mixed, large sawtimber patches
encompassing a total of 13 ha, there is no core area (i.e., no point in these patches is further than 100 m from the
patch perim eter. A lthou gh landscapes B and C have sim ilar am oun ts of m ixed, large sa wtim ber, total core area
indicates that landscape B has much less core area, suggesting a much more fragmented (greater edge-to-interior
ratio) configuration of habitat in landscape B than C.
Number of core areas (NCA) indicates that although landscape B has less than half as much mixed, large
sawtimber core area as landscape C, it has more than 3 times as many disjunct core areas. Note also the difference
between number of patches (NP) and number of core areas. The difference between landscape B and C is more
pronou nced w ith the latter index, indicatin g that the ha bitat in lan dscape B is indeed m ore fragm ented than in
landscape C.
Compared to patch density (PD ), core area density (CAD) does a much better job of characterizing the
differences in landscape structure among landscapes. For example, although landscapes A and B have similar patch
den sities, core area density differs dramatically between them. Landscape A has no core areas, indicating that the
habitat is highly fragmented into very small patches; whereas, landscape B has a comparatively high core area
density. Similarly, although land scapes B and C have similar amou nts of mixed, large sawtimbe r habitat, the core
area in landscape B is fra gm ented into several disjun ct areas, wh ereas in land scape C it is m ore contig uou s.
Althoug h the 3 landscapes v ary considerably in both am oun t and distribu tion o f mixed, large sa wtim ber h abitat, it is
difficult to interpret these landscape structural differences by core area density alone; this index is best interpreted
in conju nction w ith other indices such as class area (CA). Also, because total landscape area is similar among the
landscapes, core area density and number of core areas convey the same information.
Although mea n patch size (MPS) does a good job of ranking the 3 landscapes with respect to mixed, large
sawtimb er frag me ntation (A b eing mo st fragm ented , C being least), mean core area per patch (MCA1)
distinguishes the different stages of fragmentation even more effectively. Like mea n patch size, mean core area per
patch is most info rmative wh en interpre ted in con junction w ith other indices such as class area, patch density (PD),
and patch size variability (PSSD or PSCV). For example, it is difficult to tell from this index alone if the
differences between landscapes B and C are because of differences in habitat area or habitat pattern. However, by
interpreting both class area and mean core area per patch it beco me s clear th at the d ifferen ces are due solely to
pattern. Mean area per d isjunct core (MCA2) is consistent with mean core area per patch, but note the differences
due to th e differenc es in num ber of p atches an d numb er of disjunct core areas.
Often, variation in the amount of core area per patch or disjunct core is of greater interest than the average
con dition. Patch core area standard deviation (CASD1) and disjunct core area standard deviation (CASD2)
indicate that the absolute variation in core area size per patch and per disjunct core area, respectively, is 6 times
greater in landscape C than B. However, these indices alone do not say much about differences in structure among
the 3 landscapes without simultaneously considering the mean core area per patch or mea n area per disjunc t core,
respe ctively . Patch core area coefficient of variation (CAC V1) m easures relative variability and indicates that core
44
area variability decreases progressively from the least (C) to the most (A) fragmented landscape. This suggests that
timb er m anagem ent activities have ten ded to pro duc e greater hom oge neity in core areas for this habitat typ e.
Disjunct core area coefficient of variation (CACV2) measures relative variability among disjunct core areas and
indicates that the disjunct core areas in landscape B are slightly more variable than in landscape C. The choice
between coefficient of variation measures would depend on the application.
The total core area index (TC AI) repre sents the land scapes alon g a co ntinu um from mo st to least fra gm ented .
According to this index, only 20% of the mixed, large sawtimber in landscape B is "interior" habitat; the remaining
80% is "edg e" ha bitat. W ithout any other information, it could be dedu ced that this h abitat type is highly
fragmented in landscape B. When total core area index is interpreted in conjunction with class area or the
landscape similarity index, it becomes quite clear that landscapes B and C differ exclusively in habitat pattern and
not habitat area, and that landscape B is indeed more fragmented than landscape C. The mean core area index
(MCA I) indicates that the mixed, large sawtimber habitat in all 3 landscapes is highly fragmented (i.e., all have a
high ed ge-to-interior ra tio). According to this index, ho wev er, the mixed, large sawtim ber patches in land scapes B
and C have roughly the same average core area index. Yet, the total core area index and other indices clearly
indicate that landscape B is in fact more fragmented than landscape C. These differences illustrate some important
differences between the total and mean core area indices. The mean core area index represents the average patch
characteristic, and may not necessarily represent the overall landscape structural condition very well. This may be
appropriate and meaningful when the focus of the application is on patch-level phenomena. However, when the
focus is on landscape structure, the mean patch condition may be m isleading. For example, the mean core area
index for landscape C is affected by the great variation in core area index amon g the 3 patches. The large core area
index of the largest patch is offset by the 0 core area index of the smallest patch and the very small core area index
of the mid -sized patch . This b ias is cha racteristic of first-o rder statistics such the me an, an d is particularly
pronounced in this case because of the small sample size (n = 3 patches) in landscape C.
Lan dscape-L evel Exa mp le.--Figure 6 depicts 3 sample landscapes that vary in composition and pattern based
on a 100 m edge width for all edg e types. Total core area (TC A) in dicates that lan dscapes A , B, C contain
progressively more core area, and because total landscape area (TA) is similar, they represent a continuum from
most to least patchy. Note that all core area indices are affected by the interaction of patch size, patch shape, and
edge width. For example, with a much larger edge width (e.g., 200 m) or much smaller edge width (e.g., 10 m), the
index values would change dramatically, especially in landscapes A and B, because of the size and shapes of the
mixed, large saw timber patches in these landscapes.
Number of core areas (NC A) in dicates that althoug h landscape A has the greatest number of patches (NP ), it
doe s not h ave the greatest number of core areas because m any of the patches in landscape A do not have any core
area. Because total landscape area is similar am ong landscapes, number of core areas and core area density (CAD)
are largely redundant. Note that although landscapes A and B have fewer core areas than patches, landscape C has
more core areas than patches. The rank order of landscapes based on number of core areas is different than that
based on number of patches and total core area. This reversal occurs because of the relationship between patch
sizes an d sha pes in these landscapes and the designated edge width o f 100 m . With a much larger edg e width (e.g.,
200 m) or m uch smaller ed ge w idth (e.g., 10 m), number of core areas wo uld chan ge dram atically, especially in
landscapes A and B, because of the size and shapes of the patches in those landscapes. For this reason, particular
attention should be given to the interpretation of number of core areas, core area density, and total core area
because they can lead to a different rank ordering of landscapes along a gradient in landscape heterogeneity.
Although mea n patch size (MPS) does a good job of ranking the 3 landscapes with respect to their spatial
heteroge neity, mean core area per patch (M CA 1) distingu ishes amo ng th ese lan dscape ev en m ore d istinctly.
Because mean core area per patch is affected by patch shape, it captures an aspect of spatial pattern not captured by
mea n patch size. Like mea n patch size, mean core area per patch is mo st informa tive w hen interpreted in
conjunction o ther indices su ch as total landscape area, patch density (PD), and patch size variability (PSSD or
PSC V). Mean area per d isjunct core (MCA2) is consistent with mean core area per patch, but note the differences
45
due to the differences in number of patches and number of disjunct core areas, especially in landscape A.
Patch core area standard deviation (CASD1) and disjunct core area standard deviation (CASD2 ) indicate that
the ab solute variation in core area size per patch and per d isjunct core area, respectively, d ecrea ses pro gressively
from landscap e C to A, and in this man ner mim ic the results of patch size standard deviation. How ever, these
indices alon e do not tell u s much about diffe rences in stru cture am ong the 3 landscapes withou t simu ltaneo usly
considering the mean core area per patch or mea n area per disjunc t core, respectively . Patch core area coefficient
of variation (CACV 1) measures relative variability and, in contrast to the standard deviation, indicates that core area
variability increases progressively from the least (C) to the most (A) patchy landscap e. Thus, although patch co re
area varies less in absolute terms in landscape A than C, it varies much more in relative terms. Hence, timber
ma nag em ent activities have ten ded to pro duc e sm aller, bu t mo re variable core areas. Disjunct core area coefficient
of variation (CACV 2) measures relative variability among disjunct core areas. Among other things, this index
indicates that in landscape A the disjunct core areas are much less variable than the core areas per patch. The choice
between coefficient of variation measures would depend on the particular application.
The total core area index (TC AI) repre sents the 3 lan dscapes along a con tinuu m from mo st to least patchy .
Accord ing to this index, only 1 0% of landscape A is "interio r" habitat, the rem aining 90 % is "edg e" ha bitat.
Without any other information on landscape A, it could be deduced that landscape A contains a great deal of spatial
heterogeneity. However, the total core area index does not indicate how much total core area exists or how many
patch es the c ore area is distributed am ong and, in this respect, it is best interp reted in conjun ction with other indices.
The mean core area index (MCA I) mimics the results of the total core area index, although the values are smaller
because patches in each landscape with 0 core area contribute equally to the mean and reduce the average value.
Nearest-Neighbor Metrics
FRAGSTATS computes a few statistics based on nearest-neighbor distance at the patch,
class, and landscape levels (Table 1). Nearest-neighbor distance is defined as the distance from a
patch to the nearest neighboring patch of the same type, based on edge-to-edge distance.
Nearest-neighbor metrics quantify landscape configuration. Nearest-neighbor distance can
influence a number of important ecological processes. For 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. 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). Opdam (1991) reviewed a number of studies that
empirically demonstrated an isolation effect on bird communities in various habitat patches.
Interpatch distance plays a critical role in island biogeographic theory (MacArthur and Wilson
1967) and metapopulation theory (Levins 1970, Gilpin and Hanski 1991) and has been discussed
in the context of conservation biology (e.g., Burkey 1989). The role of interpatch distance in
metapopulations has had a preeminent role in recent conservation efforts for endangered species
(e.g., Lamberson et al. 1992, McKelvey et al. 1992). Clearly, nearest-neighbor distance can be
an important characteristic of the landscape depending on the phenomenon under investigation.
FRAGSTATS computes the nearest-neighbor distance (NEAR) and proximity index
46
(PROXIM) for each patch. The proximity index was developed by Gustafson and Parker
(1992)[see also Gustafson and Parker 1994, Gustafson et al. 1994, Whitcomb et al. 1981] and
considers the size and proximity distance 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 we use 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). According to the authors, the proximity index quantifies the
spatial context of a habitat patch in relation to its neighbors; 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. 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.
At the class and landscape levels, FRAGSTATS computes the mean proximity index (MPI)
for patches comprising the class or for all patches in the landscape. At the class level, the mean
proximity index measures the degree of isolation and fragmentation of the corresponding patch
type and the performance of the index under various scenarios is described in detail by Gustafson
and Parker (1994). We also compute the mean proximity index at the landscape level by
averaging the proximity index across all patches and patch types in the landscape, although the
performance of this index as a measure of overall landscape structural complexity has not been
evaluated quantitatively.
At the class and landscape levels, FRAGSTATS computes the mean nearest-neighbor
distance (MNN) for patches comprising the class or for all patches in the landscape. At the class
level, mean nearest-neighbor distance can only be computed if there are at least 2 patches of the
corresponding type. At the landscape level, mean nearest-neighbor distance considers only
patches that have neighbors. Thus, there could be 10 patches in the landscape, but 8 of them
might belong to separate patch types and therefore have no neighbor within the landscape. In
this case, mean nearest-neighbor distance would be based on the distance between the 2 patches
of the same type. These 2 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, this index should be interpreted carefully when landscapes contain rare patch
types.
Mean nearest-neighbor distance is a first-order statistic and may not be meaningful if the
47
distribution is complex. Variability in nearest-neighbor distance measures a key aspect of
landscape heterogeneity that is not captured by mean nearest-neighbor distance. Nearestneighbor standard deviation (NNSD) is a measure of patch dispersion; a small standard
deviation relative to the mean implies a fairly uniform or regular distribution of patches across
landscapes, whereas a large standard deviation 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 nearestneighbor standard deviation is a function of the mean nearest-neighbor distance and variation in
nearest-neighbor distance among patches. Thus, while the standard deviation 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, 2 landscapes
may have the same nearest-neighbor standard deviation, e.g., 100 m; yet 1 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 structure 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. In addition, standard deviation assumes 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 standard deviation that make assumptions about the distribution and therefore
can be misleading.
Coefficient of variation often is preferable to standard deviation for comparing variability
among landscapes. Nearest-neighbor coefficient of variation (NNCV) 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 the mean nearest-neighbor distance to interpret this metric.
Even so, nearest-neighbor coefficient of variation can be misleading with regards to landscape
structure without also knowing the number of patches or patch density and other structural
characteristics. For example, 2 landscapes may have the same nearest-neighbor coefficient of
variation, e.g., 100%; yet 1 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 structure could be very different,
even though nearest-neighbor coefficient of variation is the same; although the identical
coefficients of variation values indicate that both landscapes have the same regularity or
uniformity in patch distribution.
Because of limitations in Arc/Info (i.e., cannot calculate edge-to-edge distances), the vector
version of FRAGSTATS does not calculate nearest neighbor metrics. To compute these indices
from a vector image, the image must be rasterized first and then analyzed with the raster version
of FRAGSTATS. During the rasterization process, depending on the cell size selected, it is
possible for polygons to merge or divide. Indeed, this problem can be quite severe and lead to
erroneous results for metrics based on the number and size of patches. Therefore, considerable
care should be exercised when rasterizing a vector image to insure the desired results. The most
48
important limitation of these nearest-neighbor indices is that 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 index sums the distanceweighted area of all patches whose edges are within the specified search radius of the focal patch,
but only considers patches within the landscape boundary. Thus, the proximity index 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 a biased proximity index. In
addition, the proximity index evaluates the landscape context of patches at a specific scale of
analysis defined by the size of the search radius. Therefore, this index is only meaningful if the
specified search radius has some ecological justification given the phenomenon under
consideration. Otherwise, the results of the proximity index will be arbitrary and therefore
meaningless. Although these scaling issues are a critical consideration for all landscape metrics,
they are particularly problematic for these nearest-neighbor indices.
Patch -Level E xam ple.--Figure 4 depicts 3 patche s extracted from a sam ple lan dscape that vary in their
neighbo rhood context. Patch A has the sm allest nearest-neighbor distance (NE AR ), follow ed by patch B and C.
Sim ilarly, patch A has the largest proximity index (PROXIM) based on a 200 m search radius, followed by patch B
and C. Note the inverse relationship between nearest-neighbor distance and the proximity index. These indices
support the conclusion drawn from the landscape similarity index (LSIM) that patch A is the least insular of the 3
patch es. Patch A contains a closer n eighbor and a greater am oun t of sim ilar hab itat within its imme diate
neighborhood than either patch B or C. However, because of the relatively small landscape extent relative to patch
size, nearest-neighbor distances are probably not very meaningful in this sample landscape.
Class-Lev el Ex am ple.--Figure 5 depicts 3 sample landscapes that vary in the amount and pattern of mixed,
large sawtimb er habitat. Mean nearest-neighbor distance (MNN) is greatest in landscape A, suggesting that mixed,
large sawtimber patches are m ost isolated in this landscape, although the differences among landscapes are
relative ly sm all. Nearest-neighbor standard deviation (NNSD) and nearest-neighbor coefficient of variation
(NN CV ) are greatest in landscape B, suggesting that the dispersion of m ixed, large sawtim ber patches is least
regular in this landscape. The mean proximity index (MPI) is inversely related to mean nearest-neighbor distance
based on a 200 m search radius and indicates that mixed, large sawtimber in landscape A is most fragmented and
insular. These nearest-neighbor indices indicate that mixed, large sawtimber is less fragmented in landscape B than
C; ye t, mo st other fragme ntation indices indicate the con verse . The se diffe rences likely reflect th e relatively sm all
extent of these landscapes relative to patch size. Under these conditions, nearest-neighbor indices are not
particularly meaningful and their interpretations can be misleading.
49
Lan dscape-L evel Exa mp le.--Figure 6 depicts 3 sam ple lan dscapes that vary in com position an d pattern. Mean
nearest-neighbor distance (M NN ) is smallest in lan dscape C , sugg esting that pa tches are least insular in this
landscape. Nearest-neighbor standard deviation (NNSD) and nearest-neighbor coefficient of variation (NNC V) are
greatest in landscape A, suggesting that the dispersion of patches is least regular in this landscape. The mean
proximity index (MP I) is smallest in landscape A based o n a 20 0 m search rad ius and indicates that patch es are m ost
fragmented and insular in this landscape; although the interpretation of this index at the landscape level is somew hat
difficu lt. Because o f the relatively small extent of th ese lan dscapes, n earest-neig hbo r indices are not p articularly
me aningful.
Diversity Metrics
FRAGSTATS computes several statistics that quantify diversity at the landscape level (Table
1). These metrics quantify landscape composition. 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 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 species. These
diversity indices have been applied by landscape ecologists to measure 1 aspect of landscape
structure--landscape composition (e.g., Romme 1982, O'Neill et al. 1988, Turner 1990a).
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 types selected at random would be different
types. Thus, the higher the value the greater the likelihood that any 2 randomly drawn patches
would be different patch types (i.e., greater diversity). 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
50
have the same applicability.
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, these
diversity indices combine richness and evenness components into a single measure, even though
it is usually more informative to evaluate richness and evenness independently.
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, 2
landscapes may have very different structure yet have the same richness. For example, 1
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 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 (McGarigal and McComb, unpubl.
data).
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 composition--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
51
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 3 evenness indices (Shannon's evenness index, SHEI;
Simpson's evenness index, SIEI; modified Simpson's evenness index, MSIEI), corresponding to
the 3 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 based on an equal distribution 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. Nevertheless, it is important to note that evenness, like richness and diversity,
does not convey any information about which patch types are most or least abundant or which
may be of greater ecological significance.
Lan dscape-L evel Exa mp le.--Figure 6 depicts 3 sam ple lan dscapes that vary in com position an d pattern.
Shannon's diversity index (SH DI), Simpson's diversity index (SIDI), and the modified Simpson's diversity index
(MSIDI) largely reflect differences in patch richness and represent the landscapes along a continuum from most (A)
to least (C ) dive rse. In landscape A, Simpson's diversity index indicates that there is a 79% probab ility that 2
randomly chosen patches would represent different patch types. According to patch richness (PR), the number of
different patch ty pes v aries fro m 1 0 in lan dscape A to 3 in landscape C. B ecau se these land scapes are similar in
area a nd th e m axim um possible num ber o f patch typ es is a co nstan t, patch richness d ensity (PRD), relative patch
richness (RPR), and patch richness are largely redundant. On the average, landscape A contains 3.5 different patch
types w ithin a 100 -ha area a nd contains 37 % o f the poten tial number of p atch type s.
Although landscape C is the least diverse based on the diversity and richness indices, it has the most even area
distribution among patch types, according to Shannon's evenness index (SH EI), Simpson's evenness index (SIEI),
and the modified Simpson's evenness index (MSIEI). These 3 indices indicate that the distribution of area among
patch types is 84-91% of the ma xim um even ness in landscape C, dependin g on wh ich index is interpreted. This
illustrates the potential importance of interpreting richness and evenness independently and the importance of
interp reting even ness se parate from diversity, w hich is influenced strongly by richne ss. No te that differen ces in
evenness among landscapes based on Simpson's evenness index are less pron ounced than the other 2 evenn ess
indices, perh aps bec ause Sim pson's metric is less influenced by rare p atch type s.
Contagion and Interspersion Metrics
FRAGSTATS computes 2 indices representing patch interspersion and juxtaposition at the
class and landscape levels, although 1 index applies only to the landscape level (Table 1). These
metrics quantify landscape configuration. A contagion index was proposed first by O'Neill et al.
(1988) and subsequently it has been widely used (Turner and Ruscher 1988, Turner 1989, Turner
52
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. Both
contagion indices are designed for raster images in which each cell is individually evaluated for
adjacency, and like-adjacencies (cells not on a patch perimeter) are considered. Both indices
have been applied at the landscape level to measure landscape structure.
FRAGSTATS computes 1 of the contagion indices proposed by Li and Reynolds (1993).
This contagion index (CONTAG) is applicable only to raster images at the landscape level and it
is based on raster "cell" adjacencies, not "patch" adjacencies. This contagion index 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. 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). 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. According to the previous authors, contagion
measures the extent to which landscape elements (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. Moreover, the contagion index represents the observed level of contagion as a
percentage of the maximum possible given the total number of patch types.
We present a new interspersion and juxtaposition index (IJI) that is compatible with both
vector and raster images and applicable at both the class and landscape levels. Unlike the earlier
contagion indices that are based on raster "cell" adjacencies, our index is based on "patch"
adjacencies. 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. For raster
images, internal cells are ignored; only the patch perimeters are considered in determining the
total length of each unique edge 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
53
(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 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 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.
Unlike the contagion index, the interspersion and juxtaposition index can be applied at both
the class and landscape levels. At the class level, this index measures the juxtapositioning of a
focal patch type with all others and does not reflect the interspersion of other patch types. Again,
the index is not affected by the dispersion of the focal patch type per se, except that a well
dispersed patch type is more likely to be well interspersed as well. For example, the focal patch
type could be aggregated in 1 portion of the landscape or maximally dispersed and the value of
the index would be the same if the proportion of total edge length involving the focal patch and
each other patch type is the same.
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
juxtaposition 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 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 because it considers
only patch edges. This scale effect should be carefully considered when attempting to compare
results from different studies.
Class-Lev el Ex am ple.--Figure 5 depicts 3 sample landscapes that vary in the amount and pattern of mixed,
large sawtimber habitat. The interspersion and juxtaposition index (IJI) indicates that the mixed, large sawtimber
edg e present in landscape B is m ore equitably d istributed am ong patch types than in either land scape A or C. Note
also that although landscapes A and C contain very different numbers of patch types (10 vs. 3), the interspersion
and juxtaposition index is roughly the same, indicating that the mixed, large sawtimber edge is distributed among
the available patch types at about 50% of the maximum po ssible equitable distribution in both landscapes, even
thou gh th e absolutes am oun ts of ed ge an d propo rtions a ssociated w ith each edge type are clearly qu ite different.
Lan dscape-L evel Exa mp le.--Figure 6 depicts 3 sample landscapes that vary in composition and pattern. The
interspersion and juxtaposition index (IJI) ind icates that the interspersion of av ailable patch types is greatest in
54
landscape A and least in lan dscape C . This o ccurs because landscape C contains 2 p atch ty pes that are p resen t only
in the landscape border and the amount of edge involving these 2 types is very small. Thus, the distribution of edge
lengths among u nique types is very uneven. Accordingly, the contagion index (CONTAG ) is greatest in landscape
C and least in landscape A. This reflects both the interspersion of patch types as discussed above as well as the
larger, more contiguous patches in landscape C compared to landscape A.
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61
Appendix A. Example of the FRAGSTATS output file formatted exclusively for display
purposes (i.e., "basename".full). Each run of FRAGSTATS on a landscape produces an output
file like this one. The results reported here correspond to the landscape displayed in figure 6
(landscape B). The results obtained using the vector and raster versions of FRAGSTATS are
included separately; note the differences in indices involving edge lengths and patch perimeters.
_______________________________________________________________________________
Vector Version
Date: 07 Oct 93 13:39:26 Thursday
Coverage: ncveg
Basename For Output Files: ncveg
Patch Type Attribute: class
Edge Dist: 100
Background Class: NONE
Max Patch Types Possible: 27
Weight File: contrast.new
Patch ID Attribute: patchid
Class Names Attribute: classdesc
Input Landscape Contains a Landscape Border
Proportion of Boundary/Background to Count as Edge: 0.00
Write Patch Indices: YES
Write Class Indices: YES
AML/Program Directory: /gis/giswork/barbara/vector/
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
700
1.118
437.399
1.167
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
W
0.378
6.695
1.305
0
W
296.073
0.378
0.338
0.000
437.399
0.099
6.695
1.243
1.167
1.305
0.000
0
0.000
0.000
0.000
0.000
13.711
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con (%):
Mean Shape Index:
Double Log Fractal Index:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
1.118
0.378
1
1.118
0.000
1.477
6.695
6.695
1.167
NA
1.305
0.000
0.000
0.000
0.000
0.000
0.000
CLASS INDICES
Patch Type:
Total Area (ha):
Largest Patch Index (%):
Patch Density (#/100 ha):
Patch Size SD (ha):
Total Edge (m):
Con-Wght Edge Den (m/ha):
Mean Edge Contrast (%):
Landscape Shape Index:
Area-Weighted Mean Shape:
Mean Patch Fractal:
Core % of Landscape (%):
Number Core Areas:
Mean Core Area 1 (ha):
Core Area CV 1 (%):
Core Area SD 2 (ha):
Total Core Area Index (%):
Intersper/Juxtapos (%):
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
200
18.586
1907.330
1.248
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
MGF
8.413
80.049
1.245
62
Core Area (ha):
Core Area Index (%):
4.622
24.868
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
500
6.323
1046.888
1.174
0.016
0.248
Num Core Areas:
1
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
MGF
8.413
91.000
1.258
1
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con (%):
Mean Shape Index:
Double Log Fractal Index:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
24.908
8.413
2
12.454
49.232
9.978
83.930
82.829
1.211
1.113
1.248
4.638
0.676
2.303
2.319
99.324
12.558
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
MSH
6.082
74.276
1.231
1
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con (%):
Mean Shape Index:
Double Log Fractal Index:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
18.008
6.082
1
18.008
0.000
7.957
73.927
74.276
1.138
NA
1.231
4.612
0.338
0.000
4.612
0.000
25.610
CLASS INDICES
Patch Type:
MGF
Total Area (ha):
296.073
Largest Patch Index (%):
6.277
Patch Density (#/100 ha):
0.676
Patch Size SD (ha):
6.131
Total Edge (m):
2954.219
Con-Wght Edge Den (m/ha):
8.375
Mean Edge Contrast (%):
85.525
Landscape Shape Index:
1.655
Area-Weighted Mean Shape:
1.229
Mean Patch Fractal:
1.252
Core % of Landscape (%):
1.566
Number Core Areas:
2
Mean Core Area 1 (ha):
2.319
Core Area CV 1 (%):
99.324
Core Area SD 2 (ha):
2.303
Total Core Area Index (%):
18.619
Intersper/Juxtapos (%):
62.578
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
600
18.008
1712.001
1.138
4.612
25.610
CLASS INDICES
Patch Type:
MSH
Total Area (ha):
296.073
Largest Patch Index (%):
6.082
Patch Density (#/100 ha):
0.338
Patch Size SD (ha):
0.000
Total Edge (m):
2355.761
Con-Wght Edge Den (m/ha):
5.882
Mean Edge Contrast (%):
74.276
Landscape Shape Index:
1.452
Area-Weighted Mean Shape:
1.138
Mean Patch Fractal:
1.231
Core % of Landscape (%):
1.558
Number Core Areas:
1
Mean Core Area 1 (ha):
4.612
Core Area CV 1 (%):
0.000
Core Area SD 2 (ha):
0.000
Total Core Area Index (%):
25.610
Intersper/Juxtapos (%):
30.221
PATCH INDICES
63
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
102
28.318
2430.356
1.288
8.769
30.965
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
MLS
48.802
18.807
1.242
1
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
110
51.288
4544.994
1.790
12.336
24.052
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
MLS
48.802
24.408
1.281
3
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
104
51.332
6230.153
2.453
8.459
16.478
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
MLS
48.802
16.959
1.329
2
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
108
8.255
1893.036
1.859
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
MLS
48.802
25.391
1.333
0
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
107
5.298
912.608
1.118
0.010
0.189
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
MLS
48.802
21.105
1.253
1
CLASS INDICES
Patch Type:
MLS
Total Area (ha):
296.073
Largest Patch Index (%):
17.338
Patch Density (#/100 ha):
1.689
Patch Size SD (ha):
19.940
Total Edge (m):
15198.311
Con-Wght Edge Den (m/ha):
11.374
Mean Edge Contrast (%):
21.334
Landscape Shape Index:
3.218
Area-Weighted Mean Shape:
1.907
Mean Patch Fractal:
1.288
Core % of Landscape (%):
9.988
Number Core Areas:
7
Mean Core Area 1 (ha):
5.915
Core Area CV 1 (%):
84.772
Core Area SD 2 (ha):
5.010
Total Core Area Index (%):
20.467
Intersper/Juxtapos (%):
75.666
Class Area (ha):
144.491
Percent of Landscape (%):
48.802
Number Patches:
5
Mean Patch Size (ha):
28.898
Patch Size CV (%):
69.001
Edge Den (m/ha):
51.333
Total Edge Contrast (%):
19.311
Area-Wt Mean Edge Con (%): 20.599
Mean Shape Index:
1.702
Double Log Fractal Index:
1.519
Area-Weighted Mean Fractal: 1.292
Total Core Area (ha):
29.573
Core Area Den (#/100 ha):
2.364
Core Area SD 1 (ha):
5.014
Mean Core Area 2 (ha):
4.225
Core Area CV 2 (%):
118.578
Mean Core Area Index (%):
14.337
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
101
33.096
5744.522
2.817
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
HLS
14.474
35.092
1.362
64
Core Area (ha):
Core Area Index (%):
0.370
1.118
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
106
9.757
1937.990
1.750
0.014
0.146
Num Core Areas:
1
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
HLS
14.474
5.734
1.318
1
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con (%):
Mean Shape Index:
Double Log Fractal Index:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
42.853
14.474
2
21.427
54.463
25.471
27.136
28.407
2.284
1.779
1.352
0.384
0.676
0.178
0.192
92.580
0.632
CLASS INDICES
Patch Type:
HLS
Total Area (ha):
296.073
Largest Patch Index (%):
11.178
Patch Density (#/100 ha):
0.676
Patch Size SD (ha):
11.670
Total Edge (m):
7541.288
Con-Wght Edge Den (m/ha):
7.216
Mean Edge Contrast (%):
20.413
Landscape Shape Index:
2.256
Area-Weighted Mean Shape:
2.574
Mean Patch Fractal:
1.340
Core % of Landscape (%):
0.130
Number Core Areas:
2
Mean Core Area 1 (ha):
0.192
Core Area CV 1 (%):
92.580
Core Area SD 2 (ha):
0.178
Total Core Area Index (%):
0.897
Intersper/Juxtapos (%):
48.750
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
300
5.733
1291.624
1.522
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
COS
7.622
51.324
1.308
0
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
400
16.833
1922.240
1.322
2.347
13.944
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
COS
7.622
42.022
1.257
1
COS
296.073
5.685
0.676
5.550
2895.564
5.296
46.673
1.520
1.372
1.282
0.793
1
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con (%):
Mean Shape Index:
Double Log Fractal Index:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
22.567
7.622
2
11.283
49.186
9.780
46.407
44.386
1.422
0.738
1.270
2.347
0.338
CLASS INDICES
Patch Type:
Total Area (ha):
Largest Patch Index (%):
Patch Density (#/100 ha):
Patch Size SD (ha):
Total Edge (m):
Con-Wght Edge Den (m/ha):
Mean Edge Contrast (%):
Landscape Shape Index:
Area-Weighted Mean Shape:
Mean Patch Fractal:
Core % of Landscape (%):
Number Core Areas:
65
Mean Core Area 1 (ha):
Core Area CV 1 (%):
Core Area SD 2 (ha):
Total Core Area Index (%):
Intersper/Juxtapos (%):
1.174
100.000
0.000
10.401
55.228
Core
Mean
Core
Mean
Area
Core
Area
Core
SD 1
Area
CV 2
Area
(ha):
2 (ha):
(%):
Index (%):
1.174
2.347
0.000
6.972
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
103
11.882
2454.529
2.009
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
CLS
14.229
4.720
1.336
0
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
111
2.386
608.411
1.111
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
CLS
14.229
12.854
1.272
0
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
105
20.633
3059.747
1.900
1.308
6.341
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
CLS
14.229
3.612
1.312
1
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
109
7.227
2034.829
2.135
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
CLS
14.229
27.785
1.362
0
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con (%):
Mean Shape Index:
Double Log Fractal Index:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
42.129
14.229
4
10.532
63.894
27.902
13.426
8.595
1.789
1.626
1.325
1.308
0.338
0.567
1.308
0.000
1.585
CLASS INDICES
Patch Type:
CLS
Total Area (ha):
296.073
Largest Patch Index (%):
6.969
Patch Density (#/100 ha):
1.351
Patch Size SD (ha):
6.729
Total Edge (m):
8261.122
Con-Wght Edge Den (m/ha):
4.099
Mean Edge Contrast (%):
12.243
Landscape Shape Index:
2.267
Area-Weighted Mean Shape:
1.926
Mean Patch Fractal:
1.320
Core % of Landscape (%):
0.442
Number Core Areas:
1
Mean Core Area 1 (ha):
0.327
Core Area CV 1 (%):
173.205
Core Area SD 2 (ha):
0.000
Total Core Area Index (%):
3.106
Intersper/Juxtapos (%):
46.744
LANDSCAPE INDICES
Total Area (ha):
Largest Patch Index(%):
Number of patches:
296.073
17.338
17
66
Patch Density (#/100 ha):
5.742
Mean Patch Size (ha):
17.416
Patch Size Standard Dev (ha):
15.048
Patch Size Coeff of Variation (%):
86.404
Total Edge (m):
19821.830
Edge Density (m/ha):
66.949
Contrast-Weight Edge Density (m/ha):
21.170
Total Edge Contrast Index (%):
26.497
Mean Edge Contrast Index (%):
31.872
Area-Wght Mean Class Edge Contrast (%): 30.281
Landscape Shape Index:
3.878
Mean Shape Index:
1.635
Area-Weighted Mean Shape Index:
1.859
Double Log Fractal Dimension:
1.489
Mean Patch Fractal Dimension:
1.294
Area-Weighted Mean Fractal Dimension:
1.296
Total Core Area (ha):
42.862
Number of Core Areas:
14
Core Area Density (#/100 ha):
4.729
Mean Core Area 1 (ha):
2.521
Core Area Standard Dev 1 (ha):
6.931
Core Area Coeff of Variation 1 (%):
274.894
Mean Core Area 2 (ha):
3.062
Core Area Standard Dev 2 (ha):
7.528
Core Area Coeff of Variation 2 (%):
245.900
Total Core Area Index (%):
14.477
Mean Core Area Index (%):
8.468
Shannon's Diversity Index:
1.503
Simpson's Diversity Index:
0.704
Modified Simpson's Diversity Index:
1.218
Patch Richness:
7
Patch Richness Density (#/100 ha):
2.364
Relative Patch Richness (%):
25.926
Shannon's Evenness Index:
0.772
Simpson's Evenness Index:
0.821
Modified Simpson's Evenness Index:
0.626
Interspersion/Juxtaposition (%):
64.713
67
Raster Version
INPUT PARAMETERS:
Date: Tue Oct 26 12:41:29 1993
Image Name: ncveg.svf
Basename For Output Files: ncveg
Rows: 473
Cols: 465
Cellsize: 5.0
Data Type: 1
Edge Dist: 100.0
Max Patch Types Possible: 27
Background Class: -9999
Weight File: contrast.new
ID Image: ncvegid.svf
Descriptor File: classnames.dat
Image Includes a Landscape Border
Proportion of Boundary/Background to Count as Edge: 0.00
Diagonals Used;
Proximity Dist (m): 200.0
Nearest Neighbor Calcs
Write Patch Indices;
Write Class Indices
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
700
1.117
550.000
1.301
0.000
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
W
0.377
6.364
1.056
0
NONE
W
296.068
0.377
0.338
0.000
550.000
0.118
6.364
1.353
1.301
1.056
0.000
0
0.000
0.000
0.000
0.000
NONE
NA
13.219
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con(%):
Mean Shape Index:
Double Log Fractal Index:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
Near Neighor SD (m):
Mean Prox Index:
1.117
0.377
1
1.117
0.000
1.858
6.364
6.364
1.301
NA
1.056
0.000
0.000
0.000
0.000
0.000
0.000
NA
0.000
CLASS INDICES
Patch Type:
Total Area (ha):
Largest Patch Index (%):
Patch Density (#/100 ha):
Patch Size SD (ha):
Total Edge (m):
Con-Wght Edge Den (m/ha):
Mean Edge Contrast (%):
Landscape Shape Index:
Area-Weighted Mean Shape:
Mean Patch Fractal:
Core % of Landscape (%):
Number Core Areas:
Mean Core Area 1 (ha):
Core Area CV 1 (%):
Core Area SD 2 (ha):
Total Core Area Index (%):
Mean NearNeigh Dist(m):
Nearest Neighbor CV (%):
Intersper/Juxtapos (%):
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
200
18.595
2320.000
1.345
5.513
29.645
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
MGF
8.410
80.925
1.049
1
216.910
68
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
500
6.305
1340.000
1.334
0.310
4.917
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
MGF
8.410
91.000
1.052
1
216.910
CLASS INDICES
Patch Type:
MGF
Total Area (ha):
296.068
Largest Patch Index (%):
6.281
Patch Density (#/100 ha):
0.676
Patch Size SD (ha):
6.145
Total Edge (m):
3660.000
Con-Wght Edge Den (m/ha):
10.460
Mean Edge Contrast (%):
85.962
Landscape Shape Index:
1.805
Area-Weighted Mean Shape:
1.342
Mean Patch Fractal:
1.051
Core % of Landscape (%):
1.967
Number Core Areas:
2
Mean Core Area 1 (ha):
2.911
Core Area CV 1 (%):
89.352
Core Area SD 2 (ha):
2.601
Total Core Area Index (%):
23.384
Mean NearNeigh Dist (m):
216.910
Nearest Neighbor CV (%):
0.000
Intersper/Juxtapos (%):
61.481
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con(%):
Mean Shape Index:
Double Log Fractal:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
Nearest Neighbor SD (m):
Mean Prox Index:
24.900
8.410
2
12.450
49.357
12.362
84.613
83.476
1.340
1.015
1.050
5.822
0.676
2.601
2.911
89.352
17.281
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
MSH
6.083
74.247
1.039
1
NONE
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con(%):
Mean Shape Index:
Double Log Fractal Index:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
Near Neighor SD (m):
18.010
6.083
1
18.010
0.000
10.048
73.901
74.247
1.267
NA
1.039
5.553
0.338
0.000
5.552
0.000
30.830
NA
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
600
18.010
2150.000
1.267
5.553
30.830
0.000
CLASS INDICES
Patch Type:
MSH
Total Area (ha):
296.068
Largest Patch Index (%):
6.083
Patch Density (#/100 ha):
0.338
Patch Size SD (ha):
0.000
Total Edge (m):
2975.000
Con-Wght Edge Den (m/ha):
7.426
Mean Edge Contrast (%):
74.247
Landscape Shape Index:
1.585
Area-Weighted Mean Shape:
1.267
Mean Patch Fractal:
1.039
Core % of Landscape (%):
1.875
Number Core Areas:
1
Mean Core Area 1 (ha):
5.552
Core Area CV 1 (%):
0.000
Core Area SD 2 (ha):
0.000
Total Core Area Index (%):
30.830
Mean NearNeigh Dist(m):
NONE
69
Nearest Neighbor CV (%):
Intersper/Juxtapos (%):
NA
29.771
Mean Prox Index:
0.000
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
102
28.317
3100.000
1.456
10.977
38.766
285.044
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
MLS
48.806
19.137
1.060
1
49.497
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
110
51.273
5720.000
1.997
16.308
31.806
52.460
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
MLS
48.806
24.814
1.105
2
82.462
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
104
51.362
7810.000
2.724
11.623
22.628
200.342
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
MLS
48.806
17.213
1.152
2
25.000
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
108
8.248
2390.000
2.081
0.000
0.000
74.190
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
MLS
48.806
24.791
1.129
0
87.321
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
107
5.298
1090.000
1.184
0.255
4.814
832.616
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
MLS
48.806
20.578
1.031
1
25.000
CLASS INDICES
Patch Type:
MLS
Total Area (ha):
296.068
Largest Patch Index (%):
17.348
Patch Density (#/100 ha):
1.689
Patch Size SD (ha):
19.945
Total Edge (m):
19115.000
Con-Wght Edge Den (m/ha):
14.399
Mean Edge Contrast (%):
21.307
Landscape Shape Index:
3.565
Area-Weighted Mean Shape:
2.125
Mean Patch Fractal:
1.096
Core % of Landscape (%):
13.228
Number Core Areas:
6
Mean Core Area 1 (ha):
7.832
Core Area CV 1 (%):
83.691
Class Area (ha):
144.498
Percent of Landscape (%):
48.806
Number Patches:
5
Mean Patch Size (ha):
28.899
Patch Size CV (%):
69.015
Edge Den (m/ha):
64.563
Total Edge Contrast (%):
19.470
Area-Wt Mean Edge Con(%):
20.843
Mean Shape Index:
1.888
Double Log Fractal:
1.551
Area-Weighted Mean Fractal: 1.112
Total Core Area (ha):
39.163
Core Area Den (#/100 ha):
2.027
Core Area SD 1 (ha):
6.555
Mean Core Area 2 (ha):
6.527
70
Core Area SD 2 (ha):
Total Core Area Index (%):
Mean NearNeigh Dist (m):
Nearest Neighbor CV (%):
Intersper/Juxtapos (%):
6.658
27.103
53.856
49.979
75.795
Core Area CV 2 (%):
Mean Core Area Index (%):
Nearest Neighbor SD (m):
Mean Prox Index:
102.005
19.603
26.917
288.930
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
101
33.065
7190.000
3.126
0.900
2.722
6.245
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
HLS
14.464
35.184
1.179
1
125.000
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
106
9.758
2410.000
1.929
0.275
2.818
21.162
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
HLS
14.464
5.747
1.114
1
125.000
PATCH INDICES
CLASS INDICES
Patch Type:
HLS
Total Area (ha):
296.068
Largest Patch Index (%):
11.168
Patch Density (#/100 ha):
0.676
Patch Size SD (ha):
11.654
Total Edge (m):
9405.000
Con-Wght Edge Den (m/ha):
9.048
Mean Edge Contrast (%):
20.465
Landscape Shape Index:
2.472
Area-Weighted Mean Shape:
2.853
Mean Patch Fractal:
1.147
Core % of Landscape (%):
0.397
Number Core Areas:
2
Mean Core Area 1 (ha):
0.587
Core Area CV 1 (%):
53.191
Core Area SD 2 (ha):
0.312
Total Core Area Index (%):
2.744
Mean NearNeigh Dist (m):
125.000
Nearest Neighbor CV (%):
0.000
Intersper/Juxtapos (%):
48.817
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con(%):
Mean Shape Index:
Double Log Fractal:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
Nearest Neighbor SD (m):
Mean Prox Index:
42.822
14.464
2
21.411
54.428
31.766
27.294
28.476
2.527
1.791
1.165
1.175
0.676
0.312
0.587
53.191
2.770
0.000
13.703
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
300
5.725
1580.000
1.651
0.000
0.000
7.008
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
COS
7.627
51.902
1.092
0
155.081
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
400
16.855
2420.000
1.474
3.830
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
COS
7.627
43.157
1.064
1
71
Core Area Index (%):
Proximity Index:
22.723
2.380
Near Neigh Dist (m):
155.081
CLASS INDICES
Patch Type:
COS
Total Area (ha):
296.068
Largest Patch Index (%):
5.693
Patch Density (#/100 ha):
0.676
Patch Size SD (ha):
5.565
Total Edge (m):
3630.000
Con-Wght Edge Den (m/ha):
6.676
Mean Edge Contrast (%):
47.529
Landscape Shape Index:
1.659
Area-Weighted Mean Shape:
1.519
Mean Patch Fractal:
1.078
Core % of Landscape (%):
1.294
Number Core Areas:
1
Mean Core Area 1 (ha):
1.915
Core Area CV 1 (%):
100.000
Core Area SD 2 (ha):
0.000
Total Core Area Index (%):
16.962
Mean NearNeigh Dist (m):
155.081
Nearest Neighbor CV (%):
0.000
Intersper/Juxtapos (%):
54.242
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con(%):
Mean Shape Index:
Double Log Fractal:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
Nearest Neighbor SD (m):
Mean Prox Index:
22.580
7.627
2
11.290
49.291
12.261
47.173
45.374
1.562
0.790
1.071
3.830
0.338
1.915
3.830
0.000
11.362
0.000
4.694
PATCH INDICES
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
103
11.883
3100.000
2.248
0.000
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
CLS
14.233
4.742
1.139
0
220.511
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
111
2.390
780.000
1.261
0.000
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
CLS
14.233
13.269
1.046
0
313.050
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
105
20.610
3810.000
2.098
2.022
9.813
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
CLS
14.233
3.675
1.121
1
220.511
Patch ID:
Area (ha):
Perimeter (m):
Shape Index:
Core Area (ha):
Core Area Index (%):
Proximity Index:
109
7.258
2530.000
2.348
0.000
0.000
0.000
Patch Type:
Landscape Similarity (%):
Edge Contrast (%):
Fractal Dimension:
Num Core Areas:
Near Neigh Dist (m):
CLS
14.233
27.419
1.153
0
313.050
CLASS INDICES
72
Patch Type:
CLS
Total Area (ha):
296.068
Largest Patch Index (%):
6.961
Patch Density (#/100 ha):
1.351
Patch Size SD (ha):
6.716
Total Edge (m):
10425.000
Con-Wght Edge Den (m/ha):
5.165
Mean Edge Contrast (%):
12.276
Landscape Shape Index:
2.504
Area-Weighted Mean Shape:
2.136
Mean Patch Fractal:
1.115
Core % of Landscape (%):
0.683
Number Core Areas:
1
Mean Core Area 1 (ha):
0.506
Core Area CV 1 (%):
173.205
Core Area SD 2 (ha):
0.000
Total Core Area Index (%):
4.799
Mean NearNeigh Dist (m):
266.780
Nearest Neighbor CV (%):
17.344
Intersper/Juxtapos (%):
46.635
Class Area (ha):
Percent of Landscape (%):
Number Patches:
Mean Patch Size (ha):
Patch Size CV (%):
Edge Den (m/ha):
Total Edge Contrast (%):
Area-Wt Mean Edge Con(%):
Mean Shape Index:
Double Log Fractal:
Area-Weighted Mean Fractal:
Total Core Area (ha):
Core Area Den (#/100 ha):
Core Area SD 1 (ha):
Mean Core Area 2 (ha):
Core Area CV 2 (%):
Mean Core Area Index (%):
Nearest Neighbor SD (m):
Mean Prox Index:
LANDSCAPE INDICES
Total Area (ha):
296.067
Largest Patch Index(%):
17.348
Number of patches:
17
Patch Density (#/100 ha):
5.742
Mean Patch Size (ha):
17.416
Patch Size Standard Dev (ha):
15.048
Patch Size Coeff of Variation (%):
86.405
Total Edge (m):
24880.000
Edge Density (m/ha):
84.035
Contrast-Weight Edge Density (m/ha):
26.647
Total Edge Contrast Index (%):
26.721
Mean Edge Contrast Index (%):
32.010
Area-Wght Mean Class Edge Contrast (%): 30.538
Landscape Shape Index:
4.290
Mean Shape Index:
1.813
Area-Weighted Mean Shape Index:
2.064
Double Log Fractal Dimension:
1.491
Mean Patch Fractal Dimension:
1.093
Area-Weighted Mean Fractal Dimension:
1.109
Total Core Area (ha):
57.565
Number of Core Areas:
13
Core Area Density (#/100 ha):
4.391
Mean Core Area 1 (ha):
3.386
Core Area Standard Dev 1 (ha):
4.897
Core Area Coeff of Variation 1 (%):
144.609
Mean Core Area 2 (ha):
4.428
Core Area Standard Dev 2 (ha):
5.171
Core Area Coeff of Variation 2 (%):
152.717
Total Core Area Index (%):
19.443
Mean Core Area Index (%):
11.852
Mean Nearest Neighbor (m):
155.359
Nearest Neighbor Standard Dev (m):
90.473
Nearest Neigh Coeff of Variation (%):
58.235
Mean Proximity Index:
87.144
Shannon's Diversity Index:
1.503
Simpson's Diversity Index:
0.704
42.140
14.233
4
10.535
63.747
35.212
13.509
8.609
1.989
1.598
1.127
2.022
0.338
0.876
2.023
0.000
2.453
46.269
0.000
73
Modified Simpson's Diversity Index:
Patch Richness:
Patch Richness Density (#/100 ha):
Relative Patch Richness (%):
Shannon's Evenness Index:
Simpson's Evenness Index:
Modified Simpson's Evenness Index:
Interspersion/Juxtaposition Index (%):
Contagion (%):
1.217
7
2.364
25.926
0.772
0.821
0.626
64.587
41.358
74
Appendix B. FRAGSTATS user guidelines.
The following instructions provide the information required to install and run the vector and raster versions of
FRAGSTA TS. The input parameters are described only briefly here; the OVERVIEW OF FRAGSTA TS section
should be read to fully und erstand these guidelines and some o f the options. These instructions assume that users
hav e working k now ledge of the UNIX operating environme nt.
Vector Version
Requirements/Limitations.--The vector version of the program is an Arc/Info AML. It was developed on a
SUN workstation in a UNIX operating environment using Arc/Info version 6.1; it will not run with earlier versions
of Arc/Info. The A ML calls several C program s to perform functions that either are not available in AM L or are
difficult to implement in AML (e.g., calculating logarithms, regression computations associated with the double log
fractal dim ensio n ind ex, operations in volv ing th e optional weig ht file, an d for form atting records in the outpu t files).
These C programs were compiled with the GNU C compiler and may not compile with other compilers. Many
loops in this AM L go from the minimum to the maximum patch type value. Therefore, it is most efficient if the
patch type codes are sequ ential. For ex am ple, a cove rage with 50 p atch ty pe co des rangin g from 1 to 50 wo uld
process m uch faster than one w ith 50 codes scattered th rougho ut the rang e 1000 to 200 0. Because of lim itations in
Arc /Info (i.e., cannot calculate edg e-to-e dge distances), the vec tor ve rsion of FR AG STAT S do es no t calculate
nearest neighbor metrics. To compute these indices from a vector image, the image m ust be rasterized first and then
analyzed with the raster version of FRAG STAT S. During the rasterization process, depending on the cell size
selected, it is possible for polygons to merge or divide. Therefore, considerable care should be exercised when
rasterizing a vector image to insure meaningful results. The following instructions assume that users have working
knowledge of Arc/Info.
Installation.--To install FRAG STAT S from the DOS com patible diskette containing the FRAGSTA TS program
files (filenames have bee n shortened to 8 characters):
(1) Copy the files from the directory "vector" on the diskette to the desired DOS directory.
(2) Mov e all FRAG STAT S program files into the UNIX environment using FTP or some other file transfer
utility. Note that the U NIX utility "dos2unix " may have to be run to strip carriag e returns fro m a ll files if
the file transfer utility does not perform this function automatically.
(3) In UN IX, renam e the file fragstat.aml to fragstats.aml (mv fragstat.aml fragstats.aml).
(4) In UNIX, rename the file fragstat.doc to fragstats.doc (mv fragstat.doc fragstats.doc). This file contains
these user guidelines for the vector version of FRAGSTA TS.
(5) In UN IX, run the script makeall to build the C program s (makeall).
Running FRAGSTATS.--To run FRAGSTA TS in Arc/Info there is a single comm and line, consisting of several
argum ents (each described below ), issued from the arc pro mp t as follows:
&run fragstats coverage basename patchtype edge_dist [background] [max_classes] [weight_file]
[patch_id] [descriptor] [bound_wght] [write_patch] [write_class] [path]
NOTE: If fragstats is run without the comm and line argum ents, the user will be prom pted for all the necessary
inputs.
75
NOTE: The first 4 parameters are required; the remaining 9 parameters in square brackets are optional; use a #
in place of skipped OPT ION AL param eters; enter a carriage return fo r defaults.
NOTE: If an index is not calculated, a dot (".") will be output to the "basename.patch", "basename.class", and
"basename.land" files. The abbreviation "NA" w ill be output to the "basename.full" file.
Coverage {char}: T he nam e of the input arc/info cove rage. The coverage m ust be built for polygo ns an d lines.
Acceptable landscape formats are discussed in the FRAG STA TS O VER VIEW section (see Fig. 2).
Basename {char}: T he basenam e for th e output A SCII files. Th e extension s ".patch", ".class", ".lan d", an d ".full"
will be added to the basename. The output files contain the following information:
basename.patch: each record con tains all the patch ind ices for a give n patch separated by spa ces.
basename.class: each reco rd con tains all the class indices for a g iven class sep arated by spaces.
basename.land: each record contains all the landscap e indices for a given landscap e separated by spa ces.
basenam e.full: A file con taining patch , class, and landscape indices for a g iven landscape. Th is file is
form atted for displaying resu lts.
NOTE: The "ba sename .patch ", "basename .class" and "basenam e.land " files are in a format that sh ould
facilitate input to database management programs; they are not intended for viewing results (records
are very long). Also note that if the files already exist, the information for a given landscape will be
appended to the existing files.
Patchtype {char} : The name of the num eric attribute con taining pa tch type codes (fo r exam ple, an attribute "class"
defined as 4,4,b that contains patch type codes ranging from 1 to 50). Polygons with patch type codes greater
than or equal zero are considered to be the landscape of interest. Polygons surrounding the landscape can be
included so that indices requiring adjacency information can be calculated for polygons bordering the landscape
bound ary. These landscape bo rder polygon s should be set to a negative patch type value (see Fig. 2).
Edg e_dist {float}: The distan ce fro m p atch e dge in m eters to use fo r determining core area (i.e., interior habitat).
The core area o f a patch is the area remaining after a buffer "edge_dist" wide is removed from the edg e of a
patch.
Background {integer}: Optional; the patch type (class) value of patches to be ignored in the input landscape
[default is N ON E].
Max_classes {integer}: Optional; the maximum number of patch types (classes) that could be present in the
landscape [default is NONE]. This is needed for calculating relative patch richness. If a value is not provided,
relate patch richness will not be calculated.
Weight_ file {char}: Optional; the name of an ASC II file containing weights for each combination of patch types
(classes) [default is NONE]. Each record should contain the numeric representation of 2 patch types and a
weight, separated by commas or spaces. For example:
1,2,.25
1,3,.32
2,3,.45 etc.
76
Weights represent the magnitude of edge contrast between adjacent patch types and must range between 0 and
1. Edge contrast weights are used to calculate several edge contrast indices. If the weight file is not provided,
these indices are not calculated.
Patch_id {char}: O ption al; the nam e of an attribute that con tains uniqu e ID's for each polyg on [default is
"coverage"#]. If an attribute is not provided, the "coverage"# attribute will be used.
Descriptor {char}: Optional; the name of an attribute that contains character descriptors for each patch type code
(class) [d efault is NO NE ]. This attribute must be defin ed as 10 characters or less and m ay not contain spaces.
If provided, the character descriptors will be written to the output files. Otherwise, the numeric patch type
codes will be written to the outp ut files.
Bound_wght {float}: Optional; what proportion (equivalent to contrast weight) of the landscape boundary and
backgrou nd class ed ges sho uld be c onsidered edge [default is 0]? This affects all edge ind ices.
(0) none; do n ot count any bo undary/back ground as edge (weight = 0 ).
(1) all; count all bound ary/backgrou nd as m aximum -contrast edge (weight = 1).
(2) other; specify a fraction between 0 and 1.
If you specify a fraction between 0 and 1, then that proportion of the total edge length involving the landscape
boundary and any background class will be included as edge in the metrics based on edge length (e.g., total
edg e, edg e den sity). Also, that sam e fraction w ill be use d as the edg e con trast weight for all ed ge segm ents
involving the landscape boundary and background class in the edge contrast metrics. See the FRAGSTATS
OVERV IEW section for a more detailed discussion.
Write_patch {y/n}: Optional; should patch indices be written to the output files [default is YES]? If not, the
"basename.patch" file will not be created and the patch indices will not be written to the "basename.full" file.
Write_class {y/n}: Optional; should class indices be written to the output files [default is YES]? If not, the
"basename.class" file will not be created and the class indices will not be written to the "basename.full" file.
Path {char}: Optional; the name of the directory containing the fragstats AML 's and C programs [default is the
current directory]. If these are in a directory other than the one the user is running frag stats from, the u ser mu st
set &A MLPA TH prior to run ning frag stats.
77
Raster Version
Requirements/Limitations.--The raster version of the program was developed on a SUN workstation in the
UN IX o perating environm ent. It is w ritten in C and com piled with the G NU C co mp iler and ma y no t com pile w ith
other C compilers. In this version of FRAGST ATS the input landscape file and the patch ID file are stored as
signe d sho rts (16 bits). Th erefo re, a lan dscape m ay not contain mo re than 32 767 different patch ty pes (th is
shouldn't be a problem!). The input (or output) patch ID image is also limited to 32767 unique ID's. On DEC or
IBM machines, the option of inputting an arc/info SVF file (see below) doesn't work, due to the different
architectures o f these m achines and SUN s.
The UN IX raster version of FRAGSTA TS has also been compiled to run in the DOS environment on a personal
com puter (PC ). The PC versio n of fragstats will only ru n on a 386 or better m achine. A ma th coprocesso r also is
required. It should run under DOS or Windows. Fragstats will use disk space to allocate virtual memory. The
environmental variable TEMP must be set to tell the program where to allocate the swap file (e.g., SET
TEM P=C:\tmp). Otherwise, the PC version of fragstats is run exactly the same way as the Unix version (see
guidelines below). Be aware that the PC version FRAGS TAT S may not run successfully on very large and complex
landscapes due to memory limitations on the PC.
Installation.--To install the UNIX version of FRAGSTA TS from the DOS compatible diskette containing the
FRA GST ATS program files (filenames have bee n shortened to 8 characters):
(1) Copy the files from the directory "raster" on the diskette to the desired DOS directory.
(2) Move all FRAG STAT S pro gram files to the UN IX environm ent using ftp or so me other file transfer utility.
No te that the UNIX utility "dos2unix " may have to be run to strip carriag e returns fro m a ll files if the file
transfer utility does not perform this function automatically.
(3) In UN IX, renam e the file fragstat.c to fragstats.c (mv fragstat.c fragstats.c).
(4) In UNIX, rename the file fragstat.doc to fragstats.doc (mv fragstat.doc fragstats.doc). This file contains
these user guidelines for the raster version of FRAGSTA TS.
(5) In UN IX, renam e the file fragstat.mak to fragstats.mak e (mv fragstat.mak fragstats.make).
(6) In UNIX, build fragstats (make -f fragstats.make or gmak e -f fragstats.make).
NOTE: The DOS version of FRAGSTATS does not require any installation.
Running FRAGSTATS.--To run FRA GS TA TS there is a single com ma nd lin e, con sisting o f several argum ents
(each d escribed b elow), issued from the prom pt as follow s:
fragsta ts in_imag e out_ file cellsize edge_dist data_type [row s] [cols] [backgrou nd] [ma x_classes]
[we ight_file] [id_image] [desc_file] [bo und_ wg ht] [diag s] [prox_ dist] [nndist] [pa tch_sta ts] [class_stats]
NOTE: If fragstats is run without the comm and line argum ents, the user will be prom pted for all the necessary
inputs.
NOTE: The first 5 p aram eters are required ; the rem aining 13 parame ters in sq uare parentheses are optio nal;
use a $ in p lace of skipped O PTIO NA L para meters.
78
NOTE: If an index is not calculated, a dot (".") will be output to the "basename.patch", "basename.class", and
"basen ame.land" files. The abbreviation "N A" w ill be output to the "basen ame.full" file. For nearest
neighbo r distan ce, if a patch h as no neighbo rs, "NON E" w ill be ou tput to "basename .full" an d a dot to
the other files.
In_image {char}: T he nam e of the input landscape file. F ile form ats are d iscusse d un der d ata_ty pe below and in
the FRAG STA TS O VE RVIEW section (see Fig. 3). Patches o utside the land scape b oundary can be in cluded so
that indices requiring adjacency information can be calculated for patches bordering the landscape boundary;
these landscape border patches should be set to a negative class value.
Ou t_file {char}: Basenam e for o utpu t ASCII files. The extension s .patch , .class, .land , and .full will be added to
the basename. Note that in the PC version, the extensions have been shortened to .pat, .cla, .lnd (Note: not .lan
so as not to conflict with ERDAS file name extensions), and .ful to comply with DOS requirements. The output
files contain the following in form ation:
basename.patch: each record con tains all the patch ind ices for a give n patch separated by spa ces.
basenam e.class: ea ch record contains all the class in dices for a g iven class sep arated by sp aces.
basename.land: each record contains all the landscap e indices for a given landscap e separated by spa ces.
basename.full: a file containing patch, class, and landscape indices for a given landscape. This file is formatted
for display ing results.
NOTE: The "ba sename .patch ", "basename .class" and "basenam e.land " files are in a format that sh ould
facilitate input to database management programs; they are not intended for viewing results (records
are very long). Also note that if the files already exist, the information for a given landscape will be
appended to the existing files.
Cellsize {float}: The size o f cells in m eters in the inp ut im age. Cells m ust be squa re. Th e leng th of 1 side of a cell
should b e input.
Edg e_dist {float}: The distance from patch edge in meters used to determine core area (i.e, interior habitat). The
core area of a patch is the area remaining after a buffer "edge_dist" wide is removed from the edge of a patch.
Data_type {integer}: The typ e of inpu t image file, as follows:
(1) SVF file; this is a file created with the arc/info "gridsvf" command.
(2) ASCII file, no header. Each record should contain 1 image row. Cell values should be separated by a
com ma or a space (s).
(3) 8 bit binary file, no header.
(4) 16 bit binary file, no header.
(5) ERD AS im age files (4, 8, or 1 6 bit), not IM AG INE imag es.
(6) IDR ISI ima ge files.
Rows {integer}: Optional; the number of rows in the input image. This is only required if data_type is 2, 3, or 4.
79
Cols {integer}: Optional; the number of columns in the input image. This is only required if data_type is 2, 3, or 4.
Background {integer}: Optional; the value of backgroun d cells [default is NON E]. This is only required if there
are cells interior or exterior to the landscape of interest that should be igno red (see Fig. 3).
Max_classes {integer}: Optional; the maximum number of patch types (classes) that could be present in the
landscape [default is NONE]. This is needed for calculating relative patch richness. If a value is not provided,
relative patch richness will not be calculated.
Weight_ file {char}: Optional; the name of an ASC II file containing weights for each combination of patch types
(classes) [default is NONE]. Each record should contain the numeric representation of 2 patch types and a
weight, separated by commas or spaces. For example:
1,2,.25
1,3,.32
2,3,.45 etc.
Weights represent the magnitude of edge contrast between adjacent patch types and must range between 0 and
1. Edge contrast weights are used to calculate several edge contrast indices. If the weight file is not provided,
these indices are not calculated.
Id_image: Optional {char}; the method for assigning patch ID's to each patch in the landscape [default is 2]. Input
1, 2, or the n ame of a file, as follow s:
(1) Create and output an image that contains unique ID's for each patch. This allows the user to relate a set of
patch statistics to a specific patch in the landscape, if another user-specified ID image is not specified
(option 3). This file is named "in_image".ID an d is the same "data_type" as "in_imag e".
(2) Do not o utpu t an ID image (i.e., b ecau se it is not im portant to relate a se t of patch statistics to a specific
patch in the landscape).
(3) The name of an ID image to read. The ID associated with each patch in this image will be written to the
output files. The "data_typ e" of this file must be the same as "in_im age".
Desc_file: Optional {char} ; the nam e of an A SCII file con taining ch aracter descriptors for each patch type (class)
[default is NONE]. Each record in the file should contain a numeric patch type value and the character
descriptor for that patch type, separated by a comm a or space(s). For example:
1 shrubs
2 conifers
3 deciduous
etc.
Descriptive names can not contain spaces. Use an underscore ("_") or a hyphen ("-") in place of blanks. The
parame ter ma x_label_length in the file stats.h co ntrols the printed length of labels in the outpu t files.
FRAGSTA TS is distributed with ma x_label_length set to 10. To change this, edit the file stats.h, change the
parame ter to the desired length, then re-build FRA GST ATS . Note that if ma x_label_length exceeds 22, the
columns will not be aligned in the file "basename".ful. If this descriptor file is provided, the character
descriptors will be written to the output files. Otherwise, the numeric patch type codes will be written to the
outpu t files.
80
Bound_wght {float}: Optional; what proportion (equivalent to contrast weight) of the landscape boundary and
backgrou nd class ed ges sho uld be c onsidered edge [default is 0]? This affects all edge ind ices.
(0) none; do n ot count any bo undary/back ground as edge (weight = 0 ).
(1) all; count all bound ary/backgrou nd as m aximum -contrast edge (weight = 1).
(2) other; specify a fraction between 0 and 1.
If you specify a fraction between 0 and 1, then that proportion of the total edge length involving the landscape
boundary and any background class will be included as edge in the metrics based on edge length (e.g., total
edg e, edg e den sity). Also, that sam e fraction w ill be use d as the edg e con trast weight for all ed ge segm ents
involving the landscape boundary and background class in the edge contrast metrics. See the FRAGSTATS
OVERV IEW section for a more detailed discussion.
Diags: Optional {y/n}; sho uld d iagonal neighbors be evaluated w hen findin g the cells that make up a patch [default
is YES]? If not, then the 4 cells (not 8) surrounding the cell of interest will be evaluated.
Prox_dist: Optional {float}; the search radiu s in m eters to use fo r calcu lating th e pro xim ity indices [default is
NONE]. If a value is not provided, the proximity indices will not be calculated. Note that "nndist" (below)
mu st be "yes" if the p roxim ity indices are to b e calculated becau se they req uire the sam e calculations.
Nnd ist: Optional {y/n}; should indices based on nearest neighbor distance be calculated [default in YES]? This can
be very time consuming on landscapes with hundreds of patches per class. Note that this parameter must be
"yes" if the pro ximity indices are to b e calculated becau se they req uire the sam e calculations.
Patch_stats: Optional {y/n}; should patch indices be written to the output files [default is YES]? If not, the
"basename.patch" file will not be created and the patch indices will not be written to the "basename.full" file.
Class_stats: Optional {y/n}; should class indices be written to the output files [default is YES]? If not, the
"basename.class" file will not be created and the class indices will not be written to the "basename.full" file.
81
Appendix C. Definition and description of FRAGSTATS metrics.
In this section, each metric computed in FRAGSTA TS is described. Metrics are grouped into patch, class, and
landscape indices. Within each group, metrics are ordered in logical fashion according to the aspect of landscape
structure measured. For example, the core area metrics (i.e., those based on core area measurements) are grouped
together. Each metric is defined in mathematical terms, and the measurement units and theoretical range in values
are reported. The acronym for the metric given on the left-hand side of the equation is the field name used in the
ASCII output files. Where the vector and raster algorithms differ, we define both. A single notation scheme is used
consistently for all metrics (Table. C.1). 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 con vert a proportion to a percentage, or m ultiplied or divided by 10,000 to con vert
m 2 to hectares. T hese conversio n factors are separated out b y parenth eses ev en thoug h they m ay be facto red in to
the eq uation differently in the com putational form of the algorithm . For each me tric, the m athem atical formula is
described in narrative terms to facilitate interpretation of the formula.
Table C.1. Notation used in FRAGSTATS algorithms.
____________________________________________________________________________________________
Sub scripts
i = 1, ... , m or m N patch types (classes)
j = 1, ... , n patches
k = 1, ... , m or m N patch typ es (classes)
q = 1, ... , p disjunct core areas
s = 1, ... , n patches, within specified neighborhood
Sym bols
A=
Total landscape area (m 2).
a ij =
area (m 2) of patch ij.
a ijs =
area (m 2) of patch ijs w ithin sp ecified neighbo rhood (m) of pa tch ij.
a ijc =
core area (m 2) of patch ij based on specified buffer width (m).
a ijqc =
area (m 2) of disjunct core area q in patch ij based on specified buffer width (m).
p ij =
perim eter (m ) of patch ij.
p ijk =
length (m) of edge of patch ij adjacent to patch type (class) k.
82
Table C.1. Continued.
____________________________________________________________________________________________
E=
total length (m) of edge in landscape; includes landscape boundary and background edge segments if the
user decides to treat boundary and background as edge; otherwise, only boundary segments representing
true edge are included.
EN =
total length (m ) of ed ge in landscape; inclu des entire lan dscape boun dary and back ground edge segme nts
regardless of whether they represent true edge.
e ik =
total length (m ) of edge in landscape betw een patch types (classes) i and k; includes landscape boundary
segm ents represe nting true ed ge only in volv ing p atch ty pe i.
e Nik =
total length (m ) of edge in landscape betw een patch types (classes) i and k; includes all landscape bou ndary
and background edge segments involving patch type i, regardless of whether they represent true edge.
e NNik =
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 true edge.
d ik =
dissimilarity (edge contrast weight) between patch types i and k.
N=
total num ber of p atches in the lan dscape, exclud ing any backg roun d patch es.
NN =
total num ber of p atches in the lan dscape that have nearest neighbors.
n = n i = num ber o f patches in the lan dscape of patch typ e (class) i.
n N = n Ni =
num ber of p atches in the lan dscape of patch type (class) i that hav e nearest neighbors.
n ijc =
num ber of disjunct core areas in patch ij based on specified buffer width (m).
m=
num ber o f patch typ es (classes) present in the landscape, exc ludin g the landscape border if present.
mN =
num ber o f patch typ es (classes) present in the landscape, inclu ding the lan dscape border if pre sent.
m max =
maximum number of patch types (classes) present in a landscape.
h ij =
distance (m) from patch ij to nearest neighboring patch of the same type (class), based on edge-to-edge
distance.
h ijs =
distance (m) between patch ijs [located within specified neighborhood distance (m) of patch ij] and patch
ij, based on edge-to-edge distance.
g ik =
number of adjacencies (joins) between pixels of patch types (classes) i and k.
Pi =
proportion o f the lan dscape occupied by p atch ty pe (class) i.
____________________________________________________________________________________________
83
Patch Indices
(P1) L andsc ape ID
The first field in the patch output file is landscape ID (LID). Landscape ID is set to the name of the input
coverage (coverage) in the vector version and the name of the input image (in_image) in the raster version.
(P2) P atch ID
The second field in the patch output file is patch ID (PID). The vector version of FRAG STAT S contains an
option (patch_id) to name an attribute that contains unique ID's for each patch. If an attribute is not specified, the
"coverage"# attribute is used. Likewise, the raster version of FRAGSTATS contains an option (id_image) to name
an image that contains unique ID's for each patch. If an image is not specified, FRAGSTATS will create unique
ID's for each patch and optionally produce an image that contains patch ID's that correspond to the FRAGSTATS
outp ut.
(P3) Patch Type
The third field in the patch output file is patch type (TYPE). The vector version of FRAGST ATS contains an
option (descriptor) to name an attribute that contains character descriptors for each patch type. Likewise, the raster
version of FRAGSTATS contains an option (desc_file) to name an ASCII file that contains character descriptors for
each patch type. In both versions, if the patch type options are not used, FRAG STAT S will write the numeric patch
type codes to TYPE.
(P4) Area
Vector/Raster
Un its:
Range:
Hectares
AR EA > 0, w ithou t limit.
The range in AREA is limited by the grain and extent of the image, and in a particular application, AREA
may be further limited by the specification of a minimum patch size that is larger than the grain.
Description: ARE A equ als the area (m 2) of the patch, divided by 10,00 0 (to convert to hectares).
84
(P5) Landscape Similarity Index
Vector/Raster
Un its:
Percent
Range:
0 < L SIM # 100
LSIM approaches 0 wh en the correspo ndin g patch type (class) becom es increasingly ra re in the land scape.
LSIM = 100 w hen the entire landscape consists of the corresponding patch type; that is, when the entire
image is comprised of a single patch.
Description: LSIM equals total class area (m 2) divided by total landscape area (m 2), multiplied by 1 00 (to conve rt to
a percentage); in other words, LSIM equals the percentage of the landscape comprised of the
correspo ndin g patch type. N ote that LS IM is equivalen t to %LA ND at the class level.
(P6) Perimeter
Vector/Raster
Un its:
Meters
Range:
PERIM > 0, w ithou t limit.
Description: PERIM equals the perimeter (m) of the patch, including any internal holes in the patch.
(P7) Edge Contrast Index
Vector/Raster
Un its:
Percent
Range:
0 # EDGECON # 100
85
EDGEC ON = 0 if the landscape consists of only 1 patch and either the landscape boundary contains no
edg e (when a border is present) or the boun dary is not to be trea ted as e dge (wh en a b order is absent).
Also, EDGEC ON = 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. EDG ECON = 100 when the entire patch
perim eter is m axim um -con trast edge (d = 1). ED GE CO N < 100 wh en a p ortion of the patch perim eter is
less than maximum-contrast edge (d < 1). EDGECON is reported as "NA" in the "basename".full file and
a dot "." in the "basename".patch file if a contrast weight file is not specified by the user.
Description: ED GE CO N equa ls the sum o f the patch p erim eter seg me nt lengths (m) mu ltiplied b y their
correspo ndin g contrast w eights, divided by total patch perim eter (m ), multiplied by 1 00 (to conve rt to
a percentage). Any perimeter segment along the landscape boundary (if a border is absent) or
bordering background is assigned the edge contrast weight specified by the user (see bound_wght
option).
(P8) Shape Index
Vector
Raster
Un its:
None
Range:
SHAPE $ 1, withou t limit.
SHAPE = 1 when the patch is circular (vector) or square (raster) and increases without limit as patch shape
becom es more irregular.
Description: SHA PE equ als patch perimeter (m) divided by the square root of patch area (m 2), adjusted by a
constant to adjust for a circular standard (vector) or square standard (raster).
(P9) Fractal Dimension
Vector
Raster
Un its:
None
Range:
1 # FRACT # 2
A fractal dimension greater than 1 for a 2-d imensional patch indicates a departure from euclidean geom etry
(i.e., an increase in shape complexity). FRACT approaches 1 for shapes with very simple perimeters such
as circles or squares, and appro aches 2 for shap es with highly co nvoluted, plane -filling perimeters.
86
Description: FRACT equals 2 times the logarithm of patch perimeter (m) divided by the logarithm of patch area
(m 2); the raster formula is adjusted to correct for the bias in perimeter (Li 198 9).
(P10) Core Area
Vector/Raster
Un its:
Hectares
Range:
CORE $ 0, withou t limit.
CORE = 0 when every location within the patch is within the specified edge distance from the patch
perimeter (i.e., edge width). CORE approaches AREA as the specified edge distance decreases and as
patch shape is simplified.
Description: COR E equals the area (m 2) within the patch that is further than the specified edge distance from the
patch perimeter, divided by 10,000 (to convert to hectares). Note that raster version of FRAGSTATS
employs the 4-neighbor approach when determining which cells are core and which are in the edge
buffer.
(P11) Number of Core Areas
Vector/Raster
Un its:
None
Range:
NCORE $ 0, withou t limit.
NCO RE = 0 w hen COR E = 0 [i.e., every location within the patch is within the specified edge distance
from the patch perimeter (i.e., edge width)]. NCORE > 1 w hen, because of shape, the patch contains
disjunct core areas.
Description: NCORE equals the number of disjunct core areas contained within the patch boundary.
87
(P12) Core Area Index
Vector/Raster
Un its:
Percent
Range:
0 # CAI < 100
CAI = 0 when CORE = 0 [i.e., every location within the patch is within the specified edge distance from
the patch perimeter (i.e., edge width)]; 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.
Description: CAI eq uals the patch core area (m 2) divided by total patch area (m 2), multiplied by 100 (to convert to a
percentage); in other words, CAI equals the percentage of a patch that is core area.
(P13) Nearest-Neighbor Distance
Raster
Un its:
Meters
Range:
NE AR > 0, w ithou t limit.
NEAR is reported as "None" in the "basename.full" output file and a dot in the "basename.patch" output
file if no other patch of the same type exists in the landscape.
Description: NE AR equals the distance (m ) to the nearest neighb oring p atch of the same type, based on shortest
edge-to-edge distance.
(P14) Proximity Index
Raster
Un its:
None
88
Range:
P RO X IM $ 0.
PROX IM = 0 if a patch has n o neighb ors of the same patch type within the specified search radiu s.
PROX IM 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 and less fragmented
in distribution. The upper limit of PROXIM is affected by the search radius and minimum distance
between patches. PROXIM is reported as "NA" in the "basename".full file and a dot "." in the
"basenam e".patch file if a search radius is not specified by the user.
Description: PRO XIM equals the sum of pa tch area (m 2) divided by the nearest edge-to-edge distance squared (m 2)
between the patch an d the focal patch of all patches of the corresponding patch type w hose edges are
within a specified distance (m) of the focal patch. Note, when the search buffer extends beyond the
landscap e bou ndary , only pa tches con tained w ithin the landsc ape are c onsidered in the com putations.
89
Class Indices
(C1) Landscape ID (LID)
The first field in the class output file is landscape ID (LID); it is defined as in the patch output file (see previous
discussion).
(C2) Patch Type (TYPE)
The second field in the class output file is patch type (TYPE); it is defined as in the patch output file (see
previous discussion).
(C3) Class Area
Vector/Raster
Un its:
Hectares
Range:
CA > 0, w ithou t limit.
CA ap proaches 0 as the patch type b ecom es 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.
Description: CA eq uals the sum of the areas (m 2) of all patches of the corresponding patch type, divided by 10,000
(to convert to hectares); that is, total class area.
(C4) Total Landscape Area
Vector/Raster
Un its:
Hectares
Range:
TA > 0, w ithou t limit.
Description: TA eq uals the area (m 2) of the landscape, divided by 10,000 (to convert to hectares). TA excludes the
area of any background patches within the landscape.
90
(C5) Percent of Landscape
Vector/Raster
Un its:
Percent
Range:
0 < %LAND # 100
%LAN D approaches 0 when the corresponding patch type (class) becomes increasingly rare in the
landscape. %LAN D = 100 when the entire landscape consists of a single patch type; that is, when the
entire image is comprised of a single patch.
Description: %L AN D equ als the sum of the areas (m 2) of all patches of the corresponding patch type, divided by
total landscape area (m 2), multiplied by 100 (to convert to a percentage); in other words, %LAND
equ als the p ercen tage th e land scape com prised of the corre spondin g patch type. N ote that %LA ND is
equ ivalen t to LS IM at the patch level.
(C6) La rgest Patch Index
Vector/Raster
Un its:
Percent
Range:
0 < LP I # 100
LPI approaches 0 when the largest patch of the corresponding patch type is increasing 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% o f the landscape.
Description: LPI equals the area (m 2) of the largest patch of the corresponding patch type divided by total landscape
area, multiplied by 100 (to convert to a percentage); in other words, LPI equals the percentage of the
landscape comprised by the largest patch.
91
(C7) Number of Patches
Vector/Raster
Un its:
None
Range:
NP $ 1, withou t limit.
NP = 1 wh en the landscape contain s only 1 patch o f the corresp onding patch type; that is, whe n the class
consists of a single patch.
Description: NP equ als the number of p atches of the corresponding p atch type (class).
(C8) Patch Density
Vector/Raster
Un its:
Num ber per 100 hectares
Range:
PD > 0, w ithou t limit.
Description: PD equals the number of patches of the corresponding patch type (NP) divided by total landscape area,
multiplied by 10,000 and 100 (to convert to 100 hectares).
(C9) M ean Patch Size
Vector/Raster
Un its:
Hectares
Range:
MPS > 0, withou t limit.
The range in MPS is limited by the grain and extent of the image and the minimum patch size in the same
man ner as patch area (ARE A).
92
Description: MP S equals the sum o f the areas (m 2) of all patches of the corresponding patch type, divided by the
num ber of patches of the same typ e, divided by 10,00 0 (to convert to hectares).
(C10) Patch Size Standard Deviation
Vector/Raster
Un its:
Hectares
Range:
PSSD $ 0, withou t limit.
PSS D = 0 when all patch es in the class are the same size o r wh en there is only 1 patch (i.e., no v ariability
in patch size).
Description: PSSD equals the square root of the sum o f the squared deviations of each patch area (m 2) from the
mean patch size of the corresponding patch type, divided by the number of patches of the same type,
divided by 10,000 (to convert to hectares); that is, the root mean squared error (deviation from the
mean) in patch size. Note, this is the population standard deviation, not the sample standard deviation.
(C11) Patch Size Coefficient of Variation
Vector/Raster
Un its:
Percent
Range:
PSCV $ 0, withou t limit.
PSC V = 0 when all patch es in the class are the sam e size o r wh en there is only 1 patch (i.e., no v ariability
in patch size).
Description: PSCV equals the standard deviation in patch size (PSSD) divided by the mean patch size of the
correspo ndin g patch type (M PS), m ultiplied by 1 00 (to conve rt to percent); that is, the v ariability in
patch size relative to the mean patch size. Note, this is the population coefficient of variation, not the
sample coefficient of variation.
93
(C12) Total Edge
Vector/Raster
Un its:
Meters
Range:
TE $ 0, withou t 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 edg e be treated as edge.
Description: TE eq uals the sum of the lengths (m) of all edge segm ents involving the corresponding patch type. If
a landscape border is present, TE includes landscape boundary segments involving the corresponding
patch type and repre senting true edge only (i.e., contrast w eight > 0). If a land scape 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 background edge segments involving the corresponding patch type.
(C13) E dge De nsity
Vector/Raster
Un its:
Meters per hectare.
Range:
ED $ 0, withou t 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 edg e be treated as edge.
Description: ED equals the sum of the lengths (m) of all edge segments involving the corresponding patch type,
divided by the total landscape area (m 2), 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., contrast weight > 0). If a landscape border is absent, ED includes
a user-specified proportion o f land scape bound ary segm ents involv ing th e correspo ndin g patch type.
Regardless of whether a landscape border is present or not, ED includes a user-specified proportion of
background edge segments involving the corresponding patch type.
94
(C14) C ontrast-W eighted Edg e Density
Vector/Raster
Un its:
Meters per hectare.
Range:
CWED $ 0, withou t 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 none of the landscape
boundary and background edge be treated as edge. CWED increases as the amount of class edge in the
landscape increases and/or as the con trast in ed ges involv ing th e correspo ndin g patch type increase (i.e.,
contrast weight approaches 1). CWED is reported as "NA" in the "basename".full file and a dot "." in the
"basenam e".class file if a contrast weight file is not specified by the user.
Description: CW ED equals the sum of the lengths (m) of each edge segment involving the corresponding patch
type mu ltiplied by the correspond ing contrast weight, divided by the total landscape area (m 2),
multiplied by 10,000 (to convert to hectares). If a landscape border is present, CWE D includes
landscape bound ary segm ents involv ing th e correspo ndin g patch type an d rep resen ting tru e edg e only
(i.e., con trast weight > 0). If a land scape border is absent, all landscape boun dary edge segme nts
involving the corresponding patch type are assigned the edge contrast weight specified by the user (see
bound_wght option). This is equivalent to treating the specified proportion of all boundary edge
segmen ts involving the corresponding p atch type as maxim um-co ntrast edge. Regardless of whether a
landscape border is present or not, all background edge segments involving the corresponding patch
type are assigned the edge contrast weight specified by the user. Again, this is equivalent to treating
the specified proportion of all background edge segments involving the corresponding patch type as
maximum -contrast edge.
95
(C15) Total Edge Contrast Index
Vector/Raster
Un its:
Percent.
Range:
0 # TEC I # 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 none of the landscape
boundary and background edge be treated as edge. TECI approaches 0 as the contrast in edges involving
the co rrespond ing p atch ty pe lesson (i.e., con trast weight approaches 0 ). TE CI = 100 wh en all class edge is
maximum contrast (i.e., contrast weight = 1). TECI is reported as "NA" in the "basename".full file and a
dot "." in the "basename".class file if a contrast weight file is not specified by the user.
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
segm ents involv ing th e sam e type, multiplied by 1 00 (to conve rt to a percen tage). In the num erator, if
a landscape border is present, all edge segments along the landscape boundary involving the
corresponding patch type are treated according to their edge contrast weights as designated in the
contrast weight file. If a landscape border is absent, all landscape boundary segments involving the
corresponding patch type are assigned the edge contrast weight specified by the user (see bound_wght
optio n). N ote that this is equivalent to tre ating the specified proportion o f all bound ary edge segm ents
involving the co rrespon ding p atch type as maximum -contrast ed ge and the rem ainder as zero-contrast
edg e. Reg ardless of w hether a lan dscape border is present or not, all back ground edge segme nts
invo lving the co rrespond ing p atch ty pe are assigned the ed ge co ntrast w eight specified by the user.
Ag ain, note that this is equivalent to tre ating the specified proportion o f all backgroun d edge segm ents
involving the co rrespon ding p atch type as maximum -contrast ed ge and the rem ainder as zero-contrast
edge. In the denominator, all edges involving the corresponding patch type are included, including the
landscape boundary and background edge segments, regardless of whether they represent true edge or
not or h ow the user ch ooses to h andle b oundary and backgroun d edg es.
96
(C16) M ean Edge Contrast Index
Vector/Raster
Un its:
Percent.
Range:
0 # ME CI # 100
MECI = 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. MECI approaches 0 as the contrast in edges involving
the corresponding patch type lesson (i.e., contrast weight approaches 0). MECI = 100 when all class edge
is maximum contrast (i.e., contrast weight = 1). MECI is reported as "NA" in the "basename".full file and
a dot "." in the "basename".class file if a contrast weight file is not specified by the user.
Description: MEC I equ als the su m o f the segm ent len gths (m) of each patche s' perim eter m ultiplied by th eir
corresponding contrast weights, divided by total patch perimeter (m), summed across all patches of the
correspo ndin g patch type, divided by the num ber o f patches o f the same type, mu ltiplied b y 10 0 (to
convert to a percentage). If a landscape border is present, any patch perimeter segments along the
landscap e bou ndary are treated acc ording to their edge contrast w eights as desig nated in the contrast
weight file. If a landscape border is absent, any patch perimeter segments along the landscape
bou nda ry are assign ed the edg e con trast weight specified by the user (see bo und _w ght o ption ).
Regardless of whether a landscape border is present or not, all patch perimeter segments bordering
backgrou nd are assigned the edge co ntrast weight specified by the user.
97
(C17) Area-W eighted Mean Edg e Contrast Index
Vector/Raster
Un its:
Percent.
Range:
0 # AW ME CI # 100
AWM ECI = 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 bound ary and b ackground edge be tre ated as edg e. AW MEC I app roaches 0 as the contrast in
edges involving the corresponding patch type lesson (i.e., contrast weight approaches 0). AWM ECI = 100
when all class edge is maximum contrast (i.e., contrast weight = 1). AWM ECI is reported as "NA" in the
"basename".full file and a dot "." in the "basename".class file if a contrast weight file is not specified by the
user.
Description: AW MEC I equ als the su m o f the segm ent len gths (m) of each patche s' perim eter m ultiplied by th eir
corresponding contrast weights, divided by total patch perimeter (m), multiplied by patch area (m 2)
divided by the sum of patch areas, summ ed across all patches of the corresponding patch type,
multiplied by 100 (to convert to a percentage). If a landscape border is present, any patch perimeter
segments along the landscape boundary are treated according to their edge contrast weights as
desig nated in the contrast weight file. If a landscape border is absent, an y patch perim eter seg me nts
along the landscape boundary are assigned the edge contrast weight specified by the user (see
bound_w ght option). Regardless of whether a landscape border is present or not, all patch perimeter
segm ents bordering back ground are assigned the edge con trast weight specified by the user.
AWM ECI is similar to MECI except that each patch weighted by its size in computing the average
patch edge contrast index.
98
(C18) L andscape S hape Index
Vector
Raster
Un its:
None
Range:
LSI $ 1, withou t limit.
LSI = 1 when the landscape consists of a single patch of the corresponding type and is circular (vector) or
square (raster); LSI increases without lim it as land scape shape become s more irregu lar and/or as the length
of edg e within the landscap e of the co rrespon ding p atch type increases.
Description: LSI equ als the su m o f the lan dscape boun dary (rega rdless o f wh ether it represents tru e edg e or n ot)
and all edge segments (m) within the landscape boundary involving the corresponding patch type
(including those bordering ba ckgroun d), divided by the square root of the total landscape area (m 2),
adjusted by a constant for a circular standard (vector) or square standard (raster).
(C19) M ean Sha pe Index
Vector
Raster
Un its:
None
Range:
MS I $ 1, withou t limit.
MSI = 1 when all patches of the corresponding patch type are circular (vector) or square (raster); MSI
increases without limit as the patch shapes beco me m ore irregular.
Description: MS I equals the sum of the patch perim eter (m) divided by the squ are root of patch area (m 2) for each
patch of the correspond ing patch type, adjusted by a con stant to adjust for a circular standard (vector)
or square standard (raster), divided by the number of patches of the same type; in other words, MSI
equals the average shape index (SHAP E) of patches of the corresponding patch type.
99
(C20) Area-W eighted Mean Shap e Index
Vector
Raster
U
ni
ts:
N
on
e
R
ange:
AW MS I $ 1, withou t limit.
AW MS I = 1 wh en all patches of the corresponding patch type are circular (vector) or square (raster);
AW MS I increases without limit as the patch shapes becom e more irregular.
Description: AW MSI equals the sum, across all patches of the corresponding patch type, of each patch perimeter
(m) divided b y the square root of patch area (m 2), adjusted by a constant to adjust for a circular
standard (vector) or square standard (raster), multiplied by the patch area (m 2) divided by total class
area (sum of patch area for each patch of the corresponding patch type). In other words, AWM SI
equals the average shape index (SHAPE) of patches of the corresponding patch type, weighted by
patch are a so that larger p atches w eigh m ore than smaller patches.
(C21) Double Log Fractal Dimension
Vector/Raster
Un its:
None
Range:
1 # DLFD # 2
A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates a departure from a
euclidean geom etry (i.e., an increase in patch shape com plexity). DLFD ap proaches 1 for shap es with very
simple perimeters such as circles or squares, and approaches 2 for shapes with highly convoluted, planefilling perim eters. D LFD emp loys regression techn iques and is subject to sm all sam ple problems.
Spe cifically, DL FD ma y greatly exceed the theo retical range in values w hen the num ber o f patches is sm all
(e.g., <10), and its use should be av oided in su ch ca ses. In addition, DLFD requires patches to vary in size.
Thus, DLFD is undefined and reported as "NA" in the "basename".full file and a dot "." in the
"basename".class file if all patches are the same size or there is only 1 patch.
Description: DLFD equals 2 divided by the slope of regression line obtained by regressing the logarithm of patch
100
area (m 2) against the logarithm o f patch perimeter (m).
(C22) Mean Patch Fractal Dimension
Vector
Raster
Un its:
None
Range:
1 # MPFD # 2
A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates a departure from a
euclidean geom etry (i.e., an increase in patch shape com plexity). MPFD approaches 1 fo r shapes with very
simple perimeters such as circles or squares, and approaches 2 for shapes with highly convoluted, planefilling perimeters.
Description: MPFD equals the sum of 2 times the logarithm of patch perimeter (m) divided by the logarithm of
patch area (m 2) for each patch of the corresponding patch type, divided by the number of patches of
the same type; the raster formula is adjusted to correct for the bias in perimeter (Li 1989).
(C23) Area-Weighted Mean Patch Fractal Dimension
Vector
Raster
Un its:
None
Range:
1 # AWMPFD # 2
A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates a departure from a
euclidean geome try (i.e., an increase in p atch sh ape com plexity). AWMPFD approaches 1 for shapes with
very simple perimeters such as circles or squares, and approaches 2 for shapes with highly convoluted,
plane-filling perimeters.
Description: AWM PFD equals the sum, across all patches of the corresponding patch type, of 2 times the logarithm
of patch perimeter (m ) divided by the logarithm o f patch area (m 2), multiplied by the patch area (m 2)
divided by total class area (sum of patch area for each patch of the corresponding patch type); the
raster formula is adjusted to correct for the bias in perimeter (Li 1989). In other words, AWM PFD
101
equals the average patch fractal dimension (FRACT) of patches of the corresponding patch type,
weighted by patch area so that larger p atches w eigh m ore than smaller patches.
(C24) Core Area Percent of Landscape
Vector/Raster
Un its:
Percent
Range:
0 # C%LA ND < 100
C% LAN D app roaches 0 w hen core area of the correspon ding patch type (class) becom es increasingly rare
in the landscape, because of increasing smaller patches and/or more convoluted patch shapes. C%LAND
app roaches 1 00 w hen the en tire land scape con sists of a sin gle patch ty pe (i.e., w hen the en tire image is
comprised of a single patch) and the specified edge width approaches zero.
Description: C% LAN D equ als the sum of the core areas of each patch (m 2) of the corresponding patch type,
divided by total landscape area (m 2), multiplied by 10 0 (to con vert to a percentage); in other w ords,
C%L AND equals the percentage the landscape comprised of core area of the corresponding patch
type.
(C25) Total Core Area
Vector/Raster
Un its:
Hectares
Range:
TCA $ 0, withou t limit.
TCA = 0 when every location within each patch of the corresponding patch type is within the specified
edge distance from the patch perimeters. TCA approaches CA as the specified edge distance decreases and
as patch shapes are simplified.
Description: TCA equals the sum of the core areas of each patch (m 2) of the corresponding patch type, divided by
10,000 (to con vert to hectares).
102
(C26) Nu mber of Co re Ar eas
Vector/Raster
Un its:
None
Range:
NCA $ 0, withou t limit.
NCA = 0 when TCA = 0 (i.e., every location within patches of the corresponding patch type are within the
specified edge distance from the patch perimeters). NCA > 1 when, due to patch shape complexity, a patch
contains more than 1 core area.
Description: NCA 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.
(C27) Core Area Density
Vector/Raster
Un its:
Num ber per 100 hectares
Range:
CAD $ 0, withou t limit.
CAD = 0 when TCA = 0 (i.e., every location within patches of the corresponding patch type are within the
specified ed ge distance from the patch perim eters); in other w ords, w hen the re are no core area s.
Description: CAD equals the sum of number of disjunct core areas contained within each patch of the
correspo ndin g patch type, divided by total landscape area, m ultiplied by 1 0,00 0 and 10 0 (to conv ert to
100 hectares).
103
(C28) M ean Core Area P er Patch
Vector/Raster
Un its:
Hectares
Range:
MCA 1 $ 0, withou t limit.
Ultimately, the range in MCA 1 is limited by the grain and extent of the image and the minimum patch size
in the sam e m ann er as m ean patch size (M PS), b ut M CA 1 is also effected by the specified ed ge w idth.
MC A1 = 0 when total core area = 0 (i.e., every location within patches of the corresponding patch type are
within the specified ed ge distance from the patch p erim eters); in other wo rds, w hen there are no core areas.
MCA 1 approaches MPS as the specified edge width decreases and as patch shapes are simplified.
Description: MC A1 eq uals the sum of the core areas of each pa tch (m 2) of the corresponding patch type, divided by
the number of patches of the same type, divided by 10,000 (to convert to hectares). Note that MCA1
equals the average core area per patch, not the average size of disjunct core areas, as in MCA 2.
(C29) Patch Core Area Standard Deviation
Vector/Raster
Un its:
Hectares
Range:
CASD1 $ 0, withou t limit.
CASD1 = 0 when all patches in the class have the same core area or when there is only 1 patch (i.e., no
variability in core area).
Description: CAS D1 eq uals the square root of the sum of the squared deviations of each patch core area (m 2) from
the mean core area per patch (MCA1) of the corresponding patch type, divided by the number of
patches of the same type, divided by 10,000 (to convert to hectares); that is, the root mean squared
error (deviation from the mean) in patch core area. Note, this is the population standard deviation, not
the sam ple standard dev iation, and that CASD1 represen ts the variation in co re area am ong patches,
104
not among disjunct core areas, as in CASD2.
(C30) Patch Core Area Coefficient of Variation
Vector/Raster
Un its:
Percent
Range:
CACV1 $ 0, withou t limit.
CACV1 = 0 w hen all patches in the class have the same core area or when there is only 1 patch (i.e., no
variability in core area).
Description: CACV 1 equals the standard deviation in core area of patches (CASD1) divided by the mean core area
per patch (M CA 1) of the correspo nding patch typ e, mu ltiplied by 10 0 (to con vert to percent); that is,
the variability in core area relative to the mean core area. Note, this is the population coefficient of
variation, not the sample coefficient of variation, and that CACV1 represents the variation in core area
among patches, not among disjunct core areas, as in CACV2.
(C31) M ean Area Per Disjunct Core
Vector/Raster
Un its:
Hectares
Range:
MCA 2 $ 0, withou t limit.
Ultimately, the range in MCA 2 is limited by the grain and extent of the image and the minimum patch size
in the sam e m ann er as m ean patch size (M PS), b ut M CA 2 is also effected by the specified ed ge w idth.
MC A2 = 0 when total core area = 0 (i.e., every location within patches of the corresponding patch type are
within the specified ed ge distance from the patch p erim eters); in other wo rds, w hen there are no core areas.
MCA 2 approaches MPS as the specified edge width decreases and as patch shapes are simplified.
Description: MC A2 eq uals the sum of the disjunct core areas of each patch (m 2) of the corresponding patch type,
divid ed by the num ber o f disjun ct core area s of the sam e type, divided by 1 0,00 0 (to conv ert to
hectares). Note that MCA 2 equals the average size of disjunct core areas, not the average core area
105
per patch, as in MCA1.
(C32) Disjunct Core Area Standard Deviation
Vector/Raster
Un its:
Hectares
Range:
CASD2 $ 0, withou t limit.
CASD2 = 0 when all disjunct core areas are the same size or when there is only 1 core area (i.e., no
variability in core area).
Description: CAS D2 eq uals the square root of the sum of the squared deviations of each disjunct core area (m 2)
from the mean size of disjunct core areas (MCA2) of the corresponding patch type, divided by the
number of disjunct core areas of the same type, divided by 10,000 (to convert to hectares); that is, the
root mean squared error (deviation from the mean) in the size of disjunct core areas. Note, this is the
population standard deviation, not the sample standard deviation, and that CASD2 represents the
variation in size of disjunct core areas, not patch core areas, as in CASD1.
106
(C33) Disjunct Core Area Coefficient of Variation
Vector/Raster
Un its:
Percent
Range:
CACV2 $ 0, withou t limit.
CACV2 = 0 w hen all disjunct core areas are the same size or when there is only 1 core area (i.e., no
variability in core area).
Description: CACV 2 equals the standard deviation in the size of disjunct core areas (CASD2) divided by the mean
size of disjun ct core area s (M CA 2) of the co rrespond ing p atch ty pe, m ultiplied by 1 00 (to conve rt to
percent); that is, the variability in core area relative to the mean core area. Note, this is the population
coefficient of variation, not the sample coefficient of variation, and that CACV2 represents the
variation in size of disjunct core areas, not patch core areas, as in CACV1.
(C34) T otal Core A rea Index
Vector/Raster
Un its:
Percent
Range:
0 # TCAI < 100
TCAI = 0 when none of the patches of the corresponding patch type contain any core area (i.e., CORE = 0
for every patch); that is, when the landscape contains no core area for the corresponding patch type. TCAI
approaches 100 when the patches of the corresponding patch type, because of size, shape, and edge width,
contain mostly core area.
Description: TCA I equals the sum of the core areas of each p atch (m 2) of the corresponding patch type, divided by
the sum of the areas of each p atch (m 2) of the same type, multiplied by 100 (to convert to a
percentage); that is, TCAI equals the percentage of a patch type in the landscape that is core area based
on a specified edge width.
107
(C35) M ean Co re Area Ind ex
Vector/Raster
Un its:
Percent
Range:
0 # MCA I < 100
MCAI = 0 when none of the patches of the corresponding patch type contain any core area (i.e., CORE = 0
for every patch); that is, when the landscape contains no core area for the corresponding patch type. MCAI
approaches 100 when the patches of the corresponding patch type, because of size, shape, and edge width,
contain mostly core area.
Description: MC AI equals the sum of the proportion of each patch that is core area {i.e., core area of each patch
(m 2) divided by the area of each p atch (m 2)} of the corresponding patch type, divided by the number of
patch es of th e sam e type, multiplied by 1 00 (to conve rt to a percen tage); In oth er words, MCA I equ als
the average percentage of a patch of the corresponding patch type in the landscape that is core area
based on a specified edge width.
(C36) M ean Nearest-Neighbor Distance
Raster
Un its:
Meters
Range:
MNN > 0, w ithou t limit.
MNN is repo rted as "None " in the "basename ".full file and a dot "." in the "basenam e".class file if there is
only 1 patch of the co rrespond ing p atch ty pe. Similarly, M NN is repo rted as "NA" in the "basenam e".full
file and a dot "." in the "basename".class file if the user chooses not to calculate nearest neighbor distance.
Description: MN N equals the sum of the distance (m) to the nearest neighboring patch of the same type, based on
nearest edge-to-edge distance, for each patch of the corresponding patch type, divided by the number
of patches of the same type.
108
(C37) Nearest-Neighbor Standard Deviation
Raster
Un its:
Meters
Range:
NNSD $ 0, withou t limit.
NNSD = 0 w hen there are only 2 patches in the class or all patches have the same nearest-neighbor
distance (i.e., no variability in nearest-neighbor distance). NNSD is reported as "NA" in the
"basename".full file and a dot "." in the "basename".class file if there is only 1 patch of the corresponding
patch type. Similarly, NNSD is reported as "NA" in the "basename".full file and a dot "." in the
"basename".class file if the user chooses not to calculate nearest neighbor distance.
Description: NNSD equals the square root of the sum of the squared deviations of each patches' nearest-neighbor
distance (m) from the mean nearest-neighbor distance (MNN ) 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 patch nearest neighbor distance. Note, this is the population standard deviation, not the
sample standard deviation.
(C38) Nearest-Neighbor Coefficient of Variation
Raster
Un its:
Percent
Range:
NNCV $ 0, withou t limit.
NNCV = 0 when there are only 2 patches in the class or all patches have the same nearest-neighbor
distance (i.e., no variability in nearest-neighbor distance; NNSD = 0). NNCV is reported as "NA" in the
"basename".full file and a dot "." in the "basename".class file if there is only 1 patch of the corresponding
patch type. Similarly, NNCV is reported as "NA" in the "basename".full file and a dot "." in the
"basename".class file if the user chooses not to calculate nearest neighbor distance.
Description: NNC V equals the standard deviation in nearest-neighbor distances (NNSD ) divided by the mean
nearest-neighbor distance (M NN ) of the correspo ndin g patch type, m ultiplied by 1 00 (to conve rt to
percent); that is, the variability in nearest neighbor distance relative to the mean nearest neighbor
109
distance. Note, this is the population coefficient of variation, not the sample coefficient of variation.
(C39) M ean Proximity Index
Raster
Un its:
None
Range:
MP I $ 0
MPI = 0 if all patches of the corresponding patch type have no neighbors of the same type within the
specified search radius. MPI increases as patches of the corresponding patch type become less isolated and
the patch type becomes less fragmented in distribution. The upper limit of MPI is determined by the search
radius and minimum distance between patches. MPI is reported as "NA" in the "basename".full file and a
dot "." in the "basename".class file if the user chooses not to calculate nearest neighbor distance.
Description: MP I equals the sum of patch area (m 2) divided by the nearest edge-to-edge distance squared (m 2)
between the patch an d the focal patch of all patches of the corresponding patch type w hose edges are
within a specified distance (m) of the focal patch, summ ed across all patches of the same type and
divid ed by the total nu mb er of p atche s in the class. In other wo rds, M PI eq uals the ave rage proxim ity
index for patches in the class. Note, when the search buffer extends be yond the land scape boun dary
for focal patches near the boundary, only patches contained within the landscape are considered in the
com putations.
110
(C40) Interspersion and Juxtaposition Index
Vector/Raster
Un its:
Percent
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
"NA" in the "basenam e".full file and a dot "." in the "basename ".class file if th e numb er of p atch ty pes is
less than 3.
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, summ ed 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 max imum p ossible interspersion for the g iven nu mb er of patch types. No te, IJI
con siders all patch types prese nt on an im age, includ ing any p resen t in the landscape border, if present.
111
Landscape Indices
(L1) Landscape ID (LID)
The first field in the landscape output file is landscape ID (LID); it is defined as in the patch output file (see
previous discussion).
(L2) Total Area
Vector/Raster
Un its:
Hectares
Range:
TA > 0, w ithou t limit.
Description: TA eq uals the total area (m 2) of the landscape, divided by 10,000 (to convert to hectares). TA
excludes the area of any background patches within the landscape.
(L3) Largest Patch Index
Vector/Raster
Un its:
Percent
Range:
0 < LP I # 100
LPI appro aches 0 wh en 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.
Description: LPI equals the area (m 2) of the largest patch in the landscape divided b y total landscape area (m 2),
multiplied by 100 (to convert to a percentage); in other words, LPI equals the percent of the landscape
that the largest patch com prises.
112
(L4) Number of Patches
Vector/Raster
Un its:
None
Range:
NP $ 1, withou t limit.
NP = 1 when the landscape contains only 1 patch.
Description: NP equals the number of patches in the landscape. Note, NP does not include any background patches
within the landscape or patches in the landscape bo rder.
(L5) Patch Density
Vector/Raster
Un its:
Num ber per 100 hectares
Range:
PD > 0, w ithou t limit.
Description: PD equals the number of patches in the landscape divided by total landscape area, multiplied by
10,000 an d 100 (to con vert to 100 hectares).
(L6) M ean patch Size
Vector/Raster
Un its:
Hectares
Range:
MPS > 0, withou t limit.
The range in MPS is limited by the grain and extent of the image and the minimum patch size in the same
man ner as patch area (ARE A).
Description: MP S equals the total landscape area (m 2), divided by the total number of patches, divided by 10,000
(to convert to hectares).
113
(L7) Patch Size Standard Deviation
Vector/Raster
Un its:
Hectares
Range:
PSSD $ 0, withou t limit.
PSSD = 0 when all patches in the landscape are the same size or when there is only 1 patch (i.e., no
variability in patch size).
Description: PSSD equals the square root of the sum o f the squared deviations of each patch area (m 2) from the
mean patch size, divided by the total number of patches, divided by 10,000 (to con vert to hectares);
that is, the root mean squared error (deviation from the mean) in patch size. Note, this is the
population standard deviation, not the sample standard deviation.
(L8) Patch Size Coefficient of Variation
Vector/Raster
Un its:
Percent
Range:
PSCV $ 0, withou t limit.
PSCV = 0 when all patches in the landscape are the same size or when there is only 1 patch (i.e., no
variability in patch size).
Description: PSCV equals the standard deviation in patch size (PSSD) divided b y the mean patch size (MPS),
multiplied by 100 (to convert to percent); that is, the variability in patch size relative to the mean patch
size. Note, this is the population coefficient of variation, not the sample coefficient of variation.
114
(L9) Total Edge
Vector/Raster
Un its:
Meters
Range:
TE $ 0, withou t limit.
TE = 0 w hen there is no edge in the landscape; that is, w hen the en tire land scape 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.
Description: TE equals the su m o f the len gths (m) of all ed ge segm ents in the lan dscape. If a landscape border is
prese nt, TE includes lan dscape boun dary segm ents represe nting true ed ge only (i.e., contrast weight >
0). If a landscape border is absent, TE includes a user-specified proportion of the landscape bound ary.
Regardless of whether a landscape border is present or not, TE includes a user-specified proportion of
background edge.
(L10) Ed ge Den sity
Vector/Raster
Un its:
Meters per hectare
Range:
ED $ 0, withou t limit.
ED = 0 w hen there is no edge in the landscape; that is, w hen the en tire land scape 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.
Description: ED equals the sum of the lengths (m) of all edge segments in the landscape, divided by the total
landscape area (m 2), multiplied by 10,000 (to convert to hectares). If a landscape border is present, ED
includes landscape bou ndary segm ents representing true edge only (i.e., contrast weight > 0). If a
landscape border is absent, ED includes a user-specified proportion of the landscape bound ary.
Regardless of whether a landscape border is present or not, ED includes a user-specified proportion of
background edge.
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(L11) C ontrast-W eighted Edg e Density
Vector/Raster
Un its:
Meters per hectare
Range:
CWED $ 0, withou t limit.
CW ED = 0 when there is no edge in the landscape; that is, when the entire landscape and landscape bo rder,
if present, consists of a single patch and the user specifies that none of the landscape boundary and
background edge be treated as edge. CWED increases as the amount of edge in the landscape increases
and /or as the con trast in ed ges increase (i.e., contrast w eight approaches 1 ). CW ED is repo rted as "NA" in
the "basename".full file and a dot "." in the "basename".land file if a contrast weight file is not specified by
the user.
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 (m 2), multiplied by 1 0,00 0 (to
con vert to hectares). If a landscape border is present, CW ED includes lan dscape boun dary segm ents
representing true edge only (i.e., contrast weight > 0). If a landscape border is absent, all landscape
boundary edge segments are assigned the edge contrast weight specified by the user (see bound_wght
option). This is equivalent to treating the specified proportion of all boundary edge segments as
maximum-contrast edge. Regardless of whether a landscape border is present or not, all background
edg e segme nts are assign ed the edg e con trast weight specified by the user. A gain, this is equ ivalen t to
treating the specified proportion of all background edge segments as maximum-contrast edge.
(L12) Total Edge Contrast Index
Vector/Raster
Un its:
Percent
Range:
0 # TEC I # 100
TEC I = 0 wh en there is no edge in the landscape; that is, when the entire landscape and landscape bo rder,
if present, consists of a single patch and the user specifies that none of the landscape boundary and
backgrou nd ed ge be treated as edg e. TEC I appro aches 0 as the con trast in edges lesson (i.e., contrast
116
weight approaches 0 ). TE CI = 100 wh en all edge is maxim um contrast (i.e., contrast w eight = 1). T EC I is
reported as "NA" in the "basename".full file and a dot "." in the "basename".land file if a contrast weight
file is not specified by the user.
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 percen tage). In the num erator, if a land scape border is present, all edge segm ents
along the landscape boundary are treated according to their edge contrast weights as designated in the
contrast weight file. If a landscape border is absent, all landscape boundary segments are assigned the
edg e con trast weight specified by the user (see bo und _w ght o ption ). No te that this is equivalen t to
treating the specified proportion of the landscape boundary as maximum-contrast edge and the
rem ainder as ze ro-contrast edg e. Reg ardless of w hether a lan dscape border is present or not, all
backgroun d edge segm ents are assigned the ed ge co ntrast w eight specified by the user. A gain, note
that this is equivalen t to treating the spec ified prop ortion of a ll backgro und edge a s max imum-contrast
edge and the remainder as zero-contrast edge. In the denominator, all edges are included, including
the landscape boundary and background edge segments, regardless of whether they represent true edge
or not or how the user ch ooses to h andle b oundary and backgroun d edg es.
(L13) M ean Edge Contrast Index
Vector/Raster
Un its:
Percent
Range:
0 # ME CI # 100
ME CI = 0 w hen there is no edge in the landscape; that is, when the entire landscape and landscape b order,
if present, consists of a single patch type and the user specifies that none of the landscape boundary and
backgrou nd ed ge be treated as edg e. ME CI app roaches 0 as the co ntrast in edges lesson (i.e., contrast
weight approaches 0). MECI = 100 when all edge is maximum contrast (i.e., contrast weight = 1). MECI
is reported as "NA" in the "basename".full file and a dot "." in the "basename".land file if a contrast weight
file is not specified by the user.
Description: MEC I equ als the su m o f the segm ent len gths (m) of each patche s' perim eter m ultiplied by th eir
corresponding contrast weights, divided by total patch perimeter (m), divided by the total number of
patches, multiplied by 100 (to convert to a percentage). If a landscape border is present, any patch
perim eter seg me nts along th e land scape bound ary are treated acc ording to their ed ge co ntrast w eights
as designa ted in the co ntrast w eight file. If a landscape border is absent, an y patch perim eter seg me nts
along the landscape boundary are assigned the edge contrast weight specified by the user (see
bound_w ght option). Regardless of whether a landscape border is present or not, all patch perimeter
segmen ts bordering backgro und are assigned the edg e contrast weight specified by the user.
117
(L14) Area-W eighted Mean Edg e Contrast Index
Vector/Raster
Un its:
Percent
Range:
0 # AW ME CI # 100
AWM ECI = 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 type and the user specifies that none of the landscap e bound ary
and back ground edge be tre ated as edg e. AW MEC I app roaches 0 as the contrast in ed ges lesson (i.e.,
contrast weight approaches 0). AWM ECI = 100 when all edge is maximum contrast (i.e., contrast weight
= 1). AW MEC I is repo rted as "NA" in the "basenam e".full file and a dot "." in the "basename ".land file if
a contrast weight file is not specified by the user.
Description: AW MEC I equ als the su m o f the segm ent len gths (m) of each patche s' perim eter m ultiplied by th eir
corresponding contrast weights, divided by total patch perimeter (m), multiplied by patch area (m 2)
divided by total landscape area (m 2), sum me d across all patche s in the landscape, multiplied by 1 00 (to
convert to a percentage). If a landscape border is present, any patch perimeter segments along the
landscap e bou ndary are treated acc ording to their edge contrast w eights as desig nated in the contrast
weight file. If a landscape border is absent, any patch perimeter segments along the landscape
bou nda ry are assign ed the edg e con trast weight specified by the user (see bo und _w ght o ption ).
Regardless of whether a landscape border is present or not, all patch perimeter segments bordering
background are assigned the edge contrast weight specified by the user. AWM ECI is similar to MECI
except that each patch weighted by its size in computing the average patch edge contrast index.
118
(L15) Landscape Shape Index
Vector
Raster
Un its:
None
Range:
LSI $ 1, withou t limit.
LSI = 1 when the landscape consists of a single circular (vector) or square (raster) patch; LSI increases
without limit as landscape shape becomes more irregular and/or as the length of edge within the landscape
increases.
Description: LSI equ als the su m o f the lan dscape boun dary (rega rdless o f wh ether it represents tru e edg e or n ot)
and all edge segm ents (m) within the landscape bou ndary (including those bo rdering backgro und),
divided by the square roo t of the total landscape area (m 2), adjusted by a constant for a circular
standard (vector) or square standard (raster).
(L16) M ean Sha pe Index
Vector
Raster
Un its:
None
Range:
MS I $ 1, withou t limit.
MSI = 1 when all patches in the landscape are circular (vector) or square (raster); MSI increases without
limit as the patch shapes beco me m ore irregular.
Description: MS I equals the sum of the patch perim eter (m) divided by the squ are root of patch area (m 2) for each
patch in the landscape, adjusted by a constant to adjust for a circular standard (vector) or square
standard (raster), divided by the number of patches (NP); in other words, MSI equals the average
shape index (SHAPE) of patches in the landscape.
119
(L17) Area-W eighted Mean Shap e Index
Vector
Raster
Un its:
None
Range:
AW MS I $ 1, withou t limit.
AW MSI = 1 w hen all patches in the landscape are circular (vector) or square (raster); AW MSI increases
without limit as the patch shapes becom e more irregular.
Description: AWM SI equals the sum, across all patches, of each patch perimeter (m) divided by the square root of
patch area (m 2), adjusted by a constant to adjust for a circular standard (vector) or square standard
(raster), multiplied by the patch area (m 2) divided by total landscape area. In other words, AWM SI
equals the average shape index (SHAP E) of patches, weighted by patch area so that larger patches
weigh m ore th an sm aller on es.
(L18) Double Log Fractal Dimension
Vector/Raster
Un its:
None
Range:
1 # DLFD # 2
A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates a departure from a
euclidean geom etry (i.e., an increase in patch shape com plexity). DLFD ap proaches 1 for shap es with very
simple perimeters such as circles or squares, and approaches 2 for shapes with highly convoluted, planefilling perim eters. D LFD emp loys regression techn iques and is subject to sm all sam ple problems.
Spe cifically, DL FD ma y greatly exceed the theo retical range in values w hen the num ber o f patches is sm all
(e.g., <10), and its use should be av oided in su ch ca ses. In addition, DLFD requires patches to vary in size.
Thus, DLFD is undefined and reported as "NA" in the "basename".full file and a dot "." in the
"basename".land file if all patches are the same size or there is only 1 patch.
Description: DLFD equals 2 divided by the slope of the regression line obtained by regressing the logarithm of
patch area (m 2) against the logarithm o f patch perimeter (m).
120
(L19) Mean Patch Fractal Dimension
Vector
Raster
Un its:
None
Range:
1 # MPFD # 2
A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates a departure from a
euclidean geom etry (i.e., an increase in patch shape com plexity). MPFD approaches 1 fo r shapes with very
simple perimeters such as circles or squares, and approaches 2 for shapes with highly convoluted, planefilling perimeters.
Description: MPFD equals the sum of 2 times the logarithm of patch perimeter (m) divided by the logarithm of
patch area (m 2) for each patch in the landscape, divided by th e numb er of p atche s; the raster formu la is
adjusted to correct for the bias in perimeter (Li 198 9).
(L20) Area-Weighted Mean Patch Fractal Dimension
Vector
Raster
Un its:
None
Range:
1 # AWMPFD # 2
A fractal dimension greater than 1 for a 2-dimensional landscape mosaic indicates a departure from a
euclidean geome try (i.e., an increase in p atch sh ape com plexity). AWMPFD approaches 1 for shapes with
very simple perimeters such as circles or squares, and approaches 2 for shapes with highly convoluted,
plane-filling perimeters.
Description: AW MPFD equals the sum, across all patches, of 2 times the logarithm of patch perimeter (m) divided
by the logarithm of p atch area (m 2), multiplied by the patch area (m 2) divided by total landscape area;
the raster formula is adjusted to correct for the bias in perimeter (Li 1989). In other words, AWM PFD
equals the average patch fractal dimension (FRACT) of patches in the landscape, weighted by patch
area.
121
(L21) Total Core Area
Vector/Raster
Un its:
Hectares
Range:
TCA $ 0, withou t limit.
TCA = 0 when every location within every patch is within the specified edge distance from the patch
perimeters. TCA approaches total landscape area as the specified edge distance decreases and as patch
shapes are simplified.
Description: TCA equals the sum of the core areas of each patch (m 2), divided by 10,000 (to convert to hectares).
(L22) Number of Core Areas
Vector/Raster
Un its:
None
Range:
NCA $ 0, withou t limit.
NCA = 0 when TCA = 0 (i.e., every location within every patch is within the specified edge distance from
the patch perimeters).
Description: NCA 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.
122
(L23) C ore Area Density
Vector/Raster
Un its:
Num ber per 100 hectares
Range:
CAD $ 0, withou t limit.
CAD = 0 when TCA = 0 (i.e., every location within every patch is within the specified edge distance from
the patch perim eters); in other w ords, w hen the re are no core area s.
Description: CAD equals the sum of num ber of disjunct core areas contained within each patch, divided by total
landscape area, mu ltiplied by 10,000 and 100 (to convert to 100 hectares).
(L24) M ean Core Area P er Patch
Vector/Raster
Un its:
Hectares
Range:
MCA 1 $ 0, withou t limit.
Ultimately, the range in MCA 1 is limited by the grain and extent of the image and the minimum patch size
in the sam e m ann er as m ean patch size (M PS), b ut M CA 1 is also affected by the specified ed ge w idth.
MC A1 = 0 w hen TCA = 0 (i.e., every location within every patch is within the specified edge distance
from the patch perimeters); in other words, when there are no core areas. MCA1 approaches MPS as the
specified edge width decreases and as patch shapes are simplified.
Description: MC A1 eq uals the sum of the core areas of each pa tch (m 2), divided by the number of patches, divided
by 10,000 (to convert to hectares). Note that MCA1 equals the average core area per patch, not the
average size of disjunct core areas, as in MCA 2.
123
(L25) Patch Core Area Standard Deviation
Vector/Raster
Un its:
Hectares
Range:
CASD1 $ 0, withou t limit.
CA SD 1 = 0 wh en all p atche s in the landscape hav e the sa me core area o r wh en there is only 1 patch (i.e.,
no variability in core area).
Description: CAS D1 eq uals the square root of the sum of the squared deviations of each patch core area (m 2) from
the m ean core area p er patch (M CA 1), div ided by th e numb er of p atche s, divid ed by 10 ,000 (to
con vert to hectares); that is, the roo t mean sq uared erro r (dev iation from the m ean) in patch co re area.
Note, this is the population standard deviation, not the sample standard deviation, and that CASD1
represents the variation in core area among patches, not among disjunct core areas, as in CASD2.
(L26) Patch Core Area Coefficient of Variation
Vector/Raster
Un its:
Percent
Range:
CACV1 $ 0, withou t limit.
CA CV 1 = 0 wh en all p atche s in the landscape hav e the sa me core area o r wh en there is only 1 patch (i.e.,
no variability in core area).
Description: CACV 1 equals the standard deviation in core area (CASD 1) divided by the mean core area per patch
(MCA1), multiplied by 100 (to convert to percent); that is, the variability in core area relative to the
mean core area. Note, this is the population coefficient of variation, not the sample coefficient of
variation, and that CACV1 represents the variation in core area among patches, not among disjunct
core areas, as in CACV2.
124
(L27) M ean Area Per Disjunct Core
Vector/Raster
Un its:
Hectares
Range:
MCA 2 $ 0, withou t limit.
Ultimately, the range in MCA 2 is limited by the grain and extent of the image and the minimum patch size
in the sam e m ann er as m ean patch size (M PS), b ut M CA 2 is also effected by the specified ed ge w idth.
MC A2 = 0 when total core area = 0 (i.e., every location within patches of the corresponding patch type are
within the specified ed ge distance from the patch p erim eters); in other wo rds, w hen there are no core areas.
MCA 2 approaches MPS as the specified edge width decreases and as patch shapes are simplified.
Description: MC A2 eq uals the sum of the disjunct core areas of each patch (m 2), divided by the number of disjunct
core areas, divided by 10,000 (to convert to hectares). Note that MCA2 equals the average size of
disjunct core areas, not the average core area per patch, as in MCA1.
(L28) Disjunct Core Area Standard Deviation
Vector/Raster
Un its:
Hectares
Range:
CASD2 $ 0, withou t limit.
CASD2 = 0 when all disjunct core areas are the same size or when there is only 1 core area (i.e., no
variability in core area).
125
Description: CAS D2 eq uals the square root of the sum of the squared deviations of each disjunct core area (m 2)
from the mean size of disjunct core areas (M CA 2), divided by the n um ber of d isjunct core are as,
divided by 10,000 (to convert to hectares); that is, the root mean squared error (deviation from the
me an) in the size of disju nct co re areas. No te, this is the pop ulation standard d eviatio n, no t the sam ple
standard deviation, and that CASD2 represents the variation in size of disjunct core areas, not patch
core areas, as in CASD1.
(L29) Disjunct Core Area Coefficient of Variation
Vector/Raster
Un its:
Percent
Range:
CACV2 $ 0, withou t limit.
CACV2 = 0 w hen all disjunct core areas are the same size or when there is only 1 core area (i.e., no
variability in core area).
Description: CACV 2 equals the standard deviation in the size of disjunct core areas (CASD2) divided by the mean
size of disjun ct core area s (M CA 2), m ultiplied by 1 00 (to conve rt to percent); that is, the v ariability in
core area relative to the mean core area. Note, this is the population coefficient of variation, not the
sample coefficien t of variation, an d that CA CV2 represents the variation in size of disjunct core areas,
not patch core areas, as in CACV1.
(L30) To tal Core A rea Index
Vector/Raster
Un its:
Percent
Range:
0 # TCAI < 100
TCA I = 0 wh en none o f the patches in the landscape contain any core area (i.e., CORE = 0 for every
patch); that is, wh en the landscape contain s no co re area. TC AI ap proaches 10 0 wh en the p atches, because
of size, shape, and edge width, contain mostly core area.
Description: TCA I equals the sum of the core areas of each p atch (m 2), divided by the total landscape area (m 2),
multiplied by 100 (to convert to a percentage); that is, TCAI equals the percentage of the landscape
126
that is core area.
(L31) M ean Core Area Index
Vector/Raster
Un its:
Percent
Range:
0 # MCA I < 100
MC AI = 0 w hen non e of the patches in the landscape contain any co re area (i.e., CORE = 0 for every
patch); that is, wh en the landscape contain s no co re area. M CA I appro aches 1 00 w hen the patches,
because of size, shape, and edge width, contain mostly core area.
Description: MC AI equals the sum of the proportion of each patch that is core area {i.e., core area of each patch
(m 2) divided by the area of each p atch (m 2)}, div ided by th e numb er of p atche s, mu ltiplied b y 10 0 (to
convert to a percentage); in other words, MCAI equals the average percentage of a patch in the
landscape that is core area.
(L32) M ean Nearest-Neighbor Distance
Raster
Un its:
Meters
Range:
MNN > 0, w ithou t limit.
MN N is reported as "None" in the "basename".full file and a dot "." in the "basename".land file if none of
the patches have a nearest neighbor (i.e., every patch type consists of only 1 patch). MN N is reported as
"NA" in the "basenam e".full file and a dot "." in the "basename ".land file if the u ser chooses no t to
calculate nearest neighbor distance.
Description: MN N equals the sum of the distance (m) to the nearest patch of the same type, based on nearest edgeto-edge distance, for each patch in the landscape with a neighbor, divided by the number of patches
with a neighbo r.
127
(L33) Nearest-Neighbor Standard Deviation
Raster
Un its:
Meters
Range:
NNSD $ 0, withou t limit.
NN SD = 0 w hen all patch es have the sam e nea rest-neighbor distance (i.e., no variability in nearestneighbor distance). NNSD is reported as "NA" in the "basename".full file and a dot "." in the
"basename".class file if none of the patches have a nearest neighbor. Similarly, NNSD is reported as "NA"
in the "basename ".full file and a dot "." in the "basenam e".land file if the user choo ses no t to calcu late
nearest neighbor distance.
Description: NNSD equals the square root of the sum of the squared deviations of each patches' nearest-neighbor
distance (m) from the mean nearest-neighbor distance of the corresponding patch type (MN N), divided
by the number of patches; that is, the root mean squared error (deviation from the mean) in patch
nearest-neighbor distance. Note, this is the population standard deviation, not the samp le standard
deviation.
(L34) Nearest-Neighbor Coefficient of Variation
Raster
Un its:
Percent
Range:
NNCV $ 0, withou t limit.
NN CV = 0 w hen all patch es have the sam e nea rest-neighbor distance (i.e., no variability in nearestneighbor distance; NNSD = 0). NNCV is reported as "NA" in the "basename".full file and a dot "." in the
"basename".class file if none of the patches have a nearest neighbor. Similarly, NNCV is reported as "NA"
in the "basename ".full file and a dot "." in the "basenam e".land file if the user choo ses no t to calcu late
nearest neighbor distance.
Description: NNC V equals the standard deviation in nearest-neighbor distances (NNSD ) divided by the mean
nearest-neighbor distance (M NN ), multiplied by 1 00 (to conve rt to percent); that is, the v ariability in
nearest-neighbor distance relative to the mean nearest-neighbor distance. Note, this is the population
128
coefficient of variation, not the sample coefficient of variation.
(L35) M ean Proximity Index
Raster
Un its:
None
Range:
MP I $ 0.
MPI = 0 if no patch has a neighbor of the same type within the specified search radius. MPI increases as
patch es becom e less isolated from patch es of th e sam e type and the patch ty pes b ecome less frag me nted in
distribution. The upper limit of MPI is determined by the search radius and minimum distance between
patches. MPI is reported as "NA" in the "basename".full file and a dot "." in the "basename".land file if the
user chooses not to calculate nearest neighbor distance.
Description: MP I equals the sum of patch area (m 2) divided by the squared nearest edge-to-edge distance (m)
between the patch an d the focal patch of all patches of the corresponding patch type w hose edges are
within a specified distance (m) of the focal patch, summ ed across all patches in the landscape and
divided by the total number of patches. In other words, MPI equals the average proximity index for
patches in the landscape. Note, when the search buffer extends beyond the landscape boundary for
focal patches near the boundary, only patches contained within the landscape are considered in the
com putations.
129
(L36) Sha nnon's Diversity Index
Vector/Raster
Un its:
None
Range:
SHD I $ 0, withou t 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 mo re equitable.
Description: SHDI equals minus the sum, across all patch types, of the proportional abundance of each patch type
multiplied by that proportion.
(L37) Simpson 's Diversity Index
Vector/Raster
Un its:
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 mo re equitable.
Description: SIDI equals 1 minus the sum, across all patch types, of the proportional abundance of each patch type
squared.
130
(L38) M odified Simpson's Diversity Index
Vector/Raster
Un its:
None
Range:
MS IDI $ 0
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 mo re equitable.
Description: MSIDI equals minus the logarithm of the sum, across all patch types, of the proportional abundance of
each patch type squared.
(L39 ) Patch Richn ess
Vector/Raster
Un its:
None
Range:
PR $ 1, withou t limit
Description: PR equals the number of different patch types present within the landscape boundary.
(L40) Pa tch Richness De nsity
Vector/Raster
Un its:
Num ber per 100 hectares
Range:
PRD > 0, withou t limit
Description: PR equals the number of different patch types present within the landscape boundary divided by total
landscape area (m 2), multiplied by 10,000 and 100 (to conv ert to 100 hectares).
131
(L41 ) Relative Patc h Rich ness
Vector/Raster
Un its:
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. RPR is reported
as "NA" in the "basename".full file and a dot "." in the "basename".land file if the maximum num ber of
classes is not specified by the user.
Description: RPR equals the number of different patch types present within the landscape boundary divided by the
maximum potential number of patch types based on the patch type classification scheme, multiplied by
100 (to conv ert to percent).
(L42) Shannon's Evenness Index
Vector/Raster
Un its:
None
Range:
0 # SHE I # 1
SHDI = 0 when the landscape contains only 1 patch (i.e., no diversity) and approaches 0 as the distribution
of area amo ng the different patch types becom es 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).
Description: SHEI equals minus the sum, across all patch types, of the proportional abundance of each patch type
mu ltiplied by that pro portion, divided b y the logarithm of the nu mb er of patch types. In oth er wo rds,
the observed Shannon's Diversity Index divided by the maximum Sh annon's Diversity Index for that
num ber of p atch type s.
132
(L43) Simpson 's Evenness Index
Vector/Raster
Un its:
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 am ong patch typ es is perfectly even (i.e., proportional abundances are the sam e).
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 typ es.
(L44) M odified Simpson's Evenness Index
Vector/Raster
Un its:
None
Range:
0 # MS IEI # 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). MSID I = 1 when distribution of area among patch types is perfectly even (i.e., proportional
abund ances are the same).
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 m odified Simp son's diversity ind ex divided by the m axim um mo dified Sim pson's diversity
index for that numb er of patch types.
133
(L45) Interspersion and Juxtaposition Index
Vector/Raster
Un its:
Percent
Range:
0 < IJI # 100
IJI approaches 0 w hen the distributio n of adjacencies am ong uniq ue patch ty pes b ecome s increasing ly
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 "NA" in the "basename".full file and a dot
"." in the "basename".land file if the number of patch types is less than 3.
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, summ ed over each unique edge type;
divided by the logarithm of the nu mb er of patch types time s the num ber of p atch type s minu s 1
divided by 2; multiplied by 100 (to convert to a percentage). In other words, the observed
interspersion over the max imum p ossible interspersion for the g iven nu mb er of patch types. No te, IJI
considers all patch types present on an image, including any present in the landscape border, if a
border w as inclu ded . All backg round edge segm ents are ignored , as are landscape bound ary segm ents
if a border is not provided, because adjacency information for these edge segments is not available.
134
(L46) Contagion Index
Raster
Un its:
Percent
Range:
0 < CONTAG # 100
CONTA G approaches 0 when the distribution of adjacencies (at the level of individual cells) among unique
patch types becom es increasingly u nev en. CON TA G = 100 wh en all p atch ty pes are equally adjacent to all
other patch types (i.e., maximum interspersion and juxtaposition. CONTA G is undefined and reported as
"NA" in the "basenam e".full file and a dot "." in the "basename ".land file if the n um ber o f patch typ es is
less than 2.
Description: CONTA G equals minus the sum of the proportional abundance of each patch type multiplied by
number of adjacencies between cells of that patch type and all other patch types, multiplied by the
logarithm of the same quantity, summed over 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,
CONTA G 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 segme nts are igno red, as are lan dscape boun dary segm ents if a b order is
not provided, because adjacency information for these edge segments is not available.
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