71-24,881 ZUBROW, Ezra Barrish Winkler, 1945- A SOUTHWESTERN TEST OF AN ANTHROPOLOGICAL

71-24,881 ZUBROW, Ezra Barrish Winkler, 1945- A SOUTHWESTERN TEST OF AN ANTHROPOLOGICAL
71-24,881
ZUBROW, Ezra Barrish Winkler, 1945A SOUTHWESTERN TEST OF AN ANTHROPOLOGICAL
MODEL OF POPULATION DYNAMICS.
The University of Arizona, Ph.D., 1971
Anthropology
University Microfilms, A XEROX Company, Ann Arbor, Michigan
@COPYRIGHTED
BY
EZRA BARRISH WINKLER ZUBRCW
1971
iii
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED
A SOUTHWESTERN TEST OF AN ANTHROPOLOGICAL
MODEL OF POPULATION DYNAMICS
by
Ezra Barrish Winkler Zubrow
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF ANTHROPOLOGY
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
In the Graduate College
THE UNIVERSITY OF ARIZONA
19 7 1
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
I hereby recommend that this dissertation prepared under my
direction by
EZRA BARRISH WIMKLER ZUBROW
entitled
A Southwestern Test of an Anthropological
Model of Population Dynamics
be accepted as fulfilling the dissertation requirement of the
degree of
Doctor of Philosophy
1*0 t
*
Dissertation Direc r
Date
After inspection of the final copy of the dissertation, the
following members of the Final Examination Committee concur in
its approval and recommend its acceptance:"
21
2^
Y/ J i /l /
—
U.) t (t*
This approval and acceptance is contingent on the candidate's
adequate performance and defense of this dissertation at the
final oral examination. The inclusion of this sheet bound into
the library copy of the dissertation is evidence of satisfactory
performance at the final examination.
PLEASE NOTE:
Some pages have small, light,
and indistinct print.
Filmed as received.
UNIVERSITY MICROFILMS.
STATEMENT BY AUTHOR
This
requirements
is deposited
rowers under
dissertation has been submitted in partial fulfillment of
for an advanced degree at The University of Arizona and
in the University Library to be made available to bor­
rules of the Library,
Brief quotations from this dissertation are allowable without
special permission, provided that accurate acknowledgment of source
is made. Requests for permission for extended quotation from or
reproduction of this manuscript in whole or in part may be granted by
the copyright holder.
SIGNED:
IN MEMORIUM
Edward P. Dozier
April 23, 1916-May 2, 1971
He was a great teacher, a great scholar,
and a friend to all who were interested
in the broader study of anthropology as
a humane science.
iv
ACKNOWLEDGMENTS
This study is based on work done at various times over the
last four years. There are numerous people whose help and criticism
should be recognized. First, I want to thank the members of my com­
mittee: Dr. William A. Longacre, Dr. Jane H. Underwood, Dr. Raymond
H. Thompson, Dr. Harry T. Getty, and Dr. Thomas B. Hinton. To each
I am greatly indebted. Dr. Longacre developed my interest in and
brought into focus the theoretical issues to which model building is
hopefully a partial solution. In addition, he was instrumental in
providing me the opportunity to become associated with the Southwest
Archaeological Expedition. Dr. Underwood is responsible for my in­
terest in demographic problems and enthusiastically helped me to gain
an understanding not only of demographic theory and methodology, but
their importance to culture. She also was a willing sounding board
upon which many of the ideas of this study were first tested.
Dr. Thompson's cogent criticisms were invaluable as were his.editorial
revisions. In addition, Dr. Thompson was instrumental in my obtaining
a National Defense Education Act Fellowship and teaching assistantships
without which my graduate education would have been far more difficult.
I wish also to thank Dr. Edward P. Dozier in whose seminar I first
enunciated the basic ideas for a model of carrying capacity as a
dynamic equilibrium system. He encouraged me in the clarification of
.v
vi
the model and has continued to take an active interest in its develop­
ment.
I owe very special thanks to Dr. Paul S, Martin, Curator
Emeritus of the Department of Anthropology of the Field Museum of
Natural History, for the opportunity to work with the Southwest Archae­
ological Expedition and use the data derived therefrom for my doctoral
dissertation. His encouragement, adviee, guidance, and friendship has
made the possibility of archaeological research a meaningful reality.
. I am grateful to Pat Mail and Marilew Lord who somehow miracu­
lously transformed rough sketches and complex graphs into professional
illustrations. Hazel Gillie has given freely of her time and knowledge
in the accurate typing and formatting of this study.
I also wish to thank the following people Cor their contribu­
tions to this studyj Walter Bargen, Hermann Bleibtreu, Kenneth
Boulding, Ellen and Daniel Bowman, David Burkenroad, Connie and James
Carter, George Castile, Charles Cheek, Delia and Tom Cook, Judy Connor,
Connie Cronin, T. Patrick Culbert, Jeannie Derousseau, Bpyce Driskell,
Rosiland Duncan, Eliza and Timothy Early, Michael Ester, Michael
Everett, John Fritz, Fredrick Gorman, David Gregory, P. Bion Griffin,
Eric Gritzmacher, Vernon Grubisich, Bob Gutierrez, John Hanson,
Charles Hardilek, Bnil W. Haury, Dick Hevly and his students, James
N. Hill, Arthur Jelinek, John Johnson, Joel Klein, Thomas Kuhn, Bonnie
Laird, Mark Leone, Molly Lewis, Henri and Susan Luebermann, Mary
McCutcheon, Colleen Maley, Larry Manire, Craig Morris, Sharon Ott,
Paul Parker, Fred Plog, Steve Plog, Peggy Powers, Bill Rathje,
vii
John Rick, Scott Ryerson, Steve Saraydar, Bob Schacht, Jerry Schaefer,
Mike Schiffer, Jerry Smith, Staff of the Arizona State Museum Library,
Larry Straus, David Thompson, Dick Thompson, Sue Tracz, Joe Traugott,
David Tuggle, Alan Turner, Charles Vanasse, Colonel Waters, Norman
Whalen, Chris White, Ed Wilmsen, Aron Winchester, Tom Zanic, John
Zilen, and last but not least, the necessarily nameless prehistoric
inhabitants of the Hay Hollow valley.
The following organizations have generously provided monetary
supportinformation, cooperation, and various types of data, for
which I am grateful: Field Museum of Natural History, National Defense
Education Act, Title II, National Science Foundation and its Under­
graduate Research Participation Program, United States Air Force
Strategic Air Command, United States Bureau of Indian Affairs, United
States Forest Service, United States Geological Survey, and University
of Arizona Computer Center, Department of Anthropology and Extension
Division.
Finally, this study is dedicated to Marcia Zubrow, my wife,
Anne and Reuben Zubrow, my parents.
TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS
xi
LIST OF TABLES
XV
ABSTRACT
xvii
1. INTRODUCTION
1
A Brief Theoretical History Relating Demographic and
Resource Variables
,
Anthropological Explanations
Economic and Resource Orientation
Demographic Explanations
Delineation of the Definitions and Assumptions in the
Model
The Simplified Model
The Model and Selected Aspects of Economic and
Demographic Theory
Justification of the Model
2. THE EXPANDED MODEL
3
5
9
16
21
30
32
37
39
The Addition of Variables
Spatial Variation: Homogeneous and Hetero­
geneous Resource Bases
Temporal Variation
Migration and Population Development at the
Zonal Level
The Systemic Model: Version 2
Economic and Demographic Variables . .
Technology
Settlement Pattern
Longevity
'
Climate
Systemic Model: Version U
The Definition of the Equations and Constants of the
Model
The Definition of Equations for Resource and
Population Curves
Settlement Location . ;
viii
39
39
Ill
ill
l|6
U6
53
56
63
67
68
98
98
103
ix
TABLE OF CONTENTS—Continued
Page
Longevity
Consumption Equations and Technological
Innovation
Constants
3. HYPOTHESES
.107
110
112
Summary . .
It. DATA
106
12J>
'
Introduction
Brief Outline of Hay Hollow Prehistory
Phase 1
Phase 2 and 3
Phase U
Phase
Phase 6 and 7
Survey Data
Intensive Survey
Ecological Data
Introduction
Stages 1, 2, and 3
Stage U
Stage £
Stage 6
Stage 7
Stage 8
5. TESTS OF HYPOTHESES
First Hypothesis
Second Hypothesis
Third Hypothesis
Fourth Hypothesis
6. THE SIMULATION MODEL
The Modification of Space: The Simulation Map . . .
Operating Characteristics
The Simulations and the Archaeological Record ....
Conclusions
7. SUMMARY AND CONCLUSIONS
126
126
128
128
128
129
130
131
132
l£l
168
168
171
I®2
193
199
^02
203
208
208
223
230
235
238
239
2l»0
262
267
269
X
TABLE OF CONTENTS—Continued
Page
APPENDIX Is HAY HOLLOW VALLEY VERTEBRATE AND INVERTE­
BRATE SURVEY
27k
APPENDIX II: LISTING OF THE PROGRAM FOR SIMULATION MODEL
WITH SUMMARY DOCUMENTATION.
281
LIST OF REFERENCES
293
IIST OF ILLUSTRATIONS
Figure
Page
1. The logistic growth cycle
......
19
2. A simplified model of carrying capacity as a dynamic
equilibrium system
31
3. A simplified model of carrying capacity as a dynamic
equilibrium system ~ Systemic Model: Version 1 ..
33
U. Smallest land labor combination which will produce a
particular output
35
5. Heterogeneous resource model
1*0
6. Heterogeneous resource model with spatial and temporal
variation
U2
7. Predicted migration pattern
h3
8. Predicted population curves by microhabitat or eco­
logical zone with constant resources ........
1*5
9. Predicted population curves by microhabitat or eco­
logical zone with diminishing resources
U7
10. Systemic Model: Version 2
U8
11. Resources and net societal product
5U
12. Schumpeterian innovations
57
13. Restatement of systemic model in SETTLEMENT terms —
Systemic Model: Version 3
59
1U. Systemic Model: Version k
69
15. MacArthur's tk: a longevity alternative
108
16. Aerial photograph of part of the Hay Hollow valley . .
127
17. Map of the Hay Hollow valley
In
pocket
xi
xii
LIST OF ILLUSTRATIONS—Continued
Figure
Page
18. Intensive survey -- Site 83
19. Intensive survey — Site 137b
l£6
20. Intensive survey ~ Site 195.
21. Intensive survey — Site 196
l£8
22. Intensive survey — Site 201
159
23. Intensive survey -- Site lj.30
160
2U. Intensive survey — Site 5H
l6l
25. Comparison of pottery, pollen and radio carbon dates
for intensively surveyed sites
16?
26. The relationship between modern pollen and pollen
spectra from floors of sites in the Four Mile,
Shumway and Hay Hollow areas
206
27. Pollen profile from the Hay Hollow valley
207
28. Number of habitation rooms in the central 100^- sample .
210
29# Total number of sites in 100$ sample and both 2%%
samples
211
30. Pinyon pine pollen and the average number of rooms per
site in the 100,? survey sample
225
31. Pinyon pine pollen and average number of rooms per
site in the 100$ and both 2$% samples
226
32. The expected relationship between pinyon pine pollen,
an indirect index of resources and the average of
rooms per site
228
33. Pinyon pine pollen and average number of rooms for all
sites, the test of the generalized hypothesis ....
229
3U. The values of ra and rb through time
231
xiii
•LIST OF. ILLUSTRATIONS—Continued
Figure
Page
35. Pinyon pine pollen and the values of the nearest
neighbor statistic
23h
36. Pinyon pine pollen and average room size
236
37* Simulation map
2lp-
38. Simulation 1: population distribution by microhabitat . 2k5
39. Simulation 2: population distribution by microhabitat • 2U6
IjO. Simulation 3J
population distribution by microhabitat . 2k7
111. Simulation h: population distribution by microhabitat • 2l*8
lt2. Simulation £: population distribution by microhabitat . 2h9
k3» Simulation 6: population distribution by microhabitat . 2$0
ljU. Simulation 7'
population distribution by microhabitat . 2£l
k%. Simulation 8: population distribution by microhabitat . 2£2
U6. Simulation 1: total population and total number of
sites
2?3
U7. Simulation 2: total population and total number of
sites
25>U
U8. Simulation 3s
sites
25>5>
total population and total number of
ll9. Simulation U: total population and total number of
sites
256
J>0. Simulation $: total population and total number of
sites
2^7
51• Simulation 6: total population and total number of
sites
2^8
52. Simulation 7s
sites
2^9
total population and total number of
xiv
LIST OF ILLUSTRATIONS—Continued
Figure
£3. Simulation 8: total population and total number of
sites
Page
260
Total number of rooms by microhabitat from the actual
area covered by the simulated map
263
Total number of rooms and sites from the actual area
covered by the simulated map
26h
LIST OF TABLES
Table
Page
1. Summary of theoretical contributions
2k
2. Spengler's interacting economic and demographic
variables
ii9
3. Spengler's economic and demographic relationships ...
£2
U«
Archaeological sites in the Hay Hollow valley
£. Habitation rooms per site by sites
136
Longacre survey . . 3JU9
6. Comparison of settlement sizes .
. l£U
7. Pollen dates of intensive survey sites from Hay Hollow
valley
163
8. Carbon lit dates
16U
9. Pottery types of intensive survey sites
16?
10. Comparison of settlement dates
166
11. Tree estimates from two 90° transects compared to actual
number of trees within quadrants with variable
transect length and quadrant size
175>
12. Comparison of the tree estimates
selected so that there are two
meters with actual tree number
variable transect and quadrant
from Wo line transects
trees in the first 31
within quadrants with
size
177
13. Quadrant estimates for 68m. x 68m. quadrants based on
17m. x 17m., 3bm. x 3bm.} and 5>lm. x 3>lm. quadrants . 180
llu
Plant distribution of Microhabit 1
183
1$. Plant distribution of Microhabit 2
181;
16. Plant distribution of Microhabit 3
185
17. Plant distribution of Microhabit Ij.
186
xv
xvi
LIST OF TABLES—Continued
Table
Page
18. Plant distribution of Microhabitat 5
187
19. Plant distribution of Microhabitat 7
188
20. Total plant distribution for. all quadrants by micro­
habitat
189
21. Correlation coefficients of total numbers of plants byspecies by microhabitat
191
22. Correlation coefficients of numbers of plants by species
by microhabitat using mean data
192
23. Correlation coefficients of animal densities by micro­
habitat
193
2li. Total animal transect data
19h
25. Total animal transect data by density per square mile • 196
26. Maximal carrying capacity values derived from Odum's
estimates of biomass
21h
27. Maximal carrying capacity values using Zubrow-Hevly
ecological data
216
28. Cross-zonal ranking of resources ............ 217
29. The cross-zonal relationship between the ranked site
distribution and types of resources
219
30. The survey ra and rb values
230
31. Densities of the habitation sites and the number of
rooms by zone through time
233
32. The simulation: initial variable values
2U3
ABSTRACT
The problem of this study is to determine if a neo-Malthusian
model of carrying capacity as a dynamic equilibrium system accounts
for changes in population, settlement patterns, and resources archaeologically in the Hay Hollow valley. On the basis of the model a set
of hypotheses and predictions are generated relating demographic
variables such as population size, growth, and settlement pattern to
resource variables that limit carrying capacity. These hypotheses are
tested with archaeological and ecological survey data gathered in
east central Arizona. The vaidity of the model is determined by using
a variety of statistical tests. A version of the model is developed
into a simulation program which is run using different initial values
for demographic variables in order to try to replicate reality. The
positive testing of the model indicates that it may be applicable to
problems in other culture areas.
xvii
CHAPTER 1
INTRODUCTION
This study considers the generation and operationalization of
a model of carrying capacity as a dynamic equilibrium system. After a
consideration of the anthropological, economic, and demographic litera­
ture concerning population-resource relationships, a neo-Malthusian
model is shown to be applicable to societies which have not undergone
the major transformation entailed in the Industrial Revolution. The
Malthusian model, with the basic premise that resources limit
popu­
lation, is replaced by a more sophisticated ecological model. This
model is based upon a systemic consideration of population pressure
in a series of organized, spatially differentiated eco-systems, each
with its own level of consumption expectations based on food chains
with internal and external ecological connections.
The more sophisticated model is expanded by adding a series of
variables which include: spatial variation, temporal variation,
migration, net societal product, technology, settlement patterning,
settlement longevity, and climate. The assumptions and definitions of
the model are delineated and the operating characteristics of the model
are examined both graphically and systemically. The expanded model is
then defined in terms of equations and quantified in general terms.
From the assumption base of the expanded model, four hypotheses
are formally deduced which are to be tested on data from the Hay Hollow
1
2
Valley in east-central Arizona. The data are based upon archaeological
surveys and excavations of sites which span the time period A.D. 300lltOO and seven semi-independent microhabitats. The four hypotheses as
a group form an examination of the relationships among resources, popu­
lation aggregation, spatial aggregation, settlement size, and zonal
population development. The model is of sufficient generality as to
be productive of new hypotheses. This is demonstrated by showing that
the formal deductions are valid with an axis shift in the time-space
continuum.
After an updating of the known archaeological information from
the Hay Hollow Valley, four sets of archaeological data are used in
combination to determine the population parameters of the four hypo­
theses. These sets of data are: two peripheral 2%% surveys, a central
100$ survey, and a set of excavated sites. An intensive survey was
conducted during 1969 using a sample chosen for maximum possible error
to check the validity of the archaeological survey estimates. In order
I
to determine the resource parameters of the four hypotheses, an ecolo­
gical survey of eight stages was conducted in 1970. The results of
this survey allow the differentiation of statistically significant
floral and faunal microhabitats. In addition, the survey is used to
determine floral and faunal standing crop size by microhabitat and
floral productivity by microhabitat. Pollen analysis is used to esti­
mate through extrapolation from the modern standing crop and produc­
tivity figures their relative relationships during the prehistoric time
periods.
3
The four hypotheses are tested using both graphical and statis­
tical analyses. The results are interpreted in their relationship to
the hypotheses and the archaeological data. In addition to the testing
of the hypotheses, all the components of the model are used in a com­
puter simulation of the population growth, settlement distribution and
settlement longevity of the Hay Hollow Valley.
A Brief Theoretical History Relating Demographic
and Resource Variables
The relationship between resources and population has been a
topic of research for the past 200 years. Optimists have emphasized
the increase in resources and output which has been the result of tech­
nological development, and have used examples drawn from Western Europe
after the Industrial Revolution. Pessimists, noting the underdeveloped
areas of the world, cite countless examples where standard of living
and income per capita have been steadily falling because population is
surpassing economic production. The question is by no means moribund.
There is not only a continuing scholarly interest as a perusal of the
demographic and economic development literature shows (Duncan and
Hauser 1959; Higgens 1968) but a popular interest. Most recently,
there has been a series of popular studies which suggest that the
present exploitation of natural resources is close to the ultimate
limits and the pessimism of the authors is reflected in their titles:
Famine 1975 (Paddock and Paddock 1967), The Population Bomb (Ehrlich
1969), and Standing Room Only (Sax 1955).
a
The complexity of the population resource problem is partially
the result of the large number of variables which impinge upon the
relationship and the difficulty in differentiating them. Institutions
reflect their environment and vice versa. For example, the resources
which a population has at its disposal are not simply a function of
their presence in the environment. First, the population must be con­
scious of the potential resources as a resource. Second, there must
be a set of values and priorities which allow the population to decide
to allocate its time, land, labor and capital in exploitation of this
resource rather than another. Third, it must have political and eco­
nomic control or access to that part of the environment which contains
the resource. Fourth, it must have the technological sophistication
to exploit the resource. Fifth, it must have the social organization
to distribute the product which is obtained from the resource.
Similarly, the growth of the population is not simply a result
of biological reproduction. Wot only are there disease, genetic, and
density functions, but social and ideological components such as
hierarchies and birth control values which help to determine the amount
of growth.
This complexity is reflected in the analyses which have been
suggested to explain the relationship. At the risk of oversimplifi­
cation, I am dividing this brief history into three subsections, an
anthropological subsection, a resource or economic subsection, and a
demographic subsection in which I will discuss the contribution of
authors who have placed primary explanatory emphasis upon cultural,
economic, and demographic variables respectively.
5
Anthropological Explanations
It is interesting to note that although there has been con­
siderable theoretical analysis of the relationship between population
and resources which use cultural variables, most of this work has not
been done by anthropologists, but by economists. In fact, if one
examines the literature of the major anthropological schools, it is
difficult to discover references to the population resource question.
One often stated theoretical position in modern anthropological theory
is that of the cultural evolutionists. Competition deriving from
population pressure is a major force in evolution of social organiza­
tion. This has been espoused by Sumner and Keller (1927), Steward
(19U9), White (1959), Carnerio (1961) and, most recently, by Harner
(1970). Generally, it is suggested that the increased complexity of
social organization acts in a manner similar to an innovation to re­
lieve the pressure of the law of diminishing returns.
Earlier anthropologists, however, saw different relationships
and were by no means so unified in their positions. Spencer (18^2),
in a short article entitled "A Theory of Population," was a precursor
of Marx in suggesting man's intelligence as a means to exit from the
Malthusian dilemma. He suggested that intelligence is inversely re­
lated to fertility and thus as one moves through his evolutionary
social schema towards the perfectability of man, the Malthusian spectre
disappears•
Durkheim (1933) saw increasing population size and density as
a threat to social solidarity which may be saved only by the increasing
6
division of labor. Noting that Darwin states that competition is a
result of number, density, and similarity between species, Durkheim
transferred the concept to society. However, societies with large,
dense populations do exist. The division of labor acts not only as a
productivity mechanism but it increases the heterogeneity of the soci­
ety. Thus it diminishes the competition which is inherent in the
otherwise increasing similarity between members of the growing society.
By increasing social dependence and decreasing competition, the divi­
sion of labor functions as a social solidarity mechanism which allows
the social fabric to be maintained in the face of growing population
and competition.
Boas, in the process of increasing anthropological empiricism,
appears to take a contradictory stand. On one hand, he claims that
his kinship studies resulted in "no evidence that density of population,
stability of location, or economic status is necessarily connected with
a particular system of relationship and of behavior connected with it"
(Boas 1938)*
On the other hand, he recognized that polygyny played a
distinct role in the expansion and cultural assimilation of the 6th
and 7th century Arab population (Boas 1911). Although diffusionists
held a general interest in migration as a cultural transmitter, there
was little work in its relationship to resources or its cultural de­
terminants. Rather, the primary emphasis was placed upon the deter­
mination of when and where migrations took place and what cultural
traits were transmitted. In fact, the British diffusionist W. H.
Rivers (1922), when attempting to explain the depopulation of Melanesia
7
in an article entitled "The Psychological Factor," explained this de­
population within the limits of carrying capacity as a result of a
"loss of interest of life."
Enforced contact without recourse de­
stroyed native economic, social, and religious institutions which was
accompanied by decreasing birth rate and increasing death rate.
With the development of the culture area concept, Wissler
and more importantly, Kroeber attempted to determine empirically demo­
graphic characteristics of a specific culture area.
Kroeber, in his
classic, Cultural and Natural Areas of Native North America, published
and re-examined Mooney's figures and concluded that the existence of
agriculture did not make significant differences in population density;
indeed the coastal areas were considerably more densely populated than
any other area of native North America (Kroeber 1939).
The interest of the British structural-functionalists in the
population resource question was limited. Although Meyer Fortes (195h)
in his "Demographic Field Study of the Ashanti," placed great emphasis
upon population, his final explanation of Ashanti's high fertility rate
relied upon the value system for deriving causal variables.
One of the most directly relevant publications to the anthro­
pological population resource literature is not well known to the
United States. It is Krzywicki's (l93h) Primitive Society and Its
Vital Statistics. Krzywicki, a professor of Social History at the
University of Warsaw, devoted his intellectual talents to a demographic
analysis of primitive communities and tribes. The above work contains
the most massive compilation of historical and ethnographic population
8
references of which I am aware, summarized tribe by tribe in 238 pages.
It is difficult to encapsulate a book of this scope in a few sentences.
Utilizing this mass of data, Kryzwicki, was able to develop an evo­
lutionary framework in which to analyze consequences of the relation­
ship between social and demographic variables. He shows that the
result of social factors, such as institutional differences,contributes
to population isolation which in turn is responsible for the small size
of the units of the tribal world. Simultaneously, a social consequence
of the small size is claimed to be the high degree of social varia­
bility. Small changes in population composition force major changes
in the social structure such as clans, and lineages die out. These
factors mutually reinforce each other to keep primitive societies
small and diverse. Kryzwicki is also a precursor of the "structural
pose" concept, seeing different social and economic mechanisms affecting
population units of variable size as resource abundance fluctuates.
Frank Lorimer (195U), a demographer by profession and a struc­
tural functionalist with regard - to anthropological theory, wrote
Culture and Human Fertility. He shoira that a prerequisite for suc­
cessful expansion of pre-industrial societies is the existence of the
corporate unilineal kinship group. Simultaneously, these two factors,
corporate groups and unilineal kinship systems, are directly related
to high fertility. Lorimer notes that social and religious controls
of fertility are dependent upon the marginality, the isolation, and
limited subsistence base of a geographic area. His analysis of social
structure's function is the complement to Wrigley's. While Wrigley
(1969) sees the function of social structure as a social mechanism to
distinguish surplus population, Lorimer discovers that societies with
well developed formal social structure have higher fertility rates
than those without. In fact, he finds that to the extent contact re­
sults in social disorganization it also decreases fertility.
The role that Birdsell has played in the development of the
anthropological insights into the population resource question is two­
fold. In a study relating environmental, cultural, and demographic
variables to hunting and gathering, he shows that "for the simplest
cultural levels, the densities of human populations are primarily de­
termined by the variables of the environment" (Birdsell 1953). In the
Australian case, population density is determined by rainfall. On the
basis of this and similar studies, he developed models to explain not
only the growth, but the size and distribution of the Australian native
population. Thus, he was among the first anthropologists to use formal
models with predictive value and to test them using demographic vari­
ables over a considerable time depth. His second contribution is as
an educator, in that he has inspired a series of students to carry out
research on the population resource question.
Economic and Resource Orientation
In 1776 Adam Smith published The Wealth of Nations in which
the market as a self-regulating equilibrium system was shown to result
from two opposing forces. On one hand, self interest acts to guide
men into whatever work society is prepared to pay for. On the other,
the regulating force is competition. A man whose self interest is not
checked, finds himself in financial trouble for two reasons. If he
overcharges for his wares, he has no buyers. If he underpays his
workers, he has no employees. Furthermore, Smith suggested that the
market mechanism tends to increase production, wealth, resources, and
population for it is partially the result of the market being a milieu
which encouraged innovations, inventions, expansions, and risks. But
more importantly, this was the result of two laws (Heilbroner 1961):
the law of accumulation and the law of population. The object of
accumulation was reinvestment and thus growth. But accumulation meant
more industry, machines, and a larger labor force. Given competition,
accumulation resulted in a greater demand for labor and thus higher
wages which meant, in turn, lower profits and less accumulation. Smith
solved this problem with the law of population which states labor and
thus the number of laborers, the bulk of population, are a commodity
which follows the dictates of supply and demand. So as the labor force
increases to the new demand or if it overshoots it, competition de­
creases wages, accumulation increases, and there is a new cycle of up­
ward spiralling growth. Thus, there is to be expected a continual,
but episodic growth of resources and population. This rise in the
working class will force the population upwards and towards, but not
to,subsistence, as long as the accumulation process continues.
There was nothing in the population-resource relationship to
shake the faith of the philosophers in the rationality of the future.
This was reflected in a tract entitled Political Justice (1793) by
William Godwin whose primary importance is his inspiration of Daniel
11
Malthus, a friend of David Hume, to debate the issue with his son
Thomas Robert Malthus. His son published in 1798the famous Essay on
Population and in one book not only changed the viewpoint of the age
from optimism to pessimism, but inscribed his name with opprobrious
connotations upon intellectual history (Heilbroner 1961). Taking the
concept of equilibrium from Smith (Boulding 1959) and applying it to
population, he put forward the view that population when unchecked
will increase geometrically due to the "inherent attraction between
the sexes." But sustenance increases only in an arithmetric ratio.
Thus, the subsistence base eventually puts a limit upon the increasing
population. Or, as Malthus himself succinctly stated:
I think I may fairly make two postulata.
First, that food is necessary to the existence of man.
Second, that the passion between the sexes is necessary, and
will remain nearly in its present state.
Assuming, then, my postulata as granted, I say, that the
power of population is indefinitely greater than the power
in the earth to produce subsistence for man.
This limit is enforced through the "positive checks" of famine, dis­
ease, and war unless man utilizes what Malthus termed the "preventive
checks" deferred marriage and celibacy. In other words, growth must
end because there is increasing mortality or decreasing fertility. In
the latter, Malthus does not put too much faith, for he notes "Towards
the extinction of the passion between the sexes, no progress whatever
has hitherto been made." Thus, equilibrium is reached through in­
creasing mortality and increasing mortality means increased misery and
starvation. It is this gloomy prediction which has come to be known
as the "Dismal Theorem."
Boulding has stated it in other words, "if
12
the only ultimate check on the growth of population is misery, then
the population will grow until it is miserable enough to stop its
growth" (Boulding 1959).
The gloom is never relieved for Malthus continues that any
technical improvement such as a technological invention or an organi­
zational change can only relieve misery temporarily. The relief from
the subsistence situation will cause the population to grow until a new
equilibrium exists at subsistence. Thus, the result of innovations and
progress is simply an increase in the population which enables more
people to live in misery than before. It is this corrollary to the
Malthusian doctrine which Boulding has labeled the "Utterly Dismal
Theorem" (Boulding 1959).
The last 1J>0 years have shown errors in the Malthusian theory.
Least important, the arithmetric and geometric ratios were in error.
It is of little importance since the crucial principle is that re­
sources must limit population. Whether it takes place in 25 years or
200 is irrelevant except to those being limited. Historically, it is
interesting to note that Malthus was aware of this inadequacy for he
put far less emphasis on the ratios in his second edition of the Essay
(Malthus 1803). More importantly, his hypothesis that each advance in
technology is absorbed by a consequent increase in population,thus
preventing any increase in the standard of living, was disproved by
the industrial revolution. It is ironic that,with the exception of
19th century Ireland, the Malthusian spectre had been postponed in
North America and Western Europe, just as he was writing his essay.
In fact, the food supply has outrun the population growth as a result
of a large increase in agricultural land and the remarkable rise of
the yield of food per acre. Malthus had underestimated man's tech­
nological ingenuity and almost unlimited capacity to move himself and
his goods. Thus, the Malthusian doctrine is a valid empirical general­
ization for most of the world until the 1780's. As a general law, it
fell because of the fallacious assumption that increases in production
could never exceed increases in population. Today, its validity must
be qualified by the concept of development. The applicability of the
doctrine is inversely related to the degree of economic development a
country has sustained. In short, Malthus underestimated the degree
to which technology and transportation could increase production.
Before one simply rejects the utility of the Malthusian doc­
trine, as do Duncan and Hauser in the following quotation, one should
examine the more recent formulations of the doctrine which we will
consider later in this chapter in the demographic section. Duncan and
Hauser (1959s 13) claim that:
... the major contribution of such formulations has been to
provide a general framework for the discussion of problems of
the adjustment of population to resources and policy questions
related thereto. They have not been notably helr»ful in
identifying the immediate factors governing population
changes, predicting rates of growth or patterns of movement
in the short run, or explaining research.
A friend of Malthus, David Ricardo, contributed the next major
theoretical insight into the relationship between population and re­
sources from an economic point of view.
Ricardo (1911), in the
Principles of Political Economyragreed with the Malthusian doctrine
on population growth, but asked what will be the distribution of wealth
under Malthusian disequilibrium situations. Ricardo saw a tripartite
division of the economic world: (l) laborers labored and as recompense
were paid wages, (2) capitalists organized and risked capital and in
return received profits, and (3) the landlord received rents for the
use of the soil. In fact, the landlord's income was not checked by
competition. Rent was a return which had its origin in the fact that
not all land was equally productive. Thus, two farms equal in all
respects except soil may have different productions dependent solely
upon the soil's differential productivity. Since both farms sell the
products in the same market, the difference in productivity expressed
as market value will determine rent value of the more productive farm.
As population expands in the Malthusian disequilibrium situation,
Ricardo suggests the margin of cultivation will move out to less pro­
ductive lands. Later in this study, this theme will be developed into
the marginality hypothesis. As wages go up, the capitalists's profits
go down. So Ricardo claims the result of the Malthusian disequili­
brium is to benefit the landlords, hurt the capitalists and leave the
workers close to the subsistence margin.
The Marxian concept of the population-resource relationship
is based upon the rejection of the Malthusian doctrine which Marx
labeled a "libel on the human race." The proletariat, the future
communists, were too intelligent to allow reproduction to decrease the
standard of living. In addition, Marx's labor theory of value has
implications for the population resource relationship. The premise
that production is at the basis of society underlies the labor theory
of value which may be stated
as the value of any commodity being
dependent upon the labor involved in its production. Profit, the moti­
vating force of the capitalist system,is defined as the result of the
difference between the value the laborer is paid and the value he
produces. The latter is the larger. Expansion of the system results
in an increase of wages as the demand for labor rises. In order to
maintain profits, labor saving machinery is introduced. But, its
value is illusionary since actual profits are derived from the dimin­
ishing labor force. Labor, now underemployed, is willing to accept
substandard wages. This is the origin of the business cycle which
fluctuates in expanding booms and contracting depressions as the demand
for labor increases and decreases. So, for Marx, it is the twin forces
of capital accumulation and technological change, reinforced by exo­
genous population growth, which enlarge
the "reserve" army of the
unemployed (Ranis 1963). In short, Malthusian population pressure is
simply the result of capital accumulation, the source of the demand
of labor, increasing less rapidly than the laboring population.
The neoclassical era in economic theory entailed a de-emphasis
upon the population resource relationship as economic research was
devoted to microtheory and equilibrium analysis (Duncan and Hauser
19f>9)» Two contributions should be noted briefly. Marshall (1920)
in his Principles of Economics, while refining the equilibrium process,
emphasized the importance of time as an essential element in the work­
ing out of the equilibrium process. One of the criteria which the
data base of this study had to meet was sufficient time depth to allow
homeostatic mechanisms to act. The other recent contribution was the
model of unstable growth developed by Schumpeter* Schumpeter's (1911)
Theory of Economic Development refined an old theme: a stimulus is
necessary to cause a disequilibrium.
Development in our sense is a distinct phenomenon entirely
foreign to what may be observed in the circular flow or in the
tendency towards equilibrium. It is spontaneous and discon­
tinuous change in the channels of the flow, disturbance of
equilibrium, which forever alters and displaces the equilibrium
state previously existing (Schumpeter 1911: 6).
The discontinuous disturbance according to Schumpeter is an innovation
which is used for production.
Keynes (1936) discovered the non-homeostatic relationship of
savings and investment. This resulted in a re-emphasis upon popula­
tion growth and long term technological change in "development theory."
Harrod and Domar, two of Keynes1 students, developed a model for stable
growth. In this model, the problem of stable development was sus­
taining a high rate of capital accumulation in the face of declining
profits. Exogenous population growth functions in a reversed role to
Malthusian doctrine. Population growth no longer inexorably keeps the
standard of living down but functions as a mechanism to stimulate
investment by new consumption needs, while Schumpeterian innovations
act to frustrate diminishing returns.
Demographic Explanations
The neo-Kalthusians (for example, Peabody and Boulding) have
noted that it took an industrial revolution to disprove Maithus. Thus,
17
in conservative agricultural or underdeveloped areas (such as the pre­
historic ana ethnohistoric Pueblos in the American Southwest) where
the Industrial Revolution has not changed the potential for production
by several quantum leaps, it may be still thought to apply. Although
the concept of standard-of-living stability is rejected, the conclusion
that population growth is a correlate of technological change is viable
under pre-industrial conditions. If the economic forces are somewhat
inevitable, as some members of the "dismal" science have suggested, a
modern ecological model is appropriate. The Malthusian ratios are re­
placed by population pressure in a series of organized, spatially
differentiated ecosystems, each with its own level of consumption
expectations based upon food chains with internal and external eco­
logical connections.
A second model developed out of attempts in the United States
to test the Malthusian and neo-Kalthusian doctrine empirically. The
theory of growth cycles and transition combines "population pressure"
with mathematical analysis. Pearl (1925) suggested that population
grew not at a constant rate but with a variable rate. This viewpoint
is similar to Toynbee's theories insofar as it uses the growth curve
of biological organisms as a template. Pearl claimed:
The long run tendency of population growth can be represented
by a curve which starting from a previously established sta­
tionary level, representing the supporting capacity of its
region at the prevailing level of culture, productive tech­
nique, and the standard of living - rises at first slowly,
then at an increasine rate, finally leveling out as the curve
approaches an upper asymptote which represents the supporting
capacity of the environment at the last stage (reauoted from
Lorimer 1963: 297).
The mathematical curve which describes this growth cycle is called the
"logistic curve" /P = K/(l + ea
+
^x)7, and was suesested by P. F.
Verhulst in l8Li£. The crucial factor is spatial density and Pearl's
experiments on fruit flies gave empirical validation to his theory
(Fig. la).
Although never totally refuted in a critical attack, it was
replaced by transition theory because of its inaccurate predictions
towards the end of the elongated "s."
Its weakness was the assumption
of initial stationary growth rates and the empirical failure to locate
examples of stable populations at the "upper asymptote." Dorn (19£0)
tested the curve built from 1790-19^0 and found the prediction for
1950 in significant error. Motestein (19h?), building on Willcox
(1931)t noted that the gap caused by an initial decrease in deaths is
closed and a new eauilibrium is reached when a similar decline in
fertility takes place. This transition between ooints of dynamic
equilibrium explains the logistic curve for growth may be stimulated
by an increased birth rate or a decrease in death rate and terminated
by either a decreased birth rate or an increased death rate (Fig. lb
and 1c. Gowgill 19U9).
Although the theory fills the requirements of a high level
analysis in that it is dynamic rather than static and it takes into
account culture contact and social interaction, it has been criticized
by Duncan and Hauser (1959: 1U):
As concerns explanation and especially prediction, however,
transition theory ... has succeeded only in suggesting
certain major complexes of poorly defined influences on
1A
THE RESULT OF PEARL'S
LOGISTIC GROWTH CYCLE
IB
PROBABLE CYCLE
OF BIRTHS AND DEATHS
time
DEATH
BIRTH
IMPROBABLE
CYCLE
OF BIRTHS AND
DEATHS
OEATH
BIRT H
10
MALTHU SIAN
CYCLE
DEATH
BinTH
IE
BABY BOOM
OEATH
1. The logistic growth cycle.
CYCLE
20
components of population change .... The influences on
population growth that it postulates are closely bound up with
the particular historical circumstances of population growth
in Western countries.
A similar criticism is aoplicable to "Gini's (1930) parabolic curve."
Analytical theory, although less well known outside of actu­
arial and demographic circles, has a history longer than that of the
Malthusian theory. The theory developed in three major steps: (1)
the development of life tables, (2) the recognition of the relation
of a closed population with constant vital rates to its mortality
schedule and rate of increase, and (3) the development of the system­
atic interrelationships between births, deaths, sex, and age structure.
Halley, the astronomer, in the 1690's first produced the modern life
table. These later became known as examples of "stationary popula­
tions" (Lorimer 195>9) for the number of births equaled the number of
deaths.
In the 1760's Euler, the Swiss mathematician, made the concept
dynamic by showing that the age distribution could be determined by
age-specific mortality and fertility rates whether the closed popula­
tion was increasing, decreasing, or stationary. Finally, Lotka
developed a complete general theory of the interrelationships of the
primary biological processes, including the determinants of age and
sex structure if one assumed constant age-sex specific mortality rates
and fertility rates and a constant sex ratio at birth.
Johnston (1966) attempted to apply Lotka's models to Navaho
population with ethnographic and ethnohistoric data. He explains the
failure of these models as follows (Johnston 1966: 180):
21
In the first place, the basic mortality rates from which the
several United Nations model life tables were developed are
heavily weighted by age-specific mortality levels reported
among European countries since 1920. One can certainly auestion the degree to which these largely Eurooean rates would
pertain to the members of a population such as the Navajo,
whose entire mode and condition of life are so different.
Second, the selection of the most aporopriate model or group
of models to represent a specific population at a particular
time in its development is confronted with great difficul­
ties when we lack reliable information on precisely those
values which we need in guiding our selection ...(that
is) .. • fairly precise knowledge of the infant or early
childhood mortality.
Finally, it should be noted that this summary is incomplete
and reflects my own evaluation of what have been some of the major
contributions. The most complete summary extant is the United Nations
(1955) publication, The Determinants and Consequence of Population
Trends: A Summary of the Findings of Studies on the Relationships
Between Population Changes and Economic and Social Conditions, in which
the work of over l£00 authors is summarized. It differentiates the
economic and social causes and concomitants of growth, fertility, mor­
tality, age structure, distribution, labor consumntion, output, in
separate chapters.
Delineation of the Definitions
and Assumptions in the Model
Before one may discuss a model of carrying capacity as a dy­
namic equilibrium system, it is necessary to delineate some of the
basic assumptions and definitions of the model. The assumption-base
is partly a consequence of the definition of a model, partly of the
type of model, and partly of the data base on which the model is to
be tested.
Starting with the most general of the assumptions, a model is
a simulation of reality which involves a simplification in order to
facilitate the understanding of complex processes. More accurately,
models are sets of hypotheses which simplify complex observations by
offering a largely predictive framework which structures the observa­
tions in order to separate noise from information (Clarke 1968), This
separation process is partially accomplished by ignoring observations
outside of their defined universe. Thus, my first assumption is that
one may define a specific universe through a set of partition criteria.
For example, one of the universes which I am using is the Hay Hollow
Valley in east-central Arizona between A.D. 300-llt£0.
The second assumption is that it is possible to define a set
of variables which are sufficiently general as to allow the deductive
generation of hypotheses, but sufficiently specific as to allow an
adequate description of the system.
The type of model which is used in this study is a systems
model. Systems models are particularly applicable to problems such as
the population-resource relationship for several reasons. First,
General SystemsTheory is a level of theoretical model building between
the highly generalized construction of pure mathematics and specific
theories of specialized disciplines (Boulding 1968). It is true that
the greater the generality, the less the content. But, the special­
izations of fields and subfields result in many disciplines' not
reaching sufficient generality to allow the advances in other disci­
plines to have any effect because there is no connecting bridge.
23
Numerous theories in many disciplines have made contributions to the
resource-population question. Since systems theory acts as a connec­
tive bridge, the expanded model in this study will attempt to use some
of the specific contributions of the theoretical history previously
discussed.
Table 1 is a summary chart of some of the more important
contributions discussed earlier.
Second, General SystemsTheory has been derived both deductively
(Ashby 1968) and inductively (Bertalanffy 1968). Historically, it was
generated to answer a set of problems in the non-physical and be­
havioral sciences. It was realized that the lack of laws, with the
exception of evolution, was a result not only of the complexity of the
non-physycal variation. Although there is order, the order itself
varies in its organization, maintenance and changes. This problem is
augmented when it is noted that causality at the non-physical level
need not be a one way affair. In other words, if one may state that
social phenomena A causes B, it does not preclude that social phenomena
B may also cause A.
These problems were answered with the development of cyber­
netics, the study of homeostatic mechanisms; information theory, which
allows information to be quantified as negative entropy; and game and
decision theory, which allows competition and choices to be expressed
in quantified form. Inductively, factor analyses and a variety of
discriminant analyses has made possible the isolation of both prin­
ciple and minor components of multivariate phenomena. In short,
General System Theory allows one to operationalize concepts which are
Table 1. Summary of theoretical contributions.
Anthropology
Economics
White, Steward et al: Popula­
tion pressure as a determinant
of social organization which
relieves diminishing returns.
Smith: Equilibrium
Durkheim: the division of labor
as a density and competition
relief measure.
Ricardo: Distribution of
resources for Malthusian
disequilibrium.
Kroeber: the agriculture den­
sity non-correlation.
Marx; Exogenous population
growth.
Krzywicki: the isolation,
size, social variability, re­
inforcement mechanism.
Marshall: time depth of
equilibrium.
Lorimer: the expansion, uni­
lateral kinship group, fertility
relationship, the marginality
controlled fertility relation­
ship, the social organization
fertility relationship.
Birdsell; model building.
Malthus: Resources as a
limiting factor.
Schumpeter: Innovations as
a stimulus for disequilib­
rium.
Harrod: Exogenous popula­
tion.
Domar: Growth as a Mal­
thusian reversal.
Demography
Neo-Malthusian: the his­
torical and underdeveloped
area validity and the eco­
logical ramifications of
Malthusian doctrine.
Pearl: the lower logistic
curve and the density de­
pendence of growth.
Cowgill: logistic growth
cycles.
Lotka: stationary popula­
tion models.
applicable to organized wholes including interaction, centralization,
competition, and finality from a general definition of systems as a
complex of interacting components.
Third, General Systems Theory allows one to transcend the
boundary between living and physical sciences by having a similar
theory for open and closed systems. Closed systems are open systems
with a zero value for input.
Systems may be defined informally or formally. At the most
informal level systems are black boxes with inputs and outputs. One
attempts to define the behavior of a black box and to determine what
is in it by the input to output relationships. Hall and Fagan (1968)
have defined a system more formally. A system is a set of objects and
their relationships between the objects and between their attributes.
Objects are parts of the system. Attributes are defined as the proper­
ties of objects. The environment is the set of all objects which
change the system or are changed by it.
Hall and Fagan (1968) classify systems into five categories.
"Adaptive systems" are open systems which are not telelogical but
pseudo-telelogical. "Compatible systems" are defined as those systems
which reflect the best adaptation to environment. Any system with a
stochastic variable constitutes for Hall and Fagan a "system with
randomness." Finally, "isomorphic systems" are those systems in which
there is a one to one relationship between components and relation­
ships. The model used in this study is an open, compatible, opti­
mization system with stochastic variables.
Systems may also be defined with mathematical formality. For
example, Wayne Wymore (1967) defines a system in the following manner.
The set Z •
is a system if and only if:
S is not an empty set,
P is not an empty set,
F is an admissible set of input functions with values of P,
M is a set of functions defined on S with values in S and whose
identity mapping belongs to M,
T is the subset of real numbers including zero,
^is a function defined on the Cartesian product of F and T such
that:
1. 9"3 range and domain have a one to one correspondence.
2. For every f belonging to F, the function evaluated at f
and 0 is equal to the identity mapping.
3. If f belongs to F, and if s, t, s + t, belong to T, then
the function evaluated at the translation of f to s and
then operated upon to t, is the equivalent of operating
from f to t.
h»
If f and g belong to F, and if S belongs to T, and if f
(t)• g (t) for all t belonging to R (o + s), then
(f + s) -
(g, s).
The data base upon which the model will be tested in the pres­
ent study is a cultural tradition located in parts of the Pueblo sub­
culture area. Rather than attempt a definition of culture,in view of
the existence of almost as many definitions as anthropologists,
27
(Kroeber 19!?2), I will focus upon the broad behavioristic categories
which are directly relevant to the model.
Modifying Duncan's (l959) simplified model of human ecology,
there are four mutually articulated categories: resources, organiza­
tion, technology, and population. Resources are defined as the
aggregate of all non-human external conditions which influence or
modify the existence of the human population under consideration.
Thus, it may include non-living phenomena such as topography, climate,
and hydrology; botanical phenomena such as trees and grasses, and
zoological phenomena of all sizes. The term is differentiated from
environment which is being withheld to its specific systemic sense.
At times the two, resources and environment, may be isomorphic. How­
ever, resources will be considered as components within the system,
while environment is outside of the system.
By organization, I mean all the cultural phenomena which allow
a human population to maintain its corporate non-technological identity.
These include social structure, language and religion. More generally,
it is possible to define organization in its systemic terms. The
theory of organization is partly coextensive with the theory of func­
tions of more than one variable (Ashby 1968). Organization exists:
(1) when the relation of the variables A to B is dependent upon C's
value or state, or (2) when there is some constraint in the product
space of the variable possibilities. When organization exists (for
example, a function) there are no longer two independent variables and
the product space is limited. The two ends of the continuum are
28
respectively, organized simplicity, or chaotic complexity (Rapoport
and Hovarth 1968: 73). Organization may be measured as negative en­
tropy. Organization thus implies a decrease in potential diversity.
This is, of course, the opposite of the anthropological structural
functionalist viewpoint which maintains that organization is something
extra, something added to the basic units or variables.
The reason I have chosen to consider technology a separate
category rather than subordinating it as a subsystem of organization
is not to imply its greater importance compared to the other subsys­
tems. Rather, my justification is that one of the major connections
between the environment and the population is through the subsistence
base whose production is a function of technology. Thus, an operation­
al definition of technology would be the systematic knowledge and cultur­
ally shaped material artifacts which allow men to cope with their
environment and each other in both constructive and destructive ways.
Following Villee (1962) who defines a population as a group of
organisms of the same species which occupy a given area, i.e., a resi­
dential population, one may define a human population ecologically as
the members of Homo sapiens within the area bounded by a biotic com­
munity. Human populations, in common with all biological populations,
have characteristics which are the function of the group as a whole
and not of the individuals which compose the group. These are growth
and dispersion rates, birth and death rates, population size and
density, biotic potential, and age distribution.
One of the advantages of isolating population variables is that
the population concept is not only modern (Simpson 1957) but has wide
ramifications and applications throughout many branches of science
(Boulding 19!?0). It is easier to relate the theory of several disci­
plines in an interdisciplinary approach when, as already mentioned, a
bridge or a common unit exists. Within some of the natural sciences
(ecology, zoology, and physical anthropology), and social sciences
(demography, cultural anthropology, and economics) the generic concept
"population" is the common focus for viewing a universe of phenomena
comprising recognizable individual elements but concerned with such
group attributes as number, composition, distribution and change.
Second, the population as a unit is highly amenable to quantitative
analysis, since in the most abstract sense the concept was developed
in statistical "renewal" and "sampling" theory. The former refers to
deterministic and stochastic models of generalized accretion and de­
pletion. The latter was developed to meet the need for a criteria of
representativeness whereby rigorous inferences about the composition
and dynamics of a population may be based upon observations of a small
percentage of the population.
The final assumption derived from the cultural data base is
that it is possible to estimate prehistoric populations and resources
through indirect indices. Archaeological surveys have traditionally
served two functions. First, they provide the archaeologist with an
approximation of the unexcavated material remains. Second, they may
be used to provide an estimate of population. It is a crude estimate,
30
perhaps, of absolute population but it is less crude for estimating
relative population size. The more intensively an area is surveyed
and the more systematically it is sampled, the more refined is the
estimate. One of several effective indirect indices for monitoring
the changes in prehistoric resource systems exist in pollen analysis.
The Simplified Model
Carrying Capacity is the maximum number of organisms or amounts
of biomass which can maintain itself indefinitely in an area, in other
words, a homeostatic equilibrium point. It is a homeostatic equi­
librium in that there is a tendency toward the maintenance of a state
of balance between opposite forces or processes which result in a
diminishing net change or a stable constant. It is dynamic in that
the point at which the state of balance exists may change over time
and space.
What are the two opposing forces which determine the eauilibrium?
On the one hand, Liebig's extended law (Brouehey 1968: 2)
states population size is determined by maxima and minima of specific
resources. On the other hand, the "prime dynamic mover" appears to be
reproduction. Theoretically a population will tend to keep reproducing
and growing in size until an ultimate limit is reached which is deter­
mined by the supply of nutrients and energy. When there is a change in
the supply of nutrients and energy, a change in the carrying capacity
results, and there is a consequent growth or decrease of the biomass
until a new equilibrium is reached. In Figure 2, A denotes a carrying
capacity equilibrium point. If a change in the resource curves takes
31
t
POPULATION
J>
RESOURCE 2
POPULATION I
CO
u
o
o:
Z3
O
RESOURCE I
CO
LU
ft:
POPU LATION
Figure 2. A simplified model of carrying capacity as a dynamic
equilibrium system.
32
place, Resource 1 to Resource 2, a disequilibrium results with re­
sources being greater than population. One would expect the biomass
or population to grow along the population curve until a new equi­
librium point B is reached. Similarly, one may predict what would
happen in other cases such as a decrease in the resource curve or an
increase or decrease in the population curve.
An alternative representation of the same model is presented
in flow chart form (Fig. 3). Two points are worth noting. First, the
model is simplified and many steps are being omitted. For example, if
population is greater than resources, the negative growth rate may be
a result of a decreased birth rate, an increased mortality rate, or an
increased out migration rate. Neither the growth rate alogrithm, nor
the migration factor is being considered in this flow chart. Similarly
the term resources glosses over several problems such as what percent­
age of the resource base is actually usable. Second, by placing the
addition function (pop * pop + growth) before rather than after the
decision node, I am building into the model the possibility of greater
homeostatic fluctuation. This is justified in that the growth rate is
an a posteriori rather than an a priori function. Populations do not
usually decrease their growth rate because "they think" that the growth
will result in insufficient resources, but because the growth rate has
resulted in insufficient resources.
The Model and Selected Aspects of Economic
and Demographic Theory
The production function is a technical economic law relating
output to input. Given certain amounts of inputs such as labor, land
Input
/Has \
•es. leve
changed
Replace
resources
with new
res. level
Replace
growth rate
with new
growth rate
Calculate
population
growth
Population *
pop. + ffrowtt
Growth rate
is positive
iop. equa.
to resour
Equilibrium
.population
New negative
growth rate
Output
Figure 3. The simplified model of carrying capacity as a dynamic
equilibrium system — Systemic Model: Version 1.
and capital, there are various amounts of a particular good or output
which can be obtained. The amount varies with the level of technology.
At any one level of technology, there will always be a maximum obtain­
able amount of product for any given amount of input or, conversely,
there are a minimum set of inputs which will result in a particular
output (Samuelson 1961).
This study's model considers production to be primarily a func­
tion of labor and land and put minimum emphasis upon capital. This
emphasis is based upon the well documented lack of capital elasticity
in underdeveloped peasant subsistence population (Wolf 1966; Heilbroner
1962; Rostow 1962; Bauer and Yamey 1957; United Nations 1953). After
defining the population labor relationship, it is possible to redefine
the relationship between resources and population in terms of isoproduction curves (Fig. U).
It is important to realize that the growth of production is
not potentially infinite if one of the multiple inputs is fixed. The
law of diminishing returns states that:
An increase in some inputs relative to fixed inputs will cause
total output to increase; but after a point the extra output
resulting from the same additions of extra incuts is likely to
become less and less. This falling off of extra returns is a
consequence of the fact that the new "doses" of varying re­
sources have less and less of the fixed resources to work with
(Samuelson 1961: 26).
This has two major implications for our model. First, if one may
assume that at least one factor input for example, is fixed, then an
increasingly labor intensive solution to a Malthusian disequilibrium
caused by a population surplus is just a postponement and not a
35
Labor
Figure U. Smallest land labor combination which will produce a
particular output.
solution at all. Second, it will tend to reduce the amount of homeostatic fluctuation around the model's equilibrium points. An addition
in population not only consumes more resources, but, if it is past the
point of diminishing returns, it does not result in an eauivalent
addition to production as would an equal increase of population below
the point of diminishing returns.
In contrast to the dampening effect of the law of diminishing
returns, it is necessary to juxtapose the "increasing savings of
scale."
This refers to the increased production which results when
increasing all the factor inputs. It is not a direct contradiction
to the law of diminishing returns because none of the factors are
fixed. Often the increase of output production is greater than the
increase in factor input. This is the result of the economics of mass
production and involves the savings of increased specialization, the
use of interchangeable parts, and the breakdown of complex processes
into repetitive simple operations (Samuelson 1961: 26). However, in
the model the role of "savings of scale" will be less important than
the "law of diminishing returns." There are few operations of sub­
sistence and peasant economies which are amenable to this type of
production.
Pearl originally formulated the logistic curve as a function
of density dependence. However, it is clear that it could be rephrased
as a function of the law of diminishing returns. Population is rede­
fined into labor while space is the fixed input. Since sequential
37
increases of population result in smaller increases in production, the
rate of population growth must diminish as population catches up to
resources•
In the model, one cannot expect the converse; namely that if
the logistic curve pertains, then the law of diminishing returns is
acting. But one can argue knowing that the contrapositive follows
logically that the law of diminishing returns is not having a major
role in determining population.
Justification of the Model
As previously pointed out, the primary weakness of the original
Malthusian doctrine was its application to a universal data base. Its
application to post-industrial economies where increased "savings to
scale" and technical innovations raised the level of production to such
heights that the function of the positive and preventive checks was
virtually bypassed. However, in pre-industrial societies where a much
greater percentage of production is devoted to subsistence and where
the margin of economic error is small, the reality of the Malthusian
spectre has never been seriously challenged. The actual existence of
Malthusian disequilibriums have been documented both historically, the
Irish Potato famine, and ethnographically, the critical economic under­
development in India.
The model is not simply a restatement of the Malthusian model
which will become more apparent as the model is expanded in the next
chapter. The concept of ecological equilibrium in which each species
multiplies and then reaches through homeostatic fluctuation an
equilibrium population is an extension of the Malthusian system. In
the same way that Darwinian evolution as ecological succession is an
extension of ecological equilibrium. Small chance and adaptive bio­
logical or cultural variations produce constant and irreversible
changes in the equilibrium values of the populations of all species
or cultures (Boulding 1959)#
Neo-Malthusian models have both advantages and disadvantages.
The primary advantages are: first, given the initial conditions one
may predict the expected consequences, and second, one may quantify
both the initial conditions and the expected results. The primary
disadvantage of this type of neo-Malthusian model building is that
contemporary demographic and ecological data do not lend themselves
to testing the model. This is because the time span for which the
data exists scarcely suffices to encompass long tenri ecological pro­
cesses. Third, modern technological development with its concomitant
diversity of resources, complex trade patterns, and ease of mobility,
complicate the data to the point that it is necessary to utilize fac­
tor and discriminant analyses to remove the masking data patterns and
variables•
Archaeology and ethnohistory are thus in a unique position to
evaluate this type of model. Their data span long time periods and
some of the societies they consider have not developed the complex
resource networks, trade systems, and technologies which distinguish
our modern industrial nation states.
CHAPTER 2
THE EXPANDED MODEL
The Addition of Variables
In any reasonably sophisticated model it is difficult to find
a specific place to begin. A discussion of any concept or section of
the model may be influenced by other concepts or sections within the
model. Therefore, there are inevitably references to the preceding as
well as later chapters where these "other concepts" and supporting
data are discussed.
Spatial Variation; Homogeneous and
Heterogeneous Resource Bases
As presented initially the model is over-simplified. It may
be viewed as the relationship between two functions, a population func­
tion and a resource function. Since both functions may change through
time, their mutual solution, or graphically the point of intersection
may also change through time, thus tracing out a series of equilibria.
It does not take into account many variables such as spatial differ­
entiation or temporal change in resource patterns. First, one should
examine the implications of the spatial differentiation or resources
holding the temporal changes in the resource base constant. One may
imagine a complex heterogeneous resource pattern as exemplified by
Figure 5 where there are four distinct resources. If this complex
39
TOTAL
/
/
E 8 A+B+ C+D
POPULATION
CURVE
O
v
FOREST
POPULATION
TOTAL
G R AS S LAMD
POPULATION
R IVERIKE
POPULATION
POPULATION
Figure 5. Heterogeneous resource model.
TOTAL
RESOURCE
CURVE
ill
pattern is divided into a set of homogeneous resource spaces (which I
prefer to call resource zones), it will be easier to build the more
generalized model. The simplified model presented in Figure 2 accounts
for one resource zone. In order to account for the heterogeneous
pattern, it is necessary to sum the models of the individual resource
zones. This is exemplified in Figure 5 where the total carrying
capacity for the heterogeneous area will be the sum of the individual
resource zone carrying capacities denoted on the diagram by E being
equal to A + B + C + D.
Temporal Variation
External conditions, such as climate, may cause different re­
source curves to exist at different points in the chronology when the
temporal variable is added. Thus, over time there might be changes
in the individual resource zone curves. Simultaneously, changes in
fertility rates, abortion rates, or other demographic variables may
result in changes in the population curves. Either resource or popu­
lation curve changes will result in changes in the summation curves.
These changes need not be uniform (Figs. 6).
Migration and Population Development
at the Zonal Level
It has often been noted that the distribution of settlements
follows a definite pattern through time which is partially dependent
upon the spatial distribution of resources (Kroeber 1939; Hagget 1966).
One hypothesis to be examined is that the development of populations
in marginal resource zones is a function of optimal zone exploitation.
\f
\
R2
\/
\/
<£2
R2
p
v
)V
P
)
\
/
\
7
1 .
Forest
Population
Grassland
Population
Riverine
Population
Desert
Population
o .
TOTAL
POPULATION
Figure 6, Heterogeneous resource model with spatial and temporal
variation.
ZONE A
ZON E
POPULATION
OPTIMAL «
B
ZONE
POPULATION
C
POPULATION
MARGINAL
MIGRATION
•>
GROWTH
Figure 7. Predicted migration pattern.
4=VjJ
In order to operationalize this hypothesis in terms of the model, one
must set up a series of resource zones with consecutively diminishing
resource curves as in Figure 7.
It is easy to define at this point what is meant by optimal
and marginal resource zones within the model's framework. By optimal
is meant the resource zone with the highest resource curve. All other
zones are marginal. The lower the resource curve, the more marginal
the resource zone.
One may predict on the basis of the model what will happen as
a population starts to grow in the optimal resource zone (Fig. 7).
If the population is less than the carrying capacity, it will increase
until it reaches the carrying capacity. If the population overshoots
the carrying capacity as a result of simple population growth or as a
result of population growth combined with immigration, then the popu­
lation surplus (the distance C to A in Figure 7) has two alternatives
— gradual extinction or out-migration to the next zone
which is more
marginal. In the more marginal zone the process would repeat itself.
But each time there is movement from a zone to a more marginal zone,
less population is necessary to reach carrying capacity. If there is
no change in the resource curves over time one would expect the
following sequence of events: first, a population fills up the optimal
zone to carrying capacity; then a little later a second zone fills up
to a smaller carrying capacity, and then a little later a third zone
fills up. This process continues until all the zones are filled.
There are indications, however, discussed by Birdsell (19??), Stott
I—
<
-J
ZONE
A
ZONE
B
ZONE
C
3
CL
O
CL
TIME
Figure 8. Predicted population curves by microhabitat or ecological
zone with constant resources.
cvn
(1969) and Isard (i960) that the out-migration process might begin
shortly before carrying capacity is reached for population pressure
would have begun.
On the basis of the model, the predicted population
curves by zone would be similar to Figure 8. Note how similar these
curves are to the logistic curve (Fig. 1).
However, one must remember that the resource curves have been
held constant through time. If they should begin to drop, the result­
ing carrying capacity decrease would result in a larger out-migration.
This possibility is diagrammed in Figure 9.
The Systemic Model: Version 2
Since it is difficult to conceptualize the addition of too
many new components to the systemic model at any one time, I have
divided it into steps which reflect the method by which the model was
constructed. Figure 3 presents the original systemic model. Figure
10 presents the second version of the systemic model which includes
the addition of spatial variation, temporal variation, and migration
and population development at the zonal level.
Economic and Demographic Variables
When relating demographic and cultural variables, the situation
becomes more complex. Joseph Spengler in "Economics and Demography"
(1959) has played the role of Malinowski for this particular multidisciplinary interface. He lists primary and secondary economic and
demographic variables and shows their broad convergence. Table 2 is
an abstracted summary of the interacting cross-disciplinary variables.
I
ZONE
—ZONE
B
ZONE
C
T I M E
CARRYING CAPACITY
BEGINS TO DROP
Figure 9»
Predicted population curves by microhabitat or ecological
zone with diminishing resources.
t=-
U8
\
Input
Date • Date
+ time
increment
Set zone
counter
(J) « 7
zone couni
as
esource
zone
one U)
criane
ilesource level.
1 new re­
source
level
Resource
level
remains
constant
Has
rowth rate
for zone
c
Replace growth
Irate with new
growth rate
zone (J)
Decrease
zone counter
4
zone counter
Pop. zone (J)
zone
growth
Calculate new
pos. growth
rate
Zone (J)
Calculate
new negative
growth rate
, mzg.to
/other zonespossible-
f
Figure 10. The systemic model: version 2.
migrate pop­
ulation to
other zones
Table 2. Spengler's interacting economic and demographic variables
Demographic Variables
Economic Variables
M
F
r
M<j
Mortality (general or age-specific)
Fertility (general or age-specific)
Natural increase
Differential mortality (intergroup dif­
ferences in fertility)
Y
y
F(j Differential fertility (intergroup dif­
ferences in fertility)
e
Emigration
i Immigration
n
Net international migration
m
Internal migration
k
md Differential internal migration
T Population total or population density
Td
Internal distribution of population total
R
Ca
Cs
Cg
Rate of growth of total population
Age composition of population
Sex composition of population
Qualitative composition of population
(e.g., genetic, educational)
E
S
I
c
cc
Net national product or national income
Per capita net national product or national
income
Total stock of capital or income producing
wealth
Per capita amount of capital or incomeproducing wealth
Land or other resources per capita
International terms of trade
Functional distribution of income into wages,
interest, etc.
Distribution of income among persons com­
posing population
Index of fullness of employment
Annual volume of savings
Annual volume of investment
Consumption
Qualitative composition of consumption
Ic
Qualitative composition of investment
0C
Occupational composition of population
K
1
t
D
Dv
Cqs Qualitative composition of a component
of the total population (e.g., occu­
pational group, population of a region)
t=>o
Table-2. Spengler's interacting economic and demographic variables—continued
Economic
Variable
Demographic Variables
by Which Affected
Demographic
Variable
Y and y
R> T,
C a , Cq, Cg, and
possibly Cq s
M, F, e. i;
(r, R)
Fd, Md
m, md, Td
K and k
1
T, C a , Cq, C s
T, R, T d
D
R» T, Cq, Td
Dy
R»
t
R> Ti Cq
R» T, Cq, C a , C g , T(j
R, Cq, C a , C g , T^
S
I
E
c and cc
Ic
0C
^q> ^d, C a , C s
R, T, C a , Cq, C g , T(j
R» T, C a , Tjj
R* ^a»
^s> ^d
°q»
Cqs
Economic Variables
by Which Affected
y> ®y>
Oc, Dy, E
Oc»
^y
n
°c» y* E
c»
®ct cc
The demographic variables are differentially sensitive to changes in
the economic variables. Emigration, immigration, internal migration,
and differential internal migration, e, i, m, and m^ respectively, are
the most sensitive for the decision process of the household since
these variables are directly based upon the perceived economic situ­
ation and the potential of the area. Mortality, fertility, and total
population, M, F, T, are less directly determined.
Spengler documents several general relationships with economic
and demographic variables which I have summarized in Table 3.
Underlying this complex analysis of Spengler's are two basic
economic definitions which are based upon the circular flow of eco­
nomic goods and services within a society. First, New National Product
may be defined as the summation of consumption, investment, and
governmental expenditure (MP = C + I + G), or, second, it may be de­
fined as the summation of the factors of production-wages, interest,
profits, and rents (NNP =W+I + P + R), (Samuelson 1961).
For the purposes of the model, it is easier to use the con­
sumption rather than the earnings or income approach. It is necessary
to redefine these variables in order to make them applicable to non­
monetary societies. Consumption causes no insurmountable problems
since it may be calculated using biological necessities. Economists
define investment as the outlaying of resources and the deferring of
present consumption in order to obtain a gain in net real capital.
For the model, the definition needs to be amended by replacing the
word capital with resources. By deferring the uses of resources
Table 3. Spengler's economic and demographic relationships
A. Independent demographic variables and dependent economic variables,
1. Increases in T usually result in increases in Y because the
labor force is larger and S and K increase.
2. Increases in T cause t to fall since both exports and imports
increase but simultaneously this decrease in t operates to
make Y lower than it would normally be unless improvements in
technology give rise to increasing returns.
3. If T pushes down wages below the perceived potential in
neighboring areas e increases.
U. Up to a point an increased T results in an increased y as a
result of increased savings of scale, but eventually the law
of diminishing returns takes effect and decreases in 1 con­
stitute a drag upon y.
5. Increases in T, also result in changes in D and Dy since labor
becomes relatively less expensive than k or 1.
6. Increases in R result in a slow down of increases in k and
thus y, since population growth absorbs resources which other­
wise might be distributed to k.
7. Decreasing R is often accompanied by underemployment and de­
creasing y. This is the result of the fact that as R declines,
S increases, and I decreases because the market does not
expand.
8. Redistribution of the population TD tends to optimize economic
activities across space and thus increasing per capita output,
simultaneously increasing I and decreasing S since the
rationale for e is to increase the propensity to consume.
B. Independent economic variables and dependent demographic variables.
1. Increases in y tend to decrease M. This is offset, however,
by the degree of development and underdeveloped areas today
often have low y and low M causing their population explosion,
2. Within a socio-economic strata increases in y tend to be
directly related to F.
3. e and i are dependent upon the perceived spread of economic
opportunities available between the receiving and trans­
mitting areas•
It. md anc* m are dominated by conglomeration and aggregation of
economic activities which result in labor and hence population
attraction.
following Wittfogel (1957) one expects to receive a gain in usable
resources greater than the gain which could have been derived from the
immediate use of those deferred. The storage of a gricultural seed is an
example. Finally, the concept of governmental expenditure must be
broadened to organizational expenditure which allows for the variety
of religious and social guises that governmental forms take in non­
monetary economies. Thus, the new formula is NSP = C + I + 0 — net
societal product is equal to consumption plus investment plus organi­
zational expenditure.
Environment is defined as a systemic external variable in the
original set of definitions. Resources are defined as the potential or
real aggregate of all non-human external conditions which influence or
modify the existence of the human population under consideration.
Those resources which are actually used are the NSP. Thus, the NSP
may be less or equal to resources but never greater than resources.
The curves in Figures 1-1). should be now redefined in terms of NSP
whose relationship to resources in the model is shown in Figure 11.
Technology
Technology has often played a central role in cultural evolu­
tionary theories. Its suggested implications for cultural change have
ranged from White's almost autonomous energy moderating variable to
the "leisure theory" of development which suggests that technical in­
novations release labor from subsistence activities to participate in
cultural activities. From a systemic ecological viewpoint technology
is a limiting factor upon the production of goods and services and
ft
c
o
3
CL
O
CL
NSP
Resources
Figure 11. Resources and net societal product.
thus should be characterized by the types of inputs used, the output
mix, and the quantitative relationships between inputs and maximum
output.
I have used Schumpeter's formulation of changing technology in
the model. Schumpeter laid stress on "innovations" by which he meant
either technological progress or resource discovery. In short, it is
a change in the production function which brings about an increase in
output. Although Schumpeter emphasized innovations both as a stimulus
for disequilibrium and as the "mainspring" of autonomous investment,
it is the former which will be of interest.
Accordingly, it is possible to start the analysis with the NSP
population system in stable equilibrium. Development is the discon­
tinuous disturbance of the equilibrium in the form of an innovation.
The increase in production output is the stimulus for the Malthusian
disequilibrium.
There are two other facets of the theory. First, significant
innovations usually occur in clusters. A single innovation does not
have a major effect upon production unless it is backed up by a series
of reinforcing innovations. For example, the introduction of the in­
ternal combustion engine needed a vast number of reinforcing innova­
tions, such as the expansion of highways and the expansion of the
petroleum and rubber industries, before the automobile industry caused
an effective difference in the national product. Or, using a prehis­
toric example, irrigation had no long term effect upon agricultural
productivity unless the necessary social innovations took place which
allowed the maintenance of the canals, the distribution of water, and
the allocation of the surplus product. Once a "cluster of innovations"
has been introduced they become a competitive necessity and diffuse
widely.
Second, innovations are favored by the equilibrium state. The
stability of the system results in minimal risk of failure while the
small margin of resource surplus is the motivating force resulting in
the maximum pressure to innovate. As the intensification of the rate
of innovation increases the disequilibrium of the NSP population sys­
tem, larger margins of surplus exist and the pressure for innovation
decreases.
In terms of the graphic model, Figure 12 shows a cluster of
Schumpeterian innovations in terms of their results on the NSP curves.
Settlement Pattern
Before one may discuss alternative theories and methods behind
the generation of settlement location, it is necessary to restate the
model with zonal variables into a model with settlement variables.
Continuing the logical reductionism which began with the definition
of the heterogeneous model (Fig. £), it is possible to define two vari­
ables: settlement population and settlement threshold. One may then
apply the neo-Malthusian model to units of settlement as well as zones.
The relationships among settlement population P (I, J), zonal popula­
tion PT (J), and settlement threshold ST, the maximum population of a
settlement are:
*7
NSPl
NSPO
Resources
Figure 12. Schumpeterian innovations. This figure shows
the income in net societal product from NSPO
to NSP caused by a "cluster of innovations"
SI to Six,
$8
FT (J) -
(I, J)
P (I, J) < ST
where; P (I, J) is the population, P, of the I^1 settlement in zone J,
PT (J) is the total population of zone J,
ST is the maximum number of people that may exist in a settle­
ment.
The relationship among settlement population, zonal population, and
zonal resources is:
P (I, J) < PT (J) < NSP (J)
where: P (I, J), ST, PT (J) are the same as above
NSP (J) is the net societal product of zone J.
In diagrammatic terms, this would be the equivalent of adding
a third line of settlement population curves beneath the zonal curves
in Figure 5. In systemic terms the restatement is shown in the flow
chart of Figure 13.
Settlement pattern classifications reflect the high degree of
variability in both the settlement distributions and the theoretical
problems for which the distributions are data. Thus, there are
morphological classification of rural and urban settlements (Dickenson
196I±), size classifications (U.S. Census 19o0), and functional classi­
fications such as Christaller's central place hierarchies.
Critical, however, to all classifications is the central con­
cept of location. If one conceptualizes settlement patterns in two
dimensional space, a simplifying assumption, it is possible to quantify
the locational relationships. At one extreme are the regular patterns
59
Inputs
Date
Date + Time
increment
Tot. Pop.
Zone Pops
Zone Pop.
Settle. Pop
Zone resources
settlement
resources
Tot. resources
zone re.
Set Zone
Counter
J - 7
Is
one Counte
0
Set Settle­
ment Counter
to k
I •k
as
ettlement
esources
hange
leplace set­
tlement re­
sources with
new level
Settlement
resources
remain
constant
Decrease
Counter
I
Decrease
J by one
as
ettlement
op. growth
change
Decrease
Counter
I
«
Replace set­
tlement pop.
growth with
new erowth
rate.
Pop. (I)
pop. (I)
growth
Calculate
negative
growth
1
/
Calculate
new positive
growth
-Intra
zonal mi^.
nter
zonal mig.
possible
Intra-zonal
mig. budded
settlement
Inter-zonal
mig. budded
settlement.
Figure 13. Restatement of systemic model in SETTLEMENT terms
Systemic Model: Version 3«
including settlements which are located in a line or in lattices. At
the other extreme are the non-regular patterns, random distributions,
clusters of settlements, or even single isolated settlements.
The problem which faces the model is twofold. First, what is
the relationship between population and NSP on one hand, and settlement
location and settlement pattern on the other? Second, how may these
relationships be simulated? For the purposes of the model it is
assumed that once a settlement is located, it cannot be moved and still
remain the same settlement. Settlements grow and die at the same lo­
cation. If a settlement moves, for example, the Hano experience
(Dozier 1966), it is similar to one settlement population becoming
extinct and a new settlement being founded. The simplifying assumption
for the model is that settlement identity is equivalent to locational
uniqueness. Thus, for new settlement formation to take place within
the zone the population of a settlement must be greater than the
settlement threshold and the zonal population total must be less than
the zonal net societal product or symbolically, P (I, J)> ST and PT
(J)< NSP (J).
There are many factors which are involved in the migrant's,
P (I, J) - ST, choice of a
new settlement location. Of these,
three will be considered. First, the location may be randomly deter­
mined. Second, new settlement location is determined by the location
of other settlement locations and populations. Third, new settlement
location is based upon the location of potential resources. In cases
where P (I, J) > ST and PT (J) > NSP (J), it is possible to calculate
the best zone for the migrants to locate by looking for the zone with
the smallest PT (J)/lTSP (J) ratio. Then, the actual location within
the new zone may be determined by any of the three alternatives above.
If one turns to the problem of calculation and simulation, the
choice of a random location may be determined by the use of a pseudo­
random number generator or a random numbers table. In order to cal­
culate the new settlement location on the basis of other settlements
and populations, a population weighted "Bachi mean center of the
distribution" is used (King 1969). For the third alternative, one may
calculate the necessary resource area of existing settlement popula­
tions and locate the new settlement in that location which affords the
best resource-population combination.
Other variables, such as spatial aggregation and population
aggregation, which also concern settlement location may be tested
semi-independently of the simulation of the model. These are indirect
indices of social organization. On purely theoretical grounds their
relevance to the physical constraints on social organization may be
argued from the "Ising problem." Assume that the minimum possible
organization is manifested in random behavior. Imagine a box which
has a group of balls moving randomly in the limited volume. If one
diminishes the environment by making the walls smaller and smaller ~
eventually the balls will form a lattice. Thus, one has caused a
complex change in the motion of the balls from random to ordered be­
havior solely by decreasing the size of the environment which affects
the activity of the internal components. An analogue often occurs
62
when an elevator is loaded with people to its maximum legal capacity.
It is not difficult to substitute populations or settlements
for the balls and a limited area such as a settlement or valley for
the environment. At one level, if one begins to pack more and more
people into a limited area defined by the boundaries of the settlement,it
would begin to show more ordered behavior within its population. This
would occur even if behavior of the population was originally random,
which it is not. This phenomenon could be measured indirectly by the
population aggregation (the number of people per settlement) in combi­
nation with the areal or volumetric size of the settlement. On another
level, the decrease in the effective environment would cause settlement
location in a region to be more ordered. For example, if part of a
valley becomes non-inhabitable, then a clustering of the settlements in
the inhabitable portion is to be expected. This is possible to
measure through the nearest-neighbor statistic which scales the re­
lationship among dispersed, randomly distributed, and clustered
settlements (Hagget 1966) or the "mean crowding" statistic which
measures proximity (Monte Llcyd 1967).
The cultural implications of the physical constraints on organ­
ization should be stated. Following Steward, it may be noted if there
is a low density highly dispersed population, there is little need for
intergroup economic and social cooperation. However, as either popu­
lation pressure forces multi-specialized zonal economies, or as
environmental limitations take place, it becomes economically advan­
tageous to develop reciprocity and redistribution systems. The latter
being more efficient because: (1) distribution of goods becomes more
dependable, (2) food failures at one settlement may be offset by the
wider joint resource base, (3) greater exploitation of the total re­
source base may take place through institutionalized intervillage
specialization, (U) a basis is provided for cooperation in other areas
for such activities as construction and maintenance of simple irriga­
tion systems (Johnson 1970).
From the above one may logically continue by using Durkheim's
arguments of social solidarity and the division of labor. Increasing
population density brings greater specialization and increased division
of labor. Increased division of labor brines a higher degree of social
solidarity and social organizational complexity. Thus, from Steward's
non-cooperating, low density, highly dispersed, similarly employed
population, there has developed a highly clustered, differentially
employed, highly organized population. However, the population need
not make the organizational shift, and one would expect the density
to diminish.
Longevity
One of the major problems of settlement analyses is the ques­
tion of longevity. Why does one settlement survive when a similar
settlement fails? This problem is particularly difficult to analyze
when there are sufficient resources to maintain both. There is in­
sufficient information or theory pertaining to this question as a
perusal of the literature on the cyclical nature of culture (Toynbee
6U
1965J
Willey and Phillips 1958), its decline (Eisenstadt 1967), or
on cities (Mumford 196lj Dickenson 196U) shows. For example, Willey
in his attempt to explain the Postclassic depopulation of the Viru
Valley was forced to fall back upon the exogeneous factor of Chan
Chan's greater resource and opportunity potential as a cause for dif­
ferential settlement longevity. A second example is provided by
Rathje's argument (Rathje 1971) that differential settlement extinction
for the Maya decline is the result of differences in the import and
export of goods and services. He claims that the core area trades
social organization and services for raw resources from the peripheral
areas. Although the demand for resources continues in the core area,
the innovations in social organization and services become integrated
into the societies of the peripheral area and thus the demand for core
area commodities disappears. With the destruction of trade core area
settlements cannot exist, but peripheral area settlements survive.
McKenzie (1968) developed perhaps the most useful formulation
of causes of differential settlement extinction applicable to the
model. It may be integrated into the concept of Schumpeterian inno­
vation. He argues that, in an agricultural community, the point of
maximum development is equivalent to an ecological climax. Thus, the
community tends to remain in a balanced condition until a new element
enters the system to disturb the status quo. This disturbing innova­
tion, to use the Schumpeterian term, acts in either a positive manner,
resulting in growth, or a retractive manner resulting in emigration
and readjustment to the circumscribed economic base.
The variable length of time that settlements exist must be
accounted for. The model will attempt to use two alternative longevityfunctions. One might argue that under the conditions of decreasing
resources longevity is a function of settlement size, A minimum popu­
lation is necessary to keep a settlement in existence. This view is a
simple extension of the population aggregation arguments suggested
earlier. A larger settlement population can absorb a greater number
of losses than a settlement with less population. If the amount of
loss is constant over time and space or variable (but equally applied
to both the larger and smaller settlements), it will take a longer time
for the larger settlement to fall below the minimum level of settlement
existence than the smaller settlement. It is important to note that
if one is considering a rate of loss which is related to population
size rather than the amount of the loss, the above argument does not
hold, and is thus not used as a longevity alternative.
The first alternative is based on MacArthur's belief (MacArthur
and Connell 1966) that there is no population wh5.ch is totally safe
from extinction. A finite probability exists that every settlement
population will die. This probability is a function of existence and
not of predation or competition. MacArthur has developed a measure
of this probability, tk, which is the expected time for a population
at its carrying capacity to become extinct if the population is not
allowed to go beyond its carrying capacity. A population is considered
relatively safe if the tk value is large and in danger of extinction
if tk is small.
Instead of discussing the equation since it appears later in
this chapter, two other aspects of MacArthur's formulation will be
noted. First, tk is highly sensitive to the carrying capacity. A
small change in the carrying capacity may result in tk changing by
powers of 10. Second, the effects of predation (either inter-species
or intra-specie warfare for human populations) and competition, al­
though both possibly resulting in extinction do so through different
mechanisms. The effect of predation is to decrease the growth rate
or even make it negative by increasing mortality. Competition on the
other hand, causes a decrease in the per capita carrying capacity or,
in the terms of the model, the NSP population ratio. The former in­
creases the potential resources available to the surviving population:
the latter decreases the potential resources.
This alternative is applicable for determining longevity when
the settlement population is near equilibrium or when there is a dis­
equilibrium caused by population surplus with decreasing NSP. The
reader might argue that it is not appropriate for the MacArthur formu­
lation to be applied to the population-surplus disequilibrium. How­
ever, after the population surplus disequilibrium has begun to be
corrected by an increase in the death rate, or, preferably, by emigra­
tion, the situation has returned to an equilibrium. Thus, unlike the
growth disequilibrium the decline disequilibrium may be examined as a
set of diminishing equilibria in which the population is forced to
diminish only when necessary. In the growth disequilibrium the popu­
lation may grow for a period and not reach equilibrium, but in the
67
decline disequilibrium the population is continually forced to decrease
until the new equilibrium is attained due to the lack of resources.
The second alternative for determining longevity is based upon
a random relationship. The random relationship is calibrated to the
actual data. For example, in the Hay Hollow Valley between A.D. 300
and A.D. lU50, there is a l/lO probability that in any 100 years a
site would become extinct. It is not difficult to adjust a pseudo
random number generator to simulate this l/lO probability on the aver­
age. This is not to argue that longevity is random, but rather it
gives a base line to see how great is the deviation from random.
Climate
The rationale for isolating climactic factors is twofold.
First, it has been the most widely studied of the ecologically limiting
factors (Broughey 1968). Second, there exist considerable detailed
data over long temporal spans for the Southwest developed by palynologists such as Hevly (1970) and Martin (1963) and dendroclimatologists such as Fritts (1965). The climate is the summation of a large
number of factors including temperature, moisture, radiation, light,
air currents, and air pressure. However, a close interaction exists
between temperature and moisture which in a large measure determine
the faunal and botanical distributions. For example, using Holdridges1
19U7 system of classification of world plant formation and life zones
(MacArthur and Connell 1966) as a predictive device for the determina­
tion of major ecozones upon the Hay Hollow study area, one is able to
make a set of predictions on the basis of knowing only the altitude
and mean precipitation. The predictions that the study area is in a
warm temperate latitudinal region, in a lower, upper altitudinal zone,
in a semi-arid humidity province, and that it has thorn-scrub vegeta­
tion hold up when compared to the actual data. The Holdridge system
predicts a mean annual biotemperature of S>5°; the actual value is 51°
based on a 37 year sample.
Climatic factors will be calculated in the resource portion of
the model as a factor in resource growth. In other words, it will
push the resource curves and the NSP curves up or down depending upon
whether the climactic conditions are favorable or unfavorable to
biological growth.
Systemic Model:
Version U
Figure lit is a flow chart of the complete systemic model in­
corporating all the factors discussed in the previous sections. It
is the same as the simulation model and was prepared as part of the
simulation program for the testing of the model and is written in
F0RTRAN IV for use with an F0RTRAN EXTENDED compiler. The model
attempts to simulate carrying capacity as a dynamic equilibrium system.
It originates with a small population in a single settlement. As time
passes and ecological conditions change the population grows and a
budding process results in new settlements. The growth process con­
tinues until the settlements reach a maximum population. As resources
diminish, the populations diminish and the settlements aggregate.
69
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97
Finally, they become extinct. The simulation is based upon four com­
ponents: a population growth function, a population resource (NSP)
check, a settlement locator, and a longevity function. The population
growth function determines, at different birth, death and migration
rates, how much the population grows through a given time span. The
population resource (NSP) check defines the amount of resources which
exist, the NSP, and how much of the NSP may be used at a particular
level of technology following Schumpeter (1911), and checks the popu­
lation size against these limiting values. The settlement locator
determines which zone and where in each zone new settlements will
exist. Finally, the longevity function determines how long each set­
tlement will exist for non-resource reasons discussed above. Thus, a
population in a particular settlement may become extinct for two
reasons: (1) for resource reasons which will be calculated in the
population resource check, and (2) for non-resource reasons which will
be calculated in the longevity function.
At the most simplistic level the four components fit together
in the following way. The population growth component operates until
the population resource check component shows that the population is
too large for a single settlement as defined by the settlement thresh­
old. It then checks to see whether or not this population is too large
for the zone. If it is not, the settlement locator locates a new
settlement in the same zone as the original settlement and populates
it with the excess population. If the total population is too large
for the zone, the population resource check component calculates the
best zone for the excess population and the settlement locator locates
the site within that zone. Finally, the longevity function is called
into play. If it causes a population to become extinct at a particu­
lar time, it resets the population growth function, the population
check, and the settlement locator so that the settlement no longer
exists. When resources in terms of usable NSP diminish, the four com­
ponents act in reverse to minimize the loss.
Actually, the systemic simulation model is more complex for
three reasons. First, when there are multiple settlements growing in
multiple zones and being checked against multiple resource levels, the
number of possible variations and optimizations increases extensively,
if not geometrically. Second, the population growth component and the
population resource check component are defined by multiple equations
and are not just single relationships. Third, the settlement locator
and the longevity function components are both testing three alterna­
tive methods of determining the settlement location and two alterna­
tive methods of determining settlement longevity.
The Definition of the Equations
and Constants of the Model
The Definition of Equations for Resource
and Population Curves
Population. Following Rogers (1968), one may define four
elements of interregional population growth and distribution. These
are the initial population births, deaths, and net migration.
99
Symbolically, it is expressed w fa
+
1) = w fa) + b fa) - d fa) + n fa)
where w fa) is the population at time t, the initial population, b fa)
is the number of births between t and t + 1, d fa) is the number of
deaths between t and t + 1, and n (t) is the number of net migrants
between t and t + 1. The growth, then, is w
+
1) - w (t). Or if
one wants to determine the "growth multiplier," it is easily calculated.
Since the above equation may be rewritten w (t
+
l) = w (t) (l + B -
D + N) where B is the birth rate, D the death rate, and N the net
migration rate. The "growth multiplier" GM, is GM = (1 + B - D + N).
Often B and D are combined to give a net non-migratory growth rate,
R, R = B - D. These are the factors that are combined to allow the
quantification of the population curves of the graphical model or the
calculation of growth in the systemic model.
The above are the "crude rates." It is possible, if the age
structure and sex ratio of the population are known to determine more
accurate rates using the age cohort method (Cox 1970), However, since
the latter are based upon data which is not readily available in the
archaeological or ethnohistoric record, one may rely upon the "cruder"
formulations.
Underdeveloped societies range from R = .002 prior to the
agricultural revolution to R « .020 - .029 for modern underdeveloped
societies if calculated by averaging societal R's. Birth rates range
from .038 - .OUU while death rates range from .010 - .022. The model
originates with R • 2.5 and runs to R • l.£ per century, or approxi­
mately .0l|0 to .020 per year.
100
In order to calculate migration, two types need to be differ­
entiated. First, there is "naturally expected" migration which is a
concomitant solely of the existence of other communities and which is
in operation at all times. Second, there is migration which takes
place as the result of a population surplus disequilibrium. This
latter type operates uiscontinuously. Different assumptions and
equations are used to determine the different types of migration.
"Naturally expected" migration is based upon the following
assumptions which I believe are reasonable: (l) Goodrich (1936) has
shown that areas of low standard of living and employment tend to be
areas of net out-iaigrabion, while areas of high standard of living and
employment tend to be areas of net in-migration. It is assumed that
the general standard of living and employment rate of all the settle­
ments, based upon social, occupational, technological, and ecological
similarities, are broadly equal. (2) If two areas are in different
economic regions, Folger (1953) has shown that the relationship between
distance migrated and the number of migrants may be different from the
relationship within an economically integrated area. (3) The rate of
migration has been shown by Bogue and Hagood (1953) to vary with the
type of community or origin and destination, the direction of migration,
and the age and other characteristics of the migrant. Also, it is
clear that a high proportion of all migration streams is a flow between
communities of the same type, such as urban to urban, farm to farm
(Bogue, Shryock, and Hoermann 1957)• The settlements in the study
area are assumed to be of the same order in terms of type of
communities. (U) The size, direction, and net effects of migration
streams are not invariable in time or place but are reasonably sensi­
tive to social and economic changes occurring in the various communi­
ties of origin and destination (Bogue, Shryock, and Hoermann 19^7).
Yet, the regional pattern of net migration tends to remain constant
for
atr
least several decades reflecting the continued action of a set
of redistributive forces (Shryock and Eldridge 19h7). On the basis of
these tested hypotheses, one may assume that major trends in migration
pattern last for at least two or three decades.
Zipf (19U9) has shown that the "naturally expected" amount of
migration between any two settlements is directly proportional to the
product of the population of the two settlements and inversely pro­
portional to the distance between them, that iss Z = k (Pi) (P2)/d
where Z is the proportionality factor related to migration, PI and P2
are the population of the settlements, d is the distance between them,
and k is a constant.
Veiy sophisticated "gravity models" have been developed upon
Zipf's basic ideas and have been discussed by Isard and Bramhall (I960).
Critical, however, to all of them is the constant k which must be
determined inductively if one wishes to use the gravity model as a
predictive device.
In a recent study (Bogue, Shryock, and Hoermann 19?7), the
concept of the rate of flow or velocity of the migration stream was
defined. This is an abstract measure that takes neither the place of
origin nor destination as a starting point for the same results are
102
obtained whether one uses in-migration or out-migration rates. It is
defined as V
8
M/PO X 100 or V = M/PD X 100 where:
Wpt
po7pt
V = the rate of flow of the migration stream,
M = the number of migrants in the stream,
PO « the population in the area of origin,
PD *= the population in the area of destination
PT = the total population of all potential areas of destination
including the area of origin.
Unfortunately, streams of migration have not been calculated for ethno­
graphic populations. Thus, I am forced to fall back on modern data to
get the range of V. Analyzing urban, rural and rural non-farm streams
of migration from 1935-UO in U.S. populations, Bogue, Shryock, and
Hoermann found stream velocities ranging from U.U to 30.7 for the five
year period. Net migration velocities range from .lj-2.7. Given the
velocity, it is possible to use these equations to determine the num­
ber of migrants accurately. The model will run velocity rates from
1-2.
The second type of migration takes place when there is a
population surplus disequilibrium. The migration size is equal to the
surplus value if there is a location within a zone capable of carrying
the new population as discussed previously. The equations defining
this second type of migration are in simplified form as follows:
(a) if PT (J)< NSP (J) and if P (I, J)> ST, and if NSP (J) - PT
(J)> P (I, J) - ST, then M - P (I, J) - ST: but if NSP (J)
- PT (J) < P (I, J) - ST then M = NSP (J) - FT (J) and P (I, J)
- ST - M
8
F and F is checked as X in (b).
103
(b) if PT (J)> NSP (J) and X = PT (J) - NSP (J) and there exists
a different value of J where PT (J) - NSP (J)> X, then M =
PT (J) - NSP (J) where J has its original value. In the above:
F, X = dummy variables,
J
B
the zone,
PT (J) = the total population of the zone,
NSP (J) = the net societal product of the zone,
P (I, J) = the population of the Ith settlement of zone J.
Resources. The equation defining resources is inductively
derived and is thus very simple. Res (J) at Time 2 = Res (J) (1.0 +
RG) at time 1 where RG is the resource growth. The values of Res (J)
will be discussed briefly in this chapter and at length in Chapter li.
Settlement Location
The settlement location equations must be examined in two
parts: first, there are the zonal location equations; second, there
are intra-zonal settlement location equations. The zonal location
equations are simply a series of checks between total zone populations
PT (J) and net societal product NSP (J). If there are sufficient re­
sources in the zone in which the population disequilibrium takes place
for a new settlement, the new settlement is located within that zone.
If not, one calculates the zone which is best capable of supporting
the new population. This is accomplished by the following set of
equations•
lOli
POS (1) = PT (1)/INSP (1)
POS (2) = PT (2)/lNSP (2)
POS (3) = PT (3)/lNSP (3)
POS (U) = PT (U)/INSP (U)
POS (5) - PT (£)/lNSP (£)
POS (6) « PT (6)/lNST (6)
2 - AMINI (POS 1, POS 2, POS 3, POS U, POS 5, POS 6)
If
Z « POS
Z - POS
55 = POS
g = POS
2 = POS
2 - POS
1
2
3
U
$
6
then
BEST
BEST
BEST
BEST
BEST
BEST
=1
=2
= 3
= h
= £
-6
J « BEST
The variables are defined as above with POS 1-6, Z, and BEST as dummy
variables. AMINI is a function which chooses the smallest of the
variables within the parentheses.
Within the zone there are three alternative ways of calculating
where the settlement is located as noted previously. First, there is
simply random location. This is accomplished by setting the coordi­
nates of the site (X, Y) equal to two random numbers generated by a
pseudo-random number generator. The F0RTRA.N equations are x = 10*
RANF(O.O) and Y » 10*RANF(0.0). These X and Y values are then checked
in a look-up table to determine whether or hot they are actually in
the appropriate zone. If not, new coordinates are generated.
Second, there is location which is based upon the optimization
of the relationship of the new settlement's population with the other
populations in the zone. This is defined as the population weighted
"Bachi mean center of the distribution." Anthropomorphizing the concept,
uo$
the question is what location would allow the population of the new
settlement to be in contact with the greatest amount of population in
other existing settlements within the zone by traveling the least
distance. This is calculated by the following two equations,
n
XX =
P(I,J)XX(I,J)
PT(J)
n
YY = ^=1
P(I,J)YY(I,J)
PTTJT
where XX and YY are the coordinates of the new settlement, XX (I, J)
and YY (I, J) are the X and Y coordinates of each pre-existing settle­
ment I within zone J, P (I, J) is the population of the Ith settlement
in zone J, PT (J) is the total population of the zone J, and n is the
number of settlements in each zone. If the Bachi mean location does
not correspond to the appropriate zone (as determined by the look-up
table) for which it was calculated, one arbitrarily uses the randomly
determined coordinates.
Third, there is new settlement location which is based upon
the allocation of non-utilized resources. Each settlement which exists
in the time span immediately prior to the new settlement is using a
particular amount of resources which can be calculated in terms of
area. Thus, in order to optimize settlement location with regards to
non-utilized resources, one may calculate the areas which are necessary
to support the other villages. After centering these areas around the
villages, one randomly chooses a new location not in the areas. The
same look-up table constraints apply to these coordinates as in the
first alternative. The equations which determine this alternative
location are:
106
XXX - RANF (0.0)
YYY • RANF (0.0)
AREA. = ((2500 . P (I, J))/(U.C0N.APR0D(J)))
R = ^AREA/ 6.283153)/292.6
R
^XXX(I, J)-XXX)^ + (YYY(I, J)-YYY)2
where:
XXX and YYY are the coordinates of the new village
Area = the area needed to support the population of a village
R = the radius of the Area
P (I, J) is the population of the Ith settlement in zone J
APROD (J) is the productivity of the zone J
CON = the consumption constant
XXX (I, J), YYY (I, J) are the locations of the previous settle­
ments.
Longevity
Two
alternative sets of equations determine non-resource
settlement longevity. Similar to settlement location, the longevity
function may be expressed stochastically by a random variable.
IAA = 10.RANF(0.)
If (IAA = 6) then, P (I, J) - 0.
Since the pseudo random number generator delivers a number
between 0 and 1 with an approximately even distribution of digits,
one may expect at any given time l/lO of the settlements are becoming
extinct, on the average, but which settlement and when is uniquely
controlled by the random number generator.
107
The second alternative is based upon MacArthur's finite proba­
bility for every population at carrying capacity reaching extinction.
The function is:
TK - (D/(2.P (I, J)»R2). e
2 p
J)*log B/^
where:
TK = the time to extinction
R = the growth rate
B «= the birth rate
D *= the death rate
P (I, J) » the population of the Ith settlement in zone J
The limiting parameters on TK have a critical effect on its size. For
example, if B = 1,1, D = 1.0, P (I, J) = 10, then TK = 13, but with
the same B and D, if P (I, J) = 100, TK
a
10,000. The function TK
when graphed will generally follow the shape of Figure 15. The take­
off point is usually between P (I, J) = 100-200 which is small enough
to be common in Southwestern archaeological and ethnohistoric settle­
ments.
The third alternative is the simple settlement decline func­
tion based upon on exogeneous causes. If one postulates an external
factor to the system, e.g., disease or war, which diminishes the
population by an absolute amount, Q, longevity is a function of size
and is expressed by P (I, J) at time 2 = P (I, J) - Q at time 1.
Consumption Equations and
Technological Innovation
Net Societal Product was defined as the summation of con­
sumption, investment, and organizational expenditure. This is
108
Take
Off
TK
P(I.J)
200
Figure 15. MaoArthur's tk: a longevity alternative.
109
operationalized in the model by defining three variables: CON, INV,
ORG. These are expressed as percentages and thus NSP « RES (J)
(CON + INV + ORG).
There are only three major technological changes which have a
significant Schumpeter cluster of innovations with them in the study
area: (1) the development of agriculture which results in a resource
surplus disequilibrium, (2) the development of irrigation which is
also a resource surplus disequilibrium cause, (3) and the development
of pueblo style architecture which results in, or is a factor in, a
population surplus disequilibrium. The first two innovation clusters
are self-obvious, but perhaps the last innovation cluster needs some
further explication. Labor is a finite commodity related to popula­
tion. Pueblo architecture takes a larger investment of labor than pit
house architecture. This assumption is based upon the generally larger
size of the pueblo as a habitation-storage room combination, to the
pit house room. Secondly, since the population is considerably larger
during the periods of time when the population was housed in pueblos,
than during the periods of pit house occupation, the amount of aggre­
gate labor involved in architectural construction was probably larger.
The allocation of labor is dependent upon societal priorities. If
large quantities of labor are allocated to the production of archi­
tecture, less labor is available for subsistence activities. Thus,
the innovations of pueblo architecture may be examined as a negative
factor draining upon subsistence resources.
110
These Schumpeterian innovation clusters could be operationalized by a series of date specific equations. At A.D. 700, the model
would bring in agricultural innovations by increasing resources. This
is accomplished by multiplying RES (J) by a variable AG which is based
on a combination of world survey agricultural figures (Odum 1953),
Pueblo figures (Woodbury 1961), and ethnographic Hopi data (Stephen
1936). The equation would be RES (j) at time 2 = RES (J)(1 + AG) at
time 1.
At A.D. 900 Pueblo architecture would be brought into the model
with RES (J) at time 2 = RES (J)(1 + ARCH) where ARCH has a negative
value. Similarly, irrigation would be brought in at A.D. 1000 with
RES (J) at time 2
B
RES (J)(1 + IRR).
Constants
Finally, the picture must be completed by briefly stating what
some of the major constants are. A further discussion of constants
occurs in Chapter U. In that chapter, which is devoted to data not
only will minor constants also be discussed, but the methods by which
they are derived will become apparent. The first population settlement
to be considered in the Hay Hollow valley study area is NS 22£ which
is located on the mesa top (zone l) at coordinates 18,18 and has an
initial population of 50. The initial resource areas for the zones
are:
zone 1 - 282$h5h m.2
zone 2 «= U9659U9 m.2
zone 3 " 9U1810
Ill
zone U = 22261157 m.2
zone 5 " 1798016 m.2
zone 7
=
20720000 m.2
These zones have a standing crop of the following amounts according to
a 1970 field study which was undertaken by Zubrow and Hevly.
zone 1 = 70.7S>00± 10.2971g/m.2
zone 2 = 36.9900+ 2.6608 g/m.2
zone 3
e
26.6060± 11.8317g/m.2
zone h = 2U.2020i 9.9155 g/m.2
zone 5 - h2.h6$Ot 12.6035g/m.2
zone 7 = 62.3l*60± 7.8297 g/m.2
The same analysis which is discussed in Chapter h has shown the pro­
ductivity of the zones as beings
zone 1 = 10.0800± 2.1513 g/m2/month
zone 2 = 12.UOOOi 2.77U6 g/m2/month
zone 3
=
lli.6600i 2.3986 g/m2/month
zone U
0
7.18001 U.22U7 g/m2/month
zone 5
B
2.11*001 O.86I4O g/m2/month
zone 7 = 22.7001 13.73UO g/m2/month
This chapter has considered the addition of temporal, spatial
and cultural variables to the simplified model of carrying capacity as
a dynamic equilibrium system. It has also discussed the model's quan­
tification in general terms. In the next chapter I will consider the
hypotheses which are derived from the expanded model and its assump­
tions.
CHAPTER 3
HYPOTHESES
As noted in Chapter 1, models provide a chance to test several
hypotheses simultaneously. Scientific procedure suggests that one
deduces a series of hypotheses from the assumption base of the model.
Deduction, however, is a complex subject. As Nagel (1961)
points out, a deduction has a formal structure in which the explicandum
is a logically necessary consequence of the explanatory premises. A
question which often arises is the priority of the premises, hypoth­
eses, and deductions or observations. As pointed out previously, the
question is not critical as long as the structure holds together ex
post facto, that is, none of the canons of logic or observation were
violated in the formal analysis. A second question which add to the
complexity is whether a term may appear in the conclusion of a formal
demonstration unless it also appears in the premises. For this study,
I will take the wider interpretation of allowing new terms into the
conclusion.
There are two types of logical manipulation which will be used
in this chapter. One I will call syllogistic; the other algebraic.
The syllogistic form of deduction states that if a, then b, if b, then
c, therefore, if a, then c. The algebraic form is the manipulation of
a statement until it equals an identity or a truism. A is equal to B.
112
113
B is equal to G. C is equal to A. Therefore, since a equals a, the
system's logical consistency has been shown by identity.
Before examining the hypotheses and the deductions from which
they are derived, one should note what are the more important consider­
ations or criteria for the model's success. These are: (l) does the
model successfully simulate reality? (2) is it useful heuristically
for understanding the dynamic relationships between man, culture and
environment? (3) is it productive of new hypotheses? and (U) is it
useful in showing the limitations of the data or theory upon which it
is constructed.
In Chapter 2, there was a consideration and graphical operationalization of the hypothesis that the development of population in
marginal resource zones is a function of optimal zone population
exploitation. This hypothesis may be deduced, formally syllogistically,
from the assumptions of the model and additional propositions.
The following is the formal deduction with a verbal approxi­
mation next to each statement.
A. Pj < NSPj £ Rj
1. NSPj » K(Rj)
Assumption
The population of a re­
source zone is less than
or equal to the net
societal product, i.e.,
what a culture may pro­
duce in a resource zone
for subsistence, and this
is less than or equal to
the potential resources
of that zone.
Proposition
The net societal product
of a zone is a direct
function of the resources
of a zone.
na
Pj » K(NSPj)
Proposition
The population of a zone
is a direct function of
the Net Societal Product
of the zone.
PJ - K(Rj)
Conclusion
Therefore, the population
of a zone is a direct
function of the resources
of a zone.
a. Ra, Rb, Rc, C RJ Definition
Resource zones, a, b, c,
are members of the set of
resource zones.
b. NSPa, NSPb,
NSPc, C NSPj
Definition
Net societal products a,
b, c, are members of the
set of net societal pro­
ducts.
c. Pa, Pb, Pc,
C Pj
Definition
Populations a,
are
members of the sets of
populations.
Ra < Rb < Rc
Proposition
The resources of zone a
are less than the resources
of zone b which are less
than the resources of zone
c• Zones a and b will be
called marginal to optimal
c.
Pa < Pb < Pc
Conclusion
Therefore, the population
of zone a is less than the
population of zone b which
is less than the popula­
tion of zone c.
Gj = Pj/Tj
Proposition
The average population
growth rate of a zone is
equal to the population of
the zone divided by the
time it took to grow to
the present size.
Proposition
The time for potential
population growth in zones
at b, c, is equal.
Ta
e
Tb «= Tc
115
Conclusion
Therefore, the average
population growth rate of
zone a is less than that
of zone b which is less
than that of zone c.
Assumption
The summation of the
populations of the zones
is equal to the total
population.
Conclusion
Therefore, the population
total is equal to the sum
of the population of
zones a, b, and c.
•*•10. Pt = T(Ga + Gb + Gc) Conclusion
Therefore, the population
total is equal to the
time for population de­
velopment times the growth
rates of zones a, b, and
c summed.
•*•11. Gb + Ga = Gc - Pt/T
Therefore, the develop­
ment of the population in
the marginal 2ones, a and
b, over time is a function
of the development of the
population in the optimal
zone, c, over time and is
a function of the total
population.
.*.8. Ga <Gb < Gc
B. Pt «=
.* »9. Pt = Pa + Fb + Pc
Conclusion
Two advantages of formal deduction are apparent from the above
example. First, the number of assumptions and propositions which are
necessary to support a hypothesis is surprising. Second, the incom­
pleteness of the hypothesis may become apparent. The original nondeduced hypothesis was incomplete insofar as it did not take into
account that the development of marginal zone populations was not only
a function of the optimal zone's population development, but of the
total population.
116
The second hypothesis to be deduced is that during periods of
resource depletion, there will be a population aggregation of settle­
ments•
A. Pt
NSP t ^C*Rt
Assumption
The population at a par­
ticular time is less than
or equal to the Net Soci­
etal Product at that time,
which is less than or
equal to the potential
resources of that time.
1. NSPt - K(Rt)
Proposition
The Net Societal Product
of a particular time is a
direct function of the
resources of that time.
2. Pt = K (NSPt)
Proposition
The population at a par­
ticular time is a direct
function of the Net Soci­
etal Product of that time.
Conclusion
Therefore, the population
at a particular time is a
direct function of the
resources of that time
a. R2, R1 C Rt
Definition
Resources at time 2 and
time 1 are members of the
set of resources.
b. NSP 2, NSP 1 C
NSP t
Definition
Net Societal Products at
time 2 and time 1 are
members of the set of net
societal products.
c. P2 PI C Pt
Definition
Populations at time 2 and
time 1 are members of the
set of populations
Proposition
Resources at time 1, the
earlier period, are
greater than resources at
time 2, the later period.
In other words, a resource
depletion is taking place.
.3. Pt = K(Rt)
U. Rl> R2
117
Conclusion
Therefore, the population
at time 1 is greater than
the population at time 2.
nt (spt)
Definition
The population at a par­
ticular time is equal to
the number of settlements
at that particular time
multiplied by the average
settlement size at that
particular time.
•"•e. PI = nl (spl)
Conclusion
Therefore, the population
at time 1 equal the num­
ber of settlements at
time 1 multiplied by the
average settlement size
at time 1.
•*.f. P2 = n2 (sp2)
Conclusion
Therefore, the population
at time 2 equals the num­
ber of settlements at
time 2 multiplied by the
average settlement size
at time 2.
Proposition
The rate of population
change is greater than
the rate of settlement
change.
.*.5. Pl> P2
d. Pt
55
6. ra > rb
g. P2
a
ra(Pl)
Definition
The population at time 2,
is equal to the rate of
population change times
the population at time 1.
h. n2
B
rb(nl)
Definition
The number of settlements
at time 2 equals the rate
of settlement change
times the number of
settlements at time 1.
Conclusion
Therefore, the ratio of
the population of time 2
to the population at time
1 is greater than the
ratio of the number of
settlements at time 2 to
the number of settlements
at time 1.
•*•7. P2/P1 > n2/nl
118
,*.8. (n2 Sp2)/(nl Spl)
> n2/nl
*.9. Sp2/Spl> 1
'.10. Sp2>SPl
Conclusion
Therefore, the ratio of
the number of settlements
times the average settle­
ment size at time 2 to the
number of settlements
times the average settle­
ment size at time 1 is
greater than the ratio of
the number of settlements
at time 2 to the number of
settlements at time 1.
Conclusion
Therefore, the ratio of
the number of average set­
tlement size at time 2 to
the average settlement
size at time 1 is greater
than 2.
Conclusion
Therefore, the settlement
size at time 2 is greater
than the average settle­
ment size at time 1.
It may not be clear to the reader that I have deduced the
hypothesis that during periods of resource depletion, there will be a
population aggregation of settlements. The above deduction shows that
if resources at time 1, the earlier period, are greater than resources
at time 2, the later period, then the average settlement size at time
2 is greater than the average settlement size at time 1. In other
words, as resources decrease, average settlement sizes increase showing
the population aggregation of settlements. This is a combination of
number U and number 10 of the deduction.
The hypothesis must be qualified, however, by number six in
the deduction. The hypothesis holds if the rate of population change
is greater than the rate of settlement change. This proposition is
119
not, I believe, unreasonable. For to suggest the opposite would mean
that a relatively small amount of population would be settling a rela­
tively large number of settlements under resource depletion. This
would not appear to be a particularly efficient strategy when one con­
siders the problems of labor allocation, resource allocation, and
possible inter-village resource competition. A discussion of the more
generalized hypothesis that population aggregation is inversely related
to resources where the population ra > rb is relaxed is found in Chap­
ter 5.
The third hypothesis to be deduced is that during period of
resource depletion, there is spatial aggregation of settlements. The
deduction is similar to the deduction of the population aggregation
hypothesis. Using the same general assumption and definition base, one
may add the following statements to the previous deduction.
11. ra > rc
a. A2 = rc(Al)
Proposition The rate of population
change is greater than the
rate of resource area
change.
Definition
The resource area at time
2 is equal to the rate of
resource area change times
the resource area at time 1.
,*.12. P2/P1 > A2/A1
Conclusion
Therefore, the ratio of
the population at time 2 to
the population at time 1 is
greater than the ratio of
the resource area at time
2 to resource area at time
1.
.".13. P2/A2 ^ Pl/Al
Conclusion
Therefore, the ratio of
the population to the re­
source area at time 2,
120
i.e., the population den­
sity of the resource area
at time 2, is greater than
the ratio of the popula­
tion to the resource area
at time 1, i.e., the popu­
lation density of the re­
source area at time 1.
If the population, resources, and resource area is decreasing
while the population density and average settlement size is increasing
then the settlements must be spatially aggregating. This effect may
be accurately measured by using one of several nearest neighbor sta­
tistics. For example, there is Getis's nearest neighbor statistic
c = (f0 - re)/(P*re where re = l/(2)» 2), r0 is the measured mean
nearest neighbor distance,(T-Tq is the standard error, and 7* is the
density of a Poisson probability function. Nearest neighbor is more
accurate than simple density since it allows one to distinguish aggre­
gation even when density is decreasing. Finally, it should be noted
that this hypothesis is qualified by two propositions, ra> rb and
ra > rc.
The fourth hypothesis to be deduced is that during periods of
resource depletion, the residential area of sites decreases. The
deduction follows in which one operates independently on both sides of
the implication.
1. R1 > R2 —> RA1 > R2
Hypothesis
If there is a resource
depletion between time 1,
the earlier period, and
time 2, the later period,
then there will be a de­
crease in the residential
area of the sites.
121
2. NSPt - K(Rt) RAt =
k(LLt)
3. Pt - K(NSPt) LLt
k(Pt
h. PI > P2 —* PI > P2
Proposition
The Net Societal Product
at a particular time is a
direct function of the
resources at that time.
The residential area at a
particular time is a Amo­
tion of the labor force
at that time since this
limits residential con­
struction.
Proposition
The population at a par­
ticular time is a direct
function of the net so­
cietal product at that
time. The labor force at
a particular time is a
direct function of the
population size at a par­
ticular time.
Conclusion
Therefore, if population
at time 1 is greater than
population at time 2,
then population at time 1
is greater than at time 2
and the identity is
proved.
Man's conception of the time-space continuum which contains
elements common to the four deductions has been changed by the theory
of relativity. In an often quoted statement, Minkowski describes the
results of this change. "From henceforth space in itself and time in
itself sink to mere shadows, and only a kind of union of the two pre­
serves an independent existence."
The classic Gassendi-Newtonian concept of space was that it had
a positive objective existence without regard to the human mind.
Newton thus stated, that absolute space without regard to anything
122
external was always similar and immutable. The relationship of space
and time was that every point in space persists throughout an infinite
succession of instants of time.
Michelson and Morley's concept (Einstein 1921) of ether
allowed a meaning to be attached to the concept of absolute position in
space and when their famous experiment failed, a major hole was torn
into the assumption base of classical physics and the time-space re­
lationship which was not filled until the theory of relativity was
proposed.
Einstein recognized that every event or phenomena which occurs
could be determined by the space coordinates x, y, z, and a time co­
ordinate, t. Einstein saw that the classic view of three dimensional
space and one dimensional time was an illusion which resulted from
"simultaneity" rather than a real conflict with the four dimensional
time-space continuum. This illusion arose from the fact that one
receives news of near events almost simultaneously due to the speed of
light (Einstein 1921).
The importance of this four-dimensional construct for any
study dealing with time and space, including archaeology, will become
evident. The history of any event will be represented in the spacetime continuum as a continuous line which is called the world line.
The same world line will determine for all observers the history of the
event equally well. But each observer being in a different position or
time will map that world line with slight or even large differences on
the axes. Thus, the influence of the observer's motion, or different
123
position in the space-time continuum, is shown through their choosing
different axes of space and time. Thus, the continuum is both real and
subjective -- subjective insofar as the observer chooses the axes. The
Lorentz transformation equations express mathematically the relation­
ship between the different choices of time and space (Einstein 1921).
This relationship of time and space has been used by astrono­
mers in estimating the age of the universe. The Doopler shift (Gill
196$) showing distances of ten billion light years also indicates that
the universe is ten billion years old. Wissler and many other cultural
anthropologists and archaeologists have made rough use of this concept
in the age area hypothesis.
In the formally deduced hypotheses, the spatial axes in the
definition of variables was given by letter subscripts. The temporal
axes were given by numeric subscripts. Allowing the observer to move
one may ask the question, what happens if one replaces the numeric
subscripts with alphabetic subscripts and vice versa? In other words,
what happens if one looks at the hypotheses from the viewpoint of a
different observer who is mapping one of the spatial axes into a tem­
poral axis and vice versa?
The hypotheses were:
1. Ra < Rb < Rc —> Gb + Ga = Gc - Pt/T
2. R1 > R2 —> Sp2 > Spl
3. Rl> R2 —> P2/A2 > Pl/Al
U. R1 > R2 —> RA.1> RA2
12U
The transformed statements of the hypotheses with their verbal
equivalents are:
1. R3 < R2 < R1 —*G2 + G3 - G1 - Pt/A
If the resources at time 3 are less than the resources at
time 2 which are less than the resources at time 1, then
the spatial development of the population in times 3 and
2 are a function of the spatial development of the popu­
lation at time 1 and the total population.
2. Ra > Rb —*Spb > Spa
If the resources of zone a are greater than the resources
of zone b, then the population aggregate of b is greater
than that of a, when the cross zonal rate of population
change is greater than the cross zonal rate of settlement
change•
3. Ra > Rb—> Pa/Aa> Pb/Ab
If the resources of zone a are greater than those of zone
b, then the spatial aggregation of settlements in zone b
is greater than in zone a when the cross zonal rate of
population change is greater than the cross zonal rate of
resource change.
U. Ra > Kb —* RAa > RAb
If the resources of zone a are greater than those of zone
b, then the residential area of sites in zone a are greater
than the residential area of sites in zone b.
The formal deductions for both sets of hypotheses are the same.
Only the subscripts and spatial and temporal variables need to be
transformed. In other words, what has been suggested is that if a
hypothesis holds temporally, it should hold spatially and vice versa.
If nothing else, it is a productive way to develop new hypotheses.
12*
Summary
In summary, this chapter has formally deduced four hypotheses
from the model. They may be informally stated and combined into the
following two statements.
1. The development of population in marginal resource zones is a
function of optimal zone exploitation.
2. During periods of resource depletion, the population is living
in more clustered settlements, in larger communities in terms of
average number of rooms per site, and in smaller residential areas in
terms of the average room size.
Finally, the implications of the relationships between space
and time were examined in terms of the four hypotheses.
CHAPTER U
DATA
Introduction
The Hay Hollow Valley (Figure 16) is located on the NavajoApache county line approximately 12 miles east of Snowflake, Arizona.
Its latitude and longitude are 3U°3h', 109°!?5' respectively. Most of
the valley is owned by the James Carter family and has been used as a
cattle ranch.
The valley, as well as the Little Colorado River drainage, has
been the location of intensive archaeological work for the last 15
years. This work has been directed by Paul S. Martin and his students
and has resulted in a considerable amount of information about the pre­
history and paleo-anthropology of the area being obtained. Several
volumes of the Fieldiana Anthropology series, six dissertations, and
several articles in professional journals have reported much of the
information on this Anasazi-Mogollon transitional area. It would be
futile to attempt to recapitulate all of the data here. An outline
chart of the major prehistoric occurrences as understood in 1970 fol­
lows. It is primarily based upon William A. Longacre's "A Synthesis
of Upper Little Colorado Prehistory, Eastern Arizona" (1961*), and John
Johnson's "Settlement Systems and Cultural Adaptation in the Hay Hollow
Valley, A.D. 950-1100"(1970) although other materials are also used.
The outline is a general updating of Longacre's synthesis.
126
Figure 16. Aerial photograph of part of the Hay Hollow valley.
128
Brief Outline of Hay Hollow Prehistory
Phase 1
Name: Concho Complex (Martin and others 196U)
Date: 1000 B.C.-A.D. 200 (Johnson 1970)
Food Procurement. Centers around the collection of wild game
and plants with occasional horticulture (Martin and Fritz 1966).
Settlement Type and Pattern. Small, nonpermanent camps without
evidence of architecture (Martin and others 196U). Camps contain fire
and storage pits (Martin and Fritz 1966).
Social Organization. Inferred localized, unilateral, exogamous
groups with a single house representing the domicile of a nuclear
family (Martin and Fritz 1966).
Phase 2 and 3
Name: Incipient Agriculturalists and Initial Sedentary Agricul­
turalists (Martin and others 19610.
Dates
A.D. 200-7^0
Food Procurement. Increasing dependence on agriculture through­
out period but hunting and gathering still predominant subsistence
factors (based on quantified tool kits), (Burkenroad 1968). However,
there may be a decline in agricultural dependence after A.D. £00 based
on tool variation (Leone 1968).
Settlement T:/pes and Patterns. Small pit house villages, (1-5)
houses with associated storage pits. After A.D. £00, villages usually
located with arable land (Martin and others 196U). Beginning with
A.D. k$0f there is a trend toward greater site dispersion of habitation
129
sites approaching hexagonality near the end of the period (Gregory
1969). Up to A.D. 600, village size remained quite homogeneous (Plog
1969).
Social Organization, Similar to Phase 1 but after A.D. 500,
there is a decrease in social distance and autonomy (Leone 1968).
Also, there is little intersite complexity up to A.D. 600 (Plog 1969).
Pottery. First appearance of pottery about A.D. £00 with Alma
Plain, incised, and neckbanded, and San Francisco Red being the major
types.
Population Trends. Increasing to A.D. 500 but starts to de­
cline about A.D. 600 (Schiffer 1968; Zubrow 1970).
Phase li
Name: Established Village Farming (Martin and others 196U).
Date: A.D. 750-900 (Longacre 196U; Johnson 1970).
Food Procurement. Between A.D. 750 and 800 agriculture becomes
the predominant subsistence factor (Burkenroad 1968). This corresponds
to increasing dependence upon agriculture throughout the period (Leone
1966).
Settlement Types and Patterns. Large pit house communities of
5-15 houses (Martin and others 19610. Until A.D. 850 there was greater
site aggregation which then began to redisperse (Gregory 1969).
Social Organization. Prior to A.D. 850 none of the villages
appear to contain more than two family groups (Plog 1969). The in­
creasing aggregation of villages reflects the development of intersite
social clustering based upon pottery stylistic attributes (Cook 1970).
i30
However, with the redispersion of the settlements, there is also in­
creasing economic and social autonomy (Leone 1968).
Pottery. Black-on-white decorated pottery first appears with
White Mound and Red Mesa types, Alma Plain and Scored, Forestdale
smudged, Lino gray, Lino Black-on-gray, and San Francisco also appear.
Population Trends. Decreases until A.D. 800 and then starts
to increase with the predominance of agriculture (Schiffer 1968;
Zubrow 1970).
Phase 5
Name: Beginnings of Planned Towns (Martin and others 1961;).
Date: A.D. 900-1100.
Food Procurement. Agricultural dependence begins decreasing
until A.D. 10^0 according to Leone (1968) but not documented by Burkenroad (1968). At approximately A.D. 1000 irrigation first appears in
the valley (Plog 1969) which may be responsible for the rise in agri­
cultural dependence after A.D. 10^0 (Leone 1968), By A.D. 975>-1000
population is greater than could be supported by rainfall agriculture
(Saraydan 1970).
Settlement Patterns and Types. Pueblo architecture appears
ranging from small rectangular shapes to plaza oriented towns by the
end of the period with distinct religious structure, i.e., kivas
(usually a cluster of settlements will contain one with a great kiva).
There is general proliferation of sites which are a result of "budding
off" processes (Longacre 1970). These new sites are located in the
131
more marginal ecological zones as a result of exploitation of optimal
zones (Zubrow 1970). The result is an increased density of sites whose
pattern across space when considered as a whole is close to random
(Gregory 1969).
Social Organization. Inter and intra-site complexity increases
with Uk% of sites showing more than one local group represented (Plog
1969). Larger sites have been demonstrated to contain multi-matrilocal
residence units in one village (Longacre 196b). There are multiple
indications of intersite social organization and possible redistribu­
tion centers including the scope of irrigation and the "nuclearly
centered" clustering of sites (Johnson 1970).
Pottery. Snowflake Black-on-white, Showlow Black-on-red,
Wingate Black-on-red and various forms of corrugated pottery.
Population Trends. This is the period of maximum population
growth culminating in A.D. 102? (Schiffer 1968) although probably later
according to Longacre (196U), Plog (l969), and Zubrow (1970). After
the peak is reached, there is a rapid decline.
Phase 6 and 7
Name:
Established Towns — Beginning of Convergence and Large
Towns — Full Convergence.
Date: A.D. 1100-lliS0.
Food Procurement. An externally, i.e., environmental (Hevly
1970) and an internally, i.e., population produced strain in resource
potential resulted in decreasing potential per capita production
132
(Zubrow 1970). This may be partially and temporarily offset by the
savings of scale which are a result of the greater cooperation possible
in aggregated villages (Longacre 1970). There is a shift to greater
dependence on wild plants (Klein 1969). After 1200, the village de­
pendence on agriculture decreases (Leone 1968).
Settlement Patterns and Types. There are large masonry
Pueblos with kivas, Great Kivas or plazas, or both (Longacre 196U).
These settlements which tend to be located on the edge of the optimal
ecological zones result from the aggregation of population as the high
average number of rooms per site attests (Zubrow 1970).
Social Organization. This is the period of maximum intra-site
complexity indicating increased integration within communities but
intersite complexity was decreasing suggesting a breakdown in regional
organization (Plog 1969). This would correspond to the increased num­
ber of uxorilocal residence units demonstrated at Broken K (Hill 1970).
Pottery. Four Mile polychrome, St. Johns polychrome, Snowflake
Black and white, and various brown corrugated and textured wares.
Population Trends. Population declines with final abandonment
coming between A.D. 1350-11*00 (Schiffer 19685 Zubrow 1970).
Survey Data
Critical to any prehistoric demographic studies is the broad
areal understanding of archaeological resources which is the result of
surveys. The Hay Hollow Valley and the Little Colorado drainage have
been the scene of multiple surveys of variable intensity. These
133
include surveys by John Rinaldo of the Vernon area, by William Longacre
of the "triangular area" bounded by U.S. 60, 260, and 666, by Mark
Leone of the "central" Hay Hollow valley, by Fred Plog and Chris White
of the peripheral Hay Hollow valley, and minor "completion" surveys of
the Hay Hollow valley by Ezra Zubrow, Dave Gregory, Michael Schiffer
and John Johnson.
For the purposes of this study, the central and peripheral
surveys will have the most importance. However, all of the later
surveys owe a debt to the earlier ones, not only in occasional overlap,
but in regards to the development of efficient survey techniques.
In 1967, the "central" portion of the valley was surveyed
covering an area of £.2 square miles. This is the area marked Central
Survey on the map of post 1966 surveyed sites in the valley (Fig. 17).
This survey systematically covered 100;? of the area on foot, recording
sites defined by an explicit criterion. This criterion was that any
spatially unique sherd, lithic, or architectural cluster was to be
defined as a site. In order to acquire a site designation, the clus­
ters had to be surrounded by areas of non-cultural materials and
could not be the result of possible redeposition by water or pot
hunters. Samples of the surface cultural materials were collected
from each site. In the 100$ survey, 277 sites were found of which
198 sites were datable using the surface pottery collections.
A brief statement about the survey technique is apropos.
After the survey area was gridded, a crew of five to ten members of
the expedition would cover an individual grid unit by walking back
13U
and forth across the area in a line approximately five yards apart.
Thus, the area was covered not only systematically but completely.
In 1968, two peripheral survey areas were defined in order to
measure the amount of spatial and cultural variation.
and one. was west
of ...the..100$
One was east
sample survey. These are labeled the East
:i Vaut- peripheral'•'survey on Figure 17. Both of these surveys were
2%% samples. The same type of on foot surveying was continued and the
same criterion for the definition of sites was used. Dr. Martin dated
the potentially datable sites in the 1967 and 1968 surveys on the basis
of pottery.
,, In order to estimate the room counts of those sites which had
not been excavated, Fred Plog (Schiffer 1968) calculated two linear
regression equations which inductively related room number of sherd
scatter and room block area. This was based on the relationships which
existed in known excavated and surveyed sites in the area. The
equation for pithouse villages is R = ,llii7A + 1.2 where R is the num­
ber of rooms and A is the area in square meters of the sherd scatter.
The eqcaticn for ptteblos is R = .10B + .h where R is the number of
rooms and B is the area of the room block in square meters (Schiffer
1968).
A
second problem to be considered is the relationship between
total room count and habitation rooms. It is likely that there is a
gradual increase in the ratio of non-habitation to habitation struc­
tures through tifflu.. To take this into account, population estimates
would have to be lowered through time by an increasing factor. (For
135
a discussion of functional determination of rooms from surface remains
see Zanic 1968.) This has been done by Plog (196?), Schiffer (1968)
and others by using several ratios based inductively on known sites
such as Carter Ranch and 3roken K.
One must also consider how many of the habitation rooms were
occupied at one time. This was calculated by taking 80$ of the habi­
tation rooms at the midpoint (Plog 1969; Schiffer 1970).
As previously mentioned, the valley has been divided into
topographic and potential ecological zones which are numbered 1-7.
Topographically, these are (1) the top of the mesa, (2) the sides of
the mesa, (3) the alluvial fans at the bottom of the mesas, (U) the
second sandstone terrace, (5) the first terrace, and (6) and (7) the
bottomlands. The exact environmental composition will be discussed
later in this chapter.
Before one may understand Tables U and 5, it is necessary to
explain the site numbering systems. There are two independent number­
ing systems. Longacre has one set of numbers which corresponds to the
sites which he located in the triangle which includes the Hay Hollow
valley. A second set of numbers were used in the "New Survey" which
includes all surveys after 1966. Table k is a complete listing of the
new survey sites. Column 1 is the site number according to the new
survey. Column 2 is the pottery date based on surface collections as
given at the time of the survey by Paul S. Martin except in cases where
the site was excavated prior to 1969. In those pre-1969 excavated
cases where C]^, tree ring dates, or pollen dates caused a reanalysis
136
Table U. Archaeological sites in the Hay Hollow valley.
Site
Number
1
3
U
5
6
Date
950-1150
1*00-700
MicroHabitat
Maximum
Number of
Rooms occupied at
One Time
Number of
Rooms in
Habitation
Sites
Number of
Habitation
Rooms
6
5
U
1
1
1
5
9
U
7
3
5
1
1
1
8
6
5
1
1
1
500-800
7
7
7
3
3
7
3
2
3
3
3
7
3
3
7
16b
800-1000
7
17
18
1100-1300
3
19
21
22
900-1100
23
950-1150
7
3
3
3
2U
25
26
950-1150
3
3
950-1150
1
1
1
27
28
3
7
800-900
7
10
10
8
7
8
9
10
11
12
13
lU
15
16a
29
800-950
100-700
700-800
950-1150
1100-1200
950-1150
700-1100
950-1150
750-950
700-900
7
850-950
7
137
Table It. Archaeological sites in the Hay Hollow valley—Continued
Site
Number
Date
MicroHabitat
30
31
33
31+
35
36
37
38
39
900-1000
1100-1300
2
ko
Ilia
950-1150
950-1150
2
2
U2
950-1150
2
5
u
3
2
2
5
1
a
1
1
6
5
17
13
1
1
2
1
1
1
3
1
1
2
2
2
800-900
3
2
3
5
10*
U5
U6
U7a
700-900
950-1150
U8
U00-700
h9
950-1150
950-1150
900-1100
500-700
1000-1150
60
61
3
3
6
2
U3
52
53
5U
55
56
57
58
59
Number of
Habitation
Rooms
Maximum
Number of
Rooms occupied at
One Time
3
950-1150
950-1150
950-1150
Number of
Rooms in
Habitation
Sites
950-1150
U00-600
950-1150
950-1150
700-900
2
2
2
2
3
2
3
7
7
7
7
3
3
7
7
17
1
u
138
Table U. Archaeological sites in the Hay Hollow valley—Continued
Site
Number
62
63
6U
65a
66
67
68
69
70
71
72
73
7h
75
76
77
78
79
80
81
*83
8Ua
85
86
87a
88
89
90
91
92
Maximum
Number of
Rooms occupied at
One Time
MicroHabitat
Number of
Rooms in
Habitation
Sites
Number of
Habitation
Rooms
950-1150
950-1150
700-900
900-1000
900-1000
3
7
7
2
2
1
1
1
1
1
1
950-1150
2
2
1350-11*50
950-1150
950-1150
950-1150
950-1050
950-1150
950-1150
U00-800
U00-700
950-1150
950-1150
loou-noo
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
6
5
U
950-1150
1100-1300
2
25
15
12
950-1050
950-1050
950-1150
950-1150
7
7
7
7
7
1
1
1
650-750
650-750
550-650
600-800
7
7
7
7
3
3
Date
7
2
,
3
850-1025
7
UO
(correction by intensive survey)
2
2
139
Table lw
Site
Number
Archaeological sites in the Hay Hollow valley—Gontinued
Date
MicroHabitat
93
9k
95
96
97
98
99a
100
102
103
10U
105
107
108
109
110
700-800
500-700
500-700
700-900
850-950
850-1000
800-950
900-1000
200-500
950-1150
700-900
950-1150
111b
950-1150
112
121
950-1150
950-1150
122
123
12Ua
125
125b
127
128
129
130
131
132
950-1150
950-1150
950-1150
800-900
900-1050
3
7
3
3
6
950-1150
950-1150
7
7
3
3
3
3
7
7
7
7
7
7
7
7
7
7
7
3
3
3
Maximum
Number of
Rooms occurpied at
One Time
Number of
Rooms in
Habitation
Sites
Number of
Habitation
Rooms
3
3
2
2
2
2
5
5
5
1
1
1
2
1
1
1
1
1
u
U
3
1
1
1
1
1
1
3
2
600-700
U00-700
3
2
3
lUo
Table U. Archaeological sites in the Hay Hollow valley—Continued
Site
Number
133
13U
135a
135b
135c
136
137a
*137b
139
IhO
mi
lij.2
Hi3
HiU
1U5
11*6
1U7
Ui8
1U9
150
151a
152
153
15U
155
156
156a
157
158
*137b
Date
900-1100
500-700
950-1150
800-950
900-1000
500-700
960-1100
1000 B.C.
900-1000
900-1000
800-900
950-1000
950-1150
700-800
800-900
650-750
800-900
950-1150
950-1150
Maximum
Number of
Rooms occu­
pied at
One Time
MicroHabitat
Number of
Rooms in
Habitation
Sites
Number of
Habitation
Rooms
7
2
1
1
3
3
7
20
20
16
7
7
7
7
10
3
1
10
2
1
8
2
1
7
7
7
7
7
7
7
5
2
1
1
3
3
7
7
t
900-1000
950-1050
800-900
950-1150
1000-1050
700-800
7
7
7
7
1
1
1
7
7
2
2
2
925-97*
7
11
(correction by intensive survey)
lltl
Table U#
Site
Number
Archaeological sites in the Hay Hollow valley—Continued
Date
1$9
160
161
162
163
I6h
165
800-900
700-800
900-1000
700-800
900-1000
166
167
168
169
170
171
172
17U
175
176a
177
178
180
181
182
183
900-1050
800-900
900-1000
500-700
185
186
187
188
189
191
192
MicroHabitat
Number of
Rooms in
Habitation
Sites
Number of
Habitation
Rooms
Maximum
Number of
Rooms occupied at
One Time
850-1000
55o-65o
700-800
500-700
600-700
900-1000
800-900
700-900
950-1050
1000-1150
600-700
950-1050
600-800
1150-1282
900-1000
900-1000
900-1000
6
3
5
2
h
2
3
1
3
1
2
1
99
7
59
li6
5
6
1U2
Table U. Archaeological sites in the Hay Hollow valley-Continued
Site
Number
193
19U
*195
*196
197
199
*201
203
20U
205
206
207
208
209
210a
211
212
213
21U
215
216
217
218
220
221
222
223
22k
*195
*196
*201
MicroHabitat
Date
Number of
Rooms in
Habitation
Sites
Number of
Habitation
Rooms
Maximum
Number of
Rooms occu­
pied at
One Time
500-700
7
700-850
1000-12000
1100-1280
7
7
7
25
1
17
1
13
1
600-750
1100-1200
7
7
7
8
20
8
20
6
950-1150
950-1150
950-1150
950-1150
950-1150
950-1150
950-1150
950-1150
950-1150
1300-^00
1150-1300
900-1100
1150-121)0
1150-1225
1175-1300
— — »•
(corrections by
w
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
7
7
7
I
intensive
11
22
80
VV
survey)
16
11*3
Table k»
Site
Number
225a
226
227
228
229
230
231
232
233
231*
235
236
237
239
2U0
2U1
2U2
21*3
2UU
270
271
273
275
276
277
278
279
280
281
282
285
286
Archaeological sites in the Hay Hollow valley--»Continued
Date
300-600
900-100
MicroHabitat
Number of
Rooms in
Habitation
Sites
Number of
Habitation
Rooms
Maximum
Number of
Rooms occur
pied at
One Time
50
50
39
15
15
12
2
6
1
2
5
1
2
h
1
1
2
1
1
1
1
1100-1200
1250-1350
700-900
950-1150
250-600
500-700
850-1050
600-700
1000-1100
900-1000
900-1000
900-950
1*50-650
1000-1050
900-1000
950-1050
800-950
•
HiU
Table lu
Site
Number
Archaeological sites in the Hay Hollow valley—Continued
Date
1000-1100
301
950-1050
310
311
950-1150
312
950-1150
313
950-1150
31U
320
321a +b
322
323
900-1000
330
950-1150
331
800-900
332
200 BC-AD 300
333
800-900
33U
950-1150
33*
800-900
336
950-1150
337
MicroHabitat
7
7
7
7
7
7
h
3
7
7
7
7
5
7
7
7
7
Number of
Habitation
Rooms
1
1
1
1
1
1
1
1
1
u
U
3
20
h
15
3
12
2
338
339
Uoo
U01
U02
i|03
UOU
1(20
U21
*1*30
UUO
950-1150
950-1150
1000-1150
1000-1100
1000-1100
1000-1100
1000-1100
1000-1150
1000-1150
1000-1150
1000-1150
*1*30
1075-1100
7
7
(correction by intensive survey)
7
7
2
2
2
2
2
2
2
7
5
Maximum
Number of
Rooms occu­
pied at
One Time
Number of
Rooms in
Habitation
Sites
Table U. Archaeological sites in the Hay Hollow valley—Continued
Maximum
Number of
Rooms occupied at
One Time
Date
MicroHabitat
Number of
Rooms in
Habitation
Sites
U5o
fcSL
1000-1100
1000-1100
7
7
7
5
2
2
U60
U6l
U62
950-1050
7
7
u
9
3
2
2
1
1
1
7
5
2
2
2
2
2
2
19
a
15
3
2
2
6
Site
Number
U70
U71
U80
2*81
U82
U90
500
501
505
506
507
508
^10
*$11
512
513
515
520
521
525
530
535
5U0
5U5
*Sll
1150-1200
1000-1100
1000-1100
1000-1100
700-950
850-950
3
7
3
700-800
900-1000
7
7
2
700-900
7
1000-lii00
7
26
1000-1150
1000-1100
7
5
3
Hi
25
7
5
u
1000-1050
7
1200-1350
7
a
a
u
7
7
7
1150-1250
800-900
600-700
800-950
1000-1050
950-1150
1300-lli00
1
7
7
7
7
1200-1U50
700-1000
Number of
Habitation
Rooms
3
22
2
15
9
3
U
15
h
(correction by intensive survey)
8
19
13
1
15
7
2
3
15
10
1
12
5
2
2
1h6
Table U. Archaeological sites in the Hay Hollow valley—Continued
Site
Number
55o
5#
560
565
600
605
610
611
612
613
61U
615
616
617
620
621
622
630
631
632
63U
635
636
637
6I|0
6U1
61)2
6U3
6i0i
6Ii5
Date
1100-1300
1000-1050
950-1050
750-850
1000-1100
1000-1300
950-1100
1050-1100
1000-1150
1050-1150
950-1100
800-1000
1000-1150
1000-1150
1000-1150
1050-1150
MicroHabitat
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
1000-1150
1000-1100
7
7
7
7
7
7
7
1000-1100
5
1000-1100
5
5
7
950-1050
1000-1150
Maximum
Number of
Rooms occu­
pied at
One Time
Number of
Rooms in
Habitation
Sites
Number of
Habitation
Rooms
6
1
U
8
U
1
3
8
3
1
2
6
50
33
26
3
2
2
3
2
2
3JU7
Table U. Archaeological sites in the Hay Hollow valley—Continued
Site
Number
61*7
6U8
6h9
650
6^1
6^2
65U
655
656
657
658
659
660
661
Date
MicroHabitat
950-1050
5
1100-1200
850-950
800-900
1000-1100
950-1050
1000-1100
850-900
5
5
7
7
7
5
5
7
5
U
800-1100
5
5
662
663a
663b
670
671
200-700
200-700
1000-1100
950-1050
900-1050
5
U
U
7
7
672
673
1000-1100
1000-1150
U
7
67U
675
676
950-1200
950-1200
U
it
950-1050
800-900
850-1050
900-1050
7
7
7
7
7
1000-1150
7
677
678
679
680
681
682
950-1050
Number of
Rooms in
Habitation
Sites
Number of
Habitation
Rooms
Maximum
Number of
Rooms occu­
pied at
One Time
8
8
6
12
12
7
70
5
70
9
U
55-65
1
1
1
1
1
1
6
5
1
h
1
3
1
1
1
1
1
1
1
8
6
5
XU8
Table H. Archaeological sites in the Hay Hollow valley—Continued
Site
Number
683
68U
686
690
691
692
693
69k
695
696
700
701
702
703
70U
705
706
707
708
709
710
711
712
713
71U
715
716
717
725
Date
MicroHab tat
800-900
1050-1150
950-1050
950-1050
900-1000
1000-1050
900-1000
900-1050
800-900
1000-1100
U-5
1050-1100
U-5
1000-1100
a-5
1250-1300
u-5
1150-1250
a-5
Number of
Rooms in
Habitation
Sites
Number of
Habitation
Rooms
Maximum
Number of
Rooms occu­
pied at
One Time
2
h
1
1
8
3
1
1
1
1
6
5
1
1
1
1
1
1
1U9
Table 5. Habitation rooms per site by site: Longacre survey.
Site
Number
102
103
10U
105
106
177
186
Date
800-1000
1100-1300
700-900
900-100
1100-1300
700-900
Number of
Rooms in
Habitation
Sites
25
1
5
60
Number of
Habitation
Rooms
Maximum
Number of
Rooms occu­
pied at
One Time
175
5
h
19
1
5
U7
103
k
U
15
l
h
37
80
3
5
1
h
1
188
550-750
600-800
202
600-800
5
l
207
900-1100
5
h
3
208
900-1100
5
209
210
211
800-1000
700-900
800-1000
3
3
5
h
3
2
3
2
2
h
212
213
600-800
600-800
15
2
15
2
3
12
2
21ii
215
216
217
700-900
500-700
800-1000
800-1000
3
3
30
6
2
228
700-900
800-1000
15
5
11
h
3
230
3
22
3
2
2
18
U
9
2
150
of the site date, the amended date is used. Column 3, the location
column, indicates the ecological zone where the site occurs. Column
h -- total rooms, column 5 — habitation rooms, and column 6 — maxi­
mum occupation, are the result of calculations discussed above except
in pre-1969 excavated sites where if more accurate data exist, they
are used.
Table 5 has the sites from the Longacre survey which are within
the valley but are not part of the new survey. Column 1 is the
Longacre survey number. Column 2 is the date. Column 3 is the number
of rooms which Longacre estimated. Columns U and 5 are the habitation
rooms and the maximum occupation which Plog calculated using the same
criteria as the New Survey.
Two caveats should be noted with these data. The data have
been compiled by many people over the last eight years. Unfortunately,
a careful examination will show that inconsistencies have crept into
the data which are not correctable without extended field work. For
example, Michael Schiffer has site number £06 located within the
sample square, but the map >ihich was drawn by David Grebory originally
shows the site outside the sample square. Rather than make arbitrary
decisions which would confuse the literature even more, I have com­
piled and requoted the materials as they exist.
The second caveat is that the data were often compiled with
different problems in mind and thus the degree of data completeness
is somewhat variable. Perhaps these caveats are an argument for having
a single person gather and analyze the data for a single problem. How­
ever, in large projects this is often unfeasible because people's
l£L
interests and the relevant problems change as the field grows at un­
expectedly fast rates (Kuhn 1968). Secondly, these data were gathered
as part of the Southwest Archaeological Expedition which is a field
school devoted to teaching research methods as well as field methods.
A partial measure of a field school's success is the number of students
it is able to educate. In a sense these goals of one person gathering
and analyzing data for consistency and educating students are opposite.
However, I think that Tables U and £> are a remarkable set of data
equaled in only a few archaeological areas by data with comparable
representative qualities. This is a reflection of the efforts of
Dr. Paul S. Martin and his field program.
Intensive Survey
In the summer of 1969, I did an intensive survey of seven
sites. It was undertaken for several reasons. First, there is always
a fear that when one is using surface indications that one is over­
estimating what is under the ground. Second, there is a question of
whether the dates are accurate when based solely on surface pottery
collections. Third, more accurate data were necessary than were avail­
able for testing some of the hypotheses, such as the residential area
hypothesis. Fourth, a primary question when using survey materials is
whether or not one may estimate multi-component sites. Fifth, in the
process of surveying, several sites were found and it was considered
necessary to check them more carefully since their reality was ques­
tionable. Finally, several sites were being pot hunted extensively
and it was decided that before total destruction had taken place, as
1*2
much data as feasible would be collected in the context of the ongoing
research and then an attempt at protection would be made.
A brief comment about pot hunting is appropriate in order to
give the reader an understanding of the gravity of the situation. One
of the unfortunate consequences of maintaining a long term research
interest in a particular area is that the value of the area becomes
known to local pot hunters. The longer the expedition has been working
in the valley, the better known is the work and the more accurately is
the location of its archaeological interests pinpointed. This is the
consequence of two factors. First, an expedition such as the Southwest
Archaeological Expedition, which has been located in the same area for
If? years becomes a part of the local society and economy and its work
and personnel are discussed in the same manner as the work and per­
sonnel of the local cattle industry. Secondly, the expedition itself,
in an attempt to maintain good relations with the owners of the land
and the local population have attempted to publicize the value of the
area's archaeological resources and the reasons why they should be
excavated by professionals.
However, it appears that the expedition has failed to a certain
extent with regard to its attempts to dissuade local pot hunters. In
the three summers in which I have been associated with the expedition,
pot hunting has increased. Not only have most of the habitation sites
pot holes in them, but recently heavy machine equipment has been
brought in. At Broken K, plow and furrowing machinery were used in
the burial area to find graves. This has taken place even though the
1*3
owners of the land have attempted more than once to keep unauthorized
people off their property. At Four Mile ruin, the type site of Four
Mile Polychrome, which is located a few miles from the valley, a nine
yard front-end loader was used to remove the burial area of the site
in an attempt to find whole pots.
The intensive survey was utilized on New Survey sites 83, 137,
195, 196, 201, 1;30, and 511. These sites were not chosen randomly and
should not be considered representative. In fact, they were chosen
for multiple reasons, one of which was that they emphasized areas of
possible dating and size error. In other words, rather than being
representative, the sample was skewed to maximize the potential error
between the survey estimates and what actually occurred underground.
Thus, if there were major problems in the survey estimates, they were
sure to be found. Within this set of sites with potential errors,
NS 83 and NS 137 were chosen because there were limited reasons to
believe that they might be multi-component sites. NS 5>11 was chosen
because it was thought to be the last site in the valley. The rest of
the sites were chosen because they were near access roads and previous
archaeological work and were beginning to be pot hunted extensively.
In fact, each site had at least one pot hole in it and some had con­
siderably more damage.
The intensive survey was carried out in a series of steps.
First, the site was relocated in the field and checked against aerial
photographs and existing maps. Second, a new surface collection of
the pottery remains was made. Third, the site was analyzed for surface
15U
features. Fourth, the topsoil of approximately one to two inches
covering the top of the walls was removed and the architectural layout
was mapped. Fifth, in problematical areas, trenches were put in to
clarify the architectural features of the site. Sixth, pottery collec­
tions, tree ring specimens, C-l!| and pollen samples were taken from
the exposed floor area. Seventh, a bulldozer and a small front-end
loader were employed to gather soil from non-archaeological areas sur­
rounding the site which was then placed upon the site providing a three
to five foot sterile protective cap.
In no case was more than 11$ of a site's roomblocks and in­
terior plazas excavated. For NS 137b, the trenches make up 1% of the
site areaj for NS 201 - 6%s and for NS 83 - 11$. In all other sites,
it was possible to use existing potholes. Figures 18 through 2h are
the maps of the seven sites which were extensively surveyed. If one
compares the actual number of rooms as determined from the intensive
survey with the estimated number of rooms for the original 1967-68
surface surveys the following is the result.
Table 6. Comparison of settlement sizes.
Site
NS
NS
NS
NS
NS
NS
NS
83
137
19$
196
201
1*30
£11
Intensive Survey
Surface Survey
U3
10
11
22
76
7
lit
2$
20
25
1
20
20
lit
37
Sit* 83
10
36
39
Figure 18. Intensive survey ~ Site 83.
H
i
N
r
Site 137 B
10 Meters
Figure 19
Intensive survey — Site 137b
vn
o
I
a
3
1° J
\\
4
7
Site 195
5
6
fi '
°
I 9
, ».
—
10 Meters
Figure 20. Intensive survey — Site 195.
vn
m
oo
IO I
t-
p>
w> vo /:
W
in
vn
(M
IT
160
i
3
7
4-
i
!
2
5
6
$\ie A30
Si^e
fig0*®
23<
we
e
,s^
Site 511
10 Meters
Figure 2l|. Intensive survey — Site J>11.
162
The intensive survey shows an average of 26.1 rooms per site compared
to the 17.8 rooms per site of the 1967-68 survey for the seven sites.
Two conclusions may be drawn from these data. First, the
original survey does not overestimate the number of rooms. Instead,
it appears that it may underestimate the number of rooms. Second, if
one remembers that the sample was skewed towards areas of maximum error
and difficulty in survey estimating, then the maximum possible error
is 31% and the actual error is probably considerably lower, in the
area of 1$%.
Each of the sites was dated by pollen dating and on the basis
of pottery. Six of the seven sites were also dated by C-liu
All of
the carbon dates were done by Geochron. Unfortunately, there were
insufficient funds to run more than one date per site. Table 7 is the
pollen dating which was done by Richard Hevly. Table 8 is the C—"lit
dating and Tables 9 is the pottery counts and dates which were done
by David Gregory. The three sets of dates are graphically compared
in Figure 2£. A final date estimation was made on the basis of maxi­
mum overlap which is shown as the vertical lines on the graph.
If one examines the two sets of dates, the following compari­
son is possible.
163
Table 7. Pollen dates of intensive survey sites from Hay Hollow
valley. Pollen dating by Richard H. Hevly.
Pollen Sample No.
Site No.
AP/NAP Ratio
1-6
201
7-11
83
Insufficient
pollen
12-1 3
137b
Increased AP
575-625; 925-975;
1075-1150+ 1300+
U4-I6
195
Low AP
650-925; 975-1075;
1150-1300
17-18
511
Increased AP
575-625; 925-975;
1075-1150+ 1300+
19
U30
Increased AP
575-625; 925-975;
1075-1150; 1300+
20-22
196
Low AP
650-925; 975-1075;
1150-1300
Low AP
Dates
650-925? 975-1075;
1150-1300
16U
Table 8. Carbon lU dates.
Site No*
Geochronology
Laboratory No.
Date
Range
83
Gx-1661
1020± 85
8U5-1015
195
Gx-1660
1155± 85
1070-12U0
*196
GX-I66I4
690± 90
600-780
137
GX-1662
710i 95
610-805
201
GX-1665
136O£ 90
1*30
No C-Uj dates run
511
Gx-1663
990i 80
1270-1U50
910-1070
* The carbon material for this sample was taken from a fire pit
20 feet outside of the pueblo and may not be associated.
165
Table 9, Pottery types of intensive survey sites.
Pottery Type
83
X
Snowflake Black-onwhite
•White Mount Blackon-white
*137b
i£,\
X
-
Red Mesa Black-on-white
195
X
Sites
196
201
X
U30
511
X
X
X
X
X
X
St. Johns 31ack-on-red
X
Show Low Black-on-red,
exterior corrugated
X
Show Low 31ack-on-red
X
X
X
Wingate Black-on-red
X
X
X
X
X
X
X
San Francisco Red
Alma Plain
X
X
Plainware
Lino Gray
X
X
X
Four Mile Polychrome
X
St. Johns Polychrome
Querino Polychrome
X
X
X
McDonald Painted Corru­
gated
X
X
X
X
X
.. X
X
X
X
X
X
X
Corrugated - Plain
Corrugated - Indented
X
Painted ware - no
design elements
Black-on-white - no
design elements
Unidentifiable
Estimated Dates
X
X
X
X
X
X
X
X
X
850- 900- 1150- 1150- 1125- 1000- 13001300 1000 1250 1250 1250 1100 lliOO
* 13?b has a pithouse village component which may influence this
pottery distribution...
166
Table 10. Comparison of settlement dates.
Site Number
83
137
195
196
201
U30
511
Estimated 1967-68
Survey Date
300-1025
930-970
1150-121*0
1150-1225
1175-1300
1075-1100
1300-1U00
1100-1300
o
-^co
1
o
o
ni
NS
NS
NS
NS
NS
NS
NS
Intensive
Survey Date
1000-1200
1100-1280
1100-1200
1000-1150
1200-lli50
First I averaged the 1U intensive survey and the Hi estimated
dates. Then I subtracted the average estimated date from the average
intensive survey date. This calculation shows that the average dif­
ference between the dates for all the sites is only kO.O years. If
one excludes 137b, which is a multi-component site having both pithouses and a small pueblo, one only has a 11.6 year difference. Ex­
cluding 137b and 83, a possibly multi-component site has a l;3.5 year
difference. Two conclusions may be drawn from the above. First, the
estimated survey dates are remarkably close to the intensive survey
dates and thus may be accepted as reasonable. Second, it must be noted
that multi-component specific sites such as.137b and possibly 83, pro­
duce very poor estimates. Thus no single dating estimate should be
given a great deal of reliance unless one has evidence that the site
is not a multi-component site.
Time
.Carbon U
—
h
Pottery
— —*
Pollen
Comparison of pottery, pollen and radio carbon dates for
intensively surveyed sites.
168
Ecological Data
Introduction
During the summer of 1970 Dick Hevly and I directed an ecolo­
gical survey. Its purpose was threefold. First, we wanted to
determine if the topographic and soil zones correspond to differences
in flora and fauna. If so, were these differences sufficiently great
as to be labeled different micro-habitats? Second, we wished to de­
termine the actual amount of resources and resource productivity
available to the prehistoric population. Third, we wanted to obtain
these resource figures with sufficient representative accuracy as to
be usable in the simulation of a model of carrying capacity as a
dynamic equilibrium system. The ecological survey consisted of eight
stages.
Stage 1 was the accurate determination of the topographic and
soil zones which was accomplished by using aerial photographs, geolo­
gical and soil maps, and field survey techniques.
Stage 2 was the plotting and field location of a representative
sample of nested quadrants in each potential micro-habitat for floral
analysis.
Stage 3 was the plotting and field location of a series of
representative transects for each potential micro-habitat for faunal
analysis.
Stage U was the initial gathering of floral data. This con­
sisted of measuring by genera the number and size of trees in the 30
meter quadrants; the number and size of bushes and shrubs in the 10
169
meter quadrants; and the number and size of herbs and grasses in the
1 meter quadrant.
Stage 5 was the gathering of animal data along the transects
by five members of the expedition moving simultaneously along the
transect identifying all genera of mammal, bird and reptile life by
number for 2$ days as well as by live trapping.
Stage 6 was the final gathering of floral data. This consisted
of returning to each of the 1 meter quadrants (which had been initially
clipped at stage h) and reclipping all growth. Both sets of clippings
were sent to Northern Arizona University where their weights were
measured by genera.
Stage 7 was the planting and harvesting of three plots of corn
— one tended and irrigated, one near water, and one plot in an arid
region for agricultural data.
Stage 8 was the relating of modern resource data to past re­
source data.
Although at first glance this might seem to be a reasonably
complete resource analysis, it is incomplete. A complete analysis
would have to control both temporal and spatial data for all of the
variables in the following outline which represents a research design
for determining the prehistoric use and resources of micro-habitats
(Hevly 1970). The incompleteness of the available data should be kept
in mind when judging the finished study.
170
I. Microhabitat Identification and Characterization
A. Biotic parameters
B. Edaphic parameters
C• Climatic parameters
II. Microhabitat Resources
A. Biotic Resources
1. Plants
a. kinds
b. amounts
c. potential use
2. Animals
a. kinds
b. amounts
c• potential use
B. Edaphic Resources
1. Soil fertility
2. Mineral and non-biotic resources of aboriginal
utility
C. Climatic Resources
1. Temperature limitations on agriculture and
utilizable wild fauna and flora.
a. irrigated situations
b. dry situations
2. Moisture limitations on agriculture and utilizable
wild fauna and flora.
a. irrigated situations
b. dry situations
III, Prehistoric Exploitation and Modification of Microhabitats
A. Temporal and Spatial distribution of Dwellings and Fields
1. Prehistoric population movements and settlement
patterns.
2. Territoriality as an adaptation to localization
3. Population growth and decline
B. Patterns and Change of Plant Utilization and Cultivation
1. Agricultural history and environmental instability
2. Changing subsistence patterns
3. Economic change and diversity
C. Patterns and Change of Animal Exploitation
171
D. Environmental Modifications
1. Altered biotic composition as a result of:
a. Prehistoric exploitation (i.e., extinction)
b. Climatic change
c. Edaphic change (erosion and irrigation)
2. Altered Edaphic conditions as a result of:
a. Climatic change-erosion
b. Biotic change (induced by man and/or climate)
may result in erosion
c. Cultivation and soil disturbance by man ~
erosion and/or mineral depletion
It is impossible to complete this type of research design in a
single season or even in multiple seasons without more expertise and
expenditure of funds than the Southwestern Archaeological Expedition
had available. Thus, the eight stages was a conscious attempt to maxi­
mize information with minimum financial expenditure and maximum utili­
zation of available talent.
Stages 1, 2, and 3
Attempts were first made to determine microhabitats in the Hay
Hollow valley by Schacht in 1968. On the basis of U.S.G.S. aerial
photographs he differentiated two major ecological zones -- a highland
zone with juniper pinyon and a lowland zone which was predominantly
saltbush grasslands. He then differentiated within the highlands two
geographic and edaphic zones. The western highlands had soils derived
from basalt, while the eastern highlands had soils derived from shale.
Topographically he then divided the western highlands into the mesa
top (zone 1) and the mesa sides (zone 2) while the eastern highlands
were divided into an upper (zone h) and lower (zone 5) terrace. The
lowlands, although not divided on geographic or edaphic criteria were
172
divided topographically into upper (zone 3) and lower (zone 7) bottom­
lands. He felt but was unable to show that zones 1 and 2 on one hand
and zones U and 5 might only differ in minor detail.
The strategic air command was kind enough to present the South­
western Archaeological Expedition with a new set of aerial photographs
which had a much finer degree of detail and resolution than the
U.S.G.S. photographs. The United States Soil Conservation Service
provided us with detailed soil maps of the area. With this information
we went back to the field and made corrections in Schacht's original
formulation. Most of these corrections were minor and previously
dealt with the zone U and 5 boundaries and the zone 3 boundaries. The
corrected version is shown in the fold out map (Fig. 17).
It was decided to take a series of floral samples from each of
the potential microhabitats which would serve two functions. First,
it would provide Dick Hevly and myself with quantified data which
would allow the statistical differentiation of the actual present day
microhabitats. Second, it would allow us to quantify the actual
present day resource potential of the microhabitats.
One might object to this procedure as having no relevance to
the past. Two answers are possible to this objection. First, although
one probably would not want to suggest that the floral samples from
today are exactly equivalent to those of the past, it does give a
reasonable estimate and is far more accurate than the generalized
archaeological statements about the environment such as:
173
In general, the climate of the Southwest is dry and like most
of western North America it has grown more dessicated since
the glacial era, reaching a peak during the Altithermal, from
about 5000 B.C. to 2^00 B.C. Since then, modern conditions
have prevailed with epicycles of erosion and valley sedimen­
tation.
. ..(The Mogollon area is), in general, an environment of
mountains and valleys, covered with dry grasslands in places
and coniferous forests in others. The climate is mild
(Willey 1966: 178-9).
Second, it is possible to relate the modern environment and
floral samples to the past by using environmental indices such as
palynology (see the discussion of stage 8).
A series of problems had to be solved before it was possible
to know that our floral samples were representative. Line transects
are the easiest and quickest sampling procedure for estimates of den­
sity, frequency and cover. However, there is some question whether
it would give an accurate estimate of the plant material due to the
random aggregation of plants. Since trees show the most variation in
aggregation in small areas, it was decided to test transect versus
quadrant data on trees. Using the SAC high resolution photograph
87b
of the Broken K area we randomly selected 10 samples. Each sample
consisted of four nested quadrants. The quadrants were from smallest
to largest — 17m. x 17m., 3hm. x 3hm., 5lm. x 5lm., and 68m. x 68m.
The line transects were two boundaries of the quadrant at right angles
to each other for all four nested quadrants. Thus, the transect
lengtn for the smallest quadrant was 17m. for the next larger quadrant
3l»m., etc. The percentage error was calculated as:
% error = (transect estimate - actual quadrant number of trees)
actual quadrant number of trees/100
17U
The results are in Table 11. The 17m. x 17m. quads compared
to the 17m. transects showed an average error of -62^ calculated bysumming the individual errors and averaging. Similarly the 3ljm. x 3Um.
quads, the 5lm. x 5>lm. quads, and the 68m. x 68m. quads showed in com­
parison to their transects errors of -3h%, -33%, and -22% respectively.
In all cases the 90° transect method seriously underestimated the
number of trees and was thus rejected.
A second sample was taken in order to test if line transects
selected on a criterion of at least two trees in the first 30 meters
gives a more accurate and representative estimate. The results are
in Table 12. This method is also rejected for the error is even
greater than the first method with average errors of -79%, -hl%, -hk%,
and -US% for the 17m., 3hm., 51m., and 68m. transects respectively.
Having rejected both line transect methods, it was decided to
attempt to use quadrants as a method of sampling. The question which
arose was what is the smallest quadrant which would give valid repre­
sentative data but which was small enough to be handled by the expe­
dition's resources? In order to determine the representative qualities
of the sample, it was assumed that if the quadrant gave an accurate
representation of the number of trees in an area of more than an acre,
it was representative and sufficiently accurate. The largest quad.,
68m. x 68m., is more than an acre. The smallest quad is l/l6 of the
largest, the next largest is lAj and the next is 9/l6. The estimate
is then defined as E = l6x, E = Ipc, E » l6/9x for the 17m. x 17m.
quad, for the 3Um. x 3Um. quad, and the Sim. x £lm. quad where:
175
Table 11. Tree estimates from two 90° transects compared to actual
niunber of trees within quadrants with variable transect
length and quadrant size.
Sample
Number
Size of
Quadrant
in Meters
Estimate
of Number
of Trees from
Two Transects
Actual
Number of Trees
in Quadrant
Percent
Error
1
2
3
5
5
10
21
3h
-60
0
Hi
hi
1
3
3
U
x 0
x 2
x It
x6
3
7
17
28
-66
17
3h
51
68
l
2
3
5
x
x
x
x
l
2
3
5
3
6
11
2h
-67
-33
-18
U
17
3h
51
68
2
3
U
5
x
x
x
x
1
2
2
3
3
8
Hi
23
-33
-25
-U3
-35
x 17
x 3h
x 51
x 68
l
3
U
5
x
x
x
x
l
3
h
U
3
10
10
20
-67
-10
60
0
6a
6b
6c
6d
17 x 17
3h x 3h
51 x 51
68 x 68
l
2
3
U
x l
x 1
x 1
x1
3
6
12
28
-67
-67
-75
-86
7a
7b
7c
7d
17 x
3h x
51 x
68 x
17
3h
51
68
l
2
U
6
x
x
x
x
l
1
1
3
3
7
19
35
-67
-71
-79
-h9
8a
8b
8c
8d
17
3h
51
68
17
3l»
51
68
l
2
3
5
x
x
x
x
l
3
3
5
h
10
18
27
-75
4i0
-50
-7
la
lb
lc
Id
17 x
3h x
51 x
68 x
17
3h
51
68
2
5
8
10
2a
2b
2c
2d
17 x
3h x
51 x
68 x
17
3k
51
68
3a
3b
3c
3d
17
3h
51
68
x
x
x
x
Ua
lib
Uc
lid
17
3h
51
68
x
x
x
x
5a
5b
5c
5d
17
3h
51
68
x
x
x
x
x
x
x
x
-29
-Hi
176
Table 11. Tree estimates from two 90° transects compared to actual
number of trees within quadrants with variable transect
length and quadrant size—Continued
Sample
Number
9a
9b
9c
9d
10a
10b
10c
lOd
Size of
Quadrant
in Meters
Estimate
of Number
of Trees from
Two Transects
Actual
Number of Trees
in Quadrant
Percent
Error
17 x
3k x
51 x
68 x
17
3h
51
68
l
2
3
k
x
x
x
x
l
2
2
3
3
7
13
19
-37
17
3)4
51
68
17
3U
51
68
l
2
2
3
x
x
x
x
l
1
2
3
2
3
9
17
-50
-33
-56
-U7
Average error
x
x
x
x
a = 62$, b - 3h%t
c a
33$, d = 22%,
-67
-H3
177
Table 12. Comparison of the tree estimates from two line transects
selected so that there are two trees in the first 31 meters
with actual tree number within quadrants with variable
transect and quadrant size.
Sample
Number
Size of
Quadrant
in Meters
Selected
Transect Tree
Estimate
Actual
Number of Trees
in Quadrant
Percent
Error
la
lb
1c
Id
17 x
3h x
51 x
68 x
17
3U
51
68
1
2
3
3
x
x
x
x
1
2
3
it
2
6
10
lit
-50
-33
-10
-lit
2a
2b
2c
2d
17 x 17
3U x 3k
51 x 51
68 x 68
0
2
3
1*
x
x
x
x
1
2
3
U
1
7
13
19
-100
—it-3
-30
-16
3a
3b
3c
3d
17 x
3h x
51 x
68 x
17
3h
51
68
2
3
it
li
x
x
x
x
0
2
2
3
2
9
17
25
-100
-33
-53
-U8
Ua
lib
Uc
bd
17 x 17
3h x 3U
51 x 51
68 x 68
1
2
2
3
x
x
x
x
1
2
3
3
it
10
lit
26
-75
-60
-57
-65
5a
5b
5c
5d
17
3h
51
68
17
3h
51
68
1
2
2
3
x
x
x
x
0
2
2
2
2
8
12
20
-100
6a
6b
6c
6d
17 x 17
3U x 3h
51 x 51
68 x 68
1
2
2
2
x
x
x
x
0
2
3
it
3
10
18
27
-100
—60
-67
-70
7a
7b
7c
7d
17 x
3it x
51 x
68 x
1
2
3
it
x
x
x
x
0
2
3
5
2
10
22
32
-100
-60
-59
-37
6a
8b
8c
8d
17 x 17
3h x 3h
51 x 51
68 x 68
2 x 2
3x U
it x 5
It x 6
5
11
17
30
-20
9
17
-20
x
x
x
x
17
3h
51
68
-50
-75
-70
178
Table 12. Comparison of the tree estimates from two line transects
selected so that there are two trees in the first 31 meters
with actual tree number within quadrants with variable
transect and quadrant size—Continued
Sample
Number
Size of
Quadrant
in Meters
Selected
Transect Tree
Estimate
Actual
Number of Trees
in Quadrant
Percent
Error
9a
9b
9c
9d
17 x
3h x
51 x
68 x
17
3h
51
68
l
2
3
U
x
x
x
X
l
2
3
U
3
6
1h
30
-67
-33
-33
4i6
10a
10b
10c
lOd
17 x
3U x
51 x
68 x
17
3U
51
68
l
2
3
U
x
x
x
x
l
2
2
2
U
8
25
36
-75
-50
-76
-76
Average errors a = 79%, b = hl%, c = hk%, d = h6%.
179
E » is the estimate to be compared with the 68m. x 68m. quad.
X • is the number of trees found in the smaller quads from which
the estimate is being made.
10
^ K
n=l
x 100 where:
Er = error
E « estimate from a particular quad size excluding 68m. x 68m. quad
K « is the actual number of trees in the 68m. x 68m. quad
n = the number of samples
These estimates and errors were calculated for both sets of sample
quads which were originally presented in Tables 11 and 12. The results
are shown in Table 13•
It would appear that the quadrants are capable of producing
better estimates. However, it should be noted that in order to do
this accurate estimating it takes far larger quadrant size than the
professional biologists and ecologists usually deem necessary. For
example, Smith (1966) claims:
The size of the quadrant must be adapted to the character­
istics of the community. The richer the flora, the larger
or more numerous the quadrants must be. In forests,
quadrants of one fifth acre are established to include the
trees, while smaller quadrants can be used to study shrubs
and understory. For the latter as well as grass cover,
quadrants of one square meter are the usual size.
In other words, for rich flora such as forests one shouldn't have to
use quadrants of more than 1/5 acre. Hevly (1970) notes that common
nested quadrant sizes are 10m. x 10m. for trees, Urn. x hm. for shrubs,
bushes, and understory, and lm. for grasses. Since these values are
180
Table 13• Quadrant estimates for 68m. x 68m, quadrants based on
17m. x 17m., 3Um. x 3Um., and 5lm. x !?lm. quadrants.
Sample
17m. x 17m.
Estimate
3Uni« x 3Um.
Estimate
5lm. x 5lm.
Estimate
Actual number
of trees in
68m. x 68m.
Quadrant
UO
28
2h
32
UO
2U
28
UO
28
12
37
30
20
25
18
21
3U
32
23
16
3k
28
2U
23
20
28
35
27
19
17
26
28
36
UO
32
UO
UO
17
23
30
25
21
32
39
30
25
1U
19
25
26
20
27
32
30
30
36
Group I based on Table 11
80
1
2
U8
U8
3
U
U8
U8
5
6
U8
U8
7
8
6U
U8
9
10
32
Group II based on Table 12
1
32
16
2
32
3
6U
U
32
5
6
U8
32
7
80
8
U8
9
10
6U
Error
Group I
Group II
10156
72JS
UU
2U
32
2056
31*
UU
,h%
lOg
181
based on larger studies where quadrant size was correlated with manymore than 60 quadrant estimates, Hevly and I decided that it would be
appropriate to compromise our large quadrant size with the professional
values. Thus, we used quadrants of 30m. x 30m. for trees, 12m. x 12m.
for shrubs, bushes, and understory, and 1m. x lm. for grasses. Five
of these were randomly located in each potential microhabitat. This
exact location is plotted in the pocket fold out map. However, one
caveat should be noted. Namely, this size quadrant may have built in
errors up to 2$% as noted in the tabular evidence.
In order to determine the amount of faunal life a series of
road transects were devised which cut across the potential microhabitats in addition to live trapping. These are just two of many poten­
tial methods which could have been used. Smith (1966) suggests sample
plots, strip census, mark-recapture method, the population removal
method, live trapping, and pellet counts as alternative methods.
Each
of these have assets and disadvantages. We chose the road transect
method primarily on the basis of logistic ease and time requirements
rather than on statistical or sampling reasons.
Since animal data are quite variable, the longer the transect,
the more accurate is the relative representation of the population.
A trade-off decision was made between the isolation of the transect
and the length of the transect. The greater the isolation of the
transect the less disturbance of the fauna but the greater the logistic
problems and the less the total length of the transect. Thus to
maximize the transect's length they were taken along roads. It may be
182
reasonably argued that the automobile traffic along these roads would
result in a skewed sample. This is probably true. However, two mini­
mizing factors should be noted. One, during prehistoric times when
there was a sizeable population in the valley and the animal distri­
bution would have been affected by human activity, the skewed samples
may be to a certain degree equivalent. Two, the skewing is consider­
ably less than what might be at first expected since the roads along
which the transects were taken have very little traffic. Traffic
along the chosen road transects varied from one automobile per four
hours to one automobile per two months. The shorter periods were
ascertained by observation; the longer periods were determined by the
ranch owner.
Stage U
As was previously noted, stage U was the initial gathering of
the floral data. The number and size of trees were derived from the
30 meter quadrants, the number and size of the trees derived from the
10 meter quadrants and the number and size of the herbs and grasses
from the 1 meter quadrant. TablesU4. through 19 show the number of the
plants per nested quadrant per microhabitat. Table 20 shows the sum­
mation of the number of plants from the five quadrants per potential
microhabitat.
In order to determine the reality of the zones two tests were
made. First, a chi square test was done using the 36 species of
plants. The sum number of each species for the five quadrants in each
microhabitat was used. The observations thus formed a matrix of 38
183
Table llw
Plant distribution of Microhabit 1,
Species
Number of plants
in quadrants
2
3~
h
1
Trees
Pinyon Pine
Juniper
Shrubs
Saltbush (Atriplex)
Sagebrush (Artemisia)
Rabbitbrush (Chrysothamnus)
Prickley Pear (Opuntia)
Cholla (Opuntia)
Skunkbush (Rhus)
Barberry (Berberis)
Winter Fat (Eurotia)
Yucca (Yucca)
Beargrass (Nolina)
Other Lycium
Herbs
Grass: Aristida
Agryopyron
Bouteloua rothrocleii
Bouteloua
Hilaria
Muhlenbe Gia
Sporobolus
Orysopsis
Other Aster
Goosefoot (Chenopodium)
Snakeweed (Guteriezia)
Buckwheat (Eriogonum)
Locoweed (Astragalus)
Other: Plantago
Leptochloa
Aristida
Sphaeralceo
Moss
* Clumps
** Approximately
8
6
"IT
ii
11
1$
1^
1
3
U
1
1.
U
2
U
li
1
U
1
2
7
30
19
17
*87
1
6
1'
2
•
** 205
1
9
2
18U
Table 1$»
Plant distribution of Microhabit 2.
Species
Trees
Pinyon Pine
Juniper
Shrubs
Saltbush (Atriplex)
Sagebrush (Artemisia)
Rabbitbrush (Chrysothamnus)
Prickley Pear (Opuntia)
Cholla (Opuntia)
Skunkbush (Rhus)
Barberry (Berberis)
Winter Fat (Eurotia)
Yucca (Yucca)
Beargrass (Nolina)
Other: Berberis
Ephedra
Echinocenis
Herbs
Grass: Aristida
Agryopyron
Bouteloua
Bouteloua: Curley spikes
Bouteloua: Straight spikes
Hilaria
Muhlenbe Gia
Sporobolus: non airoides
Sporobolus
Oiysopsis
Goosefoot (Chenopodium)
Snakeweed (Guteriezia)
Buckwheat (Eriogonum)
Locoweed (Astragalus)
Other: Gramma
Arenaria
Stanleya Pinnata
* Includes Arenaria.
1
52
Number of plants
in quadrants
2
3~
It
9
28
13
13
~T"
2?
2
UO
1
U
U
1
7
3
1
1
1
6
22
9
17
1
1
16
*6
2
13
3
9
1
12
185
Table 16. Plant distribution of Microhabit 3.
Species
1
Trees
Pinyon Pine
Juniper
6
Shrubs
Wolf berry (Lycium)
Saltbush (Atriplex)
Sagebrush (Artemisia)
Sagebrush (Artemisia) Fridentata
Rabbitbrush (Chrysothamnus)
Prickley Pear (Opuntia)
Cholla (Opuntia)
Skunkbush (Rhus)
Barberry (Berberis)
Winter Fat (Eurotia)
Yucca (Yucca)
Yucca (Yucca) Narrowleaf
Beargrass (Nolina)
Other; Amorpha
Echinocerus
Forestiera
Lycium
Herbs
Grass: Aristida
Agryopyron
Bouteloua
Hilaria
Muhlenbe Gia
Sporobolus
Sporobolus: Airoides
Chrysopsis
Goosefoot (Chenopodium)
Snakeweed (Guteriezia)
Buckwheat (Eriogonum)
Locoweed (Astragalus)
Other: Artemisia wormwood
Sphaeralcea
Cryptantha
Olinithera
Number of plants
in quadrants
2
3~
h
17
2
3
3
5
3
U
^
$
118
2
2
1
1
1
1
1
1
U
U
1
1
1
1
3
12
2
32
3l|
11
1
27
U
1
U
1
5
3
186
Table 17. Plant distribution of Microhabitat k*
Number of plants
in quadrants
2
3
F"
Species
Tree3
Pinyon Pine
Juniper
Shrubs
Saltbush (Atriplex)
Sagebrush (Artemisia)
Rabbitbrush (Chrysothamnus)
Prickley Pear (Opuntia)
Cholla (Opuntia)
Skunkbush (Rhus)
Barberry (Berberis)
Winter Fat (Eurotia)
Yucca (Yucca)
Beargrass (Nolina)
Other: Ephedra
Cliff rose
Herbs
Grass: Aristida
Agryopyron
Bouteloua: tall
Hilaria
Muhlenbe Gia
Sporobolus
Orysopsis
Goosefoot (Chenopodium)
Snakeweed (Guteriezia)
Buckwheat (Eriogonum)
Locoweed (Astragalus)
Other: Boerhaavia
1
2U
12
16
1
17
32
1
3
5
2
2
h
6
3
2
Hi
2
17
20
1
2
187
Table 18. Plant distribution of Microhabitat
Species
Trees
Pinyon Pine
Juniper
Shrubs
Saltbush (Atriplex)
Sagebrush (Artemisia)
Rabbitbnish (Chrysothamnus)
Prickley Pear (Opuntia)
Cholla (Opuntia)
Skunkbush (Rhus)
Barberry (Berberis)
Winter Fat (Eurotia)
Yucca (Yucca)
Beargrass (Nolina)
Other: Cliff rose
Ephedra
Ironwood
Herbs
Grass: Aristida
Agryopyron
Bouteloua
Hilaria
Muhlenbe Gia
Sporobolus
Orysopsis
Goosefoot (Chenopodium)
Snakeweed (Guteriezia)
Buckwheat (Eriogonum)
Locoweed (Astragalus)
Other: Aster
Cryptantha
1
18
9
Number of plants
in quadrants
2
3~
U
2
11
2
9
1
12
10
IT
U
2
f>
112
3
1.
12
3
U
1
1
2
1
8
1
3
U
21 .
8
12
3
10
1
2
1
£
188
Table 19. Plant distribution of Microhabitat 7.
Species
Number of plants
in quadrants
' l'"
2
3~
h
Trees
Pinyon Pine
Juniper
Shrubs
Saltbush (Atriplex)
Sagebrush (Artemisia)
Rabbitbrush (Chrysothamnus)
Prickley Pear (Opuntia)
Cholla (Opuntia)
Skunkbush (Rhus)
Barberry (Berberis)
Winter Fat (Eurotia)
Yucca (Yucca)
Beargrass (Nolina)
Other: Lycium
Herbs
Grass: Aristida
Agryopyron
Bouteloua
Hilaria
Muhlenbe Gia
Sporobolus
Sporobolus: Non-airoides
Orysopsis
Goosefoot (Chenopodium)
Snakeweed (Guteriezia)
Buckwheat (Eriogonum)
Locoweed (Astragalus)
Other: Tumbleweed Salsala
Salsola seedlings
Cryptantha
Poa
Aster
1
12
1
II4.
3
2
2
2
2
7
17
1
1
3
3>1
Ul
1
35
30
3
1
5k
1U
3
8
189
Table 20. Total plant distribution for all quadrants by microhabitat.
Species
Trees
Pinyon Pine
Juniper
Shrubs
Saltbush (Atriplex)
Sagebrush (Artemisia)
Rabbitbrush (Chrysothamnus)
Prickley Pear (Opuntia)
Cholla (Opuntia)
Skunkbush (Rhus
Barberry (Berberis)
Winter Fat (Eurotia)
Yucca (Yucca)
Beargrass (Molina)
Other: Lycium
Berberis
Ephedra
Echinocenis
Amorpha
Forestiera
Cliff rose
Ironwood
Number of plants in all
quadrants in microhabitat
1
2~
3
U
5
~7
29
9
131
26
1
70
3
55
2
15
2
UO
8
8
1
61
9
22
30
8
13
19
1
13
3
7
2
6
1
5
a
h
l
2
1
9
h
3
Herbs
Grass: Aristida
12
Agryopyron
Bouteloua
33U
Hilaria
Muhlenbe Gia
19
Sporobolus
Orysopsis
Other: Aster
35
Boerhaavia
Goosefoot (Chenopodium) red mist 1
Snakeweed (Guteriezia)
Buckwheat (Eriogonum)
Locoweed (Astragalus)
Other; Plantain
1
Gramma
Artemisia wormwood
Sphaeralceo
Cryptantha
Aster
1
1
1
1
3
2U
1
2
3
1
7
1
9
13
3
1
1
1
15
1
6
61
3U
1U
1
35
35
33
19
20
12
33
3
10
92
1
65
1
2
1
2
15
1
h
1
1
3
2
1
5
Hi
8
190
species by six microhabitats. The resulting chi square was signifi­
cant at greater than the .0001 level. Thus, one may conclude that the
six microhabitat distributions taken as a group show the result of
factors other than chance variation as well as being as a group inde­
pendent of each other vis a vis the distribution of plants.
The second test was done in order to tell if there viere sig­
nificant relationships between the individual microhabitats when
analyzed one against the other rather than as a group. In order to do
this a series of Pearson Product Movement Correlation coefficients was
run between the various microhabitats. The correlation coefficient
was calculated according to the following formula.
nltlXiyi ' (Jl
1=1
\1=1
/
71)
^ n
1=1
-r< n)'
\1=1
/
where: r = is the correlation coefficient
n = is the number of cases
i = is the counter of the number of cases
x±= is the i^*1 value of the variable x, one of two variables
being correlated
y^= is the i^ value of the variable y, one of two variables
being correlated
In order to test the significance of r, one assumes the null
hypothesis that the deviation from the expected value of r is suf­
ficiently small that it could have happened purely by chance. In other
words, we are assuming what we wish to disprove. The proof of the
191
hypothesis of meaningful correlation is the disproof of the null
hypothesis. Under the null hypothesis (p = 0) one may state that the
sampling distribution of r is approximated by a normal curve. Its mean
and standard deviation are then equal to m = 0 and G^r **
Using
.05, the standard level of significance for scientific work, it is
possible to state that the null hypothesis is disproved, or the coef­
ficient of correlation is significant, if r exceeds 1.96 C~'T or is
smaller than -1.96
. One must reserve .judgment if r falls between
these two values. In our case where the number of species is 38, 6"^,
is equal to .161;. /l.9£/(.l6U) is equal to .3222. Thus, if r is
greater than .3222 or less than -.3222, the null hypothesis is dis­
proved and r is a significant correlation. The correlation coefficients
using the sum data is in the following table. By sum data I mean that
x± and y^ are the total number of plants of one species in the five
nested quadrants in microhabitat x and in the five nested quadrants
of microhabitat y.
Table 21. Correlation coefficients of total numbers of plants by
species by microhabitat.
Microhabitats
I
II
III
IV
V
VII
/
/
/
/
/
/
I
XXX
.i|2
.U9
.16
.17
.66
II
III
IV
V
VII
XXX
XXX
XXX
XXX
xxx
XXX
XXX
xxx
xxx
.78
.09
XXX
XXX
xxx
xxx
xxx
.11
XXX
XXX
xxx
xxx
xxx
xxx
.69
.'85
.80
.31
.lil
.E>5
The underlined values are the significant ones. If one uses mean data
rather than sum data the correlation coefficients are as follows. By
192
mean data I mean that xi and y^ are the mean number of plants of one
species for the five nested quadrants in microhabitat x and in the five
nested quadrants of microhabitat y.
Table 22. Correlation coefficients of numbers of plants by species by
microhabitat using mean data.
Microhabitats
I
II
III
IV
in
IV
V
VII
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
.61
715
.16
.68
.ao
.31 .
.5U
"31
.78
ToH
o
•
VII /
XXX
.U3
Tup
II
OO
v
/
/
/
/
I
It is interesting to note what a high degree of similarity there is
between the two sets of correlation coefficients wven to the extent
that they have identical combinations which are significant. From
these correlation coefficients it is possible to conclude the microhabitats II, IV and V have a high degree of similarity, r^ is con­
sidered to be a measure of the amount of variability explained, r^ for
II-IV, II-V, and IV-V is .66, .61;, and .61 respectively. This means
that 66% of the variability in microhabitat IV is explained by micro­
habitat II. The other values explain the variability for II-V, and
IV-V similarly. These microhabitats show the highest degree of simi­
larity of all the microhabitat combinations. It seems reasonable to
conclude on the basis of correlations whose values are approximately
.80 that the three microhabitats show sufficient similarity as to be
called one microhabitat. This is, of course, solely on the basis of
flora.
193
Stage 5
Stage $ was the gathering of animal data from the transects and
from live trapping. Each transect covered a width of l/lO mile. The
total transect area represented is:
zone
zone
zone
zone
zone
zone
zone
I
II
III
17
V
VII
VIII
...
...
...
...
...
...
...
1.380 square
.1M square
.110 square
1.6£0 square
.5>Ui square
3.0£li square
6.9 square
miles
miles
miles
miles
miles
miles
miles
Zone VIII is a continuation of potential zone IV towards Snowflake.
Tables 2k and 2£ are the summation of the transect data and
includes also the density data which was calculated by the summation
data divided by the zone areas. Pearson Product Movement correlation
coefficients were calculated on the density data by zones. The re­
sults below show that there is only one significant correlation of
sufficient size to suggest that two zones are the same animal microhabitats. These are zones IV and VIII.
Table 23. Correlation coefficients of animal densities by microhabitat.
Microhabitats
I
I
II
III
IV
V
VII
VIII
XXX
.1*2
TBI
.38
75B
TUT
73B
II
III
IV
XXX
XXX
. XXX
XXX
XXX
XXX
XXX
XXX
XXX
-.01
.31
735
-.09
.02
.15
.32
.17
-.03
M3
73?
785
V
VII
VIII
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
.63
.b2
191
Table 2U. Total animal transect data.
Microhabitats
Animals
Mammals
Deer
Antelope
Cottontail rabbit
Jack Rabbit
Coyote
Squirrel
Gray fox
Reptiles
Lizard (collared)
Lizard (striped)
Snake
Horn toad
Other lizards
Large Insects
Bug
Fly
Bee
Beetle
Grasshopper
Butterfly
Moth
Dragon fly
Cicala
Snails
Birds
ttawk, night
Buzzard, Vulture
Raven
Crow
Jay
Dove
Says Phoebe
Flycatcher
Mockingbird
Meadowlark
Sparrow, Vesper
Sparrow, Brown
2
1
3
2
1
2
1
6
U
1
1
2
1
2
3
1
1
1
1
11
2
1
1
2
1
1
2
1
7
2
11
2
£
1
1
1
1
7
5
1
2
30
1
2
5
17
1
1
20
1
1
1
1
3
1
1
17
2
21
13
7
3
13
U7
5>2
1
6
1
1
U
8
1
7
13
3
23
6
U
<?
3
3
2
2
19
6
6
Hi
75
33
195
Table 2U# Total animal transect data—Continued
Animals
"T
2
Microhabitats
3
E
5
7
5"
Birds (Continued)
Barn Swallow
1
Cliff Swallow
U
Other Hawks
1
2
Red Tail Hawk
3
1
Sparrow Hawk
3
Towee
1
Black and White Warbler
3
Speedbird
1
1
1
Towns Tanager
1
1
Thrashers
k
Peewee
1
3
Blackbird
3
3
Owls
1
Orioles
3
Plain Titmouse
6
Kingbird
3
1
Other and Unknown
26
5
25
11
10
h9
196
Table 25. Total animal transect data by density per square mile.
Animals
Mammals
Deer
Antelope
Cottontail rabbit
Jack Rabbit
Coyote
Squirrel
Gray fox
Reptiles
Lizard (collared)
Lizard (striped)
Snake
Horn toad
Other lizards
Large Insects
Bug
Fly
Bee
Beetle
Grasshopper
Butterfly
Moth
Dragon fly
Cicala
Snails
Birds
Hawk, night
Buzzard, Vulture
Raven
Crow
Jay
Dove
Says Phoebe
Flycatcher
Mockingbird
Meadowlark
Sparrow, Vesper
Sparrow, Brown
T
jT
Microhabitats
jT
TT
l.U
.7
2.2
jT
.1
1.2
.6
l.U
.7
6.9
.7
6.9
9.1
10.8
7.2
.6
1.2
3.6
5.U
.3
.3
.6
.3
.9
.3
.3
.7
.6
1.2
.3
.3
l.U
.6
U8.6
1.8
8.0
3.6
1.6
.3
.3
.1
2.0
.3
.3
.U
.U
.3
.3
2.7
.9
.9
2.0
.7
.7
5.1
3.6
.7
l.U
21.7
.7
l.U
3.6
12.3
.7
.7
1U.5
.6
.6
10.3
6.9
1.8
9.1
6.9
6.9
6.9
9.1
20.8
1.2
12.7
7.8
U.2
1.8
7.8
28.5
31.5
7.2
1U.U
1.8
12.6
U.3
1.0
7.5
2.0
1.3
1.6
10.9
U.8
197
Table 25. Total animal transect data by density per square mileContinued
Animals
1
Birds (Continued)
Barn Swallow
Cliff Swallow
Other Hawks
.7
Red Tail Hawk
Sparrow Hawk
Towee
.7
Black and White Warbler
Speedbird
.7
Towns Tanager
.7
Thrashers
Peewee
Blackbird
Owls
Orioles
Plain Titmouse
Kingbird
Other and Unknown
18.8
2
Microhabitats
3
U
$
7
^
.1
.6
.6
.3
27.3
#U
.6
.6
.1
.6
.6
,6
.1*
.1
1.8
10.8
3U.7
1.8
15.1
19.9
.3
3.3
7.1
198
was .1U5 and r had to be greater than ,28k or less than
-.28U to be significant at the .05 level. Since zone VIII is a con­
tinuation of zone IV, it is not a major surprise that the two zones
correlate sufficiently as to be described as essentially the same zone.
Using the r^ value both II and IV explain approximately 72% of the
variability of each other.
What is interesting is that unlike the floral microhabitats —
zones I-VII do not correlate with each other sufficiently that one
could claim that any combination of them are one microhabitat. Thus,
one is left in the position of having four floral microhabitats and
seven faunal microhabitats. This difference should have settlement
dispersion consequences. Namely, that during periods of hunting and
gathering economies when a greater dependence upon hunting was neces­
sary, there should be a greater dispersion of sites across the micro­
habitats•
Dick Hevly directed a hunting and trapping expedition which
took place between September 3-6 and 19-20. Both vertebrates and in­
vertebrates were collected from three areas. Habitat 1 was zones IV
and Vj habitat 2 was zone VII and zone III; and habitat 3 was zones
I and II. His report is included as an appendix. Two sets of results
from the vertebrate survey are relevant. First, the similarity co­
efficient shows that the three habitats are distinct which agrees with
the transect results. Second, since the animals were trapped and
weighed it is possible to find the amount of vertebrate biomass that
each of Hevly's habitats is capable of supporting. Habitat 1, the
199
pinyon juniper woodland, had six species trapped which were distributed
.091 grams per square meter of herbivores and .003 grams per square
meter of carnivores. Habitat 2, the grasslands, contained 11 species
which were distributed .327 grams per square meter to herbivores and
•033 grams per square meter to carnivores. The third habitat, the
juniper savanna, contained six trapped species which were distributed
.102 grams per square meter to herbivores and ,00k grams per square
meter to carnivores. The invertebrate survey showed for habitat 1,
17 species, .025 grams per square mile of herbivores, .01 grams per
square miles of carnivores; for habitat 2, 23 species, 1.05 grams per
square mile of herbivores, and .Of? grams per square meter of carni­
vores; and for habitat 3, 16 species of which .95 grams per square
meter were herbivores and .05 grams per square meter were carnivores.
Finally, it should be noted that for invertebrates that the grassland
and pinyon juniper woodland are easily distinguished from each other
but both share a compliment of species with the juniper savanna.
Thus to summarize the ecological data up to this point, there
are four floral microhabitats and seven faunal microhabitats on the
basis of quadrant and transect data. The hunting and trapping data
show clear demarcation of the three tested habitats for vertebrates
but similarity of one habitat to two distinct habitats for inverte­
brates.
Stage 6
In order to determine the potential resources, the size of the
standing crop was determined. Each of the one meter quadrants whose
200
species tabulations make up part of Table 20, were clipped during
stage U, and a sample of the species making up the 10 meter quadrants
were also clipped. These clippings were sent to Northern Arizona
University where their weights by genera per quadrant per zone were
measured under the direction of Dick Hevly, The results at the genera
specific level are on permanent file with Dick Hevly and will not be
reproduced here. The summation of the floral results are the following.
Habitat
Habitat
Habitat
Habitat
Habitat
Habitat
1
2
3
U
$
7
70.7500
36.9900
26.6060
2l>.2020
l\2.U6£0
62.3U6
±
±
±
±
±
10.2971
2.6608
11.8317
9.9155
12.6035
7.8297
g/m2
g/m2
g/m2
g/m2
g/m2
g/m2
Adding the results of the vertebrate and invertebrate survey
to the floral standing crop, it is possible to determine the total
standing crop for each zone. These are in order from habitat 1 to
habitat 7 — 71.856 g/m2, 38.096 g/m2, 27.066 g/m2, 2U.556 g/m2,
U2.819 g/m2, 62.806 g/m2. In no zone is the faunal biomass more than
2.9$ of the total biomass and it averages for all zones as 1,5% of the
total biomass. This indicates that a heavily fauna dependent economy
would be severely limited. In fact, it is even more limiting if one
calculates the relative food values of the faunal biomass to the floral
biomass. Using the U kcal/g for floral biomass from Odum (1966) and
the 2.16 kcal/g for faunal biomass derived from food composition
tables, one finds that the relative food value of the fauna is only
8% of the flora.
Prom the above one would rank the ecological zones from highest
to lowest carrying capacity 1, 7, 5, 2, 3, H. However, this is
201
somewhat misleading. The size of the standing crop influences the
capacity to produce but it is not the capacity to produce. It is anal­
ogous to capital in a bank. The capital influences how much is pro­
duced but the actual production is the result of capital and the
interest. The productivity is the amount of renewable growth similar
to the interest payments. As long as the capital or carrying capacity
stays the same one may drain off interest payments or productivity
amounts without affecting the capital or carrying capacity. Similar
strictures may be suggested for subsistence economies based on carry­
ing capacity as may be suggested to the banker who is looking for
long-term gains with minimum risk, i.e., don't dip into your capital.
In order to determine the productivity of the potential microhabitats, the same areas that were originally clipped, the 1 meter
quadrants were reclipped one month later. These second sets of clip­
pings were also sent to Northern Arizona University where they were
weighed by genera per quadrant per zone. The genera specific results
of this second set of clippings is also being kept by Dr. Hevly on
permanent file. The results were:
mlicrohabitat
microhabitat
microhabitat
microhabitat
microhabitat
microhabitat
1
2
3
h
5
7
10.0800
12.1*000
Hi.6600
7.1800
2.11*00
22.700
± 2.1513 g/m2
2,171x6 g/m2
± 2.3986 g/m2
± 1*.221*7 g/m2
± 0.361*0 g/m2
i 13.731*0 g/m2
-
It is important here to note that the productivity figures do
not exactly correspond to the carrying capacity figures. In other
words, because zone 1 has the largest standing crop does not mean it
202
has the largest productivity. Zone 7 has the largest productivity.
Unfortunately, the study was not in the field long enough to gather
data on animal productivity.
Stage 7
In order to estimate the amount of production possible from
agriculture, three plots of corn were planted. Two were planted in
microhabitat 7 and one in microhabitat U. One of the two plots in
Microhabitat 7 was located on "dry" land near the Gurley site. By dry
I mean its only source of water was rainfall and runoff. The other
was located by a water filled irrigation ditch. In each of these
sample plots the same method of planting was used. The grass was
cleared for an area of three feet in circumference around each hole
in which the corn was to be planted. Then a one foot diameter hole
was dug about 6 inches in depth. Into each hole was put 15-20 kernals
of variagated, red, green, and yellow Hopi corn. In each of the micro­
habitat 7 plots, five holes were dug and around one hole a protective
screening was placed. Each hole was watered and then covered.
The third plot of corn was planted in Mrs. Carter's garden
which is in zone U. Here two half rows of corn were planted by pushing
the corn kernals into the turned soil. Mrs. Carter watered as well as
weeded this plot.
The results of this experiment were at best ambiguous. In the
habitat 7 plot near the irrigation ditch no corn whatsoever grew. In
the "dry" habitat 7 plot only one corn plant grew.
203
The plot which was grown in Mrs. Carter's garden resulted in a
full crop producing approximately the same amount of corn as the modern
species which were being grown both in the garden and surrounding area.
Calculating then solely on the basis of modern conditions for the
county and using food composition it is possible to produce 2%.h3 g/m?
of corn kernals which is equivalent to 91.29 kcal/m^. This must be
considered as productivity since corn is an annual plant. Comparing
the corn productivity value with the total natural floral productivity
value of the most productive microhabitat, microhabitat 7> it is im­
portant to note that 91.29 kcal/m2 is only 1.01 kcal greater than the
90.28 kcal/m^ 0f the natural flora. This clearly raises the question
of why do agriculture? The answer may lie in the relative expenditure
of energy necessary to get the 90 kcal under different forms of sub­
sistence or in the fact that not all of the floral productivity is
humanly consumable. What it does show is that the change from gather­
ing to agriculture is not a major quantum leap and thus brings into
question Childe's concept of the agricultural revolution.
Stage 8
Stage 8 is an attempt to relate the modern environment to past
environments. As Jim Schoenwetter (personal communication) has pointed
out this is the most difficult and tenuous part of palynology. This
is because it is impossible accurately to determine quantitatively the
environment from the pollen rain. It is complicated due to six factors
which Butzer (19610 points out. First, there is differential repre­
sentation of pollen due to differing surface receptivity and
20U
differential preservation of pollen under different environments.
Second, there may be over or under-representation of species due to
small or excessive pollen production, insect pollination or easily de­
composed pollen. Third, there is documentation of long distance
transport of pollen by the wind. Distances sometimes exceed 100 km.
Fourth, there is possible redeposition of pollen from older sediments.
Fifth, pollen is transported by streams. Sixth, pollen sequences are
often truncated or incomplete due to fire destruction of sections and
interruptions or lateral distortion in the sedimentation process.
In order to determine quantitatively the previous biomasses
from the present biomass two parameters need to be determined. First,
one needs to find at what time in the past the present biomass existed.
This gives a base line. Second, one needs to determine the amount of
fluctuation around this base line. Several assumptions are necessary.
First and most important is that if one has modern pollen rain being
equivalent to past pollen rain, one assumes that the biomass at the
two times are equal. Second, changes in external factors such as
climate affect the microhabitats approximately equally.
Dick Hevly has constructed pollen spectra from floors of sites
in the Four Mile, Shumway, and Hay Hollow Wash archaeological areas
arranged in chronological order (Hevly 1961*)• Figure 26 is a copy of
his spectra which has been modified to show which areas of the spectra
are most similar to the modern day environment. These periods are
A.D. 275-3^0, A.D. 1100-1200, and A.D. 1350-1U00. These are the base
line figures on which will be mapped the modern environment for com­
parison.
205
In order to determine the amount of fluctuation two factors
will have to be considered. First, Hevly concludes in his dissertation
on the basis of a wide group of pollen spectra that:
The fluctuations do not appear to be random or significant
variation of aboreal pollen but can be shown to be more or
less synchronous over a wide area. Such changes may repre­
sent fluctuation of vegetation zones by as much as £00'
suggesting that movement of zones similar to that documented
historically in southern Arizona may have been occurring for
many millenia (Hevly 196U: 113-lU).
This 5>00! factor luckily happens to be the difference in alti­
tude between both zones 7 and 3 and zone 1. This difference then may
be considered the maximum difference not for two zones but for any one
zone through time. It is now possible to put the parameters on re­
source change through time. Using zone 1 and zone 3 the change in
carrying capacity limit is UJU•lJUUO g/m^ and in productivity is -It.£8
g/m^. If one uses zones 1 and 7 the change in carrying capacity over
time is 8.U0U g/m^ and in productivity is -12.62 g/m2.
Figure 27 is the pinyon pine profile from the valley which
Hevly considers to be the most sensitive independent (i.e., the pinyon
pine production is minimally affected by man) monitor of moisture and
temperature. Setting the modem day environment at A.D. 300 from the
combined pollen chart as above, one may reasonably suggest that in
800 years the peak of the pinyon pollen, the carrying capacity in­
creased a maximum of UU.lUUO g/m^ and in productivity -12.62 g/m^.
206
r
ir
ARBOREAL POUEN
• NON-ARBOREAL POLLEN •
^ECONOMIC POLLEN-|
T/ T £
,, /'* /
/
/
f
i
.
.
f
'
f
*'/«"
• .? t/ 6
* »•/
*v/ •», <7»/ f•?/' i©f o Jtidiparwi >•-/*»•''
— -/I Pmut
•J
V 0/0/
- «t«n%
UVMI
RrM
LZ£2
tCiUi OH
nRO£l
lmit
ISS332UUBEaa
Figure 26. The relationship between modern pollen and pollen
spectra from floors of sites in the Four Mile,
Shumway and Hay Hollow areas.
Jll'IOI
I008C
100 AO
300
500
700
900
1100
1300
1500
O
O
O
O
O
%
PINYON
O
O
O
O
O
PINE
7. Pollen profile from the Hay Hollow valley.
CHAPTER £
TESTS OF HYPOTHESES
To what extent do the data support the hypotheses? In a sense,
if the data support the hypotheses, they will also support the model.
This is analogous to the way the positive test of a series of theories
supports a paradigm (Kuhn 1968) Just as the theories have been deduced
from the paradigm's assumptions, the hypotheses have been formally de­
duced from the model's assumptions. Thus, the question which this
chapter will attempt to answer is to what extent do the data support
the hypotheses and the model?
First Hypothesis
The original formulation of the first hypothesis stated that
the development of population in marginal resource zones is a function
of optimal zone population exploitation. After the formal deduction
it was found necessary to restate it as follows: the development of
the population in the marginal zones is a function of the development
of the population in the optimal zones and a function of the total
population. The essential difference between the two statements of
the hypothesis is the addition of the variable of total population.
In order to test the first hypothesis, two independent tests were made.
The first utilizes the archaeological population indices from the Hay
208
209
Hollow valley, while the second estimates actual carrying capacity
values. The results of both must be compared to the predictions of
the model.
The graphic operationalization of the original first hypothe­
sis and the test implications for the population indices were discussed
in Chapter 2 in the section entitled "Migration and Population Develop­
ment." It was shown there that the predicted population curves by
zone would be similar to Figure 8 , if the resource curves were con­
stant over time. If, however, the resource curves should drop at a
particular point in the temporal sequence, the resulting carrying
capacity decrease would result in larger out-migration from the system
or increased mortality. The latter possibility was diagrammed in
Figure 9.
Solely on the basis of the density of the present flora and
the proximity to water resources, one would expect the resource curve
of zone 7 to be the highest. This would reflect the highest carrying
capacity and would deserve being labeled the optimal zone of the study
universe. The other zones may be labeled marginal. Figure 28 shows
the number of habitation rooms in the central 100% sample. The general
similarity of the shapes of the curves in Figures 8, 9,
and 28 are
clear. One may use the total number of sites, Figure 29, as an index
of population. This index shows clearly a greater similarity to
Figure 9 than to Figure 8.
Two conclusions should be drawn from
these comparisons. First, the data substantiate the hypothesis insofar
as the actual curves follow the predicted curves with the predicted
NUMBER
H*
<3
3
ro
CO
o*
®
•1
o
300
400
500
rr
oHc+
fu
600C*
H*
O
3
•1
0 m 7001
CO
800
?
o
(D
3
«+
900-
E
8
1000-
CO
tj
1
M
I 100
I 200 -i
1300
012
/
HABITATION ROOMS
NUMBER
- N W A OI
o o o oo o
- J . I
I
I
I
I
o
o
OF
SITES
OI
o
i\>
o.
o
_JL_
.. III...
100
ro
vo
r ?
I i
1 i
200
IO h3
C^"
P>
vn o
300-
= =•<<<
CO M
400
J 1
(O* c
co n>
• 1
o
H»
CO
H*
C^
500-
m
600
CI)
700
s-
800
a
CO
(D
S
P.
O*
o
dP*
900
I 000
I 100
1200
1300
1400
J>
o
112
h
w
OI
o
mi
212
relationship between the optimal and marginal zones. Second, these
results indicate that the change in the population distribution is
caused by a decrease in the carrying capacity after A.D. 11^0 or, in
the terms of the model, a decrease in the resource curves.
This decrease has been explained in an article by Schoenwetter
and Dittert (1968) as the result of a change in effective moisture
caused by a change in the seasonal rainfall pattern at approximately
this date. Hevly (1970) explains this decrease in resources with
multiple factors including (l) a change in rainfall pattern from sum­
mer dominant to winter dominant or to a biseasonal pattern, and (2) a
change in the temperature pattern from warm to cool.
It is clear, however, that the changing resource curves or
carrying capacity should be verified independently of the model and the
population indices of the valley. As was discussed under stage 8 in
Chapter 3, a series of pollen analyses were undertaken by Hevly. The
pinyon pollen which correlated to a high degree with agricultural and
gathered economic pollens is the most sensitive monitor of moisture
and temperature. Since the change in pinyon pollen is a relative index
of the change in the resource curves (Fig. 27) the pinyon pollen curve
shows independently that there is a drop in the resource curves after
A.D. ll£0.
The second test of the first hypothesis involves the estimation
of carrying capacity and population values from zonal resource data.
On the basis of predicted migration pattern (Fig. 7)j one would expect
that the zonal ordering of the population sizes would follow the
213
amounts of zonal resources when both resources and population are at
a maximum. In 1969, before the ecological data were collected by
Hevly and Zubrow, an attempt at estimating carrying capacity was made.
The area of each ecological zone was calculated from aerial photo­
graphs and maps. Somewhat arbitrarily, the amounts of dry grams of
biomass produced were taken from Odum's values for agriculture and
arid areas, and it was assumed on the basis of the United Nations
world sample that 2500 kilocalories per day were necessary and suffi­
cient to maintain an average individual in the population. Consumption
was estimated at
of the total produced biomass. This was also an
arbitrary but reasonable estimate. As long as one is interested in
the relative ordering of the zonal population estimates, rather than
the actual amounts of population, the size of the consumption figure
is irrelevant if it is applied equally across space and time. Exam­
ining Table 26, one would expect the population size to decrease by
zones in the following order: zones 7, 5, 3> U, 2, 1.
Since the areal figures of Table 26 include both land covered
in the central or 100$! and both peripheral or 2$% samples, one must
use Figure 29 to test the validity of the simulated zone ordering.
Turning to Figure 29, then, one gets the following actual distribution
of sites by zone when resources and population are at a maximum: zones
7» 2, 5, 3» U, 1. Only one zone is out of the expected sequence of
decreasing population sizes, zone 2.
There are several possible reasons for this sequence discrep­
ancy which also point out some of the simplifying assumptions in this
Table 26. Maximal carrying capacity values derived from Odum's esti­
mates of biomass.
Zones
HI
TTI
iv
Area of the zone
in mi.2
1.17
2.15
.92
1.U3
Biomass in g/m2/
day
.3
.2
.5
U.O
U.O
U.O
Kcal/g biomass
Population based
on 5% consumption
and 2J?00 kcal per
person
70
80
190
v
vTT
2.81;
9.92
.U
1.0
2.0
U.O
U.O
U.O
120
290
U110
21*
original estimation. First, I had assumed Odum's values were reason­
able. Second, I had assumed that the sites are located in the same
zone as they utilize. Third, I had assumed the geographic size of the
zones remained constant over time. Fourth, I had not attempted to
define multiple zone utilization per site.
It is now possible to relax the first assumption. Table 27
presents data based on the ecological survey by Hevly and Zubrow. The
first part of the table includes the area of the zones in square miles,
the floral standing crop, the floral productivity, the vertebrate
fauna standing crop, the invertebrate fauna standing crop, and the
total known biomass all in grams per square meter per day. The reason
I have labeled the row, total known biomass, rather than total biomass,
is that it was impossible to get vertebrate and invertebrate produc­
tivity figures because of the lack of time depth in the survey. The
second part of Table 27 presents the number of people that could be
supported using the floral standing crop, the floral productivity, the
vertebrate standing crop, the invertebrate standing crop, and the
total known biomass. It is interesting to note the size of the dis­
crepancy between the amount of population capable of being supported
by invertebrates in comparison to vertebrates. On the average, the
invertebrates are capable of supporting 10.1 times as many people as
the vertebrates. It would seem reasonable to suggest that the role
of invertebrates has been often underestimated.
On the basis of Table 27 (using the row entitled "population
based on total known resources") one would expect the population sizes
216
Table 27. Maximal carrying capacity values using Zubrow-Hevly ecolo­
gical data.
Zones
Zonal Distributions
Ar©a of th©
zones in mi.1.17
II
III
IV
V
VII
2.15
.92
1.1*3
2.8U
9.92
Floral standing
crop in g/m2/
day
2.36
1.23
.89
.81
1.U2
2.08
Floral produc­
tivity in g/mV
day
,3h
.111
.U9
,2k
.07
.76
.053
.180
,0li7
.0U7
.180
.26
.26
1.357
1.797
It.120
Vertebrate stand­
ing crop in g/m^/
day
.053
Invertebrate
standing crop in
g/m2/day
1.0
1.0
1.1
Total known biomass in g/m^/
day
3.753
2.693
2.660
Population at
1.1
Consumption
Population based
on floral stand­
ing crop
572
5U9
169
239
833
U272
Population based
on floral pro­
ductivity
8U
18U
93
71
U2
1555
Population based
on vertebrate
standing crop
13
2U
3h
lU
28
370
Population based
on invertebrate
standing crop
2^2
UU5
210
77
153
2261
Population based
on total known
biomass
911
1202
50U
U01
1056
8U58
217
v
to decrease by zones in the following order: zone 7 with the largest
population, zone 2, zone 5j zone 1, zone 3, zone it. Comparing this
with the sequence of actual distribution of sites by zone when re­
sources and population are at a maximum (Fig. 29), once again one zone is
out of sequence, zone 1. Previously, Odum's values identified Zone 2.
This discrepancy is expected to observed values for zone 1 and
zone 2 may be partially explained by the change in subsistence patterns.
Zones 1 and 2, because of the steepness of the slope and their location
on the point of the mountain, would provide the most difficulty in the
use of the major sources of water. Since agriculture became the pri­
mary form of subsistence after A.D. 7^0, this discrepancy may be a
result of the problem of access to water resources.
A second reason for the discrepancy is that all four types of
resources, floral standing crop, floral productivity, vertebrate stand­
ing crop, and invertebrate standing crop, are not equivalently ordered
by size across the zones. For example, although zone 7 has the second
highest floral standing crop, it is tied with zone 3 for the third
highest vertebrate standing crop. Table 28 shows the cross zonal
ranking by size of the four types of resources.
Table 28. Cross-zonal ranking of resources.
Standing
Crops
I
II
Zones
Floral
Floral productivity
Vertebrate
Invertebrate
1
a
3.5
3.5
a
3
3.5
3.5
III
5
2
1.5
1.5
IV
V
6
5
5.5
5.5
3
6
5.5
5.5
VII
2
1
1.5
1.5
218
The rankings range from 1, the largest biomass, to 6, the
smallest. In cases of equal biomasses the ranks have been averaged.
Computing Kendall's rank concordance for non-parametric data on the
four types of resources above, one finds a correlation of .72 which is
significant at the .01 level and which explains approximately ^0% of
variance. Since 1.0 is perfect correlation, this indicates a good but
not perfect homogeneity in the importance of the system's cross zonal
resources.
The question which should be answered is whether the site dis­
tribution reflects a particular resource, a combination of resources,
or the entire set of four resources. In order to determine the answer
to this question, the ranked site distribution was correlated with all
possible combination of resources. Table 29 shows the resulting cor­
relation coefficients by "site-resource" combination. The number of
sites was ranked by zone at the time period of maximal resources and
population. Two sets of resource rankings were used. One set was
based on the biomass figures themselvesj the other set, on the biomass
adjusted by area. I used Kendall's concordance as the primary corre­
lating technique, since it allows one to correlate any number of
variables simultaneously. One needs to make no assumptions about the
distribution, and the use of coded rankings circumvents the problems
of unit equality. An underlined coefficient indicates that it is sig­
nificant at the ,0£ level. A coefficient which is underlined twice
indicates significance at the .01 level. Since I was unable to find
any published tables for the levels of significance of Kendall's
Table 29. The cross-zonal relationship between the ranked site distribution and types of resources
Kendall's
concordance
resources not
areally adjusted
Sites and a single resource
Sites and floral stand­
ing crop
Kendall's concor­ Spearman's rho
dance resources
resources not
areally adjusted
areally adjusted
Spearman's rho
resources
areally adjusted
.51
.7U
.09
M9
Sites and floral produc­
tivity
.7h
.80
.U8
.60
Sites and vertebrate
standing crop
.91
.89
.39
.77
Sites and invertebrate
standing crop
.91
.80
.39
.60
Sites, floral standing crop
and floral productivity
,k9
.61
Sites, floral standing crop
and vertebrate standing
crop
.U7
S.
Sites, floral standing crop
and invertebrate standing
crop
.U7
.68
Sites, floral productivity
and vertebrate standing
crop
.52
.75
Sites and two resources
ro
(-»
VO
Table 29. The cross-zonal relationship between the ranked site distribution and types of resourcesContinued
Kendall's
concordance
resources not
areally adjusted
Sites, floral productivity
and invertebrate standing
crop
Sites, vertebrate stand­
ing crop, and invertebrate
standing crop
Kendall's concor­ Spearman's rho
dance resources
resources not
areally adjusted
areally adjusted
.52
.80
.67
.72
Sites, floral standing crop,
floral productivity, and
vertebrate standing crop
.£2
.59
Sites, floral standing crop,
floral productivity, and
invertebrate standing crop
.$2
.6£
Sites, floral standing crop,
vertebrate standing crop,
and invertebrate standing
crop
.^1
.62
Sites, floral productivity,
vertebrate standing crop,
and invertebrate standing
crop
.71
»71
Sites and three resources
Spearman's rho
resources
areally adjusted
Table 29. The cross-zonal relationship between the ranked site distribution and types of resourcesContinued
Kendall's
concordance
resources not
areally adjusted
Kendall's concor­ Spearman's rho
dance resources
resources not
areally adjusted
areally adjusted
Sites and four resources
Sites, floral standing
crop, floral productivity,
vertebrate standing crop,
invertebrate standing
crop
.68
.61
Spearman's rho
resources
areally adjusted
222
concordance for two variables where the number of cases is small, I
also calculated Spearman's who for which appropriate tables were avail­
able.
An examination of the significant correlation coefficients
shows that the highest correlation is between sites, floral produc­
tivity, and invertebrate standing crop.
If one considers all the sig­
nificant correlation coefficients above .70, floral standing crop is
never a resource variable.
On the basis of Table 29 it would be fair
to say that the population distribution appears to be reflecting the
floral productivity, and the vertebrate and invertebrate standing crop.
Before the discussion in the second test of the first hypothe­
sis, I should note under what conditions could the expected rankings
and the observed rankings be isomorphic.
If consumption remained at
5% for all the zones except zone 1 where it dropped to 2%, then the
expected and observed would be isomorphic. This could be a result of
the difficulty in getting access to the resources in zone 1 which is
3>00' above the valley floor.
In summary, I would claim that the data support the first hypo­
thesis in both tests.
In the first test the actual curves followed
the predicted curves with the predicted relationship between the op­
timal and marginal zones.
In the second test, although the zonal
ordering of the expected and actual population was not isomorphic,
there was only a discrepancy for one zone. The probability for the
second hypothesis being tested positively increases since the first
hypothesis has been supported.
223
Second Hypothesis
The second hypothesis is that during periods of resource de­
pletion there will be population aggregation.
Although this hypothesis
has been formally deduced in Chapter 3 it may be worthwhile to describe
verbally how I conceptualize the process happening. If the population
is above the carrying capacity point or at carrying capacity when the
resource curves begin to drop and if access to resources is related to
population size, then one would expect the smaller villages to be de­
populated first.
This would not have to be the actual carrying
capacity, but the utilizeable carrying capacity or the net societal
product.
For example, let us imagine three villages, one with a popula­
tion of 100, one with a population of UO, and one with a population of
20.
If there is a $0% decrease in resources which causes a loss of
population of $0%, the three villages would be 50, 20, and 10.
A
second £0% decrease in resources would result in populations of 2£,
10, and 5. The smallest village would no longer have sufficient man­
power to continue its functions as a village including its subsistence,
religious, and political activities. Thus, the smallest population
would migrate either to one of the other villages or out of the area
of study. If the population migrated to another village there would
be an average of 17-1/2 people per site and if the smallest village
somehow continued to exist there would be 13 people per site.
The
point to be noted here is that if small villages continue, the number
of people per village is smaller than if they do not. Thus, as
22h
resources decrease there will be fewer sites, but relatively more people
living in each site as the small villages become extinct.
I originally tested this hypothesis using the 100$ central
survey data; results appear in Figure 30. The bar graphs represent
the pinyon pollen which is the previously discussed indirect index of
resources. The line is the average number of rooms per site which is
taken to be an index of population aggregation.
During the major
period of resource depletion, from A.D. ll£0 on, the number of rooms
per site increases and then remains quite high. This indicates that
during this period there is a population aggregation.
This conclusion
is justified since the effect of the smaller sites which would have
lowered the average number of rooms per site is not exhibited.
After I formally deduced this hypothesis in Chapter 3, two
additional concepts became relevant. First, it was necessary to
assume for the formal deduction of the hypothesis as stated above
that "ra," the rate of population change, was greater than rb, the
rate of settlement change.
Second, if one relaxes two propositions
by allowing them to stand or be replaced by two alternate propositions,
the deduction generates a more generalized hypothesis.
Namely, if one
allows R1 resources at time 1 to be greater than R2, resources at
time 2, and ra to be greater than rb, to alternate with a second pair
of propositions, R1 less than R2 and ra less than rb, the deduction
shows that population aggregation is an inverse function of resources.
Figure 31 shows the relationship between the climatic index
and all the "New Survey" habitation sites in the central 100??, and
ROOMS
PER
SITE
100 BC
lOOAO
300
500
700
<;
900
1100
1300
1500
o
o
CI
o
o
%
PINYON
0>
o
a
o
PINE
Figure 30. Pinyon pine pollen and the average number of rooms per site
in the 100$ survey sample.
226
% Pinyon Pine
Rooms per Site
Figure 31. Pinyon pine pollen and average number of
rooms per site in the 100$ and both 2$%
samples•
227
both peripheral 2$% surveys.
The only known sites which are excluded
are those in the Longacre survey, Table E>.
It is interesting to note
how similar are the shapes of the average rooms per site curves in
Figure 30 and Figure 31. Figure 31 supports the hypothesis for the
same reasons that were mentioned above with regard to Figure 30.
Since the original hypothesis requires that ra be greater than rb
during the resource depletion, I calculated the average ra and rb
values for the post A,D. 1100 period. The values of ra and rb are .U9
and .37 respectively. This is the exact relationship which is neces­
sary for the hypothesis to be valid.
Turning to the more generalized hypothesis which states that
population aggregation is an inverse function of resources, one would
expect the relationship to be similar to the one illustrated in Figure
32.
This could be labeled the predicted relationship for the general­
ized hypothesis.
The two variables are an index of resources, the
percentage of pinyon pine, and an index of population aggregation, the
average number of rooms per site.
If one compares Figures 32 and 33,
the two diagrams show similarity but are not perfectly isomorphic.
This is partially due to the fact that the resource data are limited
and do not exist for the period prior to A.D. 5>00.
Secondly, there
seems to be a time lag factor between A.D. 900-1100. There is a minor
increase in average rooms per site when there should be a decrease.
However, the reality of the inverse relationship is indicated by
findings covering the period from A.D. 1100-1300, when the resource
index drops from above 80% to below $0% which is also the period when
the average number of rooms per site increases from 0.9 to 22.7
228
-70
40-
-40
20-
c
o
M
V0
c
o
Q.
£
V)
E
o
ce
o-
-20 fcS
-10
o
o
•-
o
o
M
o
o
CO
o
o
o
o
o
o
o
o
s
o
o
00
o
o
€K
o
8
o
2
o
o
<N
o
o
n
o
o
Time
ill
%. Pinyon Pine
V* Rooms per Site
Figure 32. The expected relationship between pinyon pine
pollen, an indirect index of resources and the
average of rooms per site.
229
Rooms per Site
IOOH
BC
100-
AD
300-
500©
E
h
700-
900-
1100
1300-
- % Pinyon Pine
% Pinyon Pine
Figure 33.
/A
Rooms per Site
Pinyon pine pollen and average number of rooms for all
sites, the test of the generalized hypothesis.
Figure 3h provides a comparison of the ra and rb values through
time.
This illustration is consistent with the generalized hypothesis.
When the average number of rooms per site is increasing and resources
are decreasing, ra should be greater than rb. When the average number
of rooms per site is decreasing and the resources are increasing, rb
should be greater than ra.
Periods with increasing average number of
rooms per site are A.D. 100-300, and A.D. 900-1300.
Periods with de­
creasing average number of rooms per site are A.D. 300-900 and 1300-
moo. The average values for ra and rb by time period are shown in
the following table.
Table 30. The survey ra and rb values.
Date
100-300
300-900
900-1300
1300-11*00
Expected
ra>
ra <
ra >
ra
rb
rb
rb
rb
This is what is expected.
ra
rb
5.91
1.2U
1.01
.21
2.62
1.63
.69
.33
Thus, it appears that the data
support both the specific and general hypothesis. However, prior to
A.D. $00 the resource data are non-existent.
Third Hypothesis
The third hypothesis suggests that during periods of resource
depletion there will be spatial aggregation.
In other words, at the
same periods of time that one notes population aggregation, one would
expect to find spatial aggregation. This is the result of the
6.0
1.0
-r
o
Figure 3U.
o
o
T
o
T"
o
T
o
r
O
T
t
o
o
The values of ra and rb through time.
o
232
increasing necessity for the population to utilize areas of optimal
resource production during periods of resource depletion.
First, I calculated the habitation site and room densities as
an index of spatial aggregation as suggested in the formal deduction
of the hypothesis.
Since the resource area is assumed to be constant
over time, ra, the rate of population change must be greater than rc,
the rate of resource area change.
Although the proposition base is
met, Table 31 shows that after A.D. 1100, in all cases except one,
the densities decrease. This indicates that the hypothesis is invalid
using density as a measure of spatial aggregation.
However, as briefly mentioned in Chapter 3* density is not the
most powerful tool available to the archaeologist with which to
measure spatial aggregation. For example, imagine a square mile which
contains five sites.
If the five sites are within f>0 yards of each
other or within 500 yards of each other, the density will be equal.
The densities are equal even though the former case shows far more
spatial aggregation than the latter case.
The nearest neighbor statistic allows one to measure spatial
aggregation whether or not the density is increasing or decreasing.
Thus, the density turns out to be a crude measure of spatial aggre­
gation when compared to the nearest neighbor or mean crowding statis­
tics. Figure 3$ presents the nearest neighbor statistic and the
resource index, percentage pinyon pine.
David Gregory calculated the
curve on habitation sites in the 100)2 central survey area for habi­
tation sites since nearest neighbor analysis is invalid for
233
Table 31.
Densities of the habitation sites and the number of rooms
by zone through time.
Zones
Date
"~I
TE
Til
IV
V
VT~~
Tot.Area
Density of habitation sites - number of sites per square mile
100
200
300
aoo
500
600
700
800
900
1000
1100
1200
1300
lUoo
.85
1.71
1.71
1.71
1.71
.93
.93
.93
.93
2.79
3.26
2.36
1.08
2.17
11.96
10.87
10.87
.70
.70
.70
.70
1.U0
2.10
.70
2.10
3.50
U.20
i.Uo
.70
.70
.35
.70
.70
.35
.35
.35
.35
.70
.70
.50
1.08
1.51
1.51
3.83
U.7U
3.U3
.81
.50
.10
.05
.21
.27
.33
.60
.92
1.25
1.08
3.25
3.85
3.0a
.5a
.33
.11
Density of habitation rooms - number of rooms r>er square mile
100
200
300
hoo
500
600
700
800
900
1000
1100
1200
1300
1U00
12.82
55.56
55.56
55.56
55.56
.93
.93
.93
3.26
2.79
6.98
16. Ih
15.81
9.78
16.30
U5.65
39.13
39.13
U.90
U.90
U.90
U.90
15.38
32.87
17.U8
26.57
76.22
61.5U
2.80
10.U9
10. U9
l.Ul
5.63
5.63
h.25
U.25
a.25
a.25
3.17
3.17
.70
a.33
6.15
8.27
10.38
16.73
2a. 90
3a.88
29.7a
18.55
2.62
.22
2.06
a.77
a.66
6.70
8.79
8.52
8.08
ia.6o
23.71
27.a6
16.22
10.80
2.22
NEAREST
IOOSC
NEIGHBOR
~o
>
100 AD
300
500
700
SOO
1100
1300
1500
o
w
OI
%
Figure 3$,
o>
PINYON
CD
(0
o
PINE
Pinyon pine pollen and the values of the nearest neighbor
statistic.
23*
discontinuous space. The two peripheral surveys, of course, contain
large quantities of discontinuous space.
The nearest neighbor statistic is an index of the continuum
between perfect spatial dispersion and aggregation.
Perfect aggrega­
tion, a single settlement, is 0.0; while random distribution is 1.0
on the scale. From Figure 3!? it is clear that after A.D. 700 the
spatial relationship between the sites is one of aggregation whenever
the pinyon pollen indeix is below £0%. Thus, the data show spatial
aggregation not with increasing density as predicted, but decreasing
density.
Fourth Hypothesis
The fourth hypothesis states that residential area should also
decrease during periods of resource depletion.
The rationale behind
this hypothesis is that whenever the population is above the resource
curves, this represents insufficient resources to meet the demand.
Until this demand is relaxed by out-migration or increased mortality,
a set of resource priorities will need to be established.
For example,
under these non-relaxed conditions a village should allocate more of
its labor force to subsistence tasks than to the building of large
residential structures. Thus, one would expect that residential area
will decrease during periods of resource depletion due to the priority
of the expenditure of resources on subsistence.
Although it is pos­
sible that residential area would remain stable, the smaller replace­
ment of outmoded or deteriorating structures would make stability
improbable.
The data in Figure 36 represent a sample of the 100#
R 0 0 IV!
—
o
o
ro
O
01
o
4*
o
f
•
ci
o
•
a>
o
t
o
SI Z E
(0
a
o
o
o
o
t
•
o
ro
o
O!
o
o
ci
o
IOOBC
100 AD i
300
500
700
SOO 1100 1300
1500
o
o
_
o
ro
o
w
o
o
,o
%
1
CI
o
o
o
o
PINYON
•
03
o
1
<0
o
o
o
PINE
Figure 36. Pinyon pine pollen and average room size#
to
w
Ox
237
survey chosen by time and environmental zone. The resource curve is
the same as the two previous diagrams. There is a close correlation
between residential areas as measured by average room size and the
resource curve. The results show a clear decrease in residential
area as resources decrease.
The question with which this chapter began was to what extent
do the data support the hypotheses?
The answer is that for the four
formally deduced hypotheses the data support the hypotheses. However,
it is important to note that although the data support the third
hypothesis if refined measures of analysis are used, the original
"density-based" analysis provided a negative test of the hypothesis.
CHAPTER 6
THE SIMULATION MODEL
In this study a model of carrying capacity as a dynamic equi­
librium system has been developed. From an expanded version of this
model, hypotheses were deduced. Data were gathered and the hypotheses
were tested positively.
It is possible to use the model in a second manner.
Rather
than develop hypotheses, one may use a form of the model to replicate
or simulate reality.
In order to accomplish this replication, one
uses the theoretical formulations and the interrelationships of the
variables stated by the propositions of the model.
The expanded model
in its most developed form, the systemic model version U, is the equi­
valent of the simulation model.
The simulation model has been examined in general and com­
pletely flow-charted in the discussion of the expanded model.
complete reiteration of this discussion would be redundant.
A
The
listing of the program of the simulation model has summary documenta­
tion and explanation included within it (Appendix!). Each of the
major components of the model has an explanation which precedes it.
Interspersed with the instructions of the program are comments between
lines of asterisks which explain what each section of the program does.
238
239
The Modification of Space:
The Simulation Map
The simulation makes use of a map of the Hay Hollow valley as
noted later in the documentation.
This map, which is actually repre­
sented as a 25 x 25 matrix, in the computer is derived from Figure 17.
Onto Figure 17, a 625 square grid system was overlaid so that one
boundary corresponded to the western segment of the county road. Each
square of the grid system was labeled according to microhabitat.
In
cases of multiple microhabitats in a particular grid square, the square
was labeled with the predominate microhabitat. This 25 x 25 matrix is
used in two ways in the model. First, the settlement locators locate
sites to a unique square within the grid defined by the square's
Cartesian coordinates.
Second, the settlement locators use the micro­
habitat labels of the grid squares to determine the validity of the
location of a potential "budded" settlement. In other words, it
examines the microhabitat label of the new location and a series of
alternative decisions are made on the basis of the priorities built
into the system and the particular configuration of circumstances in­
volved in the development of the newly budded settlement.
For example,
after a village is budded, the microhabitat in which it will be located
will be decided upon on the basis of the best population-to-resource
and net societal-product ratio.
If the settlement locator chooses a
pair of coordinates whose label does not correspond to this micro­
habitat, it will recalculate a new pair of coordinates until the
appropriate label match is reached.
2ho
The microhabitat distribution for the purposes of the simula­
tion is shown in Figure 37. This is similar to but not exactly
equivalent to Figure 17.
It differs in three ways. First, the borders
of the microhabitats now correspond with the nearest grid square
boundaries.
Second, some of the area immediately next to the micro-
habitat boundaries, although labeled one microhabitat, may contain
more than one microhabitat.
Third, the area which the simulated map
covers is not the total area which the fold out map (Fig. 17) covers.
Operating Characteristics
The simulation was run on a CDC 62*00 eight times in order to
examine some of the operating characteristics of the model.
of the birth rate variables were set at 3.0 and U.O.
and 1*00$ increase in the population per 100 years.
The values
This is a 300$
The death rate was
set at 1.0 or a l£0$ decrease in the population per 100 years. The
migration velocity was given values of 1.0 and 2.0. Simulations which
use the above variable values as well as the MacArthur tk and the in­
ductive probability longevity alternatives were run. The maximum
settlement population was set at 1*00.
The choice of these particular values was partially determined
by ethnographic analogy and partially inductively from the archaeolo­
gical record. After examining the range of values for birth, death,
and migration rates which occur ethnographically and ethnohistorically
in the Puebloan Southwest (Zubrow 1969), values within the range of
variation for observed reality were chosen. For example, Zuni (the
2U1
J.J I
L
wM
WMll:
2«n« ||
Figure 37. Simulation map
4
2onc VII
2ont IV
21*2
nearest Pueblo to the Hay Hollow valley) shows net growth rates of 2.2
between 1760 and i860 and 3.6 between i860 and I960.
Acoma shows
growth rates of-2.0 and 3.U for the same periods (Zubrow 1969).
Table 32 shows the various combinations of values under which
the simulation model was run.
In all cases the simulation was begun
at A.D. 200 with a single settlement of !>0 persons located at coordi­
nates (18, 18) which corresponds to a real site location with a
settlement which existed at that time. The resources and net societal
product values were based upon floral standing crop and productivity
data discussed above in Chapter I4..
Obviously, this series of simulation runs is not a complete
analysis, but given the limitations of time and money, it was suffi­
cient to demonstrate the heuristic value of the simulation model. For
a more complete analysis, single and multiple initial villages located
in all microhabitats in different locations should be used.
By initial
villages I mean the villages in existence at A.D. 200 when the simula­
tion begins.
Greater variation in the values of the birth, death, and
migration velocity rates should be examined.
There should also be
simulation runs using different values of resource growth, consumption,
and settlement maximum, as well as floral and faunal standing crop and
productivity figures used in various combinations and proportions.
For the purposes of the present study summary results will be
used in order not to burden the reader with the large number of tables
which trace the changing population of each settlement through time
and through space as populations bud and contract in each of the eight
2U3
Table 32. The simulation:
Initial
Variables
initial variable values.
Simulation
1
2
3
U
i
6
7
8
Birth rate
3.0
3.0
3.0
3.0
U.o
U.o
U.o
U.o
Death rate
1.5
1.5
1.5
1.5
1.5
1.5
1.5
1.5
Migration velocity
1.0
1.0
2.0
2.0
1.0
1.0
2.0
2.0
Longevity alterna­
tives*
I
tk
I
tk
I
tk
I
tk
Settlement maximum
Uoo
Uoo
Uoo
1*00
Uoo
UOO
Uoo
Uoo
Resource growth
.05
.05
.05
.05
.05
.05
.05
.05
Consumption
.05
.05
.05
.05
.05
.05
.05
.05
* I » Inductive random longevity alternative,
tk = MacArthur's tk longevity alternative.
2 UU
simulations. Figures 38 through k$ show the total population by microhabitat by time interval as generated by the various simulation runs.
Figures U6 through £3 show the total population and total number of
sites by time period as generated by the simulations.
Several conclusions may be drawn from an examination of these
figures. First, a birth rate of 3.0 produces a population peak or
maximum population at approximately A.D. 1000 to A.D. 1100 (Figs. 38-1*1
and by Figs. U6-U9).
A birth rate of U.O produces a much earlier large
increase in population (Figs. U2and Figs. 5>0-5>3).
The major period
of increase is approximately A,D. U00-700. The population quickly
reaches either its maximum or a high plateau value which it maintains
until approximately A.D. 1100 with limited variations.
Second, the
earlier population increase and the longer maintenance of the larger
population caused by the U.O birth rate occur both in the total popu­
lation and the total population by microhabitat analyses.
Third, the
U.O birth rate is associated with an earlier filling or development of
population in the marginal microhabitats. With a U.O birth rate the
marginal zones begin to fill at A.D. 600-700 (Figs. U2-U5), with a 3.0
birth rate the marginal zones begin to fill at A.D. 900-1100 (Figs. 38-
Ul). However, the contraction of the population into the optimal zone
takes place at approximately the same time (A.D. 1100) using either
birth rate. Fourth, the U.O birth rate emphasizes the decrease in
population which occurs after the A.D. U00-700 large increase in popu­
lation (Figs. 50-^3). Fifth, unexpectedly the 3.0 birth rate actually
produces the largest population (Figs. U6-U9).
However, it is never
2000-
19001800-
1700
1600
1500140013001200O
1100-
1000900-
4=
700600-
500400300
200-
100-
Time
Figure 38. Simulation Is population distribution by microhabitat.
The initial values of the variables are set at
B «= 3.0, D • 1.5, V « 1.0, and longevity alternative
» inductive.
220C
2100
2000
1900
1800
1700
1600
1500
1400
1300I1200
1100
1000
900
800-
700600'
500400300200100-
TImo
39. Simulation 2: population distribution by micr
The initial values of the variables are set at
B • 3.0,- D • 1.5, V • 1.0, and longevity alter
• tk.
2U7
20001900-
1800
1700
1600-
U00-
1200
c
•S IIOO
n
"5
o
Q.
1000-
«o
ra
800-
u
2
•(0
600-
500-
300-
It /
JOO100-
Time
Figure UO. Simulation 3s population distribution by microhabitat.
The initial values of the variables are set at
B • 3.0, D- c 1.5, V » 2.0, and longevity alternative
• inductive.
2U8
2000-
1800
1600
U001300-
1000900-
sn
800-
700600500400300200100-
Time
Figure Ul. Simulation U: population distribution by microhabitat. The initial values of the variables are
set at B - 3.0, D » l.S>, V • 2.0, and longevity
alternative • tk.
2h9
2000-
1800
17001600-
150014001300
1200-
c
o
a
3
noo
O
1000-
4-»
«o
900-
-C
BOO-
S
700-
o.
o
%o
se
600-
500-
400300200-
100-
Time
Figure U2.
Simulation
population distribution by microhabitat.
The initial values of the variables are set at
B • U.0, D • 1,5, V - 1.0, and longevity alternative
• inductive.
2J>0
2000-
1800
17001600-
1500
WOO1200-
c
o
1100-
3
O IOOO
CL
a TOO44
15
10
•C
O
k.
800-
W
o
a
'IS
600
500-
300200-
100-
o
Time
Figure U3.
Simulation 6: population distribution by microhabitat. The initial values of the variables are
set at B • lj.0, D • l.£, V • 1.0, and longevity
alternative - tk.
Tlmo
Figure lib*
Simulation 7: population distribution by microhabitat.
The initial values of the variables are set at
B • lj.0, D •• 1.5, V • 2.0, and longevity alternative
• inductive.
2*2
rs
a.
o
0.
JO
to
XZ
O
O
H
Time
Figure U5. Simulation 8: population distribution by microhabitat,
The initial values of the variables are set at
B • U.O, D-• 1,5, V • 1,0, and longevity alternative
- tic.
2*3
3000
« 1300"
Tofol Population
Number of Sites
8
8
r>
8
*«
8
»n
Time
Figure U6. Simulation 1: total population and total number of
sites. The initial values of the variables are set
at B • 3.0, D • l.£, V • 1,0, and longevity alterna­
tive • inductive.
2sa
3000
2900"
2800-
2700
•44
2600-
42
2500
40
2400
•30
2300-
36
2300
•34
2100
•32
2000'
30
1900
•23
leoo
-26
1700
•24
E 1600
22
20
Totol Popuiotion
Number of Sites
O
J
N
N
V
Time
Figure U7. Simulation 2: total population and total number of
sites. The initial values of the variables are set
at B • 3.0, D • 1.5, V • 1.0, and longevity alterna­
tive • tk.
3000
WOOWOOJ700
2600-
3500
2400
2300'
1200
2100'
2000'
I90CH
ieoo
WOO'
3 1500
1200
Tolol Population
' Numbvr of Sitei
Time
Figure U8. Simulation 3s total population and total number of
sites.. The initial values of the variables are set
at B • 3.0» D « 1.5, V = 2.0, and longevity alterna­
tive • inductive.
256
£ 1600<9
5 1500
& 1300
f Totol Popwloiion
Numbtr of Sit«»
t
Time
Figure l|9. Simulation U: total population and total number of
sites. The initial values of the variables are set
at B • 2.0, D » 1.5, V » 2.0, and longevity alterna­
tive « tk.
257
• WOO'
lofot Populotion
Nymfcer ©f Sitet
TX~5 § i i § TTTTTTI
Time
Figure 50. Simulation 3>: total population and total number of
sites. The initial values of the variables are set
at B • ii.O, D • 1.5, V a 1.0, and longevity alterna­
tive • inductive.
2$8
9000*
J900MOO-
•40
-36
2400*
2100'
1800-
17001600
*5 15001400-
tf)
£ 1300-
1100
lotot Popylo»ion
Number el Sitti
1000
900
eoo
70a
too
400
300700
100
o
O
R>*
8 8 8
O
(O
8
§
8
£
8
N
8
Time
Figure J>1«
Simulation 6: total population and total number of
sites* The initial values of the variables are set
at B " U.O, D • 1,5, V • 1.0, and longevity alterna­
tive « inductive.
259
9000
290028002700
u44
2600
•42
2500
-40
2400
-38
2300-
-36
2200
-34
2100
-32
2000
30
1900
23
1800
-26
1700
-24
e
o 1600
(0
"3 1500
a
'22
£
-20
•ft
tt
1400
16
1300
•16
1200
14
o
»2
1100
->2
fapuJOftOft
Number
woo
-10
900
eoo
•0
700
400
500-
6
400
300-
4
200
100
2
©
5
5
o
5
5
5
5
5
S "
J 4 S S 8 8 R 2 8 | g
w
n
«»
Time
Figure 5>2. Simulation 7s total population and total number of
sites. The initial values of the variables are set
at B • U.O, D » 1.5, V • 2.0, and longevity alterna­
tive • inductive.
</3
O
i.
o
JO
E
3
z
260
3000*
£
1600
a
1500
H
1300
X3
E
Populotion
Ngmb«f
Time
Figure 53. Simulation 8: total population and total number of
sites. The initial values of the variables are set
at B » U.0, D • 1,J>, V • 2.0, and longevity alterna­
tive • tk.
261
sustained anywhere for nearly as long a time span as the U.O rate
(Figs. 5>0-53). Thus, in over-all effect through time the h.O rate
results in a much larger sustained population. Sixth, if one compares
the two longevity alternatives, MacArthur's tk results in a larger
decrease in the number of settlements existing in the post A.D. 1100
period than does the random inductive longevity alternative (Figs. l|65>3). Finally, the increased migration velocity of 2.0 usually brings
population into one or two of the marginal zones a century or two
earlier than does a migration velocity of 1.0 (Figs. 38-U3).
It should be noted that in synergistic models such as the
simulation model it is not actually appropriate to ascribe the causes
of the above generalizations to changes in single variables. It is
more appropriate to ascribe the causes of the above generalizations to
the changes in single variables acting in conjunction with other vari­
ables which remain the same.
One generalization about the settlement locators may be made
before comparing the simulated settlement locations with the observed
archaeological record. The program repeats the randomly determined
coordinates of the village if the population weighted Bachi mean coor­
dinates are located in a non-appropriate microhabitat. The vast
majority of the weighted Bachi mean coordinates were located in non­
appropriate microhabitats which indicates its lack of utility as a
settlement locator.
262
The Simulations and the Archaeological Record
Figure 5U shows the number of rooms in each microhabitat
through time for the same area as was used in the simulation model.
The data for this figure were derived from the archaeological surveys
and excavations discussed in Chapter U. Figure 55 shows the total
number of rooms and the total number of sites for the same area.
Comparing these figures to the results of the simiation model
(Figs. 38-53), one does not find perfect agreement between any one
simulation and the archaeological record. However, all the simulations
fit the archaeological record in respect to general configuration. One
of the reasons that there is not perfect agreement is the fact that the
archaeological record is not complete. By this I do not evoke the old
"lost data" argument that states that since not everything is pre­
served, the archaeological record cannot be a data base for the testing
of hypotheses or models. Instead, I am referring to the fact that part
of the simulated area was only sampled and not totally surveyed. Since
the samples were taken in such a way as to be representative, there is
a very high probability that sites exist in the non-sampled area and
which would, if known, change Figures 5U and 55• If, on the other
hand, one used Figure 28, the number of rooms in the 100$ sample, as
a measure of the archaeological record, the two areas under considera­
tion are not exactly equal.
However, once I have admitted that the basis of comparison
between the simulated expectation and the observed reality is not per­
fect, there are several interesting inferences which may be drawn from
Figure 5>U# Total number of rooms by microhabitat from the actual
area•covered by the simulated map.
26k
550-
K55
SOO-
-SO
450'
-45
400-
"40
350-
-35
' Number of Sites
Number of Rooms
|-30
300-
V
CO
H2S ^
250200
-20
Jo
E
3
1-15 2
ISO
100-
-10
50-
-5
Time
Figure 55. Total number of rooms and sites from the actual area
covered by the simulated.map.
265
the comparison. It is clear that with respect to the distribution of
the microhabitat population, one gets a better fit with a 3.0 than a
U.O birth rate. This holds whether one uses the 100# sample (Fig. 28)
or the archaeological record from the simulated area (Fig. E>U) as the
measure of observed population. The population growth in microhabitat
VII is not sufficiently sustained for a U.O growth rate. This lack of
sustained population is also clear if one examines the total number of
rooms (Figs. U6-53) and compares them to the actual total number of
rooms (Fig. 55).
On the other hand, the observed archaeological record shows an
early small scale population movement into the marginal zones which
corresponds better to a lj.0 birth rate. However, this could be just
as easily explained by multiple initial settlements in different microhabitats, an alternative which was not simulated.
If one examines the population of each microhabitat, one notes
that different birth and migration values and longevity alternatives
fit together to come closest to the observed archaeological record.
For example, microhabitat VII is simulated best by a birth rate of 3.0,
a migration velocity of 1.0 and the inductive random longevity alter­
native while microhabitat I is best matched by a birth rate of h.O, a
migration velocity of 1.0 and the inductive random longevity alterna­
tive. Similar results may be obtained by oomparing the other microhabitats to the simulations.
This lack of identity in the initial variable values, noted
above is particularly interesting since it opens the possibility for
266
different birth, death, and migration velocity rates, and longevity
alternatives operating within each microhabitat or settlement. It is
possible to isolate the factors even further#
Once the microhabitats
are filled, the model already readjusts the mortality rates and thus
readjusts the net growth on a settlement by settlement basis. Thus,
it is possible to conclude that the different microhabitats have dif­
fering growth and migration rates and longevity alternatives prior to
microhabitat saturation.
This should be thought of as a preliminary conclusion, however,
because simulations run with more accurate adjustment of the variables
as well as multiple initial settlements might show a higher degree of
isomorphic comparison.
One may consider Figure 38 the best orer-all simulation in that it
most accurately portrays microhabitat VII, the optimal zone which
contains by far the most population. If one converts the scales be­
tween Figure 38 and Figure 5U, one finds that there are approximately
6-7 people per room. This compares with modern New Mexican Pueblos
which have 1-11 persons per room (Zubrow 1969), and Turner and Lofgren
(1966) estimates for prehistoric and ethnohistoric periods, £-7 persons
per room. The simulated figures are obviously within the appropriate
range of variation. They may be actually high because of unsampled
sites increasing the room count and thus decreasing the person-toperson ratio.
Examining the settlement locators for the same simulation, one
finds that approximately $0% of the locations are within the unsampled
267
areas, approximately 3$% of the sites are located where there are known
sites and 15% are located in areas where it is known that no sites
exist. This supports my earlier conclusion that the simulation esti­
mates are in the appropriate range of variation, but probably high.
Conclusions
It is clear that the simulation model essentially replicates
the observed archaeological record. The basis configuration of popu­
lation size, population growth, and the relationship of the microhabitat populations through time all substantiate it. The population
grows and as the resources and net societal produce limits are reached,
the marginal zones are filled in each simulation. As the resources
and net societal product diminish the population contracts back into
the optimal microhabitat. The status of the simulation model, if I
may use an analogy, is similar to that of a high quality stereo radio
tuner. A station has been tuned in but the fine adjustment tuning
necessary for perfect stereophonic listening still needs to be done.
The fine adjustment of the birth, death, and migration velocity vari­
ables, as well as the number of initial settlements and their locations
and other variables, still need to be modified before one may expect
perfect isomorphism between the simulation model and the archaeological
record.
The operating characteristics of the system have been defined.
Increased birth rates were shown to result not in larger populations,
but in a large population being sustained for a longer period of time.
It also results in an earlier expansion of the population into the
268
marginal microhabitats as well as emphasizing the decrease in popula­
tion after the first major increase in population. MacArthur's tk
longevity alternative results in a larger decrease in the number of
settlements in the post A.D. 1100 period of population contraction and
aggregation than does the inductive random longevity alternative. The
increase in the natural migration velocity from 1.0 to 2.0 resulted
in an earlier expansion into one or two of the marginal microhabitats.
The comparison of the simulations to the archaeological
reality shows that although the processes are valid, there is the
distinct possibility that each microhabitat may have different birth,
death, and migration velocity values as well as longevity alternatives
operating within its boundaries prior to the relative population
saturation of each microhabitat.
Finally, the Bachi mean locator which maximizes population
contact does not provide meaningful locations while the other two
locators place sites where known sites exist in comparison to locations
where there are no sites in a ratio of approximately two to one.
CHAPTER 7
SUMMARY AND CONCLUSIONS
In this study I have attempted to examine aspects of the term
relationships between population and resources both theoretically and
substantively with respect to a body of archaeological data from the
Hay Hollow valley in east central Arizona. A consideration of the
anthropological, economic and demographic literature indicated that a
theoretical formulation of a systemic ecological mode-l would be a
productive approach to long term population growth. It is recognized
that Malthusian and neo-Malthusian models have limitations when applied
to short term demographic studies particularly for societies whose
technology has undergone the Industrial Revolution. However, there are
strong arguments for neo-Malthusian models accurately representing long
term growth where the short term masking effects may be differentiated
from the long term underlying processes in non-industrialized socie­
ties. Thus, an ecological, neo-Malthusian model is developed which
considers carrying capacity as a dynamic equilibrium system. This
model may be expressed graphically or systemically and is not only
justified, but is related to the major parts of relevant economic and
demographic theory.
The model of carrying capacity as a dynamic equilibrium system
is expanded from its simplified form by the addition of several variables
269
270
and concepts. These variables and concepts include spatial and tem­
poral variation, migration, population development at the zonal level,
various economic and demographic variables including the definition of
a new variable called net societal product, technology which is ex­
amined from the basis of Schumpeter's theory of innovation clusters,
settlement pattern, settlement longevity and climate. At various
stages within the expansion of the model, the total model is expressed
systemically to allow the reader to see the development and the in­
creasing complexity of the system. The final systemic version of the
expanded model is the equivalent of the stimulation model. Parts of
the model are then quantified.
The expanded model of carrying capacity as a dynamic equili­
brium system has two functions in addition to being an explanation of
certain processes. First, it is used to develop a series of hypotheses
which are formally deduced from the assumptions and propositions of
the model. Second, it is used to develop the simulation model which
is used to try to replicate reality.
Four hypotheses are deduced from the assumptions of the model
of carrying capacity as a dynamic equilibrium system. They are:
1. The development of population in marginal resource zones is
a function of optimal zone population exploitation.
2. During periods of resource depletion, there will be a popula­
tion aggregation of settlements.
3. During periods of resource depletion, there will be spatial
aggregation of settlements.
271
U. During periods of resource depletion, the residential area of
sites decrease.
All four of these hypotheses are deduced in such a way as to allow the
reversal of the spatial and temporal dimensions without violating
logical consistency.
The testing of the four hypotheses produced positive results.
However, it is important to note that although the data support the
third hypothesis, it is necessary to use more refined measures of
spatial aggregation than site density. The original "density"-based
analysis provided a negative test of the hypothesis which proved
erroneous when the more refined "nearest-neighbor" analysis was used.
After an updating of the known archaeological record from the
Hay Hollow valley, four major areas of archaeological data are dis­
cussed. They are excavations, a central 100^ survey, two peripheral
2surveys, and an intensive survey. The intensive survey was done
in order to test the validity of the archaeological data. In particu­
lar, it was. necessary to show that the dating and the site size from
the surveys were accurate. Three conclusions were drawn from the in­
tensive survey which used a series of sites chosen to maximize
potential survey error. First, the original survey does not overesti­
mate the number of actual rooms in a site as was feared but, if
anything, it underestimates the room count. Second, the survey dates
are remarkably close to the intensive survey dates and thus may be
accepted as reasonable. Third, it must be noted that multi-component
sites produce poor temporal estimates when surveyed. Thus, no single
272
dating estimate should be given a great deal of reliance unless one has
specific evidence that the site is not a multi-component site.
Richard Hevly and I carried out an ecological survey which
consisted of eight stages in order to determine the reality of poten­
tial microhabitats and to determine the actual amount of resources and
resource productivity available to the prehistoric population. This
survey showed the reality of the microhabitats. Of the six potential
microhabitats, the ecological survey showed four floral and six faunal
microhabitats. Floral productivity and standing-crop data were ob­
tained as well as faunal standing crop data. The quantified resource
data were related to past resources through the pollen sequence.
Finally, it was shown that the development of agriculture was not as
significant a shift in production as has been generally assumed.
The simulation model was successfully used to replicate the
archaeological record. The basic processes of the model of carrying
capacity as a dynamic equilibrium system are shown to be operating.
Furthermore, it is shown that multiple birth, death, and migration
rates may be working prior to the population saturation of each microhabitat. Fine-scale adjustment of the initial variables will probably
produce even closer isomorphic comparison between the simulations and
the archaeological record. The simulation which comes closest to the
archaeological record uses a birth rate of 3.0, death rate of 1.5,
migration velocity of 1.0, and the inductive random longevity alterna­
tive. An examination of the archaeological data from each microhabitat
shows that particular combinations of the initial variables best
273
simulates each microhabitat. Two of the three settlement locators are
successful. Together, they locate simulated sites twice as often into
locations where real sites exist rather than into locations where there
are no sites. The third settlement locator which was based upon
locating new sites in areas to maximize potential social contact was
a failure.
In short, this study has two conclusions. First, it is pos­
sible to study successfully archaeological problems through formal
models. Second, the model of carrying capacity as a dynamic equi­
librium system explains long term population resource relationships
in the Hay Hollow valley and since it is a general model it is hoped
that it will provide explanations anywhere that the conditions for its
existence are met.
APPENDIX I
HAY HOLLOW VALLEY VERTEBRATE AND
INVERTEBRATE SURVEY
Part As
Prepared by Richard Hevly, Ezra Zubrow, and students
Date of Survey
September 3-6 and 19-20.
Weather
Generally cloudy throughout the duration of the trapping
period; however, there were several warm periods during the day.
Winds were high with a thunderstorm one night. Only one night could
be considered optimum for trapping.
Trapping Period
Two days and two nights in each habitat.
Size of Plot
One acre with traps every nine feet plus buffer zone traps.
Procedure
Mammals were trapped using live animal traps as no regular
traps were available within Museum of Northern Arizona and Northern
Arizona University Museum. Animals were removed and killed by asphyx­
iation or freezing. Animals were placed in labeled bags and stored
27U
on ice until opportunity for weighing and museum preparation. Baits
employed in the traps included dried seed and peanut butter. Reptiles
were captured by hand and frozen for future study. Birds were ob­
served by field glasses and several specimens were collected by
shooting.
No amphibians were observed. Areas of permanent water do not
occur within the valley so fish do not occur there.
Results
Microhabitat U and g. Pinyon, Juniper woodland (terraces).
Predominate vegetation: extensive stand of juniper with scattered
pinyon pine. Substrate was rocky with sandy soil and few, if any,
grasses or other herbs. Shrubs were present.
Reptiles:
Birds:
Mammals:
1 Sceloporous undulatus
1 Urosaurus sp
11 Pinyon Jay
li Pinyon mice
1 Mexican woodrat
1 Jack rabbit
10.U
..... 0.7
0.2
8£.7
113.U
.171.it
Microhabitat 3 and 7. Grasslands (Hay Hollow valley bottom)
Predominate vegetation: grass only. Substrate was semi-sandy soil
with patches of sod (Bunch grasses). A few shrubs but no trees in
the study area.
Reptiles:
Birds:
3 Phrynosoma douglasi
2 Sceloporous undulatus
3 Holbroskia maculate
1 Crotalis
2 flycatchers
2 unidentified
.... Ul.7
28.U
0.2
56.8
6£.0
276
Mammals:
10 Pinyon mice
6 Silky Pocket mice
3 Mexican woodrats
2 Kangaroo mice
1 Rabbit (cottontail)
377.6
36.2
1*25.2
2U.8
396.6
Microhabitat 1 and 2. Juniper Savana (point of the mountain,
mesa top)
Predominate vegetation:
grassland with abundant juniper.
Substrate was rocky (Malpais or basalt), thin stoney soil.
Reptiles:
Birds:
Mammals:
3 Cnemidophorus velox
1 Collared lizard
3 unidentified
2 Silky Pocket mice
7 Pinyon mice
1 Coyote
Microhabitat
U, 5 Pinyon-Juniper woodland
1, 2 Juniper Savanna
3, 7 Grassland
No. of Species
3.6
2.7
19?.0
18.5
200.5
8.8
Herbivores Carnivores
g/acre
g/acre
6
6
370.5
U13.0
11.3
15.1
11
1325.U
132.8
Part B
This survey of invertebrates was carried out September 3-6
and 19-20 on the Carter ranch near Snowflake, Arizona, Three plots
of one acre each were laid out in three distinct environments in con­
junction with a vertebrate survey. The plots included pinyon-juniper
woodland, grassland, and juniper savanna.
Tree and ground sweeps were carried out on each plot using
standard sweep procedure (50 sweeps = 1 sq. meter). In addition,
approximately four man hours were spent collecting in each habitat.
277
The families found represented are listed under miscellaneous for each
plot.
The organisms collected by sweeping were dryed and weighed to
obtain an indication of the biomass each plot was supporting. It was
found that the grassland plot supported 1.1 gm/sq. meter, the pinyonjuniper woodland 0.25 gm/sq. meter, and the juniper savanna 1.0 gm/
sq. meter. These measurements were substantiated by our personal ob­
servations while collecting.
The grassland and pinyon-juniper woodland are easily dis­
tinguished from each other but the juniper savanna shows its complement
of species with both.
Microhabitat
Wo. of Species
Herbivores Carnivores
g/acre
g/acre
kt 5 Pinyon-Juniper woodland
17
0.25
0.01*
1, 2 Juniper Savanna
16
0.95
0.05
3, 7 Grassland
(*estimate)
23
1.05
0.05
Plot 1: Pinyon-Juniper Woodland
a. Ground sweep
Class Insecta
0. Coleoptera
Tenebrionidae - darkling beetles
0. Diptera
Unidentified
0. Hemiptera
Miridae - plant bugs
Tingitidae - lace bugs
0. Homoptera
Cicadellidae - leaf hoppers
b. Tree sweep
0. Hemiptera
Miridae - plant bugs
278
0. Homoptera
Cercopidae - frog hoppers
0. Lepidoptera
Geometridae - measuring worms
c• Miscellaneous
Class Insecta
0. Hymenoptera
Braconidae - braconid wasps
Mutillidae - velvet ants
0. Isoptera
Rhinotermitidae
0. Neuroptera
Myrmeleonidae - antlions
0. Orthoptera
Gryllidae - field crickets
Locustidae - grasshoppers
Tettigonidae - wingless crickets
Class Arachnida
0. Araneae
Theraphosidae - tarantulas
0. Opiliones - harvest men
Plot 2: Grassland
a. Grassland sweep (2 sq. meters)
Class Insecta
0. Diptera
Asilidae - assassin or robber flies
0. Coleoptera
Cleridae - checkered beetles
Curculeonidae - snout beetles
Mordellidae - tumbling flower beetles
Tenebrionidae - darkling beetles
0. Hymenoptera
Chalcididae - chaleid flies
Diaprildae
0. Hemiptera
Micidae -plant bugs
0. Neuroptera
Myrmeleonidae - ant lions
279
Class Arachnida
0. Araneae
Thecidiidae lactrodectus mactans - black widow spider
Class Solpugida
b. Grassland miscellaneous
Class Insecta
0. Coleoptera
Carabidae - ground beetles
Cicindelidae - tiger beetles
Curculionidae - snout beetles
0. Hemiptera
Cydnidae - burrowing bugs
0. Orthoptera
Gryllidae - crickets
0. Hymenoptera
Braconidae - braconida wasps
Cephidae - stem sawflies
Pompilidae - spider wasps
0. Isoptera
Phino terraitidae - termites
Class Chelopoda
0. Scolopendromorpha
Scalopendridae
Class Arachnida
0. Scorpiones - scorpions
Plot 3: Juniper savanna
a. Tree sweep (2 sq. meters)
Class Insecta
0. Coleoptera
Coccinellidae - lady beetles
0. Hemiptera
Miridae - plant bugs
0. Homoptera
Cercupidae - frog hoppers
0. Hymenoptera
Formicidae - ants
Mutillidae - velvet ants
Pompilidae - spider wasps
0. Lepidoptera
Geometridae - measuring worms
Class Arachnida
0. Araneae
Unidentified small spider
Ground sweep (2 sq. meters)
Class Insecta
0. Diptera
Asilidae - assassin flies
Qmpidae - danse flies
0. Hemiptera
Miridae - plant bugs
0. Homoptera
Aphididae - aphids
Cercupidae - frog hoppers
Cicadellidae - leaf hoppers
0. Thysanoptera
Thripidae
Class Arachnida
0. Acarina - mites
APPENDIX II
LISTING OF THE PROGRAM FOR SIMULATION MODEL
WITH SUMMARY DOCUMENTATION
281
282
PROGRAM MARCIAITNPUT.OUTPUTI '
prpgrah warcta. the . simula ti on motel .consists cf foup componentsthe main pp0g?aw and thpt subroutines. the maim pr coram has the
following functions•
11 to set up ccnstants such as »t'th ano drath rates.
21 to readt in a sihlllato map of the hav hollow valley by mtc°0ha3i tat.
3> to de ermtne which longevity alternative will 3e used.
4I'I) DETERMINE THE POPULATION SI'EIS) AND LCCATIONtSJ OF THE INITIAL
VILLAGE <S>.
51 to increment simulated
timt r»0m a02r.r t0 adiscn.
the population growth
61 to calcula's
3* settlement fcp each time period
t
based on bir h and death rates a no non-pesource determined migration.
71 to calculate total population for each micrchabitat for each time
period.
e» to calculate 'he imc"eased or dec."?£asec resources and net soctetal
product for fach time perioc.
91 to check settlement population against maximum settlement si7e. if
there is excess po°ulatton it is stored for possible migration and
reloca ticn intp a nsw bud5e0 settlement. this 3ucded settlement may
be locate!? in the same 0" different mc" 0ha3itat. the former has priority
cthis type of migration is considered equivalent to resource determined
m!g r ati on).
1"> to check the
total population for eac" micrchabitat against
the net societal procuct of t,|#t m ico habtt at for that ti"e period. if
excess population exists it is st0s>£!3 cor possible migration to other
•newlv phoned settle"entst in other ntcr0ha3itats.
11.to determine availas ltty of micrqhabi ta ts wi'h sufficient net r
societal *ro-uct to allow fop migration and budded settlements. i
sufficientc amounts cf urt sociehl ppcduct are available « appropriate
!
amounts o resource determined migration are calculated.
to call t h e subroutine named sctlo" which locates new settlement s»
iti to call the su3p 0ut tne named longevt which determines the amount
of se t tle"e n" extinction and which se tt events become extinct r0r
reasons not directly related to resource's.
iwj to oe'e°"ine if all microhabttats are filled. if this is the case
the mortality a.no the ce*th r»tes are apppop riately increased.
COMMON/LEr/REEIG>.AP'>OR<GI.PllCf.3).XI ir C.S > •XX < mC.G> .X XX 110" » f I
ItYYIlCr.GJ .YYV(lCCicI.RNS°(S).PT(S ).TS(f. I .LO CKUP J .25 ».A».BR.11 J.
1YI100.E)»C0N.FLS31.FLA0?.*LAG?.IDATE»STr9.0»Q.INrp(6)
INTEGER R.PT.PTT
INITIAL CONSTANTS F0" 3IRTH.DEATH RATC,"»MIf? RATION VELOCITY.
CONSUMPTION AND rXTERNB L FACTOR REDUCTION
i a=i.ci
0=1.5
90:.OS
3 Vr2.3
« c0n =.05
6 TOATE^SCO
INITIALIZING VARIABLES TO D
TSAVE=0
JSA'/E-O
30 Gil 1=1.6
tESiiuo.n
aprcdit1=0.0
o » J S P t r i =r. o
TNSP(I>=0
prcri=o
E l l TC(IJ=0.C
do si? j=l.g
do Ei2 in.irc
xii.ji=n.r
v n . j)=c.r.
xxii.jup.c
yyii,jj=c.o
xxxir.J)=3.n
yyyii.Jim.o
READS I N SIMULATED MAP CF HAY HOLLOW VALLEY BY K I C R O H A P I T A T .
" I C P C M A a i T A T r ARE INDICATED PY THE NUMnrRC 0 ME TO S T X .
THE1 °
LOCATION I N THE MATRIX CORRESPONDS TO THE MICR OHARIT AT LOCATICH
SPATHLLY ANP ALSO CDRTSPO'nS TO MAP I N TEXT.
R E A D 1 5 1 3 • C I L O C K U P <I• J ) . J - t . ? S > . T = l . 2 5 »
<=13 F1!>1*T l ? r I l 1
e » I » I T S l l .I I f O K U P C I . j i . J = l . " . r ) . 1 = 1 . 2 5 1
61<i FORMAT I1H « ? 5 I 1 )
rETS UP
RANO™ NUMBER
7 . M =R A N F I ~ 3 C . »
9 B 3 =? A N F 1 5 ? 0 • J
FLAGS TO C " T ERMINE
*3 F L A G 1= 0 . C
FLA0?=1.0
FLAG3:0.r
»
CALLS
VHICH LON.--EVITY
ALTEPNATIVE WILL BE USED
LOCATION AND S I 7 E OF FTRST VILLAGE
Xll.l>=13.
Yll.l)=13.
Pll.ll=Sr
XXC1.11 : 1 3 .
YYJ1,1»:13.
X X X t l « l > =1 3 .
YVVI1»1»=13.
1C PRINT 11
t l FORMAT I1H •cv»»I)»»lCX..';*«lCX«.V»»lCX»»C*»10X««C0N».lCIX.»fi;G«»l"
1»»IDATE»I
12 "RINT 13 ,BtD .V .O.CON.RS. ICATE
1 3 FORMAT I1H •><XtC. I F 7 . 2 . : y | t Z 4 l
14 print is
l * FORMAT t l » U , i a X . . R E S 1-G».1CX,«APR00 1 - E O
R E A D 5 1 5 .I R E T I I J . A P R P O 1 1 1 . 1= 1 . 6 I
Ft5 fiiouat IF15.1»inX»KlP. C)
"RINT lS.IRETIUfAPROCIU.I-l.SJ
1G FORMAT 11H . I C l X . F l E . T . H X . r - l . S I
•
TIME IMCREMENTEn ANO CHECKS FOR
TEMPORALLY RELATED CHANGES I N
resource growth ahc for end of tme sestet..
17 loate^ioate•x?c
pt(1i = pt(2)=pt|^|=PTCH»rPT<SI=PT«5l=C
TFITOATE.GT.UCCI19.19
13 RSr-S.C'AnSJPGI
19 T F «rcATE . G E . l ^ C O I 2 Q . ? ?
t °rint 21
">1 format (1h .2cxi»cne tt "poral simulation ccmfleteoo
GO TO 1C01
?r OOT.jt ri.ioA'E
?3 for«at jim .«pat£ is •»it>
print icc?
lf??3 F O R "at 12h .•trace 1 passed*!
iois.i.j
1C1C FORMAT (1H
RESOURCE ANO NET SOCTETAL PRODUCT INCREMENTATION.
03 21 J- l»fi
pes(jl=re"iji*cl.s.p3>
R N S P f J != { 4 . 0 « C O N » R E S ( J ) J / 7 7 5 0 3 . 0
print js.J .pesijj.rnspiji
2 5 FORMAT (1M ,»7CNE • » I l . " > r S » . F 1 S . 2 . 2X . «NSP« . l X . F " ' . ? J
2 * CONTINUE
SETTLEMENT ANO MICP0H4OITAT T N CR
J=1
2g j=j»1
el en T A T X O H .
IFCJ.GE.7IG0 TO 1 7
ZzC
2 7 T=T*1
potmt 2cc1.i.j
2mi forvat c1h ..trace a » • T1.1 x.it i
mtgrat2on settlevent sav™ ano cut off to table pointer
ifdsavt.ea.i.ano.jsave.eo.ji
go to 291
!fip<:«j).elj.0.anc.XCr.j».e3.r'.. ano.x*(t.j>.eo.c.t28.29
23M isav£=0
jsave=0
2 3 CALL LONti'V
PRINT 731.FLAR1.FLAG2.FLA33.J
2 3 1 FORMAT I1H .'FLAGS SET • , 3 r 3 , p , , FOR ZONE • f i l l
JJ - J
PRINT 2C13.I.J
2 r i l FORMAT C1H .'TRACE T • . I'l . 3 X. I I I
ORINT 282
11
2 1 2 FORMAT 11H . • " • . 1 X | « X . , ? X . « Y » . 3 * . « Y » . 7 V , . X X » , 3 X . » v y . , .XXX • . 3X . • YYY»
PRINT 2 3 ? . CP» I . J J . X C I . J ) »YJI » J t » X X I I . J ) . YYf I . J l .XYXI I . J ) .YYYIT. J l .
11=1.751
r
213 9RMAT ( 11H . IE .£ IF5 .C. 2X I ) I
3 3 TO 2 5
•
CALCULATION CF XICROrfAHI TAT S P E C I F I C TOTAL P CPUL A TIONI PT I FROM C
2*! » M J I =3
00 291 ILL=1.75
JJ
Jl•PJILL.JI
p*l =pt«
311 CNTINUF
232 "INT 361iPMJ>
J n FORMAT CtH , r y , « P T = « i l < t l
P?TNT i n o i
lCT«t F^OMAT C1H i »TRACE 2 PASSEDO
P?It!T 1011»IiJ
mi
format ixh
CALCULATION Of 'NATURAL MIGRATION' FCR OETTTINATrPN SETTLEMENT
I^CI.GE.n)3Ci31
31 TV=0.
PC=P(IiJ)
GO TO 3*11
33 K=I
T"rO.
PD=P(IiJ J
32 °OrP C I - l • J l
M=(ViOD»o0>/!>T< J)
-M=TH*M
T=T-1
TF(I.E0.H33i32
33 UK
3<ii
jt 31.
P»:«
3 1 F"RMAT C1H . • ! : • • I 3 H J : : • . I ' , . » T M = ».FS.P>
POPULATION GTWTH FUNCTION
35 ' ' ( I i J I r J P d t J M T y i i t S - D I
cO.°
7ETTLEM EN T
CALCULATION CF "ICS 0MA3ITA T SPECIFIC T0TAL POPULATION INCLUDING
09PHTH
PT(JJ=C
DO T 3 1 I L L = l i ? 5
J):PTCJ)»P<ILL.J»
351 CONTINUE
3 r r PRINT 3 r . i . J . P ( I . J I
3C r0R"A T (1H i«\'EV POPULATION AT T= • • I 3 . ! X » » J = ».T1»
"''INT 351iPT
•TS».1X.I'»>
CMECK5 FOR 5 r T T L E M E N T P C U L A T I O N 9EING GREATER THAN NSP OR
"AXICUM
rET TLEMrNT
:FI"I ji.sT.rTis.ii 37
37 TF(PTIJI.GT.PM5PC J) >371i372
ADJUSTMENT 0^ SETTLEMENT POPULATION
SOCIETAL PRODUCT
3"*1 5 A V E - P T I J ) — P N S P I J I
" t l i J I i P J I . J1-IAVE
IFJOJI, JJ.LT.CI<>« IIJI=3
°TIJJrPTCJl-IAVE
WHEN GREATER THAN MAXIMUM
"''TNT 2CC2• I i J
2C02 FORMAT I1H i«TRACE n« i T 1 ISXII«l»
O TO US
3 7 2 3 0 TO 2 7
AOJUSTMFKT OF "SETTLEMENT POPULATION V'MFN GREATER THAN MAXIMUH
3 3 S»VE=PC IiJJ-T:T
PCItJJrST
KK=I
l=j
TF(PT(J1 , 5 T «RN?P< Jl 145• 39
J<» D" 391 1=1.10-3
ifcpj!•jj. E O . S . a M O .x(i.ji.e3. 0 ..a.10.xxii »j) . E Q . 0 . ) 3 9 2 »391
T>I CONTINUE
*92 <mt»j)=save
mctc experiment isavf.jsave
isave=i
j-;ave=j
P7INT 2C03•I*J
2CC>3 FOR»AT «1H ..TRACE C » » I 1 t 3 X » I U
CALL >ETL OC
POINT qc
<13 F1RMAT ( 1 H «»KEH 5ETTLEMENT HAS POPULATION O F P
1L0NGEVI TV* I
AS LOCATED 9EF0PE.
print <il.°c i,j|
« FORMAT (1H
P-»TNT 42tX(I.JI.YII.J)
<12 FORMAT ( 1 H « « X = • » F =
• •Y=«.F5
)
print <t3.xx(i.j> .yy «t.j)
»3 FOR»AT C1H .•XX =•.F5>•YY=«.^5.C>
pqi'.'T <m.yxx« i,ji iYYY«r«j»
<l<» FORMAT I1H .•vxyr«,F5.G«*YYY = »»F^.CI
"'INT 7CCM.I.J
20C<» FORMAT I1H ••T°ACE 0«.I<t•IX.I<l I
"etijrn from E ' i r o - o r e t•'levtnt to migrant providing settlement
AND MICROHA 3ITAT
?=KK
j=l
GO TO 2 7
stopage pf higrant providing se ttlehen t
<15 xx=z
l=j
AND
micr oha 8ita t
f'lcr
CALCULATION OF
OHAHITAT SPECIFIC TOTAL POPULATION FOR
MIGRATION DETERMINATION
15 PT«l)iPTI2J=PT( 3J;PTCm:PT(S»-PT«5l=C>
DO M61 JZ=1.6
do
«si irn.75
PT(JZ)=PTCJZIfP«IZ.JZI
4S1 CONTINUE
ijrjj PRINT <IG2.PT
<sz format c1h.sx»«kic* atton pt =».i9»
<?EAL TO INTEGER NSP CONVERSION FOR Z TEST OF HICROH An IT ATS
DO 1 6 3 I C X r l . e
TNSP(ICK)-RN«;P« ICK)
«G3 CCVTINUF
mic«ohabttat-oetesmiwatjon for newly 3u0bf0 settlement
POSl:PT«l»/INSP|l)
FILLFO
POS3:r«»TI2l/INSP|2l
POSTzPTm/IHSPIII
POSiuPTeil/TVSPiq J
P*S5=PTCr)/I'!SP<5l
Pn^SrPTtGJ/I'^PIG)
?=AMIN1 <POSl.>,O':2,POST.o0S<».POr5 .P0S6)
T f l Z . T O . o n ^ l l S f T S T ; !.
TFCZ.«:Q.POC?|OE<:T;S.
IFIZ.EC.^OS'tPEJTU.
IFITi EO.PCSIIBEST-I*.
IF( ».EG.O0S5)3ErTiS.
TFtZ.E3.P0S5IOEST=<;.
PRINT 2CC?.I.J
2CD5 FORMAT (1H .«TR»CE H».T't.3X.I«t)
TSUErl
JSUE-J
J=BEST
CHECK I F ALL -''ICR0HA3ITAtj FILLED
T^CZ.CE.l.JSl.fll
OETERMI MA T I C V CF SETTLEMENT NUMBE?
RUOREO SET7LrvCNT
WITHIN HICROHAHTT AT FOR
111 20 ">12 i-itinc
I F J P C t . J » . E O . r . A N O . X I T . J > . E O o C . . A N D . ) f * C I . J ) . E Q . C . ) c 13 . 5 1 2
512 CONTINUE
r13
n
CI•J)-SAVC
AOJ'JSTS "IGR*»JT POPULATTON TO NEW S I 7 E WHEN GREATFp THAN NET SOC*
•TETAL P3PPUCT OF HEWLV HIORATO TO MICRCM3ITAT
3AVEr5AVE»PT( J)
I F I SAVE.C.RVSPt J1I
I .J I = R N S ! > « J I - P T C J t
•
TSAVF-I
JSAVErJ
print inrs
1<!^5 POR«AT 11H t • TRACE 3 PASSFDO
•>,?I»!T I C l ^ t l f J
1D12 FORMAT ( I K . • I = » . I i t
CALL SETLflC
PRINT ?CO?.I»J
S P S S r " R » A T I 1 H . ' T R A C E E «.I t » 3 X # I q )
PRINT S i t
511 F0RPAT(1H ttVEW SETTLEMENT HAS POPULATION OF P
ILflNGEVITY* J
PRI1T £13."(I»JI
PRINT 515.XII.Jl.VI I t J I
PRIVT 51G.XXJT.JI.YYfT.JI
PRINT 517.XXX(I.J),YYYII.JI
513 FORMAT (1H . • P : » . T t »
515 FORMAT C1H ««X : « . F 5 . " . « V T » . F 5 . C I
5 1 G F O R » A T C 1 H .• v x r « , F 5 . r ,.V Y = • » c ? . r . j
5 1 7 F O R M A T I 1 H . » Y X X = « ,F * . f ! . • Y Y Y r • . F 5 . Q I
«EW SETTLEMENT I E O ^ O r o SETTLEMENT
J=L
T=KK
AS LOCATED BEFORE#
I S NOW LOCATEO
288
""INT 2C07»T»J
2rC7 FORMAT C1H ««TOACE F> . I t » 3 X . I « » l
5 0 T(J 2 7
all "tcmrhaaitat!: filled and mortality increased
<»t« j1 = ptiji -save
if<°t(ji.ct.°mspij)
i el.52
r
s3 imoi?t = savf/p'rt
0=rm07t*0
pplnt 59»rm oht » 0
r=KK
j=l
t=tsue
jsjsue
so t3 2j
5'» eavel-ptt jl
• irn
PO S6 L = 1 . I I
t=:i-l*i
ic(rwsp(j>-«""ijl-p(i.j))!5s»?7t59
55 °tij)-ptcjj-p(ltj|
55 " t l . J l r O
57 »tiji:pt(ji-p»i.ji
pci »ji:p
SAVErSAVEl-ptjj)
PO TO 5 2
53 p«i»ji=(rnspf j)-iptij)-pci.j|))
ptj j|:pt(jj-n11,j|
save-savcl-ptij)
rm3<>tsave/p'"'
3=s»r«(01t
PRINT 59tRMO*T.O
S9 F C R M ATtl H .• pkortalttvzucs . J . » D .de A T H R A T E = « » F F . JI
I-KK
J-L
trisue
j=jsue
70 to 28
10p1 continue
end
subroutine setlcc
•
S I O T ' =P T ( J I
T his SU3"CUTT« > r D E T E ° M T " E S U H E P E N E M E E L E M E N T S M I L L of L O C A T E D .
it is calleo when
settl7vent population it greater than the settlement
maximum an'0/op when the total population of the mtcroharitat ts greater
THAN THE AMOUNT O
ME SOCIETAL PRODUCT FOR THAT POPULATION. THE
appropriate
"tcpohanitat,
the amount of migration. ano the number of
t
v
budded ee tle e'jt^ 15 calculated <>y the main
program.
this subroutine locates the new «"et tle hent" "hree 'vays.
hit assumes a ra mo cm location process which it generates ustno
a pvioom number genfrat or limited by the constraints of the simulated hap
of the ha* hollow valley.
21 it calculates
point in space for thf new settlement whe«>e
the vewly Buocro settlement
will 9f in t»e maximum amount of
contact with all
ot»er pre-existing sltf- mIN the MI crcha9itat.
1
this point.th* population weighted bacht ean. is tl-c point which
allows thr population of the hew tsettlcment to be the minihun
distance from the maximum po°ula ton.
TT
C
T
3> I T
CE«;
MINIMUM AMOUNT or
CALCUL
THE
APE A SURROUNDING EACH
PRE-EXIJTTNG " I T F NECESSARY TC SUPPORT I T S POPULATION «T THE SIMULATED
-TME. AFTfR LOCATING THIS ARrfl FOR ALL PRE-EXISTING NON-EXTINCT STTES
I N THE KICCMA9TTAT.IT
THE NEW
TTLr!'ENT RAVCCMLY WITHIN THE
THAT AREA OF TH^ MICRCHA3IUT WHICH I S MOT PART OF ANOTHER SETTLEMENT'S
r'JOSISTENCE "A^E.
LOCATE-
C O P M O N / L E r / R E S C c ) .A P ^ C i r G » » F « l ! ? r , 5 ) > X ( I f ) ! 1 . 5 J.X X « 1 C P . G ) . X X X ( 1 3 C > 6 )
>.A A.B E I
. • Jt
1Yllnr.fi).CON.FLAGl.FLAG?.FLAG3.I3ATE»5T,S.D.Q.INfPI6>
TN'EGER °.PT
l . Y Y t l C P . S J » Y Y Y ( 1 2 3 . = J ,R«J<:P(K),r r 1 5 ). T S I F > . L C O K U P ) ! ? 5.
•
?»NOf« SETTLEMENT LOCATOR
CX.Y)
*»INT 233'!.I.J
2 C S 3 r o q ' « A T ( 1 H . ' T ^ A C E ! •.I t » 3 X . I M »
FLAGM-C. 2
60 IAA-IOC• *AA
TF( IAA.GT.3«;.0R.IAA .E0.CJG2.61
C2 AAS^ANFCO.!
5 0 TO GO
61 T'iBrlCC.^B
TFt IST.GT..?S.fR.I3P .T 0.? J61.6 3
SI 93:RANF JC. J
30 TC 6 1
P T I F { J . E O . L C O K U P I I M * I B 3 ) ) G6 > 6 13
6 1 3 A *= R A N F « C . I
Blr^ANF CO.)
G1 TO SO
66 IF{FLAC».ET.r.CJG7.77
67 X(I.J)=IAA
YtI.Jl=IB3
""1ST Gll.IAA
6 1 1 F OPMAT I 1 H .•:#A=».T<»»
"TINT S12.I3B
6 1 2 F C V A T ( 1 H . • I B 3= » » T 1 I
PRINT 1C3T
l " r 7 FORMAT <1H t • T P ACE G ° A S S r o « l
•
p0pULAT
11N WEIGHTED 3ACHI MEAN
PRINT 1C1H.I.J
1P1«I FOR"AT (1H • • I = » . I 1• •
rE*TLEHENT
LOCATOR I X X . Y Y I
rXrC.O
63
73
71
"•2
7*!1
SYrO.C
TI=I
20 Sft 1 = 1 . 1 1
* X = ( P « I > J I • X X ( I . J )I *SX
f.Yr ( P ( I . J ) « Y V ( I , J ) I *SY
T=IT
IF(PT«Jl.Ea.r> 71.73
TS|J)=PT(J)
00 TO 7 2
'SCJIrl.O
TIBB^SY/CI'TSCJI)
*3AA=SY/(I»T^«J)J
° R INT 7 2 1 . I S A A . I 3 B 1 . J.TS( J l . r x . S Y
F O R M A T C 1 H . » < 1 5 . 2 X J .3 1 F 5 . 1 . ? X J I
Tc,CIBn3.GT.2^.0R.IBBB.rfl.C.OR.T3AA.GT.2S.OR.I3AA.EO.CIGO TO 73
rF(LOOKO"(IGAA.I?PB >.E0.J>75»73
I
290
73
XX(I.J)=IAA
VY( I . J I = I 0 3
PRINT 71
7 1 FORfATClH .«NO 3ACHI MEAN CENTERO
SO TO 7 6
•»5 X X « I . J ) = I B A A
Y Y < I ,J ) = I B 3 B
•
-C
77
73
791
""}
701
AVAILABLE RESOURCE SETTLEMENT LOCATOR (XXX.YYYJ
A A = R A N F I T .I
BRrRANF ( C . I
F L A C M =1 . 3
•50 TO 6 0
11=1
00 70 1=1.11
A*EA= t r ^ C O P ! T . J> l/<<).P«C!)N»APROD< J> J
PRINT 73U.A9CA.Ii J . ° ( T.J)
FORMAT (1H ».AR£A =« . F 1 0 . 0 , 5 X . . I = » . I 3 . 5 X , » J = » . I 3 . « ; / . » P ( I . J ) = * . I 1 C >
" = l S O R T I A R E A / « " . 7 1 1 1 3 3 ) } / ? • ) ? .G
TF| SORT(I tXXX(I.J)-IAA) ••2>+MYYY(I.J)-TE!JI»»2)>.GT . R l ^ . ^
CONTINUE
i=i r
P U N T 7 3 1 . A ° E A . ".T • J
11H .•ATA=»«F9.2.»R=».F6.:?.*I=«.I3.»J=».I3)
XXXII.J)=IAA
Y Y Y ( I . J ) =I 3 3
RETURN
rORMAT
end
subroutine lomgev
;'tnrs
or
T H I S S U 3 R R > U T I ? ' r DETEF
WHETHER
NO' SETTLEMENT! 3EC0HE
EXT
IDG
PAR'ICULAR
"ERIOO.
OF
SETTLEMENT EXTINCTION A°C POSSIBLY EMPLGYEO DEPENDING U^ON
r
'ME DIRECTION' OF THE
PRCGRAF.
ALL OTHTR OPERATIONS ON THE
TURING A "ARTICULAR
COHPLETEP. THIS
•"IJBROUTINE t r CALLEO INTO ACTION.
ONC ME'HOD OF
'LEMENT EXTINCTION
IS
'EO UDON
V INOUC'TVELY DETRRWI:IEO 1/1C PR09A9ILTTY CF EXTINCTION.
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imct our
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end
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FIGURE 17
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HAY HOLLOW VALLEY
LEGEND
.ioo
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•711
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largt Sit< Areas
Ecological Sample Quadrants
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