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, 1945-

A SOUTHWESTERN TEST OF AN ANTHROPOLOGICAL

MODEL OF POPULATION DYNAMICS.

Anthropology

University Microfilms, A XEROX Company, Ann Arbor, Michigan

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

THE UNIVERSITY OF ARIZONA

GRADUATE COLLEGE

I hereby recommend that this dissertation prepared under my

EZRA BARRISH WIMKLER ZUBROW direction by 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:"

2^

U.) t (t*

2

1

Y/ J i /l /

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 dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to bor­ rowers under 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

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

the model and has continued to take an active interest in its develop­

vi

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

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

LIST OF ILLUSTRATIONS

Page xi

LIST OF TABLES

ABSTRACT

1. INTRODUCTION

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

XV xvii

1

3

5

9

16

21

30

32

37

39

39

39

Ill

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

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 ill l|6

U6

53

56

63

67

68

98

98

103

viii

TABLE

OF CONT

ENTS

—Continued

Longevity

Consumption Equations and Technological

Innovation

Constants

3. HYPOTHESES

It. DATA '

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

Operating Characteristics 2l»0

The Simulations and the Archaeological Record .... 262

Conclusions 267

7. SUMMARY AND CONCLUSIONS 269

Page

106

.107

110

112

12J>

126

126

128

128

128

129

130

131

132 l£l

168

168

171

2

193

199

^02

203

208

208

223

230

235

238

ix

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

X

IIST OF ILLUSTRATIONS

Figure Page

1. The logistic growth cycle ...... 19

2. A simplified model of carrying capacity as a dynamic equilibrium system

3. A simplified model of carrying capacity as a dynamic

31

U. Smallest land labor combination which will produce a particular output

5. Heterogeneous resource model

35

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

10. Systemic Model: Version 2

11. Resources and net societal product

12. Schumpeterian innovations

13. Restatement of systemic model in SETTLEMENT terms —

Systemic Model: Version 3

1U. Systemic Model: Version k

15. MacArthur's tk: a longevity alternative

59

69

108

U7

U8

5U

57

17. Map of the Hay Hollow valley

xi

In pocket

LIST OF ILLUSTRATIONS—Continued

Figure

18. Intensive survey -- Site 83

19. Intensive survey — Site 137b

Page l£6

21. Intensive survey — Site 196

22. Intensive survey — Site 201

23. Intensive survey -- Site lj.30

2U. Intensive survey — Site 5H

25. Comparison of pottery, pollen and radio carbon dates for intensively surveyed sites

26. The relationship between modern pollen and pollen spectra from floors of sites in the Four Mile,

Shumway and Hay Hollow areas l£8

159

160 l6l

16?

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

30. Pinyon pine pollen and the average number of rooms per site in the 100,? survey sample

211

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

xii

xiii

•LIST OF. ILLUSTRATIONS—Continued

Figure

35. Pinyon pine pollen and the values of the nearest neighbor statistic

36. Pinyon pine pollen and average room size

Page

23h

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

U7. Simulation 2: total population and total number of sites

U8. Simulation 3s total population and total number of sites ll9. Simulation U: total population and total number of sites

J>0. Simulation $: total population and total number of sites

51• Simulation 6: total population and total number of sites

2?3

25>U

25>5>

256

2^7

2^8

52. Simulation 7s total population and total number of sites 2^9

xiv

LIST OF ILLUSTRATIONS—Continued

Figure

£3. Simulation 8: total population and total number of sites

Total number of rooms by microhabitat from the actual area covered by the simulated map

Total number of rooms and sites from the actual area covered by the simulated map

Page

260

263

26h

LIST OF TABLES

Table

1. Summary of theoretical contributions

Page

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 136

6. Comparison of settlement sizes .

7. Pollen dates of intensive survey sites from Hay Hollow valley

. l£U

163

8. Carbon lit dates

9. Pottery types of intensive survey sites

16U

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 from Wo 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 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

16. Plant distribution of Microhabit 3

17. Plant distribution of Microhabit Ij.

181;

185

186

xv

LIST OF TABLES—Continued

Table

18. Plant distribution of Microhabitat 5

19. Plant distribution of Microhabitat 7

Page

187

188

20. Total plant distribution for. all quadrants by micro­ habitat

21. Correlation coefficients of total numbers of plants byspecies by microhabitat

189

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

2li. Total animal transect data

193

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

30. The survey ra and rb values

31. Densities of the habitation sites and the number of rooms by zone through time

32. The simulation: initial variable values

219

230

233

2U3

xvi

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.

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

5

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

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

7

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 (l

93h)

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 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 population units of variable size as resource abundance fluctuates.

Frank Lorimer (195U), a demographer by profession and a struc­

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

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

11

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. 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

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: 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 Economy r agreed with the Malthusian doctrine

on population growth, but asked what will be the distribution of wealth under Malthusian disequilibrium situations. Ricardo saw a tripartite 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 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 Keynes

1 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 + e a +

^ 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, certain major complexes of poorly defined influences on

1A

T H E R E S U L T O F P E A R L ' S

L O G I S T I C G R O W T H C Y C L E time

I B P R O B A B L E C Y C L E

O F B I R T H S A N D D E A T H S

D E A T H

BIRTH

I M P R O B A B L E C Y C L E

O F B I R T H S A N D D E A T H S

OEATH

BIRT H

1 0 M A L T H U S I A N C Y C L E

DEATH

BinTH

IE

B A B Y B O O M C Y C L E

O E A T H

1. The logistic growth cycle.

20

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) of a closed population with constant vital rates to its mortality 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 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 reaching sufficient generality to allow the advances in other disci­ plines to have any effect because there is no connecting bridge.

Numerous theories in many disciplines have made contributions to the

23

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 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

White, Steward et al: Popula­ tion pressure as a determinant of social organization which relieves diminishing returns.

Durkheim: the division of labor as a density and competition relief measure.

Kroeber: the agriculture den­ sity non-correlation.

Krzywicki: the isolation, size, social variability, re­ inforcement mechanism.

Lorimer: the expansion, uni­ lateral kinship group, fertility relationship, the marginality controlled fertility relation­ ship, the social organization fertility relationship.

Birdsell; model building.

Economics Demography

Smith: Equilibrium

Malthus: Resources as a limiting factor.

Ricardo: Distribution of resources for Malthusian disequilibrium.

Marx; Exogenous population growth.

Marshall: time depth of equilibrium.

Schumpeter: Innovations as a stimulus for disequilib­ rium.

Harrod: Exogenous popula­ tion.

Domar: Growth as a Mal­

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.

"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. 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, that:

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

(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 the existence of almost as many definitions as anthropologists,

27

which are directly relevant to the model.

Modifying Duncan's (l

959)

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: 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

t

CO

u

R E S O U R C E I

o o:

Z3

O

CO

LU ft:

R E S O U R C E 2

P O P U L A T I O N J>

P O P U L A T I O N I

P O P U L A T I O N

Figure 2. A simplified model of carrying capacity as a dynamic equilibrium system.

31

32

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

\

•es. leve changed

Replace resources with new res. level

Replace growth rate with new growth rate

Growth rate is positive

Calculate population growth

Population * pop. + ffrowtt 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

L a b o r

Figure U. Smallest land labor combination which will produce a particular output.

35

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

O

T O T A L

P O P U L A T I O N

C U R V E

/

/

T O T A L

R E S O U R C E

E

8

A + B + C + D C U R V E

v

F O R E S T

P O P U L A T I O N

G R A S S L A M D

P O P U L A T I O N

R I V E R I K E

P O P U L A T I O N

T O T A L P O P U L A T I O N

Figure 5. Heterogeneous resource model.

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.

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 v p

)

)

\

P

/

\ 7

Forest

Population

Grassland

Population

Riverine

Population

1 .

Desert

Population o .

TOTAL POPULATION

Figure 6, Heterogeneous resource model with spatial and temporal variation.

Z O N E A Z O N E B Z O N E C

P O P U L A T I O N

O P T I M A L «

P O P U L A T I O N P O P U L A T I O N

M A R G I N A L

M I G R A T I O N

• > G R O W T H

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

Z O N E A

Z O N E B

Z O N E C

I—

<

-J

3

CL

O

CL

T I M E

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

Z O N E

— B

Z O N E C

T I M E

C A R R Y I N G C A P A C I T Y

B E G I N S T O D R O P

Figure

Predicted population curves by microhabitat or ecological zone with diminishing resources.

t=-

U8

\ Input

+ time increment

Set zone counter

(J) « 7

zone couni zone counter as esource zone U) criane

Resource level remains constant ilesource level.

1 new re­ source level

Has rowth rate for zone c

Pop. zone (J) zone growth

Replace growth

Irate with new growth rate zone (J)

4

Calculate new negative growth rate

Calculate new pos. growth rate

Zone (J)

/other zonespossiblef

Figure 10. The systemic model: version 2. migrate pop­ ulation to other zones

Table 2. Spengler's interacting economic and demographic variables

Demographic Variables

M Mortality (general or age-specific)

F Fertility (general or age-specific) r Natural increase

M<j Differential mortality (intergroup dif­ ferences in fertility)

F(j Differential fertility (intergroup dif­ ferences in fertility) e Emigration i Immigration n Net international migration m Internal migration m d

Differential internal migration

T Population total or population density

Td Internal distribution of population total

R Rate of growth of total population

C a

Age composition of population

C s

Sex composition of population

Cg Qualitative composition of population

(e.g., genetic, educational)

C qs

Qualitative composition of a component of the total population (e.g., occu­ pational group, population of a region)

Economic Variables

Y Net national product or national income y Per capita net national product or national income

K Total stock of capital or income producing wealth k Per capita amount of capital or incomeproducing wealth

1 Land or other resources per capita t International terms of trade

D Functional distribution of income into wages, interest, etc.

D v

Distribution of income among persons com­ posing population

E Index of fullness of employment

S Annual volume of savings

I Annual volume of investment c Consumption c c

Qualitative composition of consumption

I c

Qualitative composition of investment

0

C

Occupational composition of population

t=-

>o

Economic

Variable

Y and y

K and k

1

D

D y t

S

I

E c and c c

Ic

0

C

Table-2. Spengler's interacting economic and demographic variables—continued

Demographic Variables by Which Affected

R>

T, C a

, Cq, Cg, possibly

Cq s

and

T, C a

, Cq, C s

T, R, T d

R» T, Cq, Td

R» ^q> ^d,

C a

, C s

R> Ti Cq

T, Cq, C a

, C g

, T(j

R,

Cq, C a

, C g

, T^

R, T, C a

, Cq, C g

, T(j

R» T, C a

, Tjj

R

*

^a»

^s> ^d

Demographic

Variable

M, F, e. i;

(r, R)

Fd, M d m, md, Td

°q»

C qs

Economic Variables by Which Affected y> ®y> c

» ®ct c c

Oc, Dy, E

Oc» ^y

°c» n y*

E

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 fined as the summation of the factors of production-wages, interest,

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 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 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

c o

3

CL

O

CL

NSP

Resources

Figure 11. Resources and net societal product. ft

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 ables: settlement population and settlement threshold. One may then apply the neo-Malthusian model to units of settlement as well as zones. 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) where; P (I, J)

1 settlement in 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:

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

Set Zone

Counter

J - 7

Is one Counte

0

Set Settle­ ment Counter to k

Tot. Pop.

Zone Pops

Zone Pop.

Settle. Pop as ettlement esources hange

Zone resources settlement resources

Tot. resources zone re.

Settlement resources remain constant

Decrease

J by one as ettlement op. growth change

Decrease

Counter

I

«

1

/

Calculate new positive growth growth leplace set­ tlement re­ sources with new level

Replace set­ tlement pop. growth with new erowth rate.

-Intra zonal mi^.

Decrease

Counter

I

Calculate negative growth 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

There are many factors which are involved in the migrant's,

P 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

the best zone for the migrants to locate by looking for the zone with 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 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 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

source base may take place through institutionalized intervillage 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 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 Holdridges

1

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 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 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) 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 between t and t + 1. The growth, then, is w

+

1) one wants to determine the "growth multiplier," it is easily calculated.

Since the above equation may be rewritten w (t

+ l)

(l + B -

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 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 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 distance migrated and the number of migrants may be different from the 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

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 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:

(J)> P (I, J)

M - P

(I, J)

- ST - M

8

103

F, X = dummy variables,

J

B the zone,

Resources. The equation defining resources is inductively 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 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 (U) = PT (U)/INSP (U)

If Z « POS 1 then BEST = 1

Z

- POS 2 BEST = 2

55 = POS 3 g = POS U

BEST = 3

BEST = h

BEST = £

BEST - 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,

the question is what location would allow the population of the new

uo$

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,

XX = n

P(I,J)XX(I,J)

PT(J) n

YY = ^

=1

P(I,J)YY(I,J)

PT

T

J

T where XX and YY are the coordinates of the new settlement, XX (I, J) 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:

XXX - RANF (0.0)

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

106

CON = the consumption constant

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.)

Since the pseudo random number generator delivers a number 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)»R

2

). e

2 p J

)* lo g

B

/^ where:

TK = the time to extinction

R = the growth rate

B «= the birth rate

D *= the death rate

The limiting parameters on TK have a critical effect on its size. For the same B and D, if P (I, J) 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

Consumption Equations and

Technological Innovation

Net Societal Product was defined as the summation of con­ sumption, investment, and organizational expenditure. This is

TK

Take

Off

108

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 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 time 1.

At A.D. 900 Pueblo architecture would be brought into the model value. Similarly, irrigation would be brought in at A.D. 1000 with

RES (J)

B

(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 initial population of 50. The initial resource areas for the zones are: zone 2 «= U9659U9 m.2

Ill

zone U = 22261157 m.

2 zone 5 "

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/m

2

/month zone 2 = 12.UOOOi 2.77U6 g/m

2

/month zone 3

= lli.6600i 2.3986 g/m

2

/month zone U

0

7.18001 U.22U7 g/m

2

/month zone 5

B

2.11*001 O

.86I4O g/m

2

/month zone 7 = 22.7001 13.73UO g/m

2

/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

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

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 for understanding the dynamic relationships between man, culture and 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.

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.

Pj » K(NSPj)

PJ - K(Rj) na

Proposition

The population of a zone is a direct function of the Net Societal Product of the zone.

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 c. Pa, Pb, Pc,

C Pj

Gj = Pj/Tj

Ta e

Tb «= Tc

Definition

Populations a, are members of the sets of populations.

Proposition The resources of zone a are less than the resources of zone b which are less than the resources of zone

Conclusion called marginal to optimal c.

Therefore, the population of zone a is less than the population of zone b which is less than the popula­ tion of zone c.

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 a t b, c, is equal.

.*.8. Ga <Gb < Gc Conclusion

115

Therefore, the average population growth rate of zone a is less than that of zone b which is less than that of zone c.

B. Pt «= Assumption

Conclusion

The summation of the populations of the zones is equal to the total population.

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

•*•11. Gb + Ga = Gc - Pt/T 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.

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.

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

A. Pt NSP t ^C*Rt

1. NSPt - K(Rt)

2. Pt = K (NSPt)

.3. Pt = K(Rt) a. R2, R1 C Rt

NSP t c. P2 PI C Pt

U. Rl> R2

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.

Proposition The Net Societal Product of a particular time is a direct function of the resources of that time.

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

Definition Resources at time 2 and set of resources.

Definition Net Societal Products at members of the set of net societal products.

Definition Populations at time 2 and 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.

117

.*.5. Pl> P2 Conclusion

Therefore, the population d. Pt

55 nt (spt)

•"•e. PI = nl (spl)

•*.f. P2 = n2 (sp2)

6. ra > rb g. P2 h. n2 a

B ra(Pl) rb(nl)

Definition

Conclusion

Conclusion the population at time 2.

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.

Therefore, the population at time 1 equal the num­ ber of settlements at time 1 multiplied by the average settlement size at time 1.

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.

Definition

The population at time 2, is equal to the rate of population change times the population at time 1.

Definition

The number of settlements at time 2 equals the rate of settlement change times the number of settlements at time 1.

•*•7. P2/P1 > n2/nl Conclusion Therefore, the ratio of the population of time 2 to the population at time ratio of the number of settlements at time 2 to the number of settlements at time 1.

118

,*.8. (n2 Sp2)/(nl Spl)

*.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 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.

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.

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 = (f

0

- r e

)/

(P*r e

where r e

= l/(2)» 2), r

0 is the measured mean nearest neighbor distance,

T

-

T q

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.

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)

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.

3.

Pt - K(NSPt) LLt k(Pt Proposition

PI

Conclusion

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.

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:

12U

The transformed statements of the hypotheses with their verbal equivalents are:

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

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•

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.

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

Apache 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$0 f 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

(Zubrow 1970). This may be partially and temporarily offset by the

132

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

and forth across the area in a line approximately five yards apart.

13U

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. One was east and one. was west

of

...the.

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 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. 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 Date

1

950-1150

3

1 *00-700

U

5

800-950

6

100-700

7

700-800

8

950-1150

9

1100-1200

10

950-1150

11 700-1100

12 950-1150

13 750-950 lU

15

700-900

16a 500-800

16b 800-1000

17 1100-1300

18

19

900-1100

21 850-950

22

23 950-1150

2U

25 950-1150

26

950-1150

27

28 800-900

29

Number of

Rooms in

Micro- Habitation

Habitat Sites

Maximum

Number of

Number of Rooms occu-

Habitation pied at

Rooms One Time

2

3

3

3

7

3

7

7

7

3

3

7

3

3

7

7

3

7

7

3

3

3

3

3

3

7

7

7

6

1

5

9

1

8

1

1

10

5

1

U

7

1

6

1

1

10

U

1

3

5

1

5

1

1

8

137

Table It. Archaeological sites in the Hay Hollow valley—Continued

Site

Number Date

30

900-1000

31 950-1150

33

950-1150

31+

950-1150

35

36

37

800-900

38

39

1100-1300

ko

950-1150

Ilia

950-1150

U2

U3

950-1150

10*

U5

700-900

U6

950-1150

U7a

U8 U00-700

h9

950-1150

52

950-1150

53

900-1100

5U

500-700

55

1000-1150

56

57

950-1150

58

U00-600

59

950-1150

60

950-1150

61

700-900

2

2

2

3

5

2

2

2

2

2

7

7

3

3

7

7

3

7

7

3

3

2

2

3

2

2

Number of

Rooms in

Micro- Habitation

Habitat Sites

Maximum

Number of

Number of Rooms occu-

Habitation pied at

Rooms One Time

3

6

3

5

2

u

2

5

1

6

17

1

2

1

3 a

1

5

17

1

1

1

2

3

1 u

13

1

1

1

2

138

Table U. Archaeological sites in the Hay Hollow valley—Continued

Site

Number Date

Number of

Rooms in

Micro- Habitation

Habitat Sites

Maximum

Number of

Number of Rooms occu-

Habitation pied at

Rooms One Time

62

950-1150

63

950-1150

6U 700-900

65a

900-1000

66 900-1000

67

68 950-1150

69 1350-11*50

70 950-1150

71 950-1150

72

950-1150

73

950-1050

7h

950-1150

75

950-1150

76

77

U00-800

U00-700

78 950-1150

79 950-1150

80

loou-noo

81 950-1150

*83

1100-1300

8Ua 950-1050

85

950-1050

86

950-1150

87a 950-1150

88

89

650-750

90 650-750

91 550-650

92

600-800

2

2

2

2

2

2

2

2

2

2

2

2

2

3

7

7

2

2

2

2

7

7

7

7

7

7

7

7

7

7

1

1

1

1

6

25

1

3

3

850-1025 7 UO

(correction by intensive survey)

1

1

1

1

5

15

1

3

2

,

1

1

1

1

U

12

1

2

2

139

Table lw Archaeological sites in the Hay Hollow valley—Gontinued

Site

Number Date

93

700-800

9k

500-700

95

500-700

96 700-900

97

98

850-950

850-1000

99a 800-950

100

900-1000

102

103

200-500

950-1150

10U

105

700-900

950-1150

107

108

109

110

111b

950-1150

112 950-1150

121

950-1150

122 950-1150

123 950-1150

12Ua 950-1150

125

800-900

125b 900-1050

127

128

950-1150

950-1150

129

130 600-700

131

U00-700

132

Number of

Rooms in

Micro- Habitation

Habitat Sites

Maximum

Number of

Number of Rooms occur-

Habitation pied at

Rooms One Time

3

2

3

3

7

3

3

6

7

7

3

3

3

3

7

7

7

7

7

3

3

3

7

7

7

7

7

7

3

2

3

2

5

1

2

1

u

1

1

3

2

5

1

1

1

U

1

1

2

2

5

1

1

1

3

1

1

lUo

Table U. Archaeological sites in the Hay Hollow valley—Continued

Site

Number

Date

133

900-1100

13U

135a

500-700

135b 950-1150

135c

800-950

136 900-1000

137a 500-700

*13

960-1100

139

1000 B.C.

IhO

900-1000 mi

900-1000 lij.2

800-900

Hi3

HiU

1U5

11*6

950-1000

950-1150

700-800

800-900

1U7

650-750

Ui8

800-900

1U9

950-1150

150

151a

950-1150

152

153

900-1000

15U

155

950-1050

156 800-900

156a

950-1150

157

1000-1050

158 700-800

7

3

3

3

3

7

7

7

7

7

7

7

7

7

7

7

7

5

7

7

7

7

7

7

7

7

Number of

Maximum

Number of

Rooms in Number of Rooms occu­

Micro- Habitation Habitation pied at

Habitat Sites

Rooms One Time

2

20

10

3

1

2

1

2

*137b

925-97* 7 11

(correction by intensive survey)

1

20

10

2

1

1

1

2

t

1

16

8

2

1

1

1

2

lltl

Table U# Archaeological sites in the Hay Hollow valley—Continued

Site

Number Date

1

$9

800-900

160 700-800

161 900-1000

162 700-800

163

I6h

165

900-1000

850-1000

166

167

168

169

170

171

900-1050

800-900

900-1000

500-700

172 55o-65o

17U

175

700-800

176a 500-700

177

178

600-700

900-1000

180 800-900

181 700-900

182

183

950-1050

1000-1150

185

600-700

186

950-1050

187

600-800

188

1150-1282

189 900-1000

191 900-1000

192

900-1000

Number of

Rooms in

Micro- Habitation

Habitat Sites

Maximum

Number of

Number of Rooms occu-

Habitation pied at

Rooms One Time

6

3

3

1

99

7

5

2

3

1

59

6

h

2

2

1

li 6

5

1U2

Site

Number

Date

Number of

Rooms in

Micro- Habitation

Habitat Sites

Number of

Habitation

Rooms

Maximum

Number of

Rooms occu­ pied at

One Time

193

500-700

19U

700-850

*195

1000-12000

*196 1100-1280

197

199 600-750

*201 1100-1200

213

21U

215

216

217

218

220

221

222

223

22k

203

20U

205

206

207

208

950-1150

950-1150

950-1150

950-1150

950-1150

209 950-1150

210a

950-1150

211 950-1150

212 950-1150

1300-^00

1150-1300

900-1100

7

7

7

7

7

7

7

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

25

1

8

20

*195

1150-121)0

7 11

*196

1150-1225

7 22

*201

1175-1300 w

80

(corrections by intensive survey)

17

1

8

20

13

1

6

16

Table k» Archaeological sites in the Hay Hollow valley--»Continued

11*3

Site

Number Date

225a 300-600

226 900-100

227

228

229

1100-1200

230

231

232

233

231*

235

236

1250-1350

237

239

2U0

2U1

2U2

21*3

700-900

950-1150

250-600

2UU

270

271

500-700

850-1050

273

275

276

277

600-700

1000-1100

900-1000

900-1000

278

282

285

286

900-950

279

1*50-650

280 1000-1050

281 900-1000

950-1050

800-950

Number of

Rooms in

Micro- Habitation

Habitat Sites

Maximum

Number of

Number of Rooms occur

Habitation pied at

Rooms One Time

50

50

39

15

2

6

1

1

2

15

2

5

1

1

1

12

2

h

1

1

1

Table lu Archaeological sites in the Hay Hollow valley—Continued

HiU

Site

Number Date

Micro-

Habitat

Number of

Rooms in

Habitation

Sites

301

1000-1100

310 950-1050

311

312 950-1150

313

950-1150

31U

950-1150

320

321a +b

322

3

323

330

900-1000

331 950-1150

332

800-900

333

33U

7

7

7

7

200 BC-AD 300

5

800-900

7

33*

950-1150

7

336

800-900

7

337

950-1150

7

338

U02

950-1150

339

Uoo

950-1150

1000-1150

U01

1000-1100

1000-1100

2

7

7

2

2 i|03

UOU

1(20

1000-1100

1000-1100

1000-1150

7

7

7

7

7

7

h

2

2

2

2 U21 1000-1150

*1*30 1000-1150

UUO

1000-1150

7

5

*1*30

1

1

1 u

20

h

1075-1100

7 7

(correction by intensive survey)

Number of

Habitation

Rooms

1

1

1

U

15

3

Maximum

Number of

Rooms occu­ pied at

One Time

1

1

1

3

12

2

Table U. Archaeological sites in the Hay Hollow valley—Continued

Site

Number Date

Number of

Rooms in

Micro- Habitation

Habitat Sites

U5o

1000-1100

fcSL

U60

U6l

1000-1100

950-1050

U62 1150-1200

U70

1000-1100

U71 1000-1100

U80

2*81

U82

1000-1100

U90 700-950

500

850-950

501

700-800

505

900-1000

506

700-900

507

1000-lii00

508 1000-1150

^10 1000-1100

*$11

1200-1U50

512

700-1000

513

515

1000-1050

520 1200-1350

521

1150-1250

525

800-900

530

600-700

535

800-950

5U0

1000-1050

5U5

950-1150

7

7

7

7 u

7

7

3

7

7

7

7

7

7

7

7

5

u

7

7 a a u

7

7

7

9

3

2

2

7

3

2

3

26

5

3

Hi

25

22

2

15

9

3

U

*Sll 1300-lli00

h

15

(correction by intensive survey)

Maximum

Number of

Number of Rooms occu-

Habitation pied at

Rooms One Time

7

2

5

2

1

1

7

2

2

2

19 a

2

8

19

13

1

15

7

2

3

1

1

5

2

2

2

15

3

2

6

15

10

1

12

5

2

2

1h6

Table U. Archaeological sites in the Hay Hollow valley—Continued

Site

Number Date

55o 1100-1300

5#

1000-1050

560 950-1050

565 750-850

600 1000-1100

605 1000-1300

610 950-1100

611 1050-1100

612 1000-1150

613 1050-1150

61U

615

950-1100

616 800-1000

617 1000-1150

620 1000-1150

621 1000-1150

622 1050-1150

630

631

632 950-1050

63U

1000-1150

635

636 1000-1150

637 1000-1100

6I|0

6U1

1000-1100

61)2

6U3

6i0i

6Ii5

1000-1100

Micro-

Habitat

Number of

Rooms in

Habitation

Sites

Number of

Habitation

Rooms

Maximum

Number of

Rooms occu­ pied at

One Time

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

7

6

1

U

8

50

3

3

U

1

3

8

33

2

2

3

1

2

6

26

2

2

7

7

7

7

7

7

7

5

5

5

7

3JU7

Table U. Archaeological sites in the Hay Hollow valley—Continued

Site

Number

61*7

6U8

6h9

Date

950-1050

1100-1200

6^1

950-1050

6^2

65U

850-950

655

800-900

656

1000-1100

657

658

950-1050

1000-1100

850-900

659

660

661 800-1100

662

200-700

663a 200-700

663b 1000-1100

670 950-1050

671 900-1050

672

673

1000-1100

1000-1150

67U

675

676

950-1200

950-1200

677 950-1050

678

679

800-900

680

850-1050

681 900-1050

682 1000-1150

Maximum

Number of

Number of

Rooms in Number of Rooms occu­

MicroHabitation Habitation pied at

Habitat Sites Rooms One Time

5

5

5

7

5

U

5

5

7

7

7

5

5

5

U

U

7

7

U

7

U it

7

7

7

7

7

7

8

12

7

70

1

1

5

1

1

1

8

8

12

5

70

1

1

6

h

1

1

1

6

6

9

U

55-65

1

1

3

1

1

1

5

XU8

Table H. Archaeological sites in the Hay Hollow valley—Continued

Site

Number Date

683

800-900

695

696

700

701

702

703

70U

705

68U 1050-1150

686

950-1050

690

950-1050

691

692

900-1000

1000-1050

693

69k

900-1000

900-1050

800-900

1000-1100

1050-1100

706

707

1000-1100

708

709

710

711 1250-1300

712

713

71U

715

716

717

725 1150-1250

Micro-

Hab tat

Number of

Rooms in

Habitation

Sites

Number of

Habitation

Rooms

Maximum

Number of

Rooms occu­ pied at

One Time

h

1

1

8

3

1

1

6

2

1

1

5

1

1

1

1

1

1

U-5

U-5 a-5 u-5 a-5

Table 5. Habitation rooms per site by site: Longacre survey.

1U9

Site

Number

102

103

10U

105

106

177

186

188

202

207

208

209

210

211

212

213

21ii

215

216

217

228

230

Date

800-1000

1100-1300

700-900

900-100

1100-1300

700-900

550-750

600-800

600-800

900-1100

900-1100

800-1000

700-900

800-1000

600-800

600-800

700-900

500-700

800-1000

800-1000

700-900

800-1000

Number of

Rooms in

Habitation

Sites

5

5

3

3

5

15

2

25

1

5

60

175

5

h

5 l

3

3

30

6

15

h

Maximum

Number of

Number of Rooms occu­

Habitation

Rooms pied at

One Time

15

2

2

3

22

h h

3

2 h

19

1

5

U7

103

k

U

5

1

5

11

3

2

2

18

U

9

2

3

2

2

3

12

2

15 l

h

37

80

3

3

h

1

3

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

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 83

NS 137

NS 19$

NS 196

NS 201

NS 1*30

NS £11

Intensive Survey

U3

10

11

22

76

7 lit

Surface Survey

2$

20

25

1

20

20 lit

37

36

39

Sit* 83

10

H

N

Site 137 B

10 Meters

Figure 19

Intensive survey — Site 137b

r

vn o

i

Site 195

10 Meters

I a

3

4

5

6

7

, ». —

195. vn

oo

m

t-

W vo /: vn in

IT

(M

IO I

3

4i

7 ! i

2

5

6

$\ie

A30 fig

0

23 < we e

Si^ e

160

Site 511

10

Meters

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.

Table 7. Pollen dates of intensive survey sites from Hay Hollow valley. Pollen dating by Richard H. Hevly.

163

Pollen Sample No.

1-6

7-11

Site No.

201

83

137b 12-1 3

U4

-I6

17-18

19

20-22

195

511

U30

196

AP/NAP Ratio Dates

Low AP 650-925? 975-1075;

1150-1300

Insufficient pollen

Increased AP 575-625; 925-975;

1075-1150+ 1300+

Low AP 650-925; 975-1075;

1150-1300

Increased AP 575-625; 925-975;

1075-1150+ 1300+

Increased AP 575-625; 925-975;

1075-1150; 1300+

Low AP 650-925; 975-1075;

1150-1300

Site No*

83

195

*196

137

201

1*30

511

Table 8. Carbon lU dates.

Geochronology

Laboratory No. Date

Gx-1661

Gx-1660

1020± 85

1155± 85

690± 90

GX-I66I4

GX-1662

GX-1665

No C-Uj dates run

710i 95

136O£ 90

Gx-1663 990i 80

Range

8U5-1015

1070-12U0

600-780

610-805

1270-1U50

910-1070

20 feet outside of the pueblo and may not be associated.

16U

165

Table

9,

Pottery types of intensive survey sites.

Pottery Type

Sites

83 *137b 195 196

201

U30 511

Snowflake Black-onwhite

•White Mount Blackon-white

i£,\

Red Mesa Black-on-white

X

St. Johns 31ack-on-red

Show Low Black-on-red, exterior corrugated

X

X

Show Low 31ack-on-red

Wingate Black-on-red

San Francisco Red

X

- X

X

X

Alma Plain

Plainware

Lino Gray

Four Mile Polychrome

St. Johns Polychrome

Querino Polychrome

X

X

X

X

X

X

X

X

X

X X

X

McDonald Painted Corru­ gated

Corrugated - Plain

X

.. X

Corrugated - Indented

X

Painted ware - no design elements

Black-on-white - no design elements

Unidentifiable

Estimated Dates

X

X

X

X

X

X

850-

1300

900-

1000

X

1150-

1250

X

X

X

X

X

1150-

1250

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

1125-

1250

1000-

1100

1300-

lliOO pottery distribution...

166

Site Number

NS 83

NS 137

NS 195

NS 196

NS 201

NS U30

NS 511

Table 10. Comparison of settlement dates.

Intensive

Survey Date

300-1025

930-970

1150-121*0

1150-1225

1175-1300

1075-1100

1300-1U00

Estimated 1967-68

Survey Date

1100-1300 c^

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.

.Carbon U

Time

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. 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

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 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 lowlands, although not divided on geographic or edaphic criteria were

172

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:

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.

173

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

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 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 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:

Table 11. Tree estimates from two 90° transects compared to actual niunber of trees within quadrants with variable transect length and quadrant size.

175

Size of

Quadrant in Meters

17 x 17

3h

x

3h

51 x 51

68 x 68

17 x 17

3h

x

3k

51 x 51

68 x 68

17 x 17

3h

x

3h

51 x 51

68 x 68

17 x 17

3h x

3h

51 x 51

68 x 68

17 x 17

3h

x

3h

51 x 51

68 x 68

17 x 17

3h

x

3h

51 x 51

68 x 68

17 x 17

3h

x

3h

51 x 51

68 x 68

17 x 17

3h

x 3l»

51 x 51

68 x 68

Sample

Number

5a

5b

5c

5d

6a

6b

6c

6d

3a

3b

3c

3d

Ua lib

Uc lid la lb lc

Id

2a

2b

2c

2d

7a

7b

7c

7d

8a

8b

8c

8d

Estimate of Number of Trees from

Two Transects

2 x 1

5 x 2

8 x 3

10 x 5

1 x 0

3 x 2

3 x It

U x 6 l x l

2 x 2

3 x 3

5 x 5

2 x 1

3 x 2

U x 2

5 x 3 l x l

3 x 3

U x

h

5 x U l x l

2 x 1

3 x 1

U x 1 l x l

2 x 1

U x 1

6 x 3 l x l

2 x 3

3 x 3

5 x 5

Actual

Number of Trees in Quadrant

3

6

11

2h

3

8

Hi

23

3

10

10

20

5

10

21

3h

3

7

17

28

3

6

12

28

3

7

19

35

h

10

18

27

Percent

Error

-60

0

Hi

hi

-66

-67

-67

-75

-86

-67

-71

-79

-h9

-29

-Hi

-67

-33

-18

U

-33

-25

-U3

-35

-67

-10

60

0

-75

4i0

-50

-7

Table 11. Tree estimates from two 90° transects compared to actual number of trees within quadrants with variable transect length and quadrant size—Continued

176

Sample

Number

9a

9b

9c

9d

10a

10b

10c lOd

Size of

Quadrant in Meters

17 x 17

3k

x

3h

51 x 51

68 x 68

17 x 17

3)4 x 3U

51 x 51

68 x 68

Estimate of Number of Trees from

Two Transects l x l

2 x 2

3 x 2 k x 3 l x l

2 x 1

2 x 2

3 x 3

Actual

Number of Trees in Quadrant

3

7

13

19

2

3

9

17

Percent

Error

-67

-H3

-37

-50

-33

-56

-U7

Average error a = 62$, b -

3h% t

c a

33$, d =

22%,

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.

Size of

Quadrant in Meters

17 x 17

3h

x 3U

51 x 51

68 x 68

17 x 17

3U x

3k

51 x 51

68 x 68

17 x 17

3h

x

3h

51 x 51

68 x 68

17 x 17

3h

x 3U

51 x 51

68 x 68

17 x 17

3h

x

3h

51 x 51

68 x 68

17 x 17

3U x

3h

51 x 51

68 x 68

17 x 17

3it x

3h

51 x 51

68 x 68

17 x 17

3h

x

3h

51 x 51

68 x 68

Sample

Number la lb

1c

Id

2a

2b

2c

2d

3a

3b

3c

3d

7a

7b

7c

7d

6a

8b

8c

8d

Ua lib

Uc

bd

5a

5b

5c

5d

6a

6b

6c

6d

1 x 1

2 x 2

3 x 3

3 x it

0 x 1

2 x 2

3 x 3

1* x U

2 x 0

3 x 2 it x 2 li x 3

1 x 1

2 x 2

2 x 3

3 x 3

1 x 0

2 x 2

2 x 2

3 x 2

1 x 0

2 x 2

2 x 3

2 x it

1 x 0

2 x 2

3 x 3 it x 5

2 x 2

3 x U it x 5

It x

6

Selected Actual

Transect Tree Number of Trees

Estimate in Quadrant

2

9

17

25 it

10 lit

26

2

8

12

20

2

6

10 lit

1

7

13

19

3

10

18

27

2

10

22

32

5

11

17

30

Percent

Error

-50

-33

-10

-lit

-100

—it-3

-30

-16

-100

-33

-53

-U8

-75

-60

-57

-65

-100

-50

-75

-70

-100

—60

-67

-70

-100

-60

-59

-37

-20

9

17

-20

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

9a

9b

9c

9d

10a

10b

10c lOd

Size of

Quadrant in Meters

17 x 17

3h x 3h

51 x 51

68 x 68

17 x 17

3U x 3U

51 x 51

68 x 68

Selected Actual

Transect Tree Number of Trees

Estimate in Quadrant l x l

2 x 2

3 x 3

U X U

l x l

2 x 2

3 x 2

U x 2

3

6

1

h

30

U

8

25

36

Percent

Error

-67

-33

-33

4i6

-75

-50

-76

-76

Average errors a =

79%,

b =

hl%,

c =

hk%,

d =

h6%.

E » is the estimate to be compared with the 68m. x 68m. quad.

179

the estimate is being made.

10

x 100 where:

^ K n=l

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

Table

13

• Quadrant estimates for

68m.

x

68m,

quadrants based on

17m.

x

17m., 3Um.

x 3Um., and 5lm. x

!?lm.

quadrants.

180

Sample

Actual number of trees in

17m. x 17m. 3Uni« x 3Um. 5lm. x 5lm. 68m. x 68m.

Estimate Estimate Estimate Quadrant

Group I based on Table 11

1

2

80

U8

3

U

U8

5

6

7

8

U8

U8

U8

U8

9

10

6U

U8

32

1

2

3

U

5

6

7

8

9

10

Group II based on Table 12

32

16

32

6U

32

U8

32

80

U8

6U

UO

28

2h

32

UO

2U

28

UO

28

12

UO

UO

UU

2U

32

26

28

36

UO

32

37

30

20

25

18

21

3U

32

23

16

17

23

30

25

21

32

39

30

25

UU

3k

28

2U

23

20

28

35

27

19

17

27

32

30

30

36

1U

19

25

26

20

Error

Group I

Group II

10156

72JS

2056

31*

,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,

Number of plants in quadrants

1 2 3~ h "IT 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 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

U

17

8 6 ii 11

1

3

1 U

30

2

1

1. li

1

7

19 1

1'

2

1

9

6

2

1$

1^

U

2

U

*87

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

Number of plants in quadrants

1 2 3~ It ~T"

9

52 28 13 13 2?

UO

1 U

22

16

2

*6

13

17

3

1

2

U

1

7 3

1

1

9

9

12

1

6

1

1

185

Table 16. Plant distribution of Microhabit 3.

Number of plants in quadrants

1 2 3~ h 5 Species

Trees

Pinyon Pine

Juniper

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

6

1

17

3

2

3l|

11

1

U

12

32

U

1

3

2

3

3

$

U

U

^

2 1

2 1

1 1

1

1

U

1

1

1

1

27

5

3

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)

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 16

17

1

5

2

32

3

2

h

12

1

6

3

2

20

Hi

2 17

1

2

186

187

Table 18. Plant distribution of Microhabitat

Number of plants in quadrants

1 2 3~ U IT 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

18

2 f>

9 2 1 2

9

3

1 .

U

21 .

2

2

11

3

1 1

12

2 8 1

1

3

U

1

12 10

12

1

U

8

3

10

1

£

Table 19. Plant distribution of Microhabitat 7.

Number of plants in quadrants

' l'" 2 3~ h Species

Trees

Pinyon Pine

Juniper

Shrubs

Sagebrush (Artemisia)

Rabbitbrush (Chrysothamnus)

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

12

2

2

1

II4.

3

2 1

2

3>1

7 17

1

5k

1

1

3

30

35

Ul

1

3

1U

3

8

188

189

Table 20. Total plant distribution for all quadrants by microhabitat.

Species

Number of plants in all quadrants in microhabitat

1 2~ 3 U 5 ~7

Trees

Pinyon Pine

Juniper

29

9

131

26

1

3

70

55

1

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

Herbs

Grass: Aristida

Agryopyron

Bouteloua

Hilaria

Muhlenbe Gia

Sporobolus

Orysopsis

12

19

Other: Aster

Boerhaavia

Goosefoot (Chenopodium) red mist

1

Snakeweed (Guteriezia)

Buckwheat (Eriogonum)

Locoweed (Astragalus)

Other; Plantain

Gramma

1

Artemisia wormwood

Sphaeralceo

Cryptantha

Aster

2

15

8

13

2

8

1

9

30

UO

8

61 22

19

1

13

3

7

2

6

1

5 a

h

l

2

1

9

1

3

2

h

3

1

3

1

1

1

1

1

1

7

1

9

13

3

15

1

h

1

1

6

61

3U

1U

12 92

33

1

35

19

35 33

3

1

20 10

65

2

1

2

1

1

2

1

3

5 Hi

8

species by six microhabitats. The resulting chi square was signifi­

190

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.

n l t l

X i y i

' ( J l

7 1

)

1=1 \1=1 /

^ n -r< n)'

1=1 \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 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

hypothesis of meaningful correlation is the disproof of the null

191

sampling distribution of r is approximated by a normal curve. Its mean and standard deviation are then equal to m = 0 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 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 II III

XXX XXX XXX

.i|2

.U9

.16

XXX XXX

.69

.'85

xxx

.17 .80 .lil

.66 .31 .E>5

IV

XXX

XXX

xxx xxx

.78

.09

V

XXX

XXX

xxx xxx xxx

.11

VII

XXX

XXX

xxx xxx xxx xxx

The underlined values are the significant ones. If one uses mean data rather than sum data the correlation coefficients are as follows. By

192

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 /

I II in IV

XXX XXX XXX XXX

.U3

Tup

715

.16

XXX

.61

XXX

XXX

XXX

XXX

.5U

XXX

.ao

"31 .78

.68

.31 .

ToH

V

XXX

XXX

XXX

XXX

XXX

VII

XXX

XXX

XXX

XXX

XXX

XXX

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 from live trapping. Each transect covered a width of l/lO mile. The total transect area represented is: zone I ... 1.380 square miles zone II ... .1M square miles zone III ... .110 square miles zone 17 ... 1.6£0 square miles zone V ... .5>Ui square miles zone VII ... 3.0£li square miles zone VIII ... 6.9 square 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

II

III

IV

V

VII

VIII

I II III

XXX XXX . XXX

.1*2

XXX XXX

TBI

-.01

XXX

.38

75B

.31

-.09

735

.02

TUT

73B

.15 .17

.32

-.03

IV

XXX

XXX

XXX

XXX

M3

73?

785

V

XXX

XXX

XXX

XXX

XXX

.63

VII

XXX

XXX

XXX

XXX

XXX

XXX

.b2

VIII

XXX

XXX

XXX

XXX

XXX

XXX

XXX

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

1

2

11

1

1

7

7

5

1

2

30

1

2

5

17

1

1

20

1

1

1

1

3

2

2

1

2

2

1

6

U

2

3

2

1

1

2

1

1

1

1

1

£

1

1

1

1

17

2

21

13

7

3

13

U7

5>2

1

U

8

1

7

6

1

1

13

3

23

6

U

<?

75

33

3

3

2

2

19

6

6

195

Table 2U# Total animal transect data—Continued

Animals

" T

Birds (Continued)

Barn Swallow

Cliff Swallow

Other Hawks

Red Tail Hawk

1

Sparrow Hawk

Towee

Black and White Warbler

1

Speedbird

Towns Tanager

Thrashers

Peewee

1

Blackbird

Owls

Orioles

Plain Titmouse

Kingbird

Other and Unknown 26

2

5

Microhabitats

3 E 5 7 5"

3

1

U

2

1

3

3

1

1

3

3

3

25 k

3

3

1

6

1

11 10 h9

196

Table 25. Total animal transect data by density per square mile.

Animals

Microhabitats

T jT jT TT jT

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 l.U

.7

2.2 l.U

.7

.7

.7 l.U

8.0

.7

.7

6.9

6.9

U8.6

5.1

3.6 6.9

.7 l.U

21.7

6.9

.7 l.U

6.9

3.6

6.9

12.3

.7

.7

1U.5

20.8

9.1

1.8

1.2

.6

.6

1.2

1.2

.6

.6

10.8

7.2

3.6

5.U

3.6

1.8

.3

.3

.6

.3

.3

.3

.3

.3

1.6

.3

.3

.1

.9

.6

.1

.6 2.0

.U

10.3

.3 .U

9.1

.3 .3

1.2

.3

12.7

7.2

U.3 2.7

7.8

.9

U.2

1.0

.9

9.1 1.8

1U.U

7.5

2.0

7.8 2.0

28.5

1.8

1.3

10.9

31.5

12.6 1.6

U.8

Table 25. Total animal transect data by density per square mile-

Continued

197

Animals 1 2

Microhabitats

3 U $ 7 ^

Birds (Continued)

Barn Swallow

Cliff Swallow

Other Hawks .7

Red Tail Hawk

Sparrow Hawk

Towee .7

Black and White Warbler

Speedbird .7

Towns Tanager

Thrashers

.7

Peewee

Blackbird

Owls

Orioles

Plain Titmouse

Kingbird

Other and Unknown 18.8 3U.7

27.3

.6

.3

.1

.6

#

U

.6

.6

.1

.6

.6

,6 .1*

.1

1.8

10.8

1.8 .3

15.1 19.9 3.3 7.1

was .1U5 and r had to be greater than

,28k

or less than

198

-.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

Dick Hevly directed a hunting and trapping expedition which took place between September 3-6 and 19-20. Both vertebrates and in­ 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

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

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 1 70.7500 ± 10.2971 g/m

2

Habitat 2 36.9900 ± 2.6608 g/m

2

Habitat 3 26.6060 - 11.8317 g/m

2

Habitat U

2l>.

2020 ±

9.9155

g/m

2

Habitat

$ l\2

.U6£0

±

12.6035 g/m

2

Habitat 7 62.3U6 ± 7.8297 g/m

2

Adding the results of the vertebrate and invertebrate survey to the floral standing crop, it is possible to determine the total habitat 7 — 71.856 g/m

2

, 38.096 g/m

2

, 27.066 g/m

2

, 2U.556 g/m

2

,

U2.819 g/m

2

, 62.806 g/m

2

. 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 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 microquadrants 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 1 microhabitat 2 microhabitat 3 microhabitat h microhabitat 5 microhabitat 7

10.0800 ± 2.1513 g/m2

12.1*000

2,171x6

g/m2

Hi.6600 ± 2.3986 g/m

2

7.1800 ± 1*.221*7 g/m

2

2.11*00 ± 0.361*0 g/m

2

22.700 i 13.731*0 g/m

2

It is important here to note that the productivity figures do not exactly correspond to the carrying capacity figures. In other

has the largest productivity. Zone 7 has the largest productivity.

202

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^

0 f 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.

In order to determine the amount of fluctuation two factors

205

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 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

ARBOREAL POUEN ir

• NON-ARBOREAL POLLEN •

^ECONOMIC POLLEN-|

/ T ,, /'* /

/ / f i .. f ' f / f ' i f

•J .? 6 V o

RrM

LZ£2

I - -

«t«n%

UVMI tCiUi OH 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 O O

% P I N Y O N

O O

P I N E

O

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

Hollow valley, while the second estimates actual carrying capacity values. The results of both must be compared to the predictions of

209

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 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

N U M B E R

H*

<3

3 ro

CO

300

400

o*

®

•1 o rr o-

Hc+ fu

C*

H*

O

3

500

600-

•1

0

m 700-

1

CO

800

? o

(D

3

«+

E

8

CO

1

M

900-

1000-

I 1 0 0

/

H A B I T A T I O N R O O M S

1300

012

- o

- J . I I I I I

N U M B E R O F S I T E S

i\> o o o o

OI o

_JL_

100

ro vo

200

IO h3 vn o

C^"

P>

CO M

300-

J 1

(O* c co n>

• 1 o

CO

H*

C^

CI)

400

500-

m

600

700 s-

a

CO

800

900

(D

S

P.

O* o d-

P*

I 0 0 0

I 100

1200

1300

1400

J> o

h

r ?

I i

1 i w

OI o

mi

112

relationship between the optimal and marginal zones. Second, these

212

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 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.

HI TTI

Zones

iv

v vTT

Area of the zone in mi.2

Biomass in g/m2/ day

Kcal/g biomass

1.17

.3

U

.O

Population based on 5% consumption and 2J?00 kcal per person

70

2.15

.2

U.O

80

.92

.5

U

.O

190

1.U3

.U

U

.O

120

2.81; 9.92

1.0

U

.O

290

2.0

U

.O

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.

II III

Zones

IV V VII

Zonal Distributions

Ar©a of th© zones in mi.- 1.17

Floral standing crop in g/m2/ day 2.36

Floral produc­ tivity in g

/mV

day

,3h

Vertebrate stand­ ing crop in g/m^/ day .053

Invertebrate standing crop in g/m2/day 1.0

2.15

1.23

.111

.92

.89

.U9

.053 .180

1.1*3 2.8U

.81 1.U2

,2k

,0li7

.07

.0U7

9.92

2.08

.76

.180

1.0 1.1 .26 .26 1.1

Total known biomass in g/m^/ day 3.753 2.693 2.660 1.357 1.797 It.120

Population at Consumption

Population based on floral stand­ ing crop 572 5U9

Population based on floral pro­ ductivity

Population based on vertebrate standing crop

8U

13

18U

2U

Population based on invertebrate standing crop 2^2

Population based on total known biomass 911

UU5

1202

169

93

3h

210

50U

239

71 lU

77

U01

833

U2

28

153

1056

U272

1555

370

2261

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. 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

Floral

Floral productivity

1 a

Vertebrate

Invertebrate

3.5

3.5

II

a

3

3.5

3.5

III

Zones

IV

5

2

1.5

1.5

6

5

5.5

5.5

V

3

6

5.5

5.5

VII

2

1

1.5

1.5

218

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

Kendall's concor­ dance resources areally adjusted

Spearman's rho resources not areally adjusted

Spearman's rho resources areally adjusted

Sites and a single resource

Sites and floral stand­ ing crop

Sites and floral produc­ tivity

Sites and vertebrate standing crop

Sites and invertebrate standing crop

Sites and two resources

Sites, floral standing crop and floral productivity

Sites, floral standing crop and vertebrate standing crop

Sites, floral standing crop and invertebrate standing crop

Sites, floral productivity and vertebrate standing crop

.51

.7h

.91

.91

,k9

.U7

.U7

.52

.7U

.80

.89

.80

.61

S.

.68

.75

.09

.U8

.39

.39

M9

.60

.77

.60

ro

(-»

VO

Table

29.

The cross-zonal relationship between the ranked site distribution and types of resources-

Continued

Kendall's concordance resources not areally adjusted

Kendall's concor­ dance resources areally adjusted

Spearman's rho resources not areally adjusted

Spearman's rho resources areally adjusted

Sites, floral productivity and invertebrate standing crop

Sites, vertebrate stand­ ing crop, and invertebrate standing crop

.52

.67

Sites and three resources

Sites, floral standing crop, floral productivity, and vertebrate standing crop .£2

Sites, floral standing crop, floral productivity, and invertebrate standing crop .$2

Sites, floral standing crop, vertebrate standing crop, and invertebrate standing crop .^1

Sites, floral productivity, vertebrate standing crop, and invertebrate standing crop .71

.80

.72

.59

.6£

.62

»71

Table 29. The cross-zonal relationship between the ranked site distribution and types of resources-

Continued

Kendall's concordance resources not areally adjusted

Kendall's concor­ dance resources areally adjusted

Spearman's rho resources not areally adjusted

Spearman's rho resources areally adjusted

Sites and four resources

Sites, floral standing crop, floral productivity, vertebrate standing crop, invertebrate standing crop .68 .61

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. and all the "New Survey" habitation sites in the central 100??, and

R O O M S P E R S I T E

100 BC lOOAO

300

500

700

<;

900

1100

1300

1500 o o o

% P I N Y O N P I N E

CI

o

0> o

a

o

Figure 30. Pinyon pine pollen and the average number of rooms per site in the 100$ survey sample.

% Pinyon Pine Rooms per Site

Figure 31. Pinyon pine pollen and average number of rooms per site in the 100$ and both

2$%

samples•

226

227 both peripheral 2$% surveys. The only known sites which are excluded 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

-70

40-

-40

20o

M

V-

0

Q.

V)

E o ce

o-

o o o

•- M CO

o o

o

o s

Time o

00 ill

%. Pinyon Pine o

€K

o o

8 2 o

<N o

n

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.

-10

c

£

-20 fcS

228

Rooms per Site

IOO

H

BC

100-

AD

300-

500-

©

E h

700-

900-

1100

1300-

- % Pinyon Pine

% Pinyon Pine

/A Rooms per Site

Figure 33. Pinyon pine pollen and average number of rooms for all sites, the test of the generalized hypothesis.

229

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 1300moo. 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> rb ra rb ra

5.91

1.2U

1.01

.21 rb

2.62

1.63

.69

.33

This is what is expected. 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 o

T o o

Figure

3U.

The values of ra and rb through time.

o

increasing necessity for the population to utilize areas of optimal

232 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.

Date "~I TE Til

Zones

IV V VT~~ Tot

Density of habitation sites - number of sites per square mile

100

200

.85

300

1.71 aoo 1.71

500 1.71

600 1.71

700

800

900

1000

1100

1200

1300 lUoo

.93

.93

.93

.93

1.08

2.79

2.17

3.26 11.96

2.36 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

12.82

300

hoo

1300

1U00

55.56

55.56

500

55.56

600

55.56

700

800

900

1000

1100

1200

.93

.93

U.90

U.90

U.90

U.90

.93

15.38

3.26

9.78 32.87

2.79

16.30

17.U8

6.98 U5.65 26.57

16.

Ih

39.13 76.22

15.81

39.13 61.5U

2.80

10.U9

10. U9 l.Ul

5.63

5.63 h.25

U.25 a.25 a .25 a.

33

6.15

8.27

10.38

3.17 16.73

3.17 2a. 90

.70 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

N E A R E S T N E I G H B O R

~o

I O O S C

>

1 0 0 A D

300

500

700

S O O

1100

1300

1500 o w

OI

o>

CD

(0 o

% P I N Y O N P I N E

Figure 3$, Pinyon pine pollen and the values of the nearest neighbor statistic.

discontinuous space. The two peripheral surveys, of course, contain

23*

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! S I Z E o

o ro

O

01 o

4* o c i o

a>

o o

a

o

(0 o o o o ro o

O! o o c i o

f

• t

t

IOOBC

100 AD i

300

500

700

SOO -

1100

-

1300

1500 o o

1

1

_

ro w CI

o

03

<0 o o o o o o o o o o o

% P I N Y O N P I N E

Figure 36. Pinyon pine pollen and average room size# to

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. A complete reiteration of this discussion would be redundant. 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 microhabitat 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. The values of the birth rate variables were set at 3.0 and U.O. This is a 300$ and 1*00$ increase in the population per 100 years. 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

L 4

wM

WMll:

2«n« ||

Figure 37. Simulation map

2onc VII 2ont IV

2U1

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 variable values.

Initial

Variables

Birth rate

1 2

3

Simulation

U

i

6

7

8

3.0 3.0 3.0

3.0

U.o U.o U.o U.o

1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 Death rate

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

Consumption

.05

.05

.05

.05

.05

.05

.05

.05

.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 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

4=

700-

600-

500-

400-

300

200-

100-

2000-

1900-

1800-

1700

1600

1500-

1400-

1300-

1200-

O 1100-

1000-

900-

Time

Figure 38. Simulation Is population distribution by microhabitat.

The initial values of the variables are set at

• .5, V « 1.0, and longevity alternative

» inductive.

1500

1400

1300

I-

1200

1100

1000

900

800-

700-

220C

2100

2000

1900

1800

1700

1600

600'

500-

400-

300-

200-

100-

TImo

39. Simulation 2: population distribution by micr

The initial values of the variables are set at

3.0,- D • 1.0, and longevity alter

2U7

2000-

1900-

1800

1700

1600-

U00-

1200

c

•S IIOO

n

"5

o 1000-

Q.

«o

ra

800u

2

•(0

600-

500-

300-

JOO-

100-

It /

Time

Figure UO. Simulation 3s population distribution by microhabitat.

The initial values of the variables are set at

B • c

1.5, V » 2.0, and longevity alternative

2000-

1800

1600

U00-

1300-

1000-

900-

800-

700-

600-

500-

400-

300-

200-

100-

sn

Time

Figure Ul. Simulation U: population distribution by microhabitat. The initial values of the variables are

2U8

2h9

2000-

1200-

c o noo

a

3

O 1000-

o.

«o

4-»

900-

-C

o

o

BOO-

S 700-

1800

1700-

1600-

1500-

1400-

1300

600-

500-

400-

300-

200-

100se

Time

Figure U2. Simulation population distribution by microhabitat.

The initial values of the variables are set at

2000-

1800

1700-

1600-

1500

WOO-

a

44

15

10

•C

O

k.

o a

1200-

c

o

1100-

3

CL

TOO-

800-

'IS

600

500-

W

300-

200-

100o

Time

Figure U3. Simulation 6: population distribution by microhabitat. The initial values of the variables are alternative - tk.

2J>0

Tlmo

Figure lib* Simulation

7:

population distribution by microhabitat.

The initial values of the variables are set at

2*2

rs a.

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

- tic.

3000

« 1300"

Tofol Population

Number of Sites

8 8 8 8 r> *« »n

Time

Figure U6. Simulation 1: total population and total number of sites. The initial values of the variables are set

2*3

3000

2900"

2800-

2700

2000'

1900

leoo

1700

E 1600

2600-

2500

2400

2300-

2300

2100

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

-26

•24

22

20

•44

42

40

•30

36

•34

•32

30

•23

2sa

3000

WOO-

WOO-

J700

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

£ 1600-

<9

5 1500

& 1300

t

f Totol Popwloiion

Numbtr of Sit«»

Time

Figure l|9. Simulation U: total population and total number of sites. The initial values of the variables are set tive « tk.

2 56

• 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

.5,

V a

1.0, and longevity alterna­

257

9000*

J900-

MOO-

2400*

•40

-36

2100'

1800-

1700-

1600

*5 1500-

1400-

£ 1300tf)

1100

1000

900

eoo

70a

too

400

300-

700

100 lotot Popylo»ion

Number el Sitti

o

O

R>*

8 8 8

Time

8 §

8 8

N

8

Figure J>1« Simulation 6: total population and total number of sites* The initial values of the variables are set tive « inductive.

2$8

9000

2900-

2800-

2700 u

44

2600

2500

2400

2300-

2200

•42

-40

-38

-36

-34

2100

2000

-32

30

23

1900

1800

-26

-24

1700 e

o 1600

(0

"3 1500 a

£

1400 o

»2 1300

1200

'22

-20

1100 fapuJOftOft

Number

woo

900

eoo

700

400

500-

400

300-

200

100

-10

•0

6

4

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

•16

14

->2

</3

O i. o

JO

E

3 z

259

3000*

£ 1600 a 1500

H 1300

Populotion

Ngmb«f

X3

E

Time

Figure 53. Simulation 8: total population and total number of sites. The initial values of the variables are set

260

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|6-

5>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.

The Simulations and the Archaeological Record

Figure

5U

shows the number of rooms in each microhabitat

262

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.

550-

S O O -

450'

400-

350-

300-

250-

200

I S O

100-

50-

' Number of Sites

Number of Rooms

K55

-SO

-45

"40

-35

|-30 V

CO

H2S ^

-20 Jo

E

3

1-15 2

-10

-5

Time

Figure 55. Total number of rooms and sites from the actual area covered by the simulated.map.

26k

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

different birth, death, and migration velocity rates, and longevity

266

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. 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 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: 1 Sceloporous undulatus 10.U

Birds:

Mammals:

11 Pinyon Jay li Pinyon mice

1 Mexican woodrat

1 Jack rabbit

0.2

8£.7

.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: 3 Phrynosoma douglasi

2 Sceloporous undulatus

3 Holbroskia maculate

Birds: 2 flycatchers

2 unidentified

28.U

0.2

56.8

6£.0

276

Mammals: 10 Pinyon mice

3 Mexican woodrats

2

Kangaroo mice

1 Rabbit (cottontail)

377.6

36.2

1*25.2

2U.8

396.6 mesa top)

Predominate vegetation: grassland with abundant juniper.

Substrate was rocky (Malpais or basalt), thin stoney soil.

Reptiles: 3 Cnemidophorus velox

Birds:

Mammals:

Microhabitat

3 unidentified

2 Silky Pocket mice

7 Pinyon mice

U, 5 Pinyon-Juniper woodland

1, 2 Juniper Savanna

3, 7 Grassland

No. of Species

6

6

11

3.6

2.7

19?.0

18.5

200.5

8.8

Herbivores Carnivores g/acre g/acre

370.5

U13.0

1325.U

11.3

15.1

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 k t

5 Pinyon-Juniper woodland

Wo. of Species

17

1, 2 Juniper Savanna

16

3, 7 Grassland

(*estimate)

23

Herbivores Carnivores g/acre g/acre

0.25

0.95

0.01*

0.05

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

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

Micidae -plant bugs

0. Neuroptera

Myrmeleonidae - ant lions

278

Class Arachnida

0. Araneae

Thecidiidae lactrodectus mactans - black widow spider

Class Solpugida b. Grassland miscellaneous

Class Insecta

Carabidae - ground beetles

Cicindelidae - tiger beetles

Curculionidae - snout beetles

0. Hemiptera

Cydnidae - burrowing bugs

0. Orthoptera

Gryllidae - crickets

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

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?a

w and thpt subroutines. the maim pr coram has the following functions•

11 to set up ccnstants such as »t'th ano d r ath rates.

21 to read in a sihlllato map of the ha v hollow valley by mtc°0ha3i tat.

3> to de t 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»

0 m a02r.r t

0 adiscn.

61 to calcula's t he population growth 3* settlement fcp each time period based on bir t 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

0ha3itat 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 socie t al procuct of t,|#t m ico habtt at for that ti"e period. if excess population exists it is st

0 s>£!3 c or possible migration to other

•newl v phoned settle"ents in other ntcr0ha3itats.

11.to determine availas t ltty of micrqhabi ta ts wi'h sufficient net societal *ro-uct to allow fop migration and budded settlements. i r sufficient amounts cf urt sociehl ppcduct are available « appropriate ! amounts o c resource determined migration are calculated. to call t h e subroutine named sctlo" which locates new settlement s» i t i to call the su3p 0u t tne named longev which determines the amount of se t tle"e n" extinction and which se t tt events become extinct r

0r 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.

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P O S 3 : r « » T I 2 l / I N S P | 2 l

P O S T z P T m / I H S P I I I

P O S i u P T e i l / T V S P i q J

P * S 5 = P T C r

) / I ' ! S P < 5 l

Pn^SrPTtGJ/I'^PIG)

? = A M I N 1 < P O S l . >

,

O ' : 2 , P O S T .

o

0 S < » . P O r 5 . P 0 S 6 )

TFCZ.«:Q.POC?|OE<:T;S.

IFIZ.EC.^OS'tPEJTU.

IFIT i

EO.PCSIIBEST-I*.

I F ( » . E G . O 0 S 5 ) 3 E r T i S .

T F t Z . E 3 . P 0 S 5 I O E S T = < ; .

P R I N T 2 C C ? . I . J

2 C D 5 F O R M A T ( 1 H . « T R » C E H » . T ' t . 3 X . I « t )

T S U E r l

J S U E - J

J = B E S T

C H E C K I F A L L - ' ' I C R 0 H A 3 I T A t j F I L L E D

T ^ C Z . C E . l . J S l . f l l

O E T E R M I M A

T

I C V C F S E T T L E M E N T N U M B E ? W I T H I N H I C R O H A H T T A T F O R

R U O R E O S E T 7 L r v

C N T

111 20 ">12 i-itinc

5 1 2 C O N T I N U E r

1 3 n

C I • J ) - S A V C

A O J ' J S

T

S " I G R * » J T P O P U L A

T

T O N T O N E W S I 7 E W H E N G R E A T F p T H A N N E T S O C *

• T E T A L P 3 P P U C T O F H E W L V H I O R A T O T O M I C R C M 3 I T A T

3 A V E r 5 A V E » P T ( J )

I F I S A V E . C . R V S P t J 1 I I .

• T S A V F - I

J S A V E r J print inrs

1 < ! ^ 5 P O R « A T 1 1 H t • T R A C E 3 P A S S F D O

• > , ? I » ! T I C l ^ t l f J

1 D 1 2 F O R M A T ( I K . • I = » . I i t

C A L L S E T L f l C

P R I N T ? C O ? . I » J

P R I N T S i t

5 1 1 F 0 R P A T ( 1 H t t V E W S E T T L E M E N T H A S P O P U L A T I O N O F P A S L O C A T E D B E F O R E #

I L f l N G E V I T Y * J

P R I 1 T £ 1 3 . " ( I » J I

P R I N T 5 1 5 . X I I . J l . V I I t J I

P R I V T 5 1 G . X X J T . J I . Y Y f T . J I

P R I N T 5 1 7 . X X X ( I . J ) , Y Y Y I I . J I

5 1 3 F O R M A T ( 1 H . • P : » . T t »

5 1 5 F O R M A T C 1 H « « X : « . F 5 . " . « V T » . F 5 . C I

5 1 7 F O R M A T I 1 H .

,

. F 5 . Q I

« E W S E T T L E M E N T I E O ^ O r o S E T T L E M E N T I S N O W L O C A T E O

J = L

T = K K

" " I N T 2 C 0 7 » T » J

2 r C 7 F O R M A T C 1 H « « T O A C E

F >

. I t » 3 X . I « » l

5 0 T ( J 2 7

• all "tcmrhaaitat!: filled and mor t ality increased

S I O T ' = P T ( J I

<»t« j1 = ptiji -save if<°t(ji.ct.°mspij) i el.52 s3 r imoi?t = savf/p' rt

0=rm07t*0 pplnt 59 »rm oht » 0 r=KK j=l t=tsue jsjsue so t

3 2j

5'» eavel-ptt jl

• irn

P O S 6 L = 1 . I I t=:i-l*i i c

(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)

P O T O 5 2

)) ptj j|:pt(jj-n11,j| save-savcl-ptij) r m

3<>tsave/p'"'

3=s»r«(01t

P R I N T 5 9 t R M O * T . O

S9 F C R M ATtl H . •

I-KK pkortalttvzucs

. J . » D

.de

J - L trisue j=jsue

70 to 28

10p1 continue end subroutine se t lcc

T his

S U 3 " C U T T « > r D E T E ° M T " E S U H E P E N E M E E

T T

L E M E N T S M I L L of

L O C A T E D . it is calleo when se t tl7 v ent population it greater than the settlement maximum an'0/o p when the total population of the mtcroharitat ts greater

T H A N T H E A M O U N T O

C

M E

T

S O C I E T A L P R O D U C T F O R T H A T P O P U L A T I O N . T H E appropriate "tcpohanitat, the amount of migration. ano the number of budded ee t tle v e'jt^ 15 calculated <>y the main program. this subroutine locates the new «"et tle hen t

" "hree 'vays. hit assumes a r a mo cm location process which it generates ustno a pvioom number genfra t 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 p re-existing sltf-

IN the

MI crcha9itat. this point.

1 population weighted bacht allows th r population of the hew sett l cment to be the minihun distance from the maximum po°ula t ton. m ean. is tl-c point which

288

3

> I T C A L C U L

CE«;

T H E

MINIMUM AMOUNT or

A P E A S U R R O U N D I N G E A C H

P R E - E X I J T T N G " I T F N E C E S S A R Y T C S U P P O R T I T S P O P U L A T I O N « T T H E S I M U L A T E D

- T M E . A F T f R L O C A T I N G T H I S A R r f l F O R A L L P R E - E X I S T I N G N O N - E X T I N C T S T T E S

I N T H E K I C C M A 9 T T A T . I T

LOCATE-

T H E N E W T T L r

! ' E N T R A V C C M L Y W I T H I N T H E

T H A T A R E A O F T H ^ M I C R C H A 3 I U T W H I C H I S M O T P A R T O F A N O T H E R S E T T L E M E N T ' S r ' J O S I S T E N C E " A ^ E .

C O P M O N / L E r

/ R E S C c ) .

1

. 5 J . l

. Y Y t l C P . S J » Y Y Y ( 1 2 3 .

= J ,R«J<:P(K)

1 Y l l n r . f i ) . C O N . F L A G l . F L A G ? . F L A G 3 . I 3 A T E » 5 T , S . D . Q . I N f P I 6 >

T N ' E G E R ° . P T

• ? » N O f « S E T T L E M E N T L O C A T O R C X . Y )

* » I N

T

2 3 3 ' ! . I . J

2 C S 3 r o q ' «

A

T ( 1 H . ' T ^ A C E ! • I t

F L A G M - C . 2

6 0 I A A - I O C • * A A

T F ( I A A . G T . 3 « ; . 0 R . I A A . E 0 . C J G 2 . 6 1

C2 AAS^ANFCO.!

5 0 T O G O

61 T'iBrlCC.^B

T F t I S T . G T . . ? S . f R . I 3 P . T 0 . ? J 6 1 . 6 3

S I 9 3 : R A N F J C . J

3 0 T C 6 1

6 1 3 A * = R A N F « C . I

B l r ^ A N F C O . )

G 1 T O S O

6 6 I F { F L A C » . E T . r . C J G 7 . 7 7

6 7 X ( I . J ) = I A A

Y t I . J l = I B 3

" " 1 S T G l l . I A A

6 1 1 F O P M A T I 1 H . • : # A = » . T < » »

" T I N T S 1 2 . I 3 B

P R I N T 1 C 3

T l " r 7 F O R M A T < 1 H t • T P A C E G ° A S S r o « l

• p

0 p

U L A T 1 1 N W E I G H T E D 3 A C H I M E A N r

E *

T

L E H E N T L O C A T O R I X X . Y Y I

P R I N T 1 C 1 H . I . J

1 P 1 « I F O R " A T ( 1 H • • I = » . I 1 • • rXrC.O

S Y r O . C

T I = I

2 0 S f t 1 = 1 . 1 1

6 3 f . Y r ( P ( I . J ) « Y V ( I , J ) I * S Y

T = I T

I F ( P T « J l . E a . r > 7 1 . 7 3

7 3 T S | J ) = P T ( J )

0 0 T O 7 2

7 1 ' S C J I r l . O

" • 2 T I B B ^ S Y / C I ' T S C J I )

* 3 A A = S Y / ( I » T ^ « J ) J

° R I N T 7 2 1 . I S A A . I 3 B 1 . J . T S ( J l . r x . S Y

T c ,

C I B n 3 . G T . 2 ^ . 0 R . I B B B .

r f l . C . O R .

T

3 A A . G T . 2 S . O R . I 3 A A . E O . C I G O T O 7 3 r F ( L O O K O " ( I G A A . I ? P B > . E 0 . J > 7 5 » 7 3

I

7 3 X X ( I . J ) = I A A

V Y ( I . J I = I 0 3

P R I N T 7 1

7 1 F O R f A T C l H . « N O 3 A C H I M E A N C E N

T

E R O

S O T O 7 6

• » 5 X X « I . J ) = I B A A

• A V A I L A B L E R E S O U R C E S E T T L E M E N T L O C A

T

O R ( X X X . Y Y Y J

B R r R A N F ( C . I

F L A C M = 1 . 3

• 5 0 T O 6 0

7 7 1 1 = 1

7 3 0 0 7 0 1 = 1 . 1 1

A * E A = t r ^ C O P ! T . J > l / < < ) . P « C ! ) N » A P R O D < J > J

P R I N T 7 3 U . A 9 C A . I i J . ° ( T . J )

7 9 1 F O R M A T ( 1 H » . A R £ 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

} / ? • ) ? .

T F | S O R T ( I t X X X ( I . J ) - I A A ) • • 2 > + M Y Y Y ( I . J ) - T E

!

J I » » 2 ) > . G T . R l ^ . ^

" " } C O N T I N U E i=i r

7 0 1 r

O R

M

A T 1 1 H . • A T A = » « F 9 . 2 . » R = » . F 6 . : ? . * I = « . I 3 . » J = » . I 3 )

X X X I I . J ) = I A A

Y Y Y ( I . J ) = I 3 3

R E T U R N end subroutine lomgev

T H I S S U 3 R R > U T I ? ' r D E T E F

E X T

;'tn r s

W H E T H E R or

N O ' S E T T L E M E N T ! 3 E C 0 H E imct our

I D G a

P A R ' I C U L A R ttme

" E R I O O . two he'hoos

O F

S E T T L E M E N T E X T I N C T I O N A ° C P O S S I B L Y E M P L G Y E O D E P E N D I N G U ^ O N

' M E D I R E C T I O N ' O F T H E math

P R C G R A F . a r te°

A L L O T H T R O P E R A T I O N S O N T H E settlements

T U R I N G A " A R T I C U L A R ttme pe'tco are

C O H P L E

T

E P . T H I S

• " I J B R O U T I N E t r C A L L E O I N T O A C T I O N . O N C M E ' H O D O F

I S set

' L E M E N T E X T I N C T I O N ba

' E O U

D

O N a

V I N O U C ' T V E L Y D E

T R

R W I : I E O 1 / 1 C P R 0 9 A 9 I L T T Y C F E X T I N C T I O N .

F R O H T H E R E A L D A T A I T I S K N O W N tha* c.

N the

A V E R A G E

9

O U T O F

If!

3

« " T T L E M E N T S

S U R V I V E E A C H 1 3 0 V E A R » F F ! I O O . T M T S M E T H O D R E P L I C A T E S T H E S E R E S U L T S .

H O W E V E R . T H E S P E C I F I C S E T T L E M E N T S W H I C H * 0 N O T S U R V I V E A R E D E T E R M I N E D

B Y

T

H E R A N D O M N U M B E R G E N E R A T O R .

T

H E C P E R A T I O N A L I 7 T . N G C F T H I S P R C C E S S U S E S

N O T O N L Y S U B R O U T I N E L C G E V

9ut

S U ? R O U T T N F P U S H . T H E S E C O V O M E T H " 0 O F

C A L C U L A T I N G T H E E X T I N C T I O N O F S E T T L E M E N T S I S B A S E D U P O N A S E R I E S O F probability rijncttons which were pevelopec iy ha^arthur. on thf pasis of birth amd death rates and "qr'ulattcn sitr the variable tk is calfulated which is defined a period. r length of t i one h'jnppec yea rs. the settlement is allowed to survive to thf next time

C O M M O N / L E

R

/ R E " ( S I . A P R O C « G » . P « I R C » S . ) .

L . Y Y I I C R . 6 ) « Y Y Y ( 1 C 0 . E J . P N - T O J P ) » P T I S |

1 Y I 1 0 0 . C ) . C O N . F L A G T . F L A G 3 . F L A G 3 . I O A T E . S T

. e

. D F S . I N S P I S

I N T E G E R P . P T

P R I N T 1 C 3 6 print 1c13.i.j

1c13 format c1h . j= i

290

T N O U C T I V E ° ? 0 9 i B I L I T V L O N G E V

T T

Y C A L C U L A T I O N S

L L L = L L = L = I I = T r F

| f L » G l . £ 3

. n

. » G 0 T O 9 5

C A L L ° U S H

<»•; I c < F L A G 2 . F 3

. r

! . l 9 5 . 3 7

" E T U

1

? ' )

9 7 3 0 3 7 2 I L K = 1 . T 5

L L L = I L K

I F C X C T L X . J ) , F O . O . ) G O T O 3 7 3

< ! • » » C O N T I N U E

T

K L O N G E V I T Y C A L C U L A T I O N S

B ^ l L L = L r I = I I = L L L

L = ?

* 1 L = L * 1 r < ? T * T 9 3 1 . 1 . J . L

9 3 1 F O R M A T t l H . » T R A C E

T

X » c

T F C I O A T E . G E . 1 X O C I G O T O • > ?

T F < P I L > J I . G E . S T ) G O T O 9 0

9 0

5 0

T

0 3 " » ff=p

( L . J > « A L O r t C B / D >

!«-(ff.e0.r. )g0 to 000 tfjp

(L» jj.eo.cmgo to 3cc

"iff.gt.700.) so

T C 3 C f l

T ^ i p . E a . D J c o to o c r

P ^ i v t e s i . r F . T K

9 0 1 F 0 H " A T ( 1 H « » F F = * . F 1 3 . 5 . S X » « T K = * » F 1 3 . F )

I F I T K . L T .

ioc. s n

T O o i

9 P 0 o t

? I N T 0 P 2 . r c , t K

9 C 2 P O S M A T C I H » » r

K S K T P P E 0 » » F 1 2 . 5 . 5 X . F 1 2 . 5 >

GO TO

31,

9 1 T r L

°2

X t l . J U X C I + l . J I xxc

IfJI x x x c i . j ) = x x x t i * i . j i

Y C I . J I = Y ( I * 1 . J )

V

»ct

. J I = » Y « 1 * 1 . J l yyyi:.jj=yyy«i*i.ji

T F l L . G E . I U S O T O 0 5

I F C T . E Q . L L ) 9 7 . 9 2 1

9 3 1 1 = 1 * 1

G O T O 9 2

9 3 T t = T I - l

L L = L L - 1

9 1 I F ( L

.eo.

1 1 ) 9 5 . 0 3

9 5 P E T O R N

E » ! 0 tuascuTiNF PUSH

C O M M O N / L E r

/ae r

C S ) . A P !

?c

,> l . Y Y C i a r . 6 1 .Y Y V | l D I . S I

."h

? P

«s

) . P T

(g icc

) . T H C S ) . L O O K U P » 2 ? . 7 < i I

1 1 6 )

" C = C

O P 9 1 K L = 1 . I

P ° I N T 2 C 1 2 . X L . J

2 C I 2 F O R W A T i1h

. ' T R A C E L « . T 1 . 3 X . I 1 )

2icc»ias

2 1 S 0 r n f ? M * r c m t « I A A L O N S E V z •

TFtrAA.NC.CI <50 TO SI

0 0 3 ? M o = K L . l f ! 0

T c

' ( P C M P . J

).p1.0.ahd

. X I K P t J

>.e

' 5

.c

. . A K 0 . X * i y P f ji.eo

.r

.)go to 81 p o » f j 7 S C l ' J f W a . J

2p1c rOR u at ijh t«trace k« • ii »3x»t1i n ( M f i J | = « M W P * 1 « J J

X t M P , J ) r * « » f P * l • J l yc n

»j)ry(yp+i»j) x * i

«f.j»=xx(»p+i.ji

Y V C P . J J r V Y l v n + l . J )

X * X I

U D

. J 1 = * X X I M P * 1 . J l

V V V I V P , J l r y y v t X P + 1 . J >

2 C'W-NUE

<u continue

7eturh end

292

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29h

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1

9h9

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1967

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296

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1

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