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Serengeti wildebeest population dynamics : regulation, limitation and implications for harvesting Mduma, Simon Abia Raphael 1996

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S E R E N G E T I W I L D E B E E S T P O P U L A T I O N DYNAMICS: R E G U L A T I O N , LIMITATION A N D IMPLICATIONS F O R HARVESTING. by SIMON ABIA R A P H A E L M D U M A B.Sc, (Hon), University of Dar es Salaam, 1987 M.Sc, University of Dar es Salaam, 1991 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L M E N T O F THE REQUIREMENTS FOR T H E DEGREE OF D O C T O R OF PHILOSOPHY in  THE F A C U L T Y OF GRADUATE STUDIES D E P A R T M E N T OF Z O O L O G Y  We accept this thesis as conforming to the required standard  UNIVERSITY OF BRITISH C O L U M B I A , C A N A D A  October 1996 © Simon A.R. Mduma, 1996  In presenting this thesis in partial fulfilment  of the requirements for an advanced  degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department  or  by his or  her  representatives.  It  is understood that  copying or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department of  z o Q L O G Y  The University of British Columbia Vancouver, Canada  Date  DE-6 (2/88)  Abstract Principal challenges in managing large mammals include methods for estimating abundance, understanding the interaction between environmental conditions, density, and reproductive success and survival, and estimation and regulation of harvest. Here I present the population dynamics of the Serengeti wildebeest  (Connochaetes taurinus)  as a case study in  exploiting large mammals. The Serengeti wildebeest population increased six fold between 1960-1977 from 0.25 to 1.4 million; thereafter it remained constant at 1.3 million. Previous studies have suggested that density dependent mortality regulates the population through food shortage during the dry season. However, little was learned about which stage(s) in the life cycle were involved in the regulation process, or of the extent of human-induced mortality. I present recent demographic data on wildebeest reproduction, recruitment, and adult mortality. I combine my results with those of previous studies to construct a life table, and use key-factor analysis to investigate the influence of density dependence, predation and food limitation on the wildebeest population dynamics. I use poaching data to estimate illegal harvesting, which has been presumed to be extensive. I develop a population dynamics model to test for the consistency of the estimated demographic components. Life table analysis suggests that the Serengeti wildebeest population is regulated through density dependent adult mortality. Fertility loss acted in a density dependent fashion but was weak. Available evidence supports the food limitation hypothesis through dry season calf and adult mortality. Dry season calf mortality was the "key factor" stage causing population fluctuations. While neonatal mortality appeared to contribute the greatest to annual reduction, its pattern was not well understood. Limitation by predators and human offtake appeared to play a minor role. Synthesis of available data suggests that the Serengeti wildebeest population has reached its environmental carrying capacity under the present rainfall regime. Changes in rainfall greatly influence population size, and the reproductive surplus available for harvesting is almost directly related to the amount of rainfall in the dry season of the year. Population dynamics models indicate that in wet years additional animals could be taken in a controlled harvesting program, but elimination of the illegal harvest is essential.  Table of contents ABSTRACT  ii  T A B L E OF CONTENTS  iii  LIST OF TABLES  vi  LIST OF FIGURES  viii  ABBREVIATIONS AND SYMBOLS  xi  PREFACE ACKNOWLEDGMENTS  xii .'  C H A P T E R I SERENGETI WILDEBEEST POPULATION DYNAMICS 1.1. General Introduction  xiii  1 1  1.2. The Study Animal  6  1.3. The Study Area  6  C H A P T E R II SERENGETI WILDEBEEST POPULATION DYNAMICS: REPRODUCTION, SURVIVAL AND REGULATION  10  INTRODUCTION  10  METHODS  10  2.2.1. Reproduction  10  2.2.2. A g e and sex counts  14  2.2.3. C a l f survival  15  2.2.4. Yearling survival  19  2.2.5. Adult natural mortality  20  2.2.6. Life table analysis  22  RESULTS  27  2.3.1. Reproduction  27  2.3.2. Age and sex counts  31  2.3.3. Calfsurvival  31  2.3.4. Yearling survival  37  2.3.5. Natural mortality  41  2.3.6. Life table analysis  51  DISCUSSION  58  Summary...  63  iii  C H A P T E R III SERENGETI WILDEBEEST POPULATION DYNAMICS: PATTERNS OF M O R T A L I T Y AND RESOURCE LIMITATION INTRODUCTION METHODS 3.2.1. Reproduction 3.2.2. Patterns of mortality 3.2.3. Rainfall and food limitation RESULTS  64 64 66 .66 66 70 72  3.3.1. Reproduction  72  3.3.2. Patterns of mortality  72  3.3.3. Rainfall and food limitation  90  DISCUSSION Summary  CHAPTER IV IS WILDEBEEST POACHING M O R T A L I T Y A N IMPORTANT LIMITING FACTOR? A PRELIMINARY REPORT  99 103  105  INTRODUCTION  105  MATERIALS A N D METHODS  106  4.2.1. Sources o f data RESULTS  106 107  4.3.1. Description of poaching  107  4.3.2. Description of anti-poaching activities  111  4.3.3. Anti-poaching achievements  113  4.3.4. Analysis of poachers off-take using "Arrest forms"  113  4.3.5. Other sources of human induced mortality  119  DISCUSSION  121  Summary  124  C H A P T E R V ESTIMATING THE LIMITS TO EXPLOITATION OF SERENGETI WILDEBEEST AND IMPLICATIONS FOR ITS M A N A G E M E N T 126 INTRODUCTION  126  MATERIALS A N D METHODS  128  5.2.1. Data sources  128  5.2.2. The population dynamics model  131  5.2.3. Estimating harvest  133  5.3.4. Fitting the model to the data  135  RESULTS  136  5.3.1. Fitting the model  136  5.3.2. Confidence bounds on current harvest  141  5.3.3. Level o f sustainable harvest  141  DISCUSSION  143  Summary  149  C H A P T E R VI G E N E R A L CONCLUSIONS  151  L I T E R A T U R E CITED  155  APPENDICES Appendix 1.  165  Progesterone levels (ng/gm) measured from wildebeest fecal samples.  165  Appendix 2.  Observed and estimated ratios of wildebeest calves per female.  167  Appendix 3.  Observed and estimated ratios of wildebeest yearlings per adult.  169  Appendix 4.  Wildebeest carcass data recorded between July 1992 and December 1994.  170  Appendix 5.  Adult wildebeest mortality rates shown at different time scales between  July 1992 and December 1994.  Appendix 6.  Steps for estimating wildebeest life table entries.  Appendix 7.  Wildebeest life-table showing population estimates used in  171 172  k-value  analysis.  Appendix 8.  Selected rain gauges with a relatively long term record of monthly rainfall shown in relation to wildebeest migration zones.  174 177  v  List of Tables Table 1.1. The wildebeest population estimates in the Serengeti Ecosystem.  3  Table 2.1. Diagnostic features used in the field to identify wildebeest sex classes.  12  Table 2.2. Diagnostic features used in the field to identify wildebeest age classes.  13  Table 2.3. Mortality stages used in the analysis of age class mortalities (^-factor).  23  Table 2.4. Wildebeest pregnancy rates between 1960 and 1994.  30  Table 2.5. Estimated number of calves per 1000 adult females in March and monthly survival rates of calves.  33  Table 2.6. Estimated number of calves per 1000 adult females in March and seasonal calf survival rates.  35  Table 2.7. Proportion of calves at 4 months and one year of age.  40  Table 2.8. Seasonal yearling survival rates estimated using lognormal model.  42  Table 2.9. Summary of yearlings per adult ratios measured between 1963 and 1994.  44  , Table 2.10. Wildebeest carcasses recorded between July 1992 and December 1994.  45  Table 2.11. Adult wildebeest survival rates from 1967-1994.  50  Table 2.12. Comparison of adult survival rates measured by carcass counts and those estimated from the life table by census difference.  52  Table 2.13. Summary of the life table analysis showing the regression results of log kvalues plotted against log initial population before the mortality occurred.  55  Table 3.1. Categories of bone marrow used to determine the health condition of an animal at the time of death  67  Table 3.2. The main mortality stages (^-factor) and sub-divisions regressed against dry season food supply.  69  Table 3.3. The frequency distribution of carcasses by age classes shown in relation to sex and causes of mortality.  75  Table 3.4. The log likelihood ratio test of adult wildebeest carcasses showing sex vulnerability in different seasons.  Table 3.5. Causes of mortality recorded in 1992-94 relative to age classes.  80 81  vi  Table 3.6. The frequency distribution of bone marrow types in relation to wildebeest age classes, causes o f mortality and seasons.  Table 3.7. Summary of the life table analysis showing means of log  83 values and  regression results from eight years that had complete set of demographic data.  92  Table 3.8. Regression results of the age class mortalities and their respective subdivisions on the per capita dry season food supply.  97  Table 4.1. The frequency distribution of poaching parameters summarized from the "arrest forms" between November 1992 and June 1994.  108  Table 4.2. Carcasses recovered from poachers camps and snares as reported in the "arrest forms" between November 1992 and June 1994.  110  Table 4.3. The frequency distribution of hunting tools summarized from poachers "arrest forms" between November 1992 and June 1994.  116  Table 4.4. Estimates of snare abundance obtained from Petersen's method of mark recapture technique and corresponding annual estimates of legal and illegal wildebeest off-take in the Serengeti region.  118  Table 4.5. Types of legal harvesting programs in areas surrounding the Serengeti National Park showing a typical wildebeest quota allocated per year.  120  Table 5.1a. Data used in the wildebeest population dynamics model.  129  Table 5.1 b. Sources of data used in the model as shown in Table 5.1a.  130  vn  List of Figures Figure 1.1. The wildebeest population changes in the Serengeti Ecosystem from 1958 through 1994.  2  Figure 1.2. The study area showing the approximate boundaries of the Serengeti Ecosystem.  7  Figure 1.3. The main study zones shown in relation to the Serengeti National Park boundaries and migratory routes.  8  Figure 2.1. Differences of progesterone levels, (ng/gm) between groups measured from wildebeest fecal samples.  28  Figure 2.2. The estimated monthly change in calves per female ratio between July 1992 through December 1994.  34  Figure 2.3. The estimated monthly change in calves per female ratio calculated using the seasonal lognormal model. Figure 2.4. Wildebeest adult sex ratio.  36 ,  38  Figure 2.5. The monthly change of calves per female ratio measured from previous studies and recalculated using the seasonal lognormal model.  39  Figure 2.6. The estimated monthly change of yearlings per adult between July 1992 through December 1994.  43  Figure 2.7. Number of adult wildebeest carcasses recorded between July 1992 and December 1994 weighted per 100 live individuals counted and per 100 k m transect length.  46  Figure 2.8. Estimates of effective carcass sighting width in meters and density per k m . 2  48  Figure 2.9. Monthly adult survival rates estimated from a model relating daily counts of adult carcasses to numbers of live animals. Figure 2.10.  49  The relationship of adult annual survival rates measured by direct mortality  estimates and by census difference in consecutive years.  54  Figure 2.11. Regression results of log k-values on log initial population size of the Serengeti wildebeest.  56  Figure 2.12. Regression results of adult mortality (log k-5) on log N divided into two phases of the wildebeest population sizes.  59  viii  Figure 2.13. Wildebeest population change (Phase II) showing anti-clockwise spiral cycles which suggests delayed mortality effect.  60  Figure 3.1. The decline of adult and yearling pregnancy rates measured between 1960 and 1994.  73  Figure 3.2. Estimates of calves and yearlings monthly mortality rates calculated using the change in calves per female ratio compared to the carcass count model.  74  Figure 3.3. Percent frequency distribution of wildebeest carcasses shown by age classes and grouped into three time periods; the 1970s, 1980s and, 1990s.  77  Figure 3.4. Percent frequency of wildebeest carcasses recorded in 1992-94 showing the distribution of sex in three age classes; calves, yearlings and adults.  78  Figure 3.5. Percent distribution of adult bone marrow condition by causes of mortality recorded in 1992-94.  82  Figure 3.6. The frequency of wildebeest marrow and age classes in relation to source o f predation (1992-94): lions and hyena. Figure 3.7. Percent frequency distribution of adult marrow condition by seasons.  86 87  Figure 3.8. Wildebeest mortality rates (%) recorded intermittently between 1960 and 1994 divided into eight stages. Figure 3.9. The wildebeest Figure 3.10.  values plotted against i^-total.  89 91  The wet and dry season rainfall patterns averaged for the Serengeti  ecosystem.  Figure 3.11. The northern Serengeti dry season rainfall pattern measured from 1961  93  through 1994, estimates of average grass (food) produced per hectare per month and, the amount of food available per animal per month.  95  Figure 3.12. The mean monthly rainfall pattern in the Serengeti between 1960 - 1994 compared to the monthly rainfall in 1993. Figure 3.13.  96  The age class mortalities (^-values) regressed against dry season per capita  monthly food supply.  98  Figure 4.1. The age structure of 147 illegal hunters arrested between November 1992 and June 1994 in the Serengeti National Park.  112  Figure 4.2. Annual numbers of arrested hunters, wildebeest recorded, and snares captured between 1957-1994.  Figure 5.1. The data and best fit population model with no harvesting.  114 138  ix  Figure 5.2. The data and best fit curve of the percentage of population that is yearlings and the adult mortality rate per month during the dry season from the model with no harvesting.  139  Figure 5.3. The calf and adult survival plotted against estimated food per animal per month.  140  Figure 5.4. The likelihood profile of total annual harvest in years 1977-94 and the sustainable wildebeest harvest.  142  x  Abbreviations and Symbols.  Unless specified otherwise, abbreviations and symbols shown below apply « = about C.I. =95%  confidence interval  CL. = 95% confidence limits c.v. = Coefficient of variation Pers. C o m m . = Personal communication S.E. = 1 standard error S N P = Serengeti National Park S R C S = Serengeti Regional Conservation Strategy Project T A N A P A = Tanzania National Parks T A W I C O = Tanzania Wildlife Corporation T W C M = Tanzania Wildlife Conservation Monitoring Project Unpubl. = Unpublished data  Preface A modified version of Chapter V (in this thesis) has been submitted for publication in the Annual Symposium Volume of the British Ecological Society (BES) titled, "Population and Community Development in the Tropics." This manuscript, jointly prepared and co-authored by S . A . R . Mdunia , R. Hilborn , and A . R . E . Sinclair , was presented in the B E S Symposium 1  2  3  held in Cambridge (1-4, April 1996) under the title "The limits to exploitation o f large tropical mammals." A preliminary manuscript of this was earlier submitted to the Serengeti Regional Conservation Strategy (SRCS) in 1994 as a report of our analysis (Hilborn, Sinclair and myself) of the wildebeest population dynamics and the potential for a sustainable harvest. Thus, views presented in Chapter V are shared by the three authors rather than my own (the use of " I " or " M y " rather than " W e " or " O u r " is for consistency). The study presented in this thesis was initiated as part of the Serengeti Regional Conservation Strategy Programme. The overall objective o f S R C S is the long-term conservation of the Serengeti-Masai Mara migratory ecosystem (Anon 1991). One of the main components o f the S R C S workplan is to provide for a sustainable controlled harvest of wildlife in areas surrounding the ecosystem for use by local people. The most abundant large ungulate in the ecosystem is wildebeest, and it is the harvest of wildebeest that is expected to provide the majority of meat in any harvesting program. I hope this thesis will add to our knowledge and provide valuable information for the management of the ecosystem, and the Serengeti migratory wildebeest in particular.  'Department o f Zoology 6270 University Boulevard University of British Columbia Vancouver, B . C . Canada and Serengeti Wildlife Research Centre P . O . B o x 3134, Arusha, Tanzania. 2  School of Fisheries W H - 1 0  University o f Washington Seattle, W A 98195 U.S.A. 3  Department of Zoology  6270 University Boulevard University of British Columbia Vancouver, B . C . Canada.  xn  Acknowledgments It is a great pleasure to thank all people and organizations that helped during the course o f this study. D r Anthony R . E . Sinclair (Tony) and M r Bakari Mbano suggested the study and went to great lengths to make it real. Tony was a constant source of ideas, help and encouragement, and he allowed me to use his unpublished data. I benefited greatly from the constructive criticism from members of my Supervisory Committee, Professors Charles Krebs, Dolph Schluter, David Shackleton, Tony Sinclair and James N . M . Smith. They offered many valuable suggestions and critically reviewed my proposal and thesis drafts. Together they provided me with the inspiration and encouragement to complete this work. Also I am greatly indebted to Dr. John Robinson, Director of the Wildlife Conservation Society ( W C S ) , N e w York, U S A , and Dr. Patricia Moehlman, W C S representative to Tanzania for their support and encouragement. The University of Dar es Salaam, my employer, granted me a leave of absence throughout the study period. The Tanzania Commission for Science and Technology ( C O S T E C H ) , Serengeti Wildlife Research Institute (SWRI) and, Tanzania National Parks (TNP) generously approved my proposal and allowed me to work in the Serengeti National Park (SNP). A t the Serengeti field station, I enjoyed the support from the Serengeti Wildlife Research Centre ( S W R C ) . Special thanks go to the Director, M r Hassan N k y a , for his innumerable assistance throughout the study. Also I am grateful to M r W . Summay, Chief Park Warden, S N P , and his senior members of staff; J. Hando, J. Magombe and J. Shemkunde for their support. I am greatly indebted to the two Directors of the Serengeti Regional Conservation Strategy ( S R C S ) , M r B . Mbano and W . Mapunda. S R C S provided me with a vehicle, and field assistance. Frankfurt Zoological Society (FZS) helped with reconnaissance flights, and many other logistical problems. I am grateful to Dr. Markus Borner and his staff for their generous support. I acknowledge Drs. K . Campbell, B . Farm and B . Woodworm of the Tanzania Wildlife Conservation Monitoring ( T W C M ) for their useful discussions and support. A l s o Drs. P. Arcese, F. Banyikwa, M . East, H . Hofer and Melody Roelke-Parker contributed useful ideas on various aspects of the study. I enjoyed many hours of discussion with John Wilmshurst, fellow student and house mate at Seronera. I thank him for his helpful insights. M y special thanks are due to all those who helped me with field work, Tony & Anne Sinclair, Ray & Ulrike Hilborn, J. Fryxell, M . Maige, Jumapili and Mahemba Shabani, A . Pesambili, C . Mufongo, J. Wilmshurst, and many other Park Rangers. In addition I thank D r M . Borner, B . Mbano, Sabastian Tham and the late Mhina who skillfully helped with aerial surveys. Many thanks to BJ0rn Figenschou (Tanzania Guides Limited) and T i m Corfield  (Tanzania Ker & Downey) for their keen interest in my work and generous support in one way or another. A t U B C , I highly appreciate the assistance provided by Zoology staff; L . Bailey, A . Blachford, K . Gorkoff, D . Mellor, T . Radzaus and I. Wingate, to mention but a few. Also I would like to thank my fellow graduate students at U B C for their useful criticism and ideas during the course of my study. Special thanks are due to L . Barrett, A . Byrom, K . Heise, L . Huato and D . Wilson. I owe special thanks to D r Ray Hilborn for helping with the statistical models. I appreciate his many hours of already overtaxed schedules to oversee my work. Despite his efforts I still fall short for not being able to accommodate many of his very useful ideas. Funding for this study came from the Natural Sciences and Engineering Research Council of Canada ( N S E R C ) operating grants to D r A . R . E . Sinclair and the Wildlife Conservation Society ( W C S ) (formerly N e w York Zoological Society). M y family has been a great source of inspiration throughout this study, especially my wife Salome and our children, Gideon and Emanuel. Initially, they endured many hours of field work in the Serengeti and later they allowed me to be away for an extended period of time while writing this work. I also thank my parents, brothers and sisters for their support and encouragement.  Thank you all for persevering ~ together we have succeeded.  xiv  Chapter I Serengeti Wildebeest Population Dynamics  1.1. G E N E R A L I N T R O D U C T I O N  Leopold (1933) and Nicholson (1933) suggested that environmental factors limit a species' potential rate o f increase. This generalization embraced the concepts o f biotic potential, density-dependence, compensatory natality and mortality. Studies on population regulation in large mammals have been reviewed by Fowler (1987), while Sinclair (1989) considered regulation of animals in general. Although there are still only limited data for large ungulates, the basic concepts proposed by Leopold and Nicholson have been supported. The essence of these ideas is: (/') variation in environment causes fluctuations in populations, (ii) resources are limited and set the mean density of populations, and (iii) as population density increases, competition among individuals for available resources increases. Ultimately, population growth is slowed either by increased mortality and/or dispersal, by decreased reproduction, or both, until growth ceases. Thus, a negative feedback operates on the population. A classic example of population growth that matches theoretical predictions is the Serengeti wildebeest  (Connochaetes taurinus).  This population has been studied for more than  30 years and much is known about its dynamics (Watson 1967; Norton-Griffiths 1973; Sinclair & Norton-Griffiths 1979, 1982; Sinclair 1985; Dublin  etal. 1990;  Sinclair 1995; Campbell &  Borner 1995). The eruption of the Serengeti wildebeest resulted from the disappearance of a major mortality factor, the viral disease rinderpest, in the early 1960s (Sinclair 1977a, 1979c). Thereafter the population showed a classic logistic increase from 0.25 million in 1961 to 1.4 million in 1977: it remained more or less stable from 1977 to 1991 (Figure 1.1 and Table 1.1). This increase and leveling out in the population provides a unique opportunity to investigate  1  2.0  F i g u r e 1.1. 1994.  n  The wildebeest population changes in the Serengeti Ecosystem from 1957 through  A marked population decline in 1994 was a result of massive starvation after a  prolonged period of drought that occurred in 1993.  The drop was not statistically  significant. Vertical lines indicate 1 standard error (sources are shown in Table 1.1).  2  Table 1.1.  The wildebeest population estimates in the Serengeti Ecosystem. The standard  error (S.E.) for 1991 estimate was recalculated by Farm & Woodworth (1994).  Year  Estimate  S. E.  Source  1957  190,000  -  Swynnerton(1958)  1961  263,362  -  Sinclair (1973)  1963  356,124  -  Sinclair (1973)  1965  439,124  -  Sinclair (1973)  1967  483,292  -  Sinclair (1973)  1971  692,777  28,825  Sinclair (1973)  1972  773,014  76,694  Sinclair & Norton-Griffiths (1982)  1977  1,440,000  200,000  Sinclair & Norton-Griffiths (1982)  1978  1,248,934  354,668  Sinclair & Norton-Griffiths (1982)  1980  1,337,979  80,000  Sinclair & Norton-Griffiths (1982)  1982  1,208,711  271,935  Sinclair et al. (1985)  1984  1,337,879  138,135  Dublin et al. (1990)  1986  1,146,340  133,862  Dublin etal. (1990)  1991  1,221,783  177,240  Campbell & Borner (1995)  1994  917,204  173,632  Farm & Woodworth (1994)  3  the processes that regulate large ungulate populations by comparing present dynamics with the information collected by Talbot and Talbot (1963), Watson (1967) and Sinclair (1977a, 1979c and unpublished data) during the increase phase. Although much is known about the population dynamics during the increase phase (1961-1977), the demography after 1977 has yet to be analyzed, particularly age-specific survival and recruitment. Recent studies have suggested that density-dependent adult mortality regulates the population through food shortage during the dry season (Sinclair 1977a, Sinclair et al. 1985, Fryxell 1987, Dublin et al. 1990). The "food hypothesis" proposes that as ungulate population density increases, food availability per individual declines, individual growth is delayed, and the proportion of body weight lost during critical periods of food shortage (dry season) increases. If this weight loss is prolonged the animal ultimately starves. Several studies have shown that population size and food supply are related to the dry season mortality rate (Sinclair & Norton-Griffiths 1982, Sinclair 1985, Sinclair et al. 1985, Fryxell et al. 1988). These studies, however, did not investigate which stages in the life cycle were involved in the regulation process. Population models developed by Hilborn and Sinclair (1979) suggest that density dependence operates through juvenile survival. These models, however, were based on information collected during the increase phase. M y main question is to determine what factors are responsible for the observed pattern of wildebeest population growth and levelingoff, and their implications for a sustainable harvesting program. In this thesis I first ask i f the slowing of population growth and leveling is caused by density dependent factors (Chapter 2). Throughout population growth different age classes could have responded differently to resource limitations. The "regulation hypothesis" predicts that one or several stages in the life cycle acted in a density dependent fashion. The first possible stage is conception; but we have no evidence for density dependence in conception rate in any African ungulate. The second life stage is juvenile survival. Sinclair (1979c) reported that a major cause for the increase in wildebeest population was the increase in survival rate of yearlings after rinderpest disappeared in the Serengeti region. However, as the population increased, calf (< 1 year of age) survival declined, suggesting that the low juvenile  4  survival was a major regulatory mechanism. It remains to be seen whether the survival of this age group was density-dependent during the leveling out in population size, or whether other age groups were involved, and whether these differed by sex. Evidence from other ungulate studies suggests that this stage could be regulating the population (Houston 1982, CluttonBrock et al. 1985, Owen-Smith 1990). Thirdly, adult mortality might be regulating as shown  for African buffalo Syncerus coffer (Sinclair 1977a). In Chapter 3,1 consider the "food limitation hypothesis" which proposes that environmental factors play a major role in limiting further population growth. Previous studies have shown that the amount of dry season rainfall is strongly correlated with adult survival rates (Sinclair & Norton-Griffiths 1982, Sinclair et al. 1985, Fryxell et al. 1988). The amount of dry season rainfall determines the amount of food available to wildebeest during the critical dry period of the year. Similar ungulate studies conducted elsewhere support this hypothesis (Clutton-Brock et al. 1982, Owen-Smith 1990). The resource limitation hypothesis is supported i f demographic parameters change in relation to resource availability. In Chapter 4,1 use preliminary poaching data to estimate the exploitation of the wildebeest population by humans. In particular, I ask whether poaching mortality plays a major role in wildebeest population dynamics as reported by recent studies (Hofer et al. 1993, Campbell & Hofer 1995) and unpublished reports. I compare estimates of human off-take to natural causes described in Chapter 3 (predation and non-predation) to determine their role in the population dynamics. In Chapter 5,1 synthesize the demographic data collected between 1960 through 1994 to explore, (/) the current levels of illegal off-take, and (if) the possibility of a sustainable wildebeest harvesting program. I test the consistency of the model by using the independent estimates of legal and illegal human off-take concluded in Chapter 4. I then discuss how a legal harvesting program might be managed in the context of low level traditional exploitation practices. Finally, I summarize the findings of this study in Chapter 6.  5  1.2. T H E S T U D Y A N I M A L  Wildebeest  Connochaetes taurinus  is a medium-sized ungulate which congregates in  the Serengeti to form one of the largest ungulate populations in the world. The large biomass is sustained by a migratory system which provides seasonal grazing while avoiding competition with other ungulates for part of the year (Maddock 1979, Sinclair 1979c, Fryxell & Sinclair 1988). The wildebeest is a pure grazer, preferring short grass (5-10 cm) of high protein value, but it can live in longer grass savannas. It occurs in mesic and semi-arid rainfall (500-1000 m m p.a.) regions of eastern and southern Africa (Kingdon 1982, Estes 1991). The Serengeti wildebeest population has a well defined and highly synchronized calving period which typically lasts for 6 weeks during the wet season (mid January to early March) after a gestation period of 8 months (Sinclair 1977a, Kingdon 1982). Adult male wildebeest weigh 150-270 kg and females 118-208 kg. The sexes can be distinguished by horn pattern and external genitalia. A detailed account of the natural history and habitat choice of the wildebeest is given elsewhere (Estes 1966, 1969, 1976, 1991, Watson 1967, Kreulen 1975, Sinclair 1977a, 19776, Leuthold 1977, and Kingdon 1982).  1.3. T H E S T U D Y A R E A  The Serengeti Ecosystem (25,000 km ) is defined as the area bounding the annual 2  migration of wildebeest. The area lies between 1° and 3° 30" South and 3 3 ° 50" to 3 6 ° East (Figure 1.2). The migration is driven by rainfall which determines the availability o f green grass and drinking water (Maddock 1979, Sinclair 1979a, Fryxell et al. 1988), and specific nutrients (Kreulen 1975, Murray 1995). I divided the Serengeti ecosystem into three main regions based on areas where wildebeest spend long periods during their migration (Figure 1.3). These are: The Serengeti Plains. The migratory wildebeest moves onto the Serengeti plains ( « 5,500 km ) following the onset of the short rain season in November and December. They remain on 2  the plains as long as food is available. Local movements are determined by food availability and the avoidance of waterlogged areas. Calving normally occurs in this area between January and March. 6  F i g u r e 1.2.  The study area (l°-3° 30"S., and 3 3 ° 5 0 " - 3 6 ° E.) showing the approximate  boundaries of the Serengeti Ecosystem  line).  (dotted line),  and the Serengeti National Park  (solid  Shaded area shows mountains and hills (after Sinclair 1979a)  7  34*E  36'E  .  Loliondo G.C.A.  iiijiSerengeti •^National Park  3*  Ngorongoro "onservation Area  L3*S  Serengeti plains s e a s o n  ^  ^  Western corridor (Early dry season) North extension (Dry season)  F i g u r e 1.3. The main study zones shown in relation to the Serengeti National Park boundaries and migratory routes (after Campbell 1989). Open and solid arrows shows respectively, the main routes towards dry and wet season ranges. Minor movements during the wet season are shown with small double headed arrows. Solid lines numbered 1 to 4 show the approximate locations of four permanent transects in the western corridor.  8  Serengeti Western Corridor. A major part of the wildebeest population moves westwards into the corridor once the plains dry out in M a y or June. Unlike the rest of the migration route, this area also harbors a small resident population of wildebeest of about 25,000 (Watson 1967, Georgiadis 1995). The much larger migratory population moves through the area in the early part of the dry season (May-August). A s a result of this overlap, local wildebeest density -2  -2  varies from 1.2 k m to 785 k m . Although my focus was on the migratory population, I could not distinguish individuals belonging to the two sub-populations when they were mixed together. I, therefore, assumed a single population and ignored the resident population, which constituted only about 2% of the much larger migratory population. Northern Serengeti. From around September to mid-November, the migratory population moves into the northern extension of the Serengeti Ecosystem. O n average this area receives more rainfall and has permanent rivers which support the wildebeest through the rest of the dry season (Norton-Griffiths et al. 1975, Maddock 1979).  9  Chapter II Serengeti Wildebeest Population Dynamics: Reproduction, Survival and Regulation  INTRODUCTION In this chapter I present a method of estimating calf and yearling survival rates, and adult mortality by using the proportion of animals found dead to those alive. The analyzed data were collected in the Serengeti from July 1992 through December 1994, and from previously unpublished sources (Sinclair, Unpubl.). I then present available demographic data on wildebeest reproduction and survival for the years 1961-94. I use these data to explore which stage(s) in the life cycle regulates the Serengeti wildebeest population. Estimates of reproduction and mortality over a wide range of population densities are necessary to test for regulation. These usually require long term studies especially for large long lived mammals.  Regulation  is demonstrated if there is sufficiently strong density dependence in reproduction or  mortality to account for the population leveling off. While the patterns and mechanisms of animal mortality are closely related, I restrict my discussion to aspects of density dependence and consider the causes and patterns of mortality in Chapter 3.  M E T H O D S  2.2.1. R E P R O D U C T I O N  Measuring pregnancy rate. In this section I describe the measurement of reproductive status of females. This information will be used to investigate changes in pregnancy rate and neonatal survival. Pregnancy rate was determined by non-invasive radioimmunoassays technique (T. Gross Pers.  10  com., Gross 1992). This method, employed here on wildebeest for the first time, provides information on the reproductive cycle of an individual by measuring progesterone hormone levels in fecal samples. I used samples from individuals with known reproductive status to calibrate hormone levels. The calibration process included samples from known pregnant and non-pregnant females, and from males, collected and autopsied at different times of the year.  Field identification, sample collection and preservation. Field identification of age and sex was based on horn shape and size, body size, and coat color, as described in Watson (1967) and summarized in Tables 2.1 and 2.2. Five sets of fecal samples were collected. (/) Non-pregnant adult females, were identified during the time period following parturition and before conception. In theory these females had calves aged three to six weeks old. This normally occurred from mid-March through April before the beginning of the rutting season. Sampling was carried out three weeks following parturition by which time progesterone levels would have dropped. Samples from autopsied non-pregnant females were collected in October and November to check for seasonal differences in progesterone levels. ( H ) Fecal samples from known pregnant females were collected from the rectum o f culled animals. I sampled from September through December about 120 days after conception when progesterone levels should have build up. (iii) T o estimate pregnancy rates in the population, a number o f fecal samples was collected randomly (see below) from adult females between September and December. A t this time all pregnant females should have been more than four months pregnant, and their progesterone levels should have been higher than those of non-pregnant females. A few fecal samples were collected between September and December from (iv) yearling females to test for age of maturity, and (v) from adult males for calibration o f progesterone levels. Fecal samples for categories (iii) and (iv) above were collected randomly from large groups of wildebeest. Without focusing on any particular individual I searched for a defecating  11  Table 2.1. Diagnostic features used in the field to identify wildebeest sex classes (after Watson 1967).  Characteristic 1  Male  Female  Horn shape and pattern - larger  - smaller  - massively built, especially at the base  - slender  - form a well pronounced boss  - base forms a narrow peduncle  -external genitalia (penis sheath, and scrotum pouch  2  Body size  - relatively larger  3  Territorial behaviour - actively defend a territory  - relatively smaller  - passive  12  T a b l e 2.2. Diagnostic features used in the field to identify wildebeest age classes (after Watson 1967).  A g e class  Approximate  Size and patterns  age 1.  2.  3.  Horn shape and pattern N e w born  < 1 month  no horns  Quarter size  1-3 months  horn humps to spike-like horns, but shorter than ear  H a l f size  4-12 months  horns spike or bracket-like, longer than ears  Yearling  1-2 years  horns curve outwards without a well defined boss  Adult  >2 years  horns spread out, tips curve inwards  N e w born  < 1 month  reddish brown to brown  Quarter size  1-3 months  brown turning light grey  H a l f size  4-12 months  light grey to dark grey  Yearling  1-2 years  light black with a well developed white mane  Adult  >2 years  as yearlings, longer mane and beards  N e w born  < 1 month  small body, back just reaches mother's belly  Quarter size  1-3 months  calf back reaches midway up its mothers body  H a l f size  4-12 months  calf head just appearing above mothers back  Yearling  1-2 years  close to adult height but slighter build body size  Adult  >2 years  larger and more massively built than yearling  Coat color  Relative bodv size  13  animal; once I located one, I determined its age and sex. If the individual suited my criteria (adult female for (iii) or yearling female for (iv)) I collected about 150-300 gm of wet fecal material in a paper bag. Culled animals were chosen randomly and shot from large groups o f wildebeest by members of the Serengeti Regional Conservation Strategy Project outside the Park during harvesting operations. Fecal samples were either sun dried, or oven dried at 38-42 ° C for 24 to 36 hours. A few samples were preserved in methanol and then air dried in a fume chamber before being analyzed for progesterone content  N o significant differences were  found between duplicate samples preserved in these two ways, so results were pooled.  Chemical analysis Progesterone levels were determined at the Centre for Biotechnology Research, Biotechnologies for the Ecological, Evolutionary and Conservation Sciences ( B E E C S ) program, University of Florida, Gainesville. Fecal samples from wildebeest were analyzed for progesterone using radioimmunoassay (RIA) following the procedure of Gross (1992, and T . Gross, Pers. com.).  2.2.2. A G E A N D S E X C O U N T S  I followed the wildebeest migration to measure the population age and sex structure at different times of the year. Non-permanent transects were conducted from a vehicle by driving through large herds of wildebeest during their migration. Transect lines were chosen after mapping the distribution of migratory herds during reconnaissance flights. When an aircraft was not available, preliminary surveys were made from the ground. Depending on the distribution and abundance of wildebeest, transects through major herds were carried out approximately every two weeks. In the western corridor I also established four permanent transects each 20 to 22 km long (Figure 1.3). These transects were surveyed year round at an average interval of two weeks. The day after reconnaissance, the wildebeest population was sampled randomly by counting animals from a stationary vehicle within a semi-circular area o f 100 m radius, 1 8 0 ° in front of the observer. The radius was judged by eye after repeated training with a range finder or set markers at known distance. A t intervals, a range finder was used to check the accuracy 14  of my distance estimates in actual counting. The starting point of a transect was picked randomly using the vehicle odometer. Counting stations were thereafter spaced systematically every 500 m along the transect. Stations were spaced 1,000 m apart when larger herds were spread over a wide area. Double counting was avoided by setting transects parallel to each other and at least 2 k m apart. Counts were conducted between 0730 - 1130 hours, when animals were active and visible. Driving speed between stations was below 30 km/h to minimize disturbance. Counts were recorded on tape and transcribed later in the day. Sex and age identification (Tables 2.1 and 2.2) were aided by using binoculars.  Age and sex ratios From observed numbers of calves (<1 year) and adult females (>2 years) in the transect samples, I calculated monthly ratios of calves per 100 females. I used changes in this ratio as an index of calf survival. Unlike calves, yearlings (1 < 2 years) mix freely in both nursery and male groups, and may even form groups of their own. Therefore, I used the monthly change in yearling per adult ratio to estimate the yearling survival rate. I divided my survival data into "wet" and " d r y " seasons to test for seasonal shifts in survival. I assumed the wet season lasted from January to June and the dry season from July to December. Typically the wet season commences in November and continues through June, with a short dry spell in January and February (Norton-Griffiths et al. 1975).  2.2.3. C A L F S U R V I V A L .  I explored two statistical models to estimate (/) the annual survival rate for calves and yearlings,  (ii) seasonal changes in calf and yearling survival rates (i.e., from January through  June, and July to December), and, (iii) the reliability of these estimates. I chose the best model to estimate the calf and yearling survival rates. Each of the 1992, 1993 and 1994 cohorts was treated separately to an age of about 2 years.  15  The  Model. The purpose of the model was to predict how many calves should have been seen,  given a specified number of observed females. The data represented a small sample of absolute counts from the total population. I assumed that the observed age and sex categories were reliable. Thus, the sources of variation in data were the potential for different calf survival between different age classes of wildebeest. The model assumes that in each month (m) the herd of wildebeest contained adult females (F ), m  females (sp)  and calves (C ). m  I also assumed that there are monthly survival rates of adult  and calves (SQ). Subsequent monthly numbers of females and calves, and the  expected ratio (R ) m  are given by,  Fm+l=F sp  (2-1)  m  Cm+1 = C sc  (2.2)  m  m  R  = n/ m C  <-)  F  2  3  The adult female survival rate (sp) is estimated from adult mortality data (section 2.2.5). M y objective was to estimate the calf survival rate (SQ). For the model, the absolute observed numbers of females and calves in the population are not important so long as I set an arbitrary number which is large enough relative to my sample. I set the number of females alive in the first month equal to an arbitrary value of 1,000. I then needed one additional parameter, the number of calves in the first month Cj  to predict the ratio of calves per female  each month. I used the model to estimate Cj, the best fit to the calves per female ratio, and the estimated survival rate. Given a starting number of females in the first month, an adult female survival rate per month (sp), the number of calves in the first month (Cj, to be estimated), I could predict the ratio of calves per adult female (R ). m  (X ), m  M y data consisted of the number of adult females seen  and the number of calves seen (Y ). m  Given the number of females seen, the expected  number of calves E(Y„) is E(YJ=X R m  m  (2.4) 16  Selecting the bestfitmodel The simplest statistical approach to estimate calf survival rate is to use ordinary least squares regression, and minimize the square of the difference between the observed and expected ratio of calves per female. While the regression approach is reasonably simple, and sum o f squares (SSQ) is a robust procedure, I needed to consider the assumptions behind SSQ more carefully because I intended to perform statistical tests to evaluate confidence limits on the survival rate estimates, and to ask i f the survival rate changed seasonally. The principle problem with SSQ is that it assumes a normal distribution with a constant variance, which means that months with large sample sizes receive much more weight than months with low sample sizes. Further, it also allows counts to be negative, which is obviously impossible. Because of these limitations of SSQ most statistical analyses of count data use other methods. The lognormal distribution is preferable to the normal because, in the lognormal distribution, the variance increases with increasing sample size. A s a brief review, the n o r m a l model assumes that the difference between the observed and the expected is normally distributed. (2.5)  Y = E(Y ) + e, m  H  /II  where  This simply says that the observed value of Y is the expected value plus a deviation (e) which is normally distributed with a mean of zero and a standard deviation of a . Y  In contrast, the  lognormal error assumes that the logarithm of the observed value o f F i s the logarithm of the expected value, plus a deviation (e), which is normally distributed with a mean of zero and a standard deviation of cr . Y  ln(Y )=ln(E(Y ))+e m  m  i  m  (2.6)  where  With a lognormal distribution, an observed value of 200 with an expected of 400 receives the same weight as an observed value of 2000 and an expected of 4000. 17  The Log-likelihood Method I assumed that the counts are log normally distributed and applied maximum likelihood methods for statistical testing and estimation of confidence bounds. The likelihood of the predicted ratio (P), given the observed ratio (O) under lognormal model is 1  L{P\G) =  exp  (ln(Q)-ln(P)) 2cr  2  (2.7)  2  The standard deviation (a) is estimated as  cr =  E[ln(Q)-ln(P)] n-  2  (2.8)  p  where n is the number of months, and p is the number of parameters estimated, these being C] and srj in this case.  Seasonal changes in calf survival rates In the next step I asked i f there was evidence for a change in survival rates between wet and dry season. To do this I used two survival rate parameters instead of one. The computations were exactly the same as the log-likelihood model for annual survival explained above (equations 2.7 and 2.8), except that in addition to estimating the initial number of calves Cj, I also estimated the wet season survival (wet srj), and the dry season survival (dry  srj)  rates.  Estimating confidence bounds of the calf survival rate I obtained  confidence bounds on the estimated calf survival rate srj by likelihood  profile as follows. First, I calculated the likelihood corresponding to the maximum likelihood estimate for srj using equations 2.7 and 2.8.  I then computed the negative log likelihood,  which is minus the logarithm of the likelihood given in equation 2.7. Negative logarithms are normally used when working in likelihoods, and the analog for equation 2.6 for the negative log likelihood denoted -£(P\0)  -£(P\0)  =-In  is  1  +  (ln(O)-ln(P)) 2cr  2  2  (2.9)  18  Equation 2.9 excludes the constant term y (Lindley 1965). Omission of this constant has no effect on the estimates of the survival rates. However, absolute values of presented negative log likelihoods are arbitrarily scaled; only the difference between likelihoods o f alternative model fit to the same data are relevant. If the maximum likelihood is L , best  then to use the method of likelihood profile, I  needed to calculate the likelihood of other values of SQ. T O do this I set the calf survival equal to a specific value  (e.g., between 0.85 and 0.95), and then searched over the value o f the  parameter(s) to find the values that maximized the likelihood. I denoted this quantity L . The s  95% support limits for a parameter (analogous to 95% confidence interval, C.I.) include all values of the parameter having a negative log likelihood within 1.96 units of the maximum (Zar 1984: 94).  Testing the significance of seasonal survival model I used the difference of the maximum negative log likelihood, L  d  to test whether there  was a significant change of survival between the wet and the dry seasons. This was done by A/  where L  best  =  (T  hesl  •annual )  ( ^best seasonal  )  (2.10)  i is the maximum negative log likelihood obtained from the annual (single)  annua  survival estimate model, and L  besU  s e a s o n a l  is calculated from the seasonal (two) survival model.  Twice the difference (L ) is chi-square distributed under the null hypothesis of no survival d  differences between seasons. Probability levels are obtained from standard chi-square statistical tables (similar to log likelihood ratio test).  2.2.4. Y E A R L I N G S U R V I V A L  The Lognormal model I used the maximum likelihood method to estimate the yearling survival rate. I used the same lognormal model outlined earlier (equations 2.7-8), but used the change in yearling per adult ratio instead of calves per female ratio. Hence in all previous equations (2.1 through  19  2.8) yearling survival (sy) was substituted for calf survival  (srf),  and adult survival (s^) for  adult female survival (sp). The computations remained the same. Estimating  seasonal survival rates and confidence bounds  I carried out the same computations as for calves in section 2.2.3; "Seasonal change of calf survival" and "estimating confidence bounds of the calf survival rate" to examine seasonal changes in yearling survival.  2.2.5. A D U L T N A T U R A L M O R T A L I T Y  Carcass  counts In the Serengeti, large numbers of wildebeest live and move together in cohesive  groups. In any given day a small fraction of these die, and their remains were encountered in the field. I used the daily ratio of carcasses located per live animals counted along transects to estimate mortality rate. Carcass and live animal counts (Method 2.2.2. above) were collected concurrently along the same transects. Daily mortality rates of different age classes were based on the ratio of carcasses to live animals. Such mortality data were collected only when there was no apparent change of live animal abundance at least within the last 24 hours. The change was judged by animal movements; unidirectional movements at a fast pace suggested a rapid change of animal density and composition. Occasionally carcass data were collected within 48 hours prior to, or, after the live animal count when this condition was met. Carcasses were either observed directly from vehicles or their presence was indicated by predators or vultures. Whenever possible I adjusted my transect survey time to take advantage of when vultures were active which was normally after 07.30 hours. Early surveys during the day were especially important for locating predator kills because large predators usually hunt after dusk and leave their kills to find shade early the next day. Once a carcass was located, I recorded date, locality, and sighting distance. A g e was assigned as for live animals. Only carcasses less than 24 hours since death were considered.  20  Estimating carcass density. I used the transect length and effective sighting distances to estimate the area searched. Perpendicular sighting distance from the transect to the carcass was estimated in meters. The frequency of sighting distances were grouped into six classes; five classes o f 100 m interval and one class for counts that were beyond 500 m (centered at 1000 m). Transect length was measured from vehicle odometer in kilometers. I assumed that carcasses were randomly distributed with respect to distance from the transect and used the program  DISTANCE  ® Version 2.2 to calculate the effective sighting width  and carcass density (Buckland et al. 1993, Laake et al. 1994). Each transect was analyzed separately (cumulative distance and carcasses per sighting distance classes). Pooled estimates of effective search width and density were used if transect estimates were not significantly different.  Analysis of carcass data. The basic statistical theory for analyzing the carcass data in relation to the live animal count (Method 2.2.2) is as follows. Given a population of live individuals in the area searched, a certain number died each day. Since the proportion that died was very small, the number dying should follow a Poisson distribution (Steel & Torrie, 1980, p.395). The binomial distribution would give identical answers provided the proportion dying remained small. The Poisson distribution is  P r ( J ^ ) ~  (2.11)  where Pr (k) is the probability of k deaths, given the expected number u. The number of carcasses found (k) is known from data, and I needed to find the overall daily mortality rate (m ) that is most consistent v/ith the data. The expected number o f d  carcasses  (u)  is the number of animals in the area searched  (rif), times the  daily mortality rate  (m ). For a single transect, the mortality rate that will maximize the probability (Pr (k)) is the d  number of carcasses (k) divided by the number of animals (ni) in the area searched. This approach provides a simple estimate of the expected mortality rate. However, I wanted to  21  calculate the maximum likelihood estimator of the survival rate. T o do this I used complex models of the mortality rate.  The log-likelihood model I used the log-likelihood model to estimate adult survival rate m . The log-likelihood d  uses negative logarithms, which i f taken from the Poisson distribution gives  -£(u/k)  = u-k-\n(u) + \n(k^  (2.12)  k is the number of carcasses found in a given transect. Minimizing the sum of these negative log-likelihoods over all transects yielded the maximum likelihood estimate of u. The estimated mortality rate was given by  u  TD  = N -m TD  (2.13)  d  Where: uj £> is the expected number of carcasses to be found on transect T, and date D, ND T)  m  d  i t s  n e  number of live individuals in the searched area for that transect T and date D,  is the "overall" daily mortality rate (computed for the first transect and month).  I used a non-linear function  SOLVER  in M i c r o s o f t ®  EXCEL VERSION  5 to fit the model.  2.2.6. L I F E T A B L E A N A L Y S I S . I used estimates of pregnancy rate (method 2.2.1), and, calf, yearling and adult survival rates (methods 2.2.3, 2.2.4 and 2.2,5 respectively) in conjunction with census estimates (Table 1.1) to construct life table schedules. Life table, as used here, refers to patterns of the demographic data based on the series of annual censuses. It should not be confused with composite life tables showing the probabilities of survivorship  (e.g.,  Lowe  1969). Life tables were analyzed to examine the contribution of each life cycle stage (Table 2.3) to the change in the wildebeest population over time, and to seek evidence of density dependence at any stage. The proportion of animals dying at each stage was analyzed by k-  22  Table 2.3. Mortality stages used in the analysis of age class mortalities (^-factor).  Life cycle/Age class  1  2  Fertility loss  Wet season calf mortality  Approx. age (months)  Difference between potential  k-l k-2  Estimate  Data points  8  and estimated pregnancy rate 1-7  Calves dying between March  8  and June. 3  D r y season calf mortality  £-3  5-12  Calves dying between July  16  and December. 4  Annual yearling mortality  k-4  10-24  Yearlings dying between  4  January and December. 5  Annual adult mortality  k-5  > 2 yrs  Difference between (Nf + recruitment) and  34  Nf+1  23  factors (Varley & Gradwell 1960, 1968 and Varley et al 1973). Background information suggested that fluctuations in the Serengeti wildebeest population could be accounted for by births and deaths, because there was no evidence of immigration and emigration. The wildebeest life-table included estimates of annual population size (aerial censuses), fertility rates, and juvenile and adult survival rates.  Estimates of wildebeest population size I used annual censuses (Table 1.1) to construct the Serengeti wildebeest life-table. In years when no census was conducted, I estimated the population size by interpolation. For book-keeping purposes, I assumed all censuses were conducted in March when wildebeest were on the short grass plains. The population estimates from censuses did not include newborn calves, because these were not visible in aerial photographs due to their small size and light coat color. Except in 1992-93, where the cause and estimates of population decline were known, the population trajectory was fitted by a smoothing curve interpolation (Microsoft Excel 1993-1994). The 1994 census estimates suggested a 25% decline in numbers compared to that o f 1991. Between April 1991 (after the 1991 census was conducted) and June 1993, the Serengeti region experienced average weather and there were no reports of increased wildlife mortality. However, the 1992-93 wet season was shorter than normal and the NovemberDecember 1993 short rains were late or failed altogether in some parts. This resulted in prolonged severe drought that caused high mortality rates. Based on this background information and independent mortality estimates (Method 2.2.5), I calculated the 1993 population size retrogressively by adding the estimated loss to the 1994 estimate.  Adult sex and age class ratios. Adult sex ratios were estimated from systematic ground transects run through the whole population when on the plains in the wet season. Data were combined from the years 1971-72, 1980, and 1992-94. The same data sets were used to calculate the yearling to adult ratio in the 1970s through 1980s when this was not measured in the field. I used the actual numbers of animals counted to estimate the mean and standard error of adult sex and age class ratios. From Cochran (1977) and Krebs (1989), the mean ratio of females (or yearlings) (R) was given as 24  Where x is the number of animals in the class of interest (females for sex ratios, yearlings for age class) and y the number of all other animals in the sample (males for sex ratio, adults for age class). The standard error, SE of the estimated ratio is  (2.15)  Where n is the number of samples (transects in this case). The proportionp (of females or yearlings) as a percentage in the population is given by;  (2.16)  Life stage mortalities (k-factors). The annual change in numbers could be divided into five stages (Table 2.3). These stages included: loss of fertility, neonatal mortality, and seasonal mortality of calves, yearlings and adults. A t each stage I calculated the proportional loss in terms of the initial number (I) and final number ( F ) before and after that reduction occurred. The mortalities (&-values) were calculated as l v a l u e = log(7) - log(F)  (2.17)  i) Fertility loss (A-i). The decrease in fertility rate measures the proportion of adult females that did not become pregnant in year t\ relative to the potential maximum. For wildebeest, the potential maximum included all females 2 years and older (Sinclair 1977a). The fertility rate was obtained from autopsies and fecal samples (Method 2.2.1) for 1992-1994, and previous studies conducted by Watson (1967) and Sinclair (1977a). Thus I estimated the number of potential mothers (7) as I=N P <i-r r  A  s  (2.18)  25  and the number of adult females which were not pregnant (F) as F=I-(\-r )  (2.19)  P  Where: Nf = population size in year i (census estimate), p = M  r  s  proportion of adults in year i, = proportion of females (>2 years) in the population, i.e.: Females/(Females  + Males); and, r  p  = pregnancy rate.  The wildebeest rutting season is well defined and occurs towards the end of the wet season (May-July). Calves are born after a gestation period of 8 months between January and March (Watson 1967, Sinclair 1977a). The conception rate has never been measured. T w o scenarios could affect pregnancy rate. The first is the assumption that fetus resorption and/or abortions in the population are rare, so that there is no difference between conception and birth rates. The alternative assumption is that fetus resorption and/or abortions could be induced by physiological stress during the dry season, thus altering the birth rate. Published literature on ungulates suggests that fetus resorption and abortion are rare (Sadlier 1969, Sinclair 1977a). In the absence of known conception rates this problem could not be disentangled and I assumed the first hypothesis applied. Wildebeest pregnancy rates were measured between October and January. However, for book-keeping purposes I assumed all measurements were taken in March and represent the birth rate. ii)  Neonatal mortality, (k-i). Neonatal mortality refers to the number of calves that  died before they were four months old, i.e., those that did not survive through June. This period provides estimates o f wet season survival rates. Neonatal loss (k-i) was calculated as the difference between number of calves born (I) (from method 2.2.1) and those which survived through June (F). I used changes in the ratio of calves per female to estimate calf survival over time (Method 2.2.3.).  iii) Dry season calf mortality, (k-i).  Dry season calf mortality represents the  proportion o f calves dying during the dry season of their first year (July through December).  26  Thus the initial number (I) was the number of calves at the beginning of the dry season June and, final number F was the number of calves in December (based on Method 2.2.3.).  iv) Yearling  mortality, (k-4).  Previous estimates (Watson 1971, Sinclair Unpubl.)  expressed yearling survival as a proportion of adults at the end of the wet and dry seasons. I used these proportions to estimate annual yearling mortality. The number of yearlings at the beginning o f each year (7) was estimated from the number of calves alive in December of the previous year, and F was the number of yearlings in the following December.  v) Adult mortality, ks. Adult mortality was calculated as the difference between surviving adults in consecutive census estimates. The estimated annual mortality was thereafter expressed on a monthly basis and used to calculate life table schedules. The mortality rate from the life table was compared to independent measurements (Method 2.2.4, and Sinclair 1979c). The initial population size I, was the number of adults in January plus the number of yearlings of the previous year and F was the number o f adults in December.  Population regulation. Density dependence was detected by regression of the  k-values for each  stage against  log of the initial population size before the mortality occurred. The ensuing slope (b), intercept (a) and coefficient of determination (r^) of the regression were used to determine the role of mortality at each life stage in the regulation of the Serengeti wildebeest population.  RESULTS  2.3.1.  REPRODUCTION.  Fecal samples Progesterone levels varied among sex and, classes of pregnant and non pregnant females. Figure 2.1 shows the distribution of progesterone levels (ng/gm) analyzed from 142 wildebeest. Levels for each individual wildebeest are shown in Appendix 1. Non-pregnant  27  50  40  \-  30  \-  20  L  10  L  B s ~  01 •mm  e  2 &>  1> OH  2  0  9s  Figure  9S  5  9s  9s  Z  £  fS 9s  f*^ 9s  9s  2.1. Differences of progesterone levels (ng/gm) between groups measured from  wildebeest fecal samples. The dashed line shows the 8 ng/gm pregnant cut-off point. Abbreviations represent: ML, males; YG, Yearlings; LT, Lactating females; NP, Non pregnant females; PG, known pregnant females; and, PT, adult female samples for "Pregnancy test." Years when samples were collected are shown by their last two digits. PT'94 include autopsy samples, NP '94 and PG '94. The notch represent the median of the data array and hinges shows values within 25th and 75th percentiles. The whiskers, asterisks and open circles shows values within 1.5, 1.5-3.0 and beyond 3.0 interquartiles respectively. The 95% lower and upper confidence intervals are shown where the notch returns to full width. Notice that some of the outer confidence limits extend beyond the hinges.  28  females had progesterone levels about half (x = 5.46 ± 1.04 ng/gm S.E. n = 6) those o f pregnant females (x = 11.01 ± 1.41 ng/gm S.E.n = 8, two-sample Mest P = 0.012, d.f. = 12). Males had significantly lower progesterone levels than non-pregnant females (x = 1.93 ± 0.52 ng/gm  S.E., two-sample t-test P = 0.007, d.f. = 12). Yearling females had mean progesterone  levels o f 4.27 ± 1.20 ng/gm S.E., similar to non-pregnant adult females (two-sample Mest P = 0.469 d.f,  =9).  Calibration for pregnancy hormone assays. In October-November 1994, six autopsied non-pregnant females had progesterone hormone levels ranging from 1.34 to 7.56 ng/gm (Appendix 1, col. 4). The other eight pregnant females showed only one value (5.92 ng/gm) below the maximum o f the nonpregnant sample (Appendix 1, col. 5). The threshold between non-pregnant and pregnant giving the smallest overlap was 8 ng/gm. This value was then used to identify pregnancy in random fecal samples from the population (Figure 2.1).  Pregnancy rate. I randomly collected 116 fecal samples from females over a three year period. Fourteen o f these were collected from the autopsied females noted above. Pregnancy rates were 82.9%, 88.6% and 81.3% in 1992, 1993 and 1994 respectively (Table 2.4 and Figure 2.1.); the differences were not significant ( £ = 0.911; p = 0.634, d.f. = 2). One of the five yearling females had 8.94 ng/gm progesterone level suggesting a 20% yearling pregnancy rate in 1993. Fertility rates of autopsied yearling and adult wildebeest were previously measured by Watson (1967) and Sinclair (1979c). Adult fertility rates always exceeded 80% and were higher in the 1960s.and 1970s (>88%) compared to the 1990s (Table 2.4). The lowest adult fertility rate (81%) was recorded in 1994. Yearling fertility rates were variable i n the 1960s (4 - 83%>) and somewhat less so thereafter (6 - 20%).  29  Table 2.4. Wildebeest pregnancy rates between 1960 and 1994. Sample sizes are shown parentheses.  Year  Yearling pregnancy rate  Adult pregnancy rate  1960  0.83 (6)  0.95 (51)  Watson (1967)  1964  0.22 (9)  1.00 (32)  Watson (1967)  1965  0.44 (9)  0.95 (40)  Watson (1967)  1968  0.04 (26)  1970  0.11 (11)  1.00(14)  Sinclair (1979c)  1971  0.06(18)  0.88 (41)  Sinclair (1979c)  1991  0.82 (22)  Boutin, S. (Pers. com.)  1992  0.83 (35)  This study  0.89 (44)  This study  0.81 (32)  This study  1993 1994  0.20 (5)  Source  Sinclair (1979c)  f  2.3.2. A G E A N D S E X C O U N T S .  The wildebeest recruitment rates were determined from age and sex ratios recorded at different times of the year. A total of 134,327 individuals from the migratory population were counted over 30 months (July 1992 - December 1994). Among these, 20,301 were calves (< 1 year), 9,404 yearlings (1 < 2 years), 68,008 adult females, and 36,614 adult males. Each monthly sample was the sum of 3 to 17 transect counts which ranged from 10 to 70 k m in length. Transect length was determined by the distribution of wildebeest and accessibility of the terrain.  2.3.3. C A L F S U R V I V A L .  Statistical analyses and modelling of calf survival rates. Figures 2.2 and 2.3 shows observed and estimated ratios of calves per female between July 1992 and December 1994. Raw data and sample sizes are given in Appendix 2. The monthly change in ratio of calves per female went through three phases. First, the calves per female ratio increased between January and March. This indicates the calving season which typically began in mid-January and covered six weeks with a peak in its third week (Watson 1967, Sinclair 1977a). The first two months in this phaie were not used in the calculations o f calf survival for two reasons; (/) while neonates were being added to the population some were also dying, thus confounding estimates of both calving and survival rates; (if) females with neonates tended to segregate themselves, and this could have produced a counting bias. In the second phase, March through June (late wet season), the ratio declined slowly indicating low early calf mortality. It dropped rapidly in the third phase during the dry season (August through December) indicating late calf mortality.  Model for estimating annual calf survival. I used the lognormal model (equation 2.7) and the negative log likelihood profile (equation 2.9) to calculate the annual calf survival rates and their 95% confidence limits (C.L.) respectively. The estimated calf survival rates for 1992, 1993, and 1994 are summarized in  31  Table 2.5 and plotted in Figure 2.2. The sample sizes and observed ratios are shown in Appendix 2. The lognormal model suggests that the average monthly survival rates were lowest in 1993 (80.0%), followed by 89.1% in 1994 and highest in 1992 (95.9%). The initial ratio o f calves per female was highest in 1993 (78.3%) and much lower in 1994 (28.3%). N o counts were made in the early part o f 1992 but estimates in July 1992 suggest that the ratio could be higher or at least similar to that of 1993. This model suggests first year recruitment rates of 17.3%, 6.2% and 7.3% for 1992, 1993 and 1994 respectively.  Modelfor estimating seasonal calf survival rates. The seasonal calf survival model (modified equations 2.7 and 2.8) provides different survival rates for the wet and dry seasons. This model also provides a better fit to the observed data than the annual survival model, as judged by its smaller negative log likelihood values. However, in 1994 the observed monthly change of calves per female between March and August was ambiguous (Appendix 2) and suggested an unrealistic survival rate (wet and dry season survival rates =1.10 and 0.88 respectively, -log likelihood = -3.12). T o correct for this apparent anomaly I added another parameter that would constrain the survival estimate < 1. This increased the negative log likelihood to -1.67 (Table 2.6, column 4). O n average calf survival rates were higher during the wet season (March - June) than during the dry season (July - December) (Table 2.6 and Figure 2.3). In 1993 the monthly calf survival rate dropped sharply from 98.5% to 73% between the wet and dry seasons, but this drop was not statistically significant (log likelihood ratio test P = 0.125, d.f. =1).  The drop in  survival rate was consistent with the low rainfall in 1993 (Chapter 3, Figure 3.10). Survival rates also declined between seasons in 1994 (from 99.9% to 89.9%) and this drop was significant (log likelihood ratio test P = 0.016, d.f. = 1). In 1992, monthly survival rate was estimated for only the dry season and this was 96%.  Previous estimates of calf survival. Proportions of calves per adult did not differ drastically between 1960 - 1994 (Table 2.7) suggesting that calf survival rates were similar. Watson (1967) and Sinclair (1977a, 1979c) counted animals from oblique photographs taken from systematic aerial surveys. 32  T a b l e 2.5. Estimated number of calves per 1000 adult females in March ( C / ; July for 1992) and monthly survival rates of calves (srj) estimated by using the lognormal model.  Year  1992  1993  1994  373  783  387  0.959  0.800  0.891  95% C . L . lower limit  0.896  0.725  0.835  95% C . L . upper limit  1.026  0.881  0.951  0.973  0.963  0.995  -5.079  5.125  -2.040  Calves per 1000 females in the first month (C,) Monthly calf survival rate (SQ)  Monthly adult female survival rate (sp) -log likelihood  33  1993  1992  0.8  0.8  CD  0.6  ra 0.6 E 0.4  •  -A—A_  at  o_ 0.2  I  •  0.2  co  o  •  0.4  0  ~I  Jan  0.8 -, re • I 0.6 E  1  1  1  1  1  1  1  1  Mar May Jul Sep  1  ~ i — i — i — i — i — i — i — i — i — i —  1  Nov  •  Jan  Mar May Jul  Month  Month  1994  1992-94  Sep  Nov  0.8 0.6  -I  tat 0.4  0.4  cu  Q.  $ 0.2 > ns - 1 — i — i — i — i — i — i — i — i — O nJan Mar May Jul Sep  Month  0.2 i — i  Nov  l  Jan  I  l  l  i  l  Mar May Jul  I  i  i  Sep  i  i  Nov  Month  Figure 2.2. The estimated monthly change in calves per female ratio (solid line) between July 1992 through December 1994 using the lognormal model. Data for January and February were not included in the model fits. Observed ratios are shown as triangles (1992), diamonds (1993) and circles (1994).  34  T a b l e 2.6. Estimated number of calves in March (Cj; July for 1992) and seasonal calf survival rates (srj) from July 1992 through December 1994 computed by using the seasonal lognormal model.  Year  1992  1993  1994  Calves per 1000 females in the first month (CI)  373  578  263  no data  0.985  1.00  (0.73 - 1.0)  (0.95 - 1.0)  0.730  0.900  Monthly wet season calf survival rate (sCw) 95% C.L. Monthly dry season calf survival rate (sCd)  0.959  95% C.L. (0.89- 1.0) (0.63 - 0.84) (0.86 - 0.94) Adult female monthly survival rates  -log likelihood  - wet season (sF)  no data  0.980  0.995  - dry season (sF)  0.973  0.946  0.994  -5.079  4.183  -1.673  35  1992 Q)  E  0.8 0.6  5 0.4 Q.  $ 0.2 >  <3 Ives per Femal  CD  (0  o  i  Jan o.o  Mar May  1  Jul  1  r  S e p Nov  Jan  Mar  May  Month  0.8  0.6 -  0.6  0.4 -  0.4  0.2 -  0.2  00 -  1992-94  • — • — • — •  0.0 Mar May  Jul  Month  S e p Nov  Month  0.8  Jan  Jul  S e p Nov  ~i  Jan  1  Mar  r  n  May  1  Jul  1  1  1  1  1  S e p Nov  Month  Figure 2.3. The estimated monthly change in calves per female ratio calculated using the seasonal lognormal model. Data for January and February were not included in the model fits. Observed ratios are shown as triangles (1992), diamonds (1993) and circles (1994).  36  Other data were collected from ground transects by Sinclair (Unpubl.) from 1984 through 1990.  The previous methods used to collect data are similar to those used in this study and  errors are comparable (Table 2.7). Although aerial photographs provided large sample sizes (Appendix 2), it was not possible to distinguish the sexes, nor yearlings from adults. Because these differences were necessary to estimate the calf per adult female ratios, the sex ratio from extensive ground transect data collected in 1971, 1972 and 1980 was used (using equations 2.15,16 and 17). The adult sex ratio (Figure 2.4) was close to 50% females in the 1970s and 1980s. Thus, where sex ratio was not measured directly, I assumed this value for data collected before 1990.  Results from 8 years of ground counts where yearlings could be distinguished, suggest  that between 1962 and 1989, yearlings aged 20 ± 2 months constituted 9.8% ± 2.3% CL. of the population (sample sizes = 3,229 yearlings, 32,713 adults). Thus, I assumed yearlings constituted 10% and adult females 45% in years when yearlings were not counted. Using these estimates I applied the lognormal model to calculate the monthly change in calves per adult female ratio where there were sufficient animal count data collected for more than 5 months in a year. Results for the model fits are shown in Figure 2.5. Table 2.7 summarizes the calves per adult ratios when calves were about 4 and 12 months old measured since 1960. The ratios were estimated using the seasonal lognormal model. The observed ratios given by Sinclair (1979c) were recalculated using the lognormal model (Figure 2.5) and the estimated ratios were similar.  2.3.4. Y E A R L I N G  SURVIVAL.  For practical reasons, I assumed that calves became yearlings in January of their second year, when the next cohort of calves was about to be born. Compared to the calves per female ratio, the monthly yearling to adult ratio fluctuated widely, particularly in the wet season of 1993 (Figure 2.6; Appendix 3). In 1994 the yearling to adult ratio was small and varied over a narrow range.  37  100 --  75 1 (0 _3>  re E  50  4  25  -i  1971  r  1972  1980  1990s  Year  Figure 2.4. Wildebeest adult sex ratio. Vertical bars represent one standard error. Data for 1971, 1972 and 1980 from Sinclair (Unpubl.).  38  1965  1966 to E  0)  a  to CO  > (J  Month  1971  1972  1973  1984  F i g u r e 2.5. The monthly change of calves per female ratio measured from previous studies and recalculated using the seasonal lognormal model. Solid circles represent the observed calves per female ratios. Data for January and February are not included i n the model fits. Sources o f data: 1965, 1966 (Watson 1967); 1971-73 and 1984 (Sinclair, Unpubl. data).  39  Table 2.7.  Proportion of calves at 4 months and one year of age. The estimates in brackets  from Sinclair (1979c) and beside them are proportions calculated using the lognormal model. Sources: a, Watson (1967); b, Sinclair (1979c); c, Sinclair (Unpubl); and, d, This study.  Year  Calf: adult ratio at 4 months  Calf: adult ratio at 1 year  Source  1960  0.180  0.080  a  0.230  a  1962 1963  0.220  0.160  a  1964  0.190  0.170  a  1965  0.125 (0.13)  0.093 (0.09)  a  1966  0.129 (0.12)  0.112(0.11)  a  1967 .  0.160  0.100  b  1968  0.190  0.130(0.125)  b  1969  0.170  1970  0.140  0.110  b  1971  0.175 (0.17)  0.139(0.12)  b  1972  0.200 (0.18)  0.139(0.125)  b  1973  0.164 (0.18)  0.097 (0.13)  b  0.140  b  0.146  b  1978  0.114  c  1980  0.094  c  1982  0.145  c  1983  0.103  c  0.111  c  1986  0.109  c  1989  0.156  c  1990  0.135  c  1976 1977  1984  0.170  0.346  b  1992  0.192  0.173  d  1993  0.211  0.062  d  1994  0.131  0.073  d  The seasonal log-normal model for yearling survival. A s with calves, the seasonal lognormal survival model indicates that yearlings sometimes survived better during the wet season than during the dry season (Table 2.8, Figure 2.6). In 1993 and 1994 monthly survival was 96% and 95% respectively during the wet season (January - June). The dry season monthly survival dropped significantly (log-likelihood ratio test P = 0.017, d.f. = 1) to 73.6% in 1993. However, in 1994 the dry season monthly survival rates remained high at 96% (log-likelihood ratio test P = 0.897, d.f. = 1). The dry season monthly survival rate for 1992 was 73.4%.  Previous studies. Besides my results, estimates of yearling:adult ratios were only made in 1963 (Watson 1963) and in 1971 (Sinclair, unpubl.). The results for present and previous studies are shown in Table 2.9. The general pattern for the five estimates is similar; the highest recruitment rate (to ~ 2 years, old) was recorded in 1971 (17.4%) followed by 13.5% in 1992 and the lowest was 4% in 1993. The difference between the proportion of yearlings in January and December ranged from about 1% in 1994 to 16.6% in 1993 suggesting large differences in survival rates.  2.3.5. N A T U R A L  MORTALITY.  A total o f 373 wildebeest carcasses were recorded from July 1992 through December 1994 (Table 2.10; Figure 2.7). These carcasses were counted from a total of 151 transect surveys, while no carcasses were sighted in 81 other surveys. More than 45% (171) of the carcasses were recorded in 1994, 44.2% (165) in 1993 and only 9.9% (37) in part of 1992 (Figure 2.7). However, when weighted by search effort, 1993 recorded the highest toll. Sixty four percent of recorded deaths occurred during the 4 dry season months (July through October).  Effective sighting width and carcass density. The surveyed transects represented three main vegetation zones; the Serengeti short grass plains, the central and western  Acacia savanna,  and the northern Serengeti mixed Acacia  and broad leafed woodlands. Perpendicular sighting distances ranged from 0 to 1500 m from 41  T a b l e 2.8. Seasonal yearling survival rates estimated using the seasonal lognormal model. First month (YI) refers to July in 1992 and January for other years.  Year  1992  1993  1994  Yearlings per 1000 adults month 1 (71)  148  207  65  Wet season yearling survival rate (sYw)  no data  0.959  0.948  (0.85 - 1.0)  (0.84 - 1 0)  0.736  0.959  95% C L . Dry season yearling survival rate (sYd) 95% C L .  0.928  (0.84-1.0) (0.65 - 0.83) (0.87 - 1 0)  Monthly adult survival rate - wet season  no data  0.980  0.995  - dry season  0.973  0.946  0.994  -0.395  0.677  0.912  -log likelihood  42  1992  ^  1993  0.3  0-3  8.0.2  0.2  co «?0.1  S o.o  >-  •  0.1 ~1  1  1  1  1  1  1  1  1  1  1  Jan Mar May Jul Sep Nov  0.0  ~\  1  1  1  •  1  r  ~\  1  1  1  Jan Mar May Jul Sep Nov  Month  Month  1994  1992-94  13 0.3  Hco 0.2  «? 0.1 a> 0.0 w  >-  "I  I  I  I  I  I  I  I  I  I  1  Jan Mar May Jul Sep Nov  Jan Mar May Jul Sep Nov  Month  Month  Figure 2.6. The estimated monthly change o f yearlings per adult ratio between July 1992 through December 1994 calculated by using the seasonal lognormal model (solid lines). The observed ratio in December 1993 was abnormally high due to an unusual group o f yearlings i n one transect, and was excluded i n the model fit.  43  Table 2.9.  Summary of yearlings per adult ratios measured between 1963 and 1994.  Year  Jan/Feb  Jun./Jul.  December  1963  0.307  0.307  0.174  Watson (1971)  1971  0.096  0.095  0.049  Sinclair (Unpubl)  0.148  0.117  This study  1992  Source  1993  0.207  0.186  0.041  This study  1994  0.065  0.057  0.056  This study  44  T a b l e 2.10.  Wildebeest carcasses recorded between July 1992 and December 1994.  Age class  Total  Percent  1 N e w Born  20  5.4%  2 Quarter size  21  5.6%  3 Half Size  110  29.5%  4 Yearlings  45  12.1%  177  47.5%  373  100.0%  5 Adult Total  Figure 2.7. Number of adult wildebeest carcasses recorded between July 1992 and December 1994 weighted per 100 live individuals counted (bars) and per 100 k m transect length (solid line). The number o f adult carcasses per live adult counted (bars) was highest in 1993 indicating a high mortality rate.  46  the transect line. Estimates of effective sighting distances were similar across transects (Figure 2.8 top). T o estimate the effective area searched per transect, I used a pooled estimate of search width (shown as P in Figure 2.8). This was 226 m (196 - 259 m 95% C.I.) on each side of the transect and was rounded to 250 m ; hence the effective search width was 500 meters. The effective searched area varied with transect length, ranging from 5 to 35 k m per transect. 2  A summary of carcasses counted per transect per sighting distance class is shown in Appendix 4. The density of carcasses was similar across transects and the pooled estimate was 0.2 carcasses km" (0.16 - 0.25 95% CL; Figure 2.8 bottom). In general, densities were slightly 2  higher in western Serengeti (transects 1 -4) followed by the north (transect 7), and then central woodlands (transects 11 and 12).  Adult mortality rate. I divided carcasses into different age classes and used equation 2.12 and 2.13 to estimate mortality rates. Appendix 5 summarizes results from the adult mortality model at different time levels; daily, monthly, seasonal and annual mortality rates. Figure 2.9 compares these rates to monthly rainfall. The results suggest lower adult mortality during the wet season. Also seasonal survival rates varied substantially between years. Adult mortality was highest (28.1%) during the extended dry season of 1993 consistent with record low rainfall received (25.2 mm) over the last 35 years (Chapter 3, Figure 3.10). The highest monthly mortality rate was in November of 1993 (9.7%) during the peak of the drought. About 0.34 % (~ 3,000) o f the adult population died every day during this month. Three other months with heavy mortality rates during the dry season were; October 1992, October 1993 and September 1992 in declining rank (Figure 2.9 and Appendix 5). The 1993 mortality rate was the highest recorded since the late 1960s (Table 2.11). Survival rates were higher during the wet season in all years except 1971 and 1972, after an abnormally high dry season rainfall (>200 m m ; Sinclair 1979c; Table 2.11).  47  4  6  7  Transects  Figure 2.8.  Estimates of effective carcass sighting width in meters (top) and density per k m  2  (bottom) shown for each transect and when pooled, P for transects conducted between July 1992 and December 1994.  Vertical lines show 95% confidence intervals.  48  F i g u r e 2.9.  Monthly adult survival rates  {squares) estimated from a model relating  daily  counts of adult carcasses to numbers of live animals. The survival curve follows the rainfall regime  (open bars) with about one  month time lag. Rainfall data for July and September  1994 are missing.  49  Table 2.11. Adult wildebeest survival rates from 1967-1994. The annual monthly survival rates are not shown in years where only the dry season mortality was measured.  Year  Wet season monthly survival  Dry season monthly survival  Average annual monthly survival  1967  99.2  98.4  98.9  Sinclair (1979c)  1968  99.3  98.2  98.9  Sinclair (1979c)  1969  99.5  98.8  99.3  Sinclair (1979c)  1971  99.1  99.2  99.1  Sinclair (1979c)  1972  99.1  99.6  99.3  Sinclair (1979c)  1982  -  97.3  -  Sinclair et al. (1985)  1983  -  97.9  -  Sinclair et al. (1985)  97.3  -  This study  1992  Source  1993  98.0  94.7  96.3  This study  1994  99.6  99.4  99.5  This study  50  2.3.6. L I F E T A B L E A N A L Y S I S .  The population life table. The intermittent sampling over the last 34 years provided estimates of survival rates for five life cycle stages: pregnancy rate, neonatal survival, late calf survival, yearlings, and adults (methods 2.2.1, 2.2.3, 2.2.4 and 2.2.5 respectively). Appendix 6 shows how I estimated numbers in different age classes for the life table schedules. I calculated survival estimates based on available data in those years where only a few parameters were missing. These included population size, sex and age ratios. I estimated the population size by interpolation in those years where a census was not conducted. The mean ratio of yearlings per adult was 9.8% ± S.E. 2.3%. Thus, I assumed yearlings (12 ± 2 months) constituted 10% of the total population. Ninety percent of the remaining adults constituted 45% females for estimates prior to 1990 (sex ratio 1:1) and 58% from 1990 onwards (sex ratio 1.85 females: 1 male) (Figure 2.4). Estimated figures for the wildebeest life table based on present and previous demographic data are shown in Appendix 7. I used the wildebeest life table to determine the average instantaneous rate o f increase r (where r = natural log of wildebeest population size regressed against years). The wildebeest population has gone through two main phases over the last 34 years. First, between 1960 and 1977 the population increased logistically from 0.25 to about 1.4 million. The mean instantaneous rate o f increase r was 0.103 per year. The second phase, covering 1977 to 1993, exhibited variable net growth rates and r was -0.008 per year. This caused the population to remain between 1.1 and 1.3 million. Finally in 1994 the population declined to 0.9 million after extensive deaths during the 1993 drought.  Life cycle mortality estimates. Estimates of animals dying at each life cycle stage were derived from the wildebeest life table (Appendix 7). Adult mortality was obtained by subtracting the number of adults alive in year t+1 from previous year plus recruitment (number of calves in December). I call this method "estimates by census difference". Table 2.12 compares adult survival estimates  51  Table 2.12. Comparison of adult survival rates measured by carcass counts and those estimated from the life table by census difference (Appendix 7). Sources of data refer to independent estimates only. Values in parenthesis are 1 S.E. where this could be estimated. The 1992 independent annual survival estimate was extrapolated based on dry season results.  Annual survival rate Year  Independent estimate  Estimate by difference  Difference  Source  1967  0.877  0.976  -9.9%  Sinclair (1979c)  1968  0.880 (0.44)  0.967  -8.7%  Sinclair (1979c)  1969  0.915  0.968  -5.3%  Sinclair (1979c)  1971  0.899  0.977 (0.04)  -7.8%  Sinclair (1979c)  1972  0.917 (0.29)  1.022 (0.1)  -10.5%  Sinclair (1979c)  1992  0.720 *  0.822  -10.2%  This study  1993  0.636  0.692  -5.6%  This study  1994  0.936  0.936  0.0%  This study  52  measured independently (Table 2.11) with those calculated by census difference. Although independent survival estimates were consistently lower, results from the two methods are similar, and always within 1 standard error (S.E.) of each other when an S.E. could be estimated (Figure 2.10).  Population regulation The role of each life cycle mortality factor (^-values) in the regulation of the Serengeti wildebeest was examined by plotting the ^-values for each stage against l o g  10  of the population  size before the mortality occurred. Density dependence is shown i f the relationship is positive and relatively statistically significant. The adult mortality (k-5) and fertility loss (k-\) were positively related to population size and were relatively significant (k-5: P = 0.0009 and k-l: P = 0.031) consistent with the density dependent hypothesis (Table 2.13, Figure 2.11). However, the slopes were small (k-5: b = 0.073 and k-\:b = 0.094) suggesting weak density dependence. Neonatal ( £ - 2 ) and dry season calf (k-3) mortalities were positively related to population increase but were not statistically significant (k-2: b = 0.011, P = 0.954 and, k-3: b = 0.175, P = 0.335). Yearling mortality (k-4) had a steep slope, but it was not statistically significant (k-4: b = 0.57, P = 0.52). The problem with calculating A:-values by difference between log / and log F, is that an error in either parameter (e.g., too small log I), will automatically mean that k will be too large. Since k is plotted against log I, the same error may exist on both axes. The way to check this is to plot both log I against log F, and log F against log / . If the slopes of both regressions are less than 1 (not zero but unity) then there is no bias in estimates of the ^-values (Varley & Gradwell 1968). Results for this test shows that there could be some dependence in adult mortality ( £ - 5 ) values (log F on log / slope = 1.057 and log / on log F slope = 0.927). Thus the results for adult mortality stage should be considered tentative. The test of independence was necessary for adult mortality data (k-5) because its estimates were obtained by difference from sequential censuses. Other ^-values were obtained from independent measurements o f mortality.  53  .1.5 -,  o  (0  15 >  1.0  E  3 (0  __ 0.5 3 TJ <  0.0 00 CO CO  CD CD ^—  CD CO CD  CN CD T—  CD T—  C\l CD CO T—  co CO  co ——  CD CO  Figure 2.10. The relationship of adult annual survival rates measured by direct mortality estimates  (solid square)  Vertical bars represent  and by census difference in consecutive years  (open circles).  1 S.E. estimated from Sinclair (Unpubl) (solid line) and census error  (open bars) where these were  available.  54  Table 2.13.  Summary of the life table analysis showing the regression results of log  values  plotted against log initial population before the mortality occurred, A. The adult mortality and fertility loss were density dependent as shown by the relative significance level and the coefficient of their regressions (slope). Part B shows the results of adult mortality divided into two phases (see Figure 2.12 center and bottom).  (1) Mortality stage A Fertility loss  B  (2)  (3)  Slope  Intercept  (5) (6) (4) Adjusted Relative Observ r P -ations 2  k-1  0.094  -0.505  0.437  0.031  9  Neonatal mortality  k-2  0.011  0.337  -0.166  0.954  8  Dry season calf mortality  k-3  0.175  -0.812  0.000  0.335  16  Yearling annual mortality  k-4  0.571  -2.990  -0.156  0.521  4  Adult annual mortality  k-5  0.073  -0.394  0.297  0.0009  31  Adult mortality (1960-1971)  k-5a  -0.073  0.435  0.738  0.0004  11  Adult mortality (1975-1994)  k-5b  0.180  -1.040  0.014  0.276 '  20  Delayed adult density  k-5c  0.336  -1.999  0.139  0.086  16  dependence (1975-1994)  55  F i g u r e 2.11.  Regression results of log k-values on log initial population size of the Serengeti  wildebeest. The slope, intercept and significance levels are shown in Table 2.13. Densitydependent mortality was shown in adult mortality (relative significance levels: k-5,p = 0.0009) and fertility loss (k-l,p  = 0.031). Figures represent years shown by their last two  digits except for £-5 which is too crowded instead, years are shown in F i g 2.12 and 2.13.  (... next page.)  56  Figure 2.11. Fertility Io SS 0.12 -  V  .94  0.08 -  _3  71  •  0.00 -  ^  6 0  —2——-  *64  •  • 93  7 0  -0.04 -  r =0.437 2  Neonatal iTiortality 0.6 -. ^  91 992  0.4-  94  g> 0 . 2 -  • S 93  71  #  • 60  9 2  • 72  _l  0.0 J  r =-0.166 2  Dry seaso n calf mortality 0.8 -. co  1 Ui  5  r  0.6 -  0.2 0.0 -  67 65»  63  0.4 .63  0.2 -  •  7 1  • 94  r =0.156 2  r =0.297 2  0.15 -  •  0.10 u> 0.05 -  o  0  0.6 -  Adult mort;ality  —  0  93  0.0 -  2  0  7  #  1Ui 5  0  « m r>  Yearling mortality 0.8 <«•  =  93 • 84  •  OA.  2  o 00  •  5  2  «%• • • • . i  i  i  5.4  5.6  w  5.8  •  • i  6.0  i  6.2  logN  57  Adult mortality exhibited under-compensating density dependence with data points clumped into two groups. The first clump, Phase 1, represents the period when the population was below one million (1960s through 1971), and the second, Phase 2, when it was above a million (1975 to 1994). There was an inverse density dependence during Phase 1 (b = -0.073, P = 0.0004; Table 2.13 B; Figure 2.12 top). During Phase 2 the slope was positive but not significant (Figure 2.12  center, b =  0.180,  P = 0.276).  When data points are linked in their  temporal sequence they show some evidence of anti-clockwise spirals (Figure 2.13). Three possible cycles of 5 to 8 years are; 1975 - 80, 1980 - 84 and 1985 - 92 which suggests a delay in the density dependent effect. To test for this, k-5 was regressed against density in the previous year. The delayed density dependence was not statistically detectable but provided a slightly better fit (b = 0.336, P = 0.086) than the immediate density dependence (Figure 2.12;  center and bottom).  Figure 2.11  (bottom) can  also be interpreted as suggesting a curvilinear  density dependence with the strength of regulation accelerating at higher densities.  DISCUSSION  Tests ofpredictions. I now compare my results with the predictions of the regulation hypothesis set out in the introduction. I expected one or more density dependent mortalities to explain the growth and leveling-off of the wildebeest population between 1960 and 1994. The ^-factor analysis detected density-dependence in two life stages, fertility loss (AM) and adult mortality (k-5). Contrary to predictions in the 1970s (Sinclair 1979 c), changes in calf survival were not related to population increase. A l l age classes had higher mortality rates during the dry season than during the wet season except in years with abnormally high rainfall. The decline in adult pregnancy rate may reduce the populations' growth rate. The reduced pregnancy could result from changes in calving interval or delayed sexual maturity. Several empirical studies have shown that fecundity rates are reduced when the population approaches the environmental carrying capacity  (e.g.,  Laws 1968, Caughley 1970,  58  Phase I; 1960-72 adult mortality  5.45  5.55  5.65  5.75  5.85  5.95  Log N Phase II; 1975-94 adult mortality Within year mortality  r =-0.012 2  0.16 •  0.12  Ui  0.08  o  0.04 0.00 Delayed adult mortality  r =0.139 2  0.08 •  Ui  O  0.04 0.00 6.05  6.10  Log N  6.15  6.20  Figure 2.12. Regression results of adult mortality (log k-5) on log N divided into two phases of the wildebeest population sizes. The slope of Phase I (1960-72; top) suggest inverse density dependence (b = -0.073, relative significance p = 0.0004). While the within year mortality in Phase II (1972-94; centre) appeared to be density independent, the delayed adult mortality was weakly related to previous year's population size (bottom: b - -0.336, relative significance p = 0.086).  59  F i g u r e 2.13.  Wildebeest adult mortality (Phase II) showing anti-clockwise spiral cycles which  suggests delayed mortality effect.  60  Leader-Williams 1988, Houston 1982, Clutton-Brock et al. 1982, 1991, Owen-Smith 1990). Delayed sexual maturity, as suggested by the drop in yearling pregnancy rate (Table 2.5), could result from reduced growth rate, caused in turn by poor food quality (nourishment) and quantity. I consider these factors in Chapter 3. The present evidence suggests that density dependent adult mortality constitutes the main negative feedback on the population growth rate. These results are consistent with previous studies, which suggested that the major cause of adult mortality was intraspecific competition for food resources (Sinclair 1977a, Sinclair et al. 1985, Sinclair & Fryxell 1988, Sinclair & Arcese 1995a). Also, adult mortality compensates for calf fluctuations in the population due to its proportional large effect. Although the reproductive output was density dependent, its influence in the regulation process could have been affected by high calf mortality which appeared to be density independent. Regulation through density dependent adult mortality was also shown in the African buffalo (Sinclair 1977a). However, although Hanks (1981) suggested that an increase in adult mortality rate is the final indicator o f a declining population o f large mammal, only a few studies have found that adults are the main age group where density dependence acts. The inverse density dependent adult mortality in the 1960s through early 1970s suggests that rinderpest was holding the population below the environmental carrying capacity prior to 1962. Although the negative adult mortality slope at low densities (1960-1971) could result from artifacts relating to construction of the wildebeest life-table, the rapid population increase during this period was apparent (Sinclair 1979c). Since there is no evidence o f immigration, the increase in population size can be accounted for by two factors: (i) improved recruitment and adult survival rates following the removal of rinderpest in the early 1960s, and (if) increased dry season rainfall, and hence food, in the early 1970s which caused a second increase. Sinclair (1979c) provides a detailed account of the increase of ruminants after rinderpest was eradicated in the Serengeti region. After 1977 the average dry season rainfall declined to around 150 m m coincident with the population leveling off. Between 1977 and 1992 the population trend shows, on average, a slight negative rate of increase (r = -0.008) probably because of under-compensating effects. The importance of rainfall on the population dynamics o f wildebeest will be considered in Chapter 3.  61  Two population processes could not be established reliably. First is a possible curvilinear density dependent adult mortality between the 1960s and 1993.  This model  proposes that the intensity of density-dependent effects increases at higher population densities. This model, suggested by Fowler (1987), Sinclair (1989) and Caughley & Sinclair (1994) has not been demonstrated to this point. Second, is the delayed density dependence effects after 1975.  The severe drought in 1993 which reduced the population by almost 40% provides  another natural perturbation experiment. The regulation hypothesis will be confirmed i f the population size stabilizes at its previous level of about 1.3 million (assuming normal weather conditions). Apparently, the annual adult mortality rate in 1994 dropped to only 6.3% compared to « 40% in 1993 probably as a result of near average dry season rainfall (103 mm) and reduced wildebeest population size. Possible errors in demographic data. Small sample sizes are prone to sampling error. Hence, the small samples I used to estimate adult pregnancy rates, x -32  individuals per year, compared to a population of about  0.4 million adult females. However, the samples were random and did not fluctuate greatly from year to year, which provides some confidence in their values. Less confidence is placed in the 1993 yearling pregnancy rate as this was based on five animals and only one was slightly above the 8 ng/gm progesterone cut-off point. A n error in calibration would mean zero pregnancy rate in this age class. Based on autopsy results, the estimation of pregnancy rate using fecal samples is reliable to within a 12% error for pregnant females being classified as non-pregnant. This underestimate could be corrected (or at least reduced) in future studies by using a larger sample for both calibration and pregnancy test samples. In some years the adult sex ratio was obtained from data sets which were not specifically designed for that purpose. Adult males could have been under-represented since both, solitary and small male groups may not be sampled by transects placed through the main herds. Thus, the estimated recruitment rate as a percent of the population would be slightly over-estimated. Although very young calves could have been missed in large tightly packed aggregations (hidden behind adults), this is not likely to cause a significant error in calf survival estimates.  Occasionally immature males may have been mistaken for adult females.  62  This would cause an underestimate of the calf ratio. Between January and April yearlings could have been slightly overestimated by mistakenly including small two-year-olds. Overall, however, these errors in counting are not likely to change my results drastically.  S U M M A R Y  1. I described methods of estimating; (i) pregnancy rates, (/'/') calf and yearling survival rates from random samples of age and sex counts, and (iii) adult mortality rates from random samples of carcass and live animal counts conducted concurrently. 2. I examined the effects of various mortality stages acting on the wildebeest population by analyzing intermittent data collected between 1960 and 1994. Life table analysis has shown that the dry season mortality was higher than wet season mortality in all age classes except in years with particularly high dry season rainfall (1971-76). However, the within year seasonal differences were not necessarily statistically significant. 3. Using the A>factor analysis, I found that: (/') fertility loss (k-1) and (ii) adult mortality (£-5) were density dependent. However, there was no evidence for density dependence in (iii) Neonatal mortality (k-2) and (iv) dry season calf mortality (Ar-3) suggesting that early age stages were sensitive to other environmental effects such as diseases. Data were insufficient to test for density dependence in yearling mortality (k-4). 4. These results suggests that the wildebeest population was regulated through adult mortality. The rapid population increase in the 1960s through the early 1970s and stability in numbers after 1977 is associated with eradication of a viral disease, rinderpest in the early 1960s and changes in annual rainfall. The influence of rainfall on the dynamics of the wildebeest population is considered in Chapter 3.  63  Chapter III Serengeti Wildebeest Population Dynamics: Patterns of Mortality and Resource Limitation.  INTRODUCTION Resource limitation requires that intraspecific competition for resources increases as population density increases. Such limiting factor(s) reduce the population's rate o f increase and ultimately set the upper limit of population size. Previous studies on the Serengeti wildebeest have shown that adult mortality during the dry season was inversely related to food supply (Sinclair 1979c, Sinclair et al. 1985, Fryxell 1987, Dublin et al. 1990, Sinclair & Arcese 1995a). A s the amount of food available per individual declines, the proportion of body weight lost during the dry season increases, and animals in poor condition become more susceptible to other forms of mortality such as diseases and predation (Sinclair 1977a, LeaderWilliams 1988, Sinclair & Arcese 1995a). These previous studies, however, did not measure the impact of various causes of mortality on each age group. In this study I consider eight age groups to see whether they are affected differently as a function o f different energy reserves and physiological demands during periods of food stress. Environmental factors affect the reproductive output of a population through delayed maturity, reduced pregnancy rates and calf survival (Schaffer 1974, Charlesworth 1980, Clutton-Brock et al. 1988). A n y factor affecting body size may exert a major influence on different components of reproduction (Clutton-Brock et al. 1982, Fowler 1987, Sand & Cederlund 1996). The importance of body size in determining age of maturity has been demonstrated in many studies  {e.g.,  Reimers 1983, Albon  et al.  1986, Green & Rothstein 1991  and Gaillard et al. 1992). Among ungulates, the variation in age of maturity is size dependent with the probability of early reproduction increasing with body size (Albon et al. 1983, Clutton-Brock et al. 1988, Skogland 1983). Recent work by Berrigan & Charnov (1994)  64  emphasized the importance of climate and food quality as proximate factors that influence the evolution o f age at maturity. Thus, variation in a population's reproductive patterns depends on nutritional well-being of both immatures and adults. In turn, factors affecting food quality are strongly influenced by increasing population density or changes in environmental elements or both (Sinclair 1977a, Clutton-Brock et al. 1983, Skogland 1983, 1989, Fowler 1987). Alternatively, predators can play a major role in the regulation o f a prey population  (e.g.,  Ballard  et al.  1987, Gasaway  et al.  1992). In other instances, predation may constitute a  significant limiting factor although the prey itself varies in density as a result o f some other factors  (e.g.,  Peterson 1996). However, studies in the Serengeti have shown that predation  plays a minor role in limiting the wildebeest population size (Hilborn & Sinclair 1979, Sinclair et al. 1985, Sinclair & Arcese 1995a, Dublin et al. 1990). The wildebeest anti-predator strategy o f long distance migration and birth synchronization ensures that only a small fraction of the population is killed by predators each year. Long distance migration also prevents predators' numerical response (Maddock 1979, Fryxell & Sinclair 1988, Fryxell et al. 1988). In Chapter 2,1 showed that changes in fertility and adult survival were negatively related to density. The question remains; what factors caused the observed population patterns? In this chapter I explore causes and patterns of mortality in relation to age, sex and, condition o f animals. I examine the relative contribution of mortality o f each age class towards the total annual mortality. Then, I consider the food limitation hypothesis and test whether mortality in different life stages is related to food availability. The food limitation hypothesis is supported i f food supply is significantly inversely related to one or several of the mortality stages, or to reproduction. Other forms of mortality not related to food shortage should constitute a relatively small proportion of the total mortality.  65  METHODS  3.2.1. R E P R O D U C T I O N  Wildebeest fertility rates were estimated using methods described in Chapter II (2.2.1.), and compared with data from previous studies. I tested for a change in fertility rate between the 1960s through 1994 by logistic regression and iteratively re-weighted least squares in  NONLIN  o f the  SYSTAT®  package.  3.2.2. P A T T E R N S O F M O R T A L I T Y  A g e and sex specific mortality were estimated from two methods described in Chapter II; (/) carcass counts (Method 2.2.5), and, (if) age and sex counts (Methods 2.2.3-4). The estimated number of animals dying at different ages was used to determine patterns o f mortality and to test predation and food limitation hypotheses.  Mortality estimates from carcass counts. I recorded date, locality, age, sex, probable cause of death and condition of the animal at the time of death for each carcass located (conducted concurrently with Method 2.2.5). A g e and sex were assigned as for live animals (Table 2.1 and 2.2). In addition, tooth eruption in calves and yearlings, and wear patterns in adults, were used to age animals by methods given in Watson (1967) and Attwell (1980). Only carcasses less than 24 hours following death were considered. The condition of the animal at the time of death was determined by marrow fat reserves from its long bones (Sinclair & Duncan 1972, Sinclair 1977a, Sinclair & Arcese 1995a). Five categories of bone marrow condition were scored according to texture and color judged by visual criteria. These included; solid white fatty (SWF), white opaque gelatinous ( W O G ) , translucent gelatinous (TG), red gelatinous (RG) or absent ( A B S ) when lacking. The marrow categories are summarized in Table 3.1 and are hereafter referred to as healthy, moderate, and poor for S W F , W O G , and T G respectively.  66  Table 3.1. Categories of bone marrow used to determine the health condition of an animal at the time o f death summarized from Sinclair & Arcese (1995a). Values in bracket show ± 1 S.E. R B C refers to red blood cells.  Bone marrow condition 1  Solid white fatty  SWF  Mean % fat values  Animal health and remarks  88.5 (0.9) %  Above average; animal in good condition referred to as "Healthy"  2  White opaque gelatinous W O G  55.7 (2.4) %  Below average; animal undernourished referred to as "Moderate"  3  Translucent gelatinous  TG  15.9 (2.1)%  Very poor; animal highly undernourished referred to as "Poor"  4  Red gelatinous  RG  -  Ambiguous; active R B C in long bones  5  Absent  ABS  -  Absent; bone marrow not found  67  Efforts were made to establish the  cause of death by using all signs and clues  available within the proximity of the carcass. Causes were grouped into four main classes. (i)  Confirmed predation. Clues for a predator kill included; claw marks or bites especially around the neck and/or face, predators' footprints on the ground, signs of struggling in defense, blood trails and site of disembowel relative to the rest of the carcass. Predator species was recorded including pack size, sex and age where possible. Most large predators dismembered their kills and pulled out the rumen. Hyaena kills were more dismembered and had bones broken. The presence of predators on a carcass by itself was not considered sufficient to explain the cause of death  (ii)  Unconfirmed predation was recorded where predation was suspected as the cause of death but the predator species could not be identified.  (iii)  Miscellaneous causes included rare sources of mortality, for example; road kills, stuck in mud, drowned in rivers, and other environmental hazards.  (iv)  Non-predation deaths were decided when dead bodies were found fairly intact with the viscera inside the rib cage and gut cavity. This class included other natural causes not mentioned above. Detailed postmortem examinations were not conducted but animals in this category were suspected to have died from starvation, dehydration, and/or pathogens. I used Chi-square (X ) and log-likelihood ratio (G) tests (Zar 1984) to analyze the 2  frequency distributions of age, sex, marrow condition and causes of mortality. The William's or Yates' correction (X  c  2  or G ) was used where appropriate. I assumed equal chances of c  locating a carcass regardless of age class (except calves), sex, and causes of mortality. Mortality estimates from live animal age and sex counts. I estimated calf and yearling mortality by monthly change in calves per adult ratio (Methods 2.2.3-4). I subdivided the total annual mortality into five age classes and four subdivisions as shown in Table 3.2. I used the log-likelihood ratio test to analyze the mortality patterns of calves and yearlings (equation 2.7).  68  Table 3.2. The main mortality stages (Mactor) (A) and four sub-divisions (B) regressed against dry season (July - October) food supply, (t refers to year; 0 = present year; -1 previous year, and +1 = next year).  (1)  Life cycle/Age class  (2)  Abbreviation  (3)  (4)  Time span (from - through)  (5)  Dry Data season points regressed (YearO  A. Mortality stages 1 Fertility loss  k-l  May  January  2  k-2  March  June  k-3  July  December  k-4  January  - December  k-5  January  - December  Wet season calf  (/ )  mortality 3  Dry season calf mortality  4  Annual yearling mortality  5  Annual adult mortality  +!  'o  8  t-i  8  to  16  to to  4 34  B. Mortality sub-divisions 6 7  Neonatal mortality  A:-2new  Birth  March  u  4  Late neonatal  k-2 late  March  June  t-1  8  A>4wet  January  - June  t-1  4  £-5dry  July  mortality 8  Wet season yearling mortality  9  Dry season yearling mortality  December  to  5  Key factor analysis. I used the key factor analysis after Varley & Gradwell (1960) to determine the relative importance of each age class mortality. Life stages used and their respective A:-values were identical to those in Method 2.2.6. The reductions occurring at each stage were transformed in the form of log A:-values (equation 2.18) and the total annual mortality £-total, was the sum of all k values. The mean of each A>value shows the  relative strength o f its contribution to the  overall annual mortality. The regression slope of each A:-value against K-to\a\ indicates its contribution to the total annual mortality. The mortality stage with the largest slope value is the  key factor contributing most to population fluctuations. This mortality stage has a  regression coefficient close to unity because its A>value tends to fluctuate closely with .K-total in both size and direction (Varley & Gradwell 1960; Podoler & Rogers 1975).  3.2.3. R A I N F A L L AND FOOD LIMITATION. The most important environmental variable affecting grass production in the Serengeti is rainfall (McNaughton 1979, Sinclair 1979c). The amount of grass growth, and hence food supply to grazers, depends on the amount and distribution of rainfall. A typical wet season receives sufficient rainfall and food supply is not limiting then (Sinclair 1977a, 1979c; Maddock 1979). In contrast, the above studies have shown that food supply is sometimes inadequate during the dry season. I estimated grass production during the dry season using the regression equation for grass growth on monthly rainfall given by Sinclair (1979c Figure 4.4) and later modified by Hilbornef a/. (1994). G =\.25R y  y  (3.1)  Where: Gy is the amount of grass produced measured in kilograms per hectare per month (kg/ha/mo); and, Ry the dry season (July - October) rainfall measured in m m and averaged over the northern Serengeti region.  70  Rainfall data were obtained from the Tanzania Wildlife Conservation Monitoring ( T W C M ) data base in Seronera. Wet and dry seasons were defined as November - June and July - October respectively. I used monthly rainfall data from 21 rain-gauges that had over 85% continuous records going back to the early 1960s. I divided the rain gauges into three zones in relation to wildebeest migration pattern (Appendix 8). The average monthly rainfall was calculated for the three areas and for the total area. The amount o f food-per-animal (Fy) is the total grass grown per month per hectare, times the number of hectares utilized in the dry-season (approximately 0.5 x 10 measured from 6  a 1:250,000 scale map), divided by the total number of wildebeest in that year (Ty). G 0.5xl0 v  6  F =^—z  (3-2)  y  y The total number of wildebeest (Ty) was obtained from aerial censuses and interpolated estimates (Appendix 7, column 3).  Food limitation. The food limitation hypothesis was tested by plotting the life cycle mortality stages in the form o f log ^-values (equation 2.18) against (/) the overall amount o f food available and (ii) the amount of food available per individual wildebeest. The mortality stages k-l to k-5 are described in section 2.2.6 of Chapter II. The Bonferroni corrected ^-values were used to test the significance o f each stage with reference to when the mortality occurred relative to the dry season period (Table 3.2). Mortality occurring during the wet season was regressed against previous years' dry season food supply so as to detect delayed effects, i f any. C a l f survival is likely to be influenced by maternal effects in the previous dry season (e.g., weak or underweight newborns, and/or, mothers producing less or low quality milk). Therefore, I plotted neonatal mortality (k-i) against previous years' dry season food supply to determine i f any relationship existed.  71  RESULTS  3.3.1. R E P R O D U C T I O N .  The pregnancy rates of yearlings and adults measured intermittently between 1960 and 1994 are shown in Table 2.5. Wildebeest pregnancy rates declined significantly from the early 1960s to 1994 (Figure 3.1). Adult pregnancy rate declined from 94.6% to 83.5% ( ± 9.8% asymptotic standard error, logistic regression P = 0.003). The yearling pregnancy rate changed dramatically from 83% in 1960 to slightly over 20% in 1964 and remained low thereafter. This decline was significant but with a larger error margin than that for adults; from 34%) in the 1960s to 5.6% in the 1990s ( ± 17.4% asymptotic standard error, logistic regression P = 0.005).  3.3.2. P A T T E R N S O F M O R T A L I T Y .  Patterns of mortality in the first two years of life are based on two models;'(/) the monthly change of calves per adult ratio, and (ii) carcass counts (Methods 2.2.3-5). The two methods gave similar results for both first and second year mortality estimates except for yearlings in 1993 dry season (Figure 3.2). In 1993 the carcass count model significantly underestimated yearling mortality by 6%. One would expect that small carcasses, like those o f calves, would disappear more quickly compared to adults, particularly when the cause is predation, since carcasses can be easily dismembered, eaten, or carried away. Thus, the carcass count model would consistently under-estimate juvenile mortality. Caution must be taken, therefore, when dealing with causes of juvenile mortality, since these have inherent biases. MORTALITY ESTIMA TES FROM CARCASS COUNTS.  Age specific mortality. The frequency distribution of carcasses by age is shown in Table 3.3. Calves (<1 year) constituted 40.5% of all carcasses, while 12.1% were yearlings and 47.4% adults (>2 years). The middle-aged adult class (5-8 years old) was represented at a higher proportion than  72  F i g u r e 3.1. The adult  (squares)  between 1960 and 1994  and yearling  (P < 0.005;  (triangles) pregnancy  logistic regression  rates declined significantly  (solid lines). Dotted lines  interpolate  missing data points.  73  < •  1  _  (  o  M  o  CO  o  )  I  O  Monthly mortality rate  Calves 04  !  Yearlings 04 as  i  "ci  r • •  n 1  c  1  £  i  1992 dry  I 1  0  I  <  0.2 -  Mon  o  1993  wet  1993 dry  T  :  1994  wet  1994 dry  Season  Figure 3.2.  Estimates of calves  (top) and yearlings (bottom) monthly mortality rates calculated  using the change in calves per female ratio (or yearlings per adult ratio), compared to the carcass count model,  open circles. Within-year  estimates were similar within 95% confidence limits of each other calves in 1994 and yearlings 1993.  solid squares,  seasonal mortality  (vertical bars)  except for  Carcass model appeared to underestimate yearling  mortality in the 1993 dry season.  74  Table 3.3.  The frequency distribution of carcasses by age shown in relation to sex and causes  of mortality. Natural mortality include predation, non-predation and miscellaneous causes. (Data for the 1970s and 1980s from Sinclair & Arcese 1995a).  Calf  Yearling  (<1)  (1-2)  Age class (years) Young Middle Old adult Very old adult age (2-4)  (5-8)  (9-12)  Total  (>12)  Carcass sex 1992-94 Female  24  16  13  29  21  6  109  Male  52  17  12  39  45  9  174  75  11  1  2  1  0  90  151  44  26  70  67  15  373  9  30 27 57  Unidentified Total Predator kills 1992-94  1  5  3  12  14  3  1  3  6  -  15  8  4  15  15  -  1970s  -  36  52  56  28  -  20  192  1980s  19  63  90  64  50  286  35  26  70  67  15  213  -  90  141  216  159  85  691  -  9  8  11  9  40  1980s  -  3  9  21  42  30  28  130  1990s  -  24  20  48  52  11  155  42  49  101  91  42  325  10  42  48  34  22  156  11  6  17  14  3  51  21  48  65  48  25  207  Lion Hyaena Total Natural mortality  1990s Total Non-predation 1970s  Total Predation  -  1980s 1990s Total  75  that of young adults (2-5 years). Few older adults (>9 years) died, but this could be a reflection of their relatively smaller proportion in the population. There was no clear pattern o f age specific mortality among adults and further analysis was not possible because the age structure of the live population was not known. The frequency distribution of carcasses by age classes in the 1990s differed significantly from those reported by Sinclair & Arcese (1995a) in the 1970s and 1980s ( G = 54.293, d.f. = 8, P < 0.001) (Table 3.3, Figure 3.3 top). In the 1970s when the population was increasing the frequency of young animal carcasses (1-4 years) was higher than those o f old adults (> 9 years). This pattern was reversed in the 1980s when adults (> 5 years) became more frequent than expected for a population that was leveling off (Sinclair & Arcese 1995a). However, the age class mortality pattern in the 1990s changed again (see below). The nonpredation sample in the 1990s was similar to that of the 1970s ( G = 3.366, d.f. =4,P> but different from that of 1980s ( G = 18.944, d.f. = 4,P<  0.25)  0.001) (Figure 3.3, center). The  similarity between 1970s and 1990s was mainly the result of a proportional increase of yearling mortality and a reduced mortality of very old adults in the later period compared to the 1980s. A l s o mortality o f young adults (2-4 years old) was much lower in the 1990s than at any other time. Mortality of middle aged animals (5-8 years old) has been proportionately higher since the 1970s. The age class frequencies of animals killed by predators in the 1990s was also different from that of the 1980s ( G - 14.909, d.f. = 4, P < 0.005) (Figure 3.3 bottom). While yearling kills were proportionately well represented in the 1980s, they were least represented in the 1990s. Instead, their position was taken by young adult carcasses. Similar to the nonpredation sample, middle-aged adults were more frequent than any other class. Calves were excluded in this analyses because of possible under-counting biases.  Sex specific mortality. Sex could not be identified from 90 (24.1%) carcasses (Table 3.3). A m o n g these, only 3 (<1%) were adults and the rest were < 2 years old (Figure 3.4). Thus, I omitted calves and yearlings in analyses of sex specific mortality because the sex of 44.4% of carcasses in these classes could not identified. Adult male mortality was significantly higher than that o f adult 76  Figure 3 . 3 . Percent frequency distribution of wildebeest carcasses by age classes showing the difference of mortality patters in three time periods ( G > 13.277, P < 0.01 for each test) (1970s and 1980s from Sinclair & Arcese 1995a, and 1990s from this study)  77  30  n  Calf  Yearling  Adult  ED Female DMale H Un-identified  Figure 3.4. Percent frequency of wildebeest carcasses recorded in 1992-94 showing the distribution of sex in three age classes (calves: < 1 year; yearlings: 1-2 years; and adults: > 2 years).  78  females in all seasons except for 1992 dry and 1994 wet seasons (G > 7.879, d.f. = c  \,P<  0.005) (Table 3.4). The expected values of adult males and females were based on live animal counts conducted concurrently with carcass transects (Method 2.2.2).  Causes of death Non-predation deaths during the 1990s accounted for most mortality (74%) and were significantly higher than predation in all age classes ( G > 5.024, d.f. = 1, P < 0.025) except for c  very old adults, probably because of a small sample size (Table 3.5). Predation accounted for 24.1% of the total mortality in the following composition: lion, 8.1%; hyena, 7.3%; cheetah, 0.8%; and, unidentified predators, 8%. However, predation on calves may have been under represented due to inherent biases. Miscellaneous causes of deaths contributed 1.9% (3 road kills and 4 poached animals). While these results are contrary to the predator limitation hypothesis, they are consistent with the food limitation hypothesis.  Marrow class and predation The frequency of adult marrow categories varied significantly between predation and non-predation carcasses ( G = 11.623, d.f. =2,P<  0.01). Animals in poor condition ( T G )  contributed the largest proportion (45.6%) in the non-predation sample followed by moderate ( W O G , 38.4%) and healthy individuals ( S W F , 16%) (Figure 3.5 top). This pattern was reversed in the predation sample with only 22.2% in poor condition and 41.7% in good health. Animals with moderate marrow condition contributed 36.1% of the predation sample. Individuals with healthy marrow in the non-predation (12.4%) sample were more numerous than the 9.3% in the predation sample. This pattern further supports the food limitation hypothesis; that animals dying from non-predation causes are proportionately i n poorer condition than those dying from predation. These results are consistent with marrow frequencies in the 1970s and 1980s (Sinclair & Arcese 1995a). The frequency o f marrow condition within sex class (Table 3.6), suggests that predators were significantly selecting healthier males than those that died from other causes ( G = 16.284, d.f. = 2, P < 0.001, Figure 3.5 bottom). This difference was not detected in females probably because of a small sample size ( G = 0.957, d.f. =2,P>  0.50). A m o n g the two  important predators, lions selected for healthy adults, while hyenas killed animals in poor  79  Table 3.4. The log likelihood ratio test of adult wildebeest (> 2 years) carcasses showing sex vulnerability in different seasons. Expected values were based on proportions o f live animal counts. (* * * = P < 001; * * = P < 0.01; and, ns = not significant, G test.).  Year/ Season  1992 dry  1993 wet  1993 dry  1994 wet  1994 dry  Carcass count Female  Male  Observed  10  14  Expected  15.16  8.85  Observed  18  27  Expected  36.37  8.63  Observed  15  23  Expected  25.30  12.70  Observed  11  15  Expected  15.51  10.49  Observed  15  26  Expected  26.61  14.39  Total (n)  69  105  Live animal count Female  Male  Total  G value  24  0.63  0.37  6743  2.240  45  0.81  0.19  38  0.67  26  41  Total  174  d.f.  c  ns  1  17463  33.952 * * *  1  0.33  7496  9.336 * *  1  0.60  0.40  51130  0.870  ns  1  0.65  0.35  21790  14.431 * * *  1  104622  80  Table 3.5. Causes of mortality recorded in 1992-94 relative to age classes. (***=/*< 0 0 1 , * = P < 0.05, and, ns = not significant: d.f. = \,G tests).  Age class  NonPredation predation  Total  Calf  114  37  151  Yearling  31  13  44  5.28 *  Young adult  20  6  26  5.65 *  Middle age  48  17  65  13 10 * * *  Old  52  14  66  20.98 * * *  Very old  11  3  14  2.56 ns  276  90  366  Total  38.87 * * *  81  Overall carcasses 50 n  Non predation  • Healthy  Predation  • Moderate O Poor  Figure 3.5. Percent distribution of adult bone marrow condition by causes of mortality recorded in 1992-94. Overall (top) poor marrow was more important in non-predation mortality and healthy condition in predation carcasses (G = 11.623, P < 0.005). This difference was significant in males (G = 16.284, P < 0.001) but not in females  (bottom)  (center) ( G = 0.957, P > 0.50).  Table 3.6.  The frequency distribution of bone marrow types in relation to wildebeest age  classes, causes of mortality and seasons recorded i n 1992-94. Calves and yearlings were omitted i n marrow analysis because of the red gelatinous (RG) class which is a poor index of body condition.  83  Bone marrow class Healthy Moderate Poor RG  Absent  Total  Age classes Calf  1  0  2  133  15  151  Yearling  6  9  17  11  2  45  Young adult  7  11  7  0  1  26  Middle age  20  25  24  0  1  70  O l d adult  10  23  28  0  5  66  3  4  6  0  2  15  47  72  84  144  26  373  14  12  3  1  1  31  2  3  4  14  4  27  16  15  7  15  5  58  21  34  44  99  Wet 1  6  14  15  35  Wet 2  13  15  6  34  40  63  65  168  14  28  52  94  3  11  14  28  6  14  6  26  23  53  72  148  Very old Total Predator kills Lion Hyaena Total Adult marrow Dry  Total  Adult non-predation mortality Dry Wet 1 Wet 2 Total  Adult predation mortality Dry  9  8  6  23  Wet 1  2  6  3  11  Wet 2 Total  7  4  1  12  18  18  10  46  9  32  30  71  13  7  4  24  22  39  34  95  11  16  26  53  5  4  11  21  30  64  Adult males Nonpredation Predation Total Adult females Nonpredation Predation Total  2 13  '  condition and mostly juveniles (age; G = 31.148, d.f. = 4, P < 0.001, and, marrow; G = 21.227, d.f. = 4, P < 0.001, Figure 3.6). These results differ from those o f Sinclair & Arcese (1995a) for data collected between 1968 and 1991. Sinclair and Arcese reported no differences in marrow condition among different classes of predator kills, and lions selected for younger animals than hyenas. Marrow class in relation to age The red gelatinous (RG) bone marrow constituted 73.5% of juvenile (<2 years) carcasses (Table 3.6). This category, is not a good indicator of animal health but rather a sign of active production of red blood cells in the bone marrow (Sinclair 1977a). R G was exclusively found in animals less than 18 months old and to eliminate this confounding factor, calves and yearlings were omitted in this analysis, together with nine adult carcasses that were missing bone marrow ( A B S ) . The most frequent marrow category among adults was poor ( T G , 36.7%) followed by moderate ( W O G , 35.6%) and healthy (SWF, 22.6%) (Table 3.6). Disregarding causes o f mortality, the occurrence of each marrow class was similar among adult age classes and sex (age: G = 5.000, d.f. = 6,P>  0.05, and sex: G = 2.868, d.f = 2,P>  0.10).  The frequency of high marrow fat classes was significantly lower in natural deaths (predation and non-predation) recorded between 1992 -94 than in the shot animals "live sample" measured between 1968-73 ( G = 128.99, d.f. = 4, P < 0.001) (Sinclair and Arcese c  1995a). These results suggest that animals dying from natural causes are generally in poorer condition than live animals, consistent with the predictions of the food limitation hypothesis, and the results of previous studies (Sinclair & Arcese 1995a). Seasonal marrow  condition.  Three seasons were used in the analysis of marrow frequencies: dry season (July October), early wet season (November-February) and, late wet season (March-June). A m o n g adults, marrow frequencies were significantly different across seasons ( G = 10.074, d.f. = 4, P <0.05; Figure 3.7, top). Poor marrow was more frequent during the dry season and slightly less  85  Marrow class • Lion  • Lion  U Hyaena  M Hyaena  Figure 3.6. The frequency of wildebeest marrow (top) and age (bottom) classes in relation to source of predation between 1992-94. While lions selected for healthy and mature individuals, hyenas killed young and under nourished animals (age: G =31.148, P < 0.001; and, marrow: G =21.227, P < 0.001). R G marrow class refers to red gelatinous.  86  50 -i 40 30 i_ o 20 CQ O 10 \0 o -I  Overall  CO CD CO CO CO  <>>  Non predation  w 50 n co 40 CO  20-I 104 0  2  50 i  8 o  30  8 " co 30-  Predation  4 0  £ 20 S i 0o -  • Jul - Oct Dry • Healthy  Nov - Feb Wet1  Mar - J u n Wet 2  • Moderate  ^Poor  Figure 3.7. Percent frequency distribution of adult marrow condition by seasons. Poor and moderate conditions were important during the dry and late wet seasons (Wet 2) respectively (top : G = 10.074, P < 0.05; and, non-predation: G = 9.649, P < 0.05). There was no seasonal difference in the predation sample  {bottom:  G = 4.973, P > 0.25)  87  so in the early part of the wet season. Moderate was well represented in all seasons but was proportionately more important in the wet season between March and June. Animals dying in healthy condition were more frequent during the wet season than in the dry season (Figure 3.7 top). While the frequency of low marrow fat classes was higher in the non-predation deaths during the dry season ( G = 9.649,  d.f. = 4,P < 0.05; Figure 3.7 center),  the frequency of  marrow classes in the predation sample was more similar across seasons ( G = 4.973, d.f. = 4, P > 0.25, Figure 3.7;  bottom).  These results support the predictions o f food limitation in that the  non-predation mortality was (/') important during the dry season and, (ii) animals dying during this period were, on average, in poorer condition than those dying during the wet season. MORTALITY ESTIMA TES FROM LIVE ANIMAL COUNTS.  I used the live sex and age ratio counts for estimates of seasonal calf and yearling mortality. Unlike carcass counts, this method is free of inherent biases. In general, low mortality rates occurred during the wet season (Figure 3.2 a and b). However, seasonal mortality rates within years differed only in 1993 and 1994 for yearlings and calves respectively. The highest calf mortality rates occurred in the dry season o f 1993. Mortality estimates and their respective 95%  C.L. were  computed using Methods 2.2.3-4  (see also  Table  2.6 and 2.8).  Key factor analysis. I followed the 1993 cohort from pregnancy in late 1992 until individuals were about 2 years old in December 1994 as they were recruited into the adult age class. This is the cohort that was severely affected by the 1993 drought and of all calves born, only about 9% survived through December 1994 to their second birthday. Unexpectedly, the highest loss (48.9%) occurred in the 1993 wet season followed by another 30.3% loss during the drought in 1993. Other cohorts between 1992 and 1994 were represented for only part of their first two years in life. I used the key factor analysis to explore the importance of mortality occurring at eight life stages (Table 3.2). Figure 3.8 shows mortality rate as a percentage of total mortality at each age class measured between 1960 and 1994 (Watson 1967, Sinclair 1979c, Unpubl., and this study). The  88  40  4-  &  30  o E  20 X  c o o © Q.  10 A  •  3  4  5  6  8  Mortality stages  Figure 3.8. Wildebeest mortality rates (%) recorded intermittently between 1960 and 1994 divided into eight stages (Table 3.2). Percentages represent mortality rates i n three age classes (i.e., 2-4 per calves born, 5-6 per yearlings, and, 7-8 per adults. Data points are staggered for clarity. (Sources: Watson 1967, Sinclair 1979c, Unpubl. and this study). Key for mortality stages: 1 = fertility loss (k-l), 2 = early neonatal (k-2 new) 3 = late neonatal loss (k-2 late) 4 = dry season calf loss (A>3)  5 6 7 8  = = = =  yearling wet season loss (k-4 wet) yearling dry season loss (k-4 dry) adult wet season mortality (k-5 wet) adult dry season mortality (k-5 dry)  89  percent loss at each life stages is based on three age class mortalities; calves (<1 year), yearlings (1<2 years) and adults (>2 years). Neonatal mortality (< 2 months) was consistently higher than other stages and yearling mortality was the bast (Figure 3.2). The relative importance of mortality occurring at each stage i n determining population change was obtained by calculating its contribution i n log ^-values to the annual total, log Ktotai.  Figure 3.9 shows the regression of log ^-values against  ^T-totai  for eight years that had  complete demographic data sets. The regression results are given i n Table 3.7. The mean of the  values (Table 3.7, column 2) indicates the relative strength of the  various mortality stages contributed to the total annual mortality. Neonatal mortality had the highest mean k-value (k-2, x = 0.401) and therefore, the most important reduction stage. This was followed by dry season calf mortality (k-i, x = 0.221). Adult mortality (k-5, x = 0.040) and fertility loss (A;-i x = 0.039) were closely related and on average contributed the least to total mortality. Yearling mortality (A>4) was omitted in this analysis because few data points were available. The regression coefficient o f ^-values on  A^-totai  (Table 3.7 column 3) indicates  the importance of the mortality stage i n determining the population change. A regression coefficient close to unity suggests a stage that fluctuates closely with  X-totai.  Thus, dry season  calf mortality, with the highest regression coefficient (b = 0.64), was the "key factor" influencing population change. Neonatal (b = 0.155) and adult (b = 0.141) mortalities were second and third respectively. Fertility loss was the least (b = 0.064), probably because of its low contribution to total mortality rates (3c = 0.039) rather than random loss.  3.3.3. RAINFALL AND FOOD LIMITATION.  The wet and dry season rainfall averaged across the Serengeti ecosystem are shown i n Figure 3.10. The mean wet and dry season rainfall between 1960 and 1994 were 679 m m and 139 m m respectively. The mean annual rainfall was 781 mm. These records are similar to those reported in Norton-Griffiths et al. (1975) for rainfall data collected between the 1930s and early 1970s. A n additional shift i n the mean annual rainfall was noted in northern Serengeti (a decline from 1100 to 870 mm) but this decline was not statistically significant compared to the 1930-1970s (variability ± 25%, Norton-Griffiths et al. 1975).  90  Neonatal mortality 0.6 -, oi• Ui  o  71  0.4  94 66. .65 93  60 ,72  0.2  6=0.155  0.0 Dry season calf mortality 0.6 n  <? Ui  O _l  93  0.4  60 m  0.2  65  71  66-  0.0  94  6=0.640  9 2  6=0.141  Adult mortality 0.16  93  to• Ui  o  0.4  0.6  0.8  K-total  1.0  1.2  Figure 3.9. Wildebeest age class mortalities (^-values) plotted against total mortality (X-totai). D r y season calf mortality (£-3) had the highest coefficient of regression (b = 0.640) and therefore was the key factor. The yearling mortality (k-4) was omitted because data were insufficient. Data labels show years by their last two digits.  91  Table 3.7. Summary of the life table analysis showing means of log  values and regression  results from eight years that had complete sets of demographic data. While neonatal mortality ( £ - 2 ) contributed most in the total annual mortality (highest x ), late calf mortality (£-3)  was the  key factor (highest b value).  (1)  (2)  (3)  (4)  Mortality stage  Mean (X)  Slope (b)  Observati ons  Fertility loss  k-i  0.039  0.064  8  Neonatal mortality  k-2  0.401  0.155  8  Dry season calf  k-3  0.221  0.640  8  k-s  0.040  0.141  8  0.700  1.000  mortality Adult mortality  Total  92  1000  E E  800  A  600  A  400  A  200  A  (0  c E 'co  0  o  CO CD i —  ID CO CD  O  un  CD  CD  i —  • Wet season  o  00 CD T—  m  CO CD .  O CD CD T—  I Dry season  Figure 3.10. The wet and dry season rainfall patterns averaged for the Serengeti ecosystem. Rainfall data for 1960-63,1973-75 wet season and 1961-62 dry season were not available.  In 1993 the lowest dry season rainfall in 34 years (25 mm) occurred (Figure 3.11, top). This resulted in the lowest estimated amount of dry season food per hectare and available per individual (Figure 3.11,  bottom).  Effectively, the migratory animals experienced reduced  rainfall starting in April and a severe reduction from June through November (Figure 3.12). The estimated low in food availability was consistent with high mortality rates recorded between A p r i l and November 1993 ( « 3 0 % ) .  Food limitation. The 1993 record low rainfall, and hence food supply, provided a natural perturbation experiment that enabled us to understand the influence of reduced amounts of food on high levels of wildebeest density. Results for the ^-values against per-capita food supply are shown in Table 3.8 and plotted in Figure 3.13. The same test on the overall amount of dry season food availability (not per capita) showed no significant relationship with any life stage mortality over the last 30 years.  Adult mortality (ks)  was significantly negatively related to  per capita food supply during the dry season (b = -0.053, P = 0.0005). This relationship was detected even when 1993 was excluded from the regression equation (b = -0.036, P = 0.039). The reduced amount of food per animal during the dry season also significantly influenced the  dry season calf mortality (ks: b = -0.322, P = 0.002).  However this  relationship was not significant i f 1993 was excluded from the regression fit (b = -0.301, P = 0.153). There was a weak inverse relationship between dry season food supply and the annual  yearling mortality  (k-r.  b=  -0.410,  P = 0.063).  Sub-dividing this stage into seasons did not  change the results (Table 3.8 B) probably because data were limited; the wet season yearling mortality regressed against previous years' dry season provided P = 0.191, and, dry season mortality against dry season per capita food supply and  neonatal mortality (k-2)  P=  0.084. Although pregnancy  loss (k-\)  showed negative relationship to the dry season per capita food  supply, these were not statistically significant (k-\: b = -0.100, P = 0.34 and, k-r. b = -0.017, P = 0.617). A further subdivision of k-2 did not change the results (k-2 new P = 0.470 and k-2 late P = 0.969). Thus, adult mortality (k-5) and dry season calf mortality ( £ - 3 ) in particular were consistent with the food limitation hypothesis.  94  Figure 3.11.  The northern Serengeti dry season rainfall pattern (top) used to estimate the  amount of grass (food) produced (bottom, circles) and, the per capita food available (bottom, squares).  150  Figure 3.12.  The mean monthly rainfall pattern i n the Serengeti between 1960 - 1994  (squares) compared to the monthly rainfall in 1993 (triangles). The 1993 dry season was much drier than usual and persisted for a longer period (July through November).  96  T a b l e 3.8. Regression results of the age class mortalities between 1992-94 (A) and their respective subdivisions (B) on the per capita dry season food supply. Late calf ( £ - 3 ) and adult (ks) mortalities were significantly negatively related to the dry season food availability (B onferroni corrected P < 0.01).  (1) M o r t a l i t y stage A  B  (2)  (3)  (4)  (5)  (6)  Slope  Adjusted r2  P  d.f.  n.  Fertility loss  k-l  -0.017  -0.115  0.617  1  8  Neonatal mortality  k-2  -0.100  0.018  0.341  1  7  Late calf mortality  k-3  -0.322  0.481  0.002  1  15  Yearling annual mortality  k-4  -0.410  0.816  0.063  1  4  Adult annual mortality  k-5  -0.053  0.311  0.0005  1  32  Neonatal mortality  k-2 new  -0.097  -0.079  0.470  !  6  Late neonatal mortality  k-2 late  -0.003  -0.200  0.969  1  7  Yearling wet season  k-4 wet  -0.052  0.482  0.191  1  4  k-4 dry  -0.375  0.580  0.084  1  5  *k-4 dry  -0.548  0.989  0.048  1  3  mortality Yearling dry season mortality * Yearling dry season mortality  97  p=0.543 r =0.078  Fertility loss  2  0.08 O) 0.04  o 0.00 p=0.341 r =0.018  Neonatal mortality  2  0.6 -, CM •  D) O  0.4 0.2  Late calf  p =0.002 r =0.481  mortal jjyg to •  2  0.4 0.2 0.0 -  Yearling mortality  p =0.063 r =0.816 2  0.8 -. 0.6 -  o  -1  0.4 0.2 0.0 p=0.000 r =0.311  Adult mortality  in Ui O  _J  2  0.15 -. 0.10 0.05 0.00 1.5  L o g food  Figure 3.13.  The age class mortalities  2.0  2.5  values) regressed against dry season per capita  monthly food supply in 1992-94. Late calf (k-i) and adult (k-i) mortalities were significantly negatively related to the dry season food availability (Bonferroni corrected P < 0.01).  98  DISCUSSION The data presented above support the food limitation hypothesis but reject the predation hypothesis. In particular, a low per capita amount of food available during the critical period (dry season) has a negative effect on reproduction and survival of the wildebeest population. I now consider the influence of food limitation on the demographic parameters.  Reproduction. The decline in yearling pregnancy rate from 34% to 5.6% suggests a delay in sexual maturity. In most vertebrate species the attainment of maturity is determined by size rather than by age  (e.g.,  Geist 1971, Laws 1981, Clutton-Brock  et al.  1982, 1988, Leader-Williams  1988, Owen-Smith 1990). According to these studies, the mechanisms that reduce an individual's body growth rate are mainly related to food quality (nourishment) and quantity. Hence, at high densities less food per individual results in reduced growth rate and, therefore, in delayed maturity. In this study, however, there was no significant correlation between the change in yearling pregnancy rate and food available per individual. The ^-factor analysis may have failed to detect the correlation for two possible reasons. First, the change in age of maturity, was the first demographic parameter to be negatively affected by the population growth. A major decline in yearling pregnancy rate occurred before the population had doubled in 1971 and remained low thereafter. Second, the decline had a minor effect on the population growth rate. The estimated contribution of yearlings to the total number of calves born per year was about 3% compared to 83% contributed by adult females (>2 years). The decline in adult pregnancy rate was density dependent but was not related to food availability. Reduced pregnancy rate could be a result of one or a combination of the following; (f) a further delay in age of maturity beyond 2 years, (ii) increasing calving interval, (iii) increasing abortion incidents, (iv) increasing female infertility, or, (v) inadequate males to impregnate receptive females — (as a result of infertility or skewed sex ratio). Except for skewed sex ratio, other processes may be influenced by one or several environmental factors. One environmental factor often implicated is nutrition.  99  The delayed sexual maturity and reduced fertility are consistent with population growth models proposed by Caughley (1970) and Houston (1982) and supported by several studies (Laws 1968, Geist 1971, Sinclair 1977a, Clutton-Brock et al. 1982). These models predict a decline in fertility rate as the population approaches its environmental carrying capacity. Other factors that may affect fertility rates include diseases and harsh weather conditions. N o data were available to test these alternative factors. Food limitation. Adult mortality (k-5) and dry season calf mortality (k-3) were negatively related to the amount of food available per individual during the dry season, which is consistent with the food limitation hypothesis. Wildebeest that died during the dry season showed low fat reserves on average suggesting that the most probable cause of mortality was poor nutrition, consistent with previous studies of the Serengeti wildebeest (Sinclair 1979c, Sinclair et al. 1985, Sinclair & A r c e s e 1995a). First year mortality. Neonatal mortality constituted the highest proportional loss compared to other life cycle stages (Table 3.7, Figure 3.8).  This stage was neither correlated to dry season food  availability, nor was it the "key factor." These results suggest that neonatal mortality was sensitive to random mortality agents. Nutrition is often implicated as influencing the size, vigor, and survival of new born calves and undernourished calves become more susceptible to diseases and predation. However, such effects appear to result from changes that are not necessarily related to density. Studies conducted on ungulates elsewhere have shown a strong relationship between reproductive success and the female's nutritional status. For example, in the white tailed deer (Odocoileus  virginianus) the nutritional state of the pregnant female greatly influenced the  growth of her fetus and, therefore, its chances of survival at birth (Verme 1963, 1967, 1969 and 1977). In these and other ungulate studies (e.g., Caughley 1970, Geist 1971, Grubb 1974, Sinclair 1977a, Clutton-Brock etal. 1982,1991, Leader-Williams 1988, Owen-Smith 1990), individuals' nutritional levels were negatively correlated with population density. However, a density-dependent effect was not detected in this study.  100  C a l f mortality in dry season was the "key factor" influencing population fluctuations and was the second most important reduction segment. This stage was negatively correlated with food supply but was not density dependent. Dry season calf mortality was much higher than adult mortality which was density dependent. These results suggest that wildebeest calves were more sensitive to environmental changes, particularly rainfall, than were adults. Similar results were seen in buffalo (Sinclair 1977a), and kudu  Tragelaphus strepsiceros  (Owen-Smith  1990). In temperate regions, calf mortality appears to be sensitive to harsh weather conditions  e.g., red deer Cervus elephus  (Clutton-Brock  et al.  1982) and Soay sheep  Ovis aries  (Clutton-  Brock et al. 1991). Despite fluctuations in calf survival rates, changes in the overall population size were dampened by adult survival which was more numerous and relatively less sensitive to environmental changes.  Adult mortality. Fluctuations in adult mortality were dependent on nutritional well-being as influenced by rainfall relative to density. Thus, increasing population density reduced the amount o f food available per individual during the dry season resulting in loss of body weight and increased susceptibility to other forms of mortality like diseases and predation (Sinclair 1977a, Sinclair & Arcese 1995a). Hence, intraspecific competition for food was the probable cause o f mortality. This condition was exacerbated in the prolonged and intense dry season in 1993. During 1993, all age classes were seriously affected. Large die-offs resulting from starvation and dehydration are not unusual in ungulates  (e.g., Klein  & Olson 1960, Caughley 1970,  Leader-Williams 1980, Owen-Smith 1990 and Clutton-Brock etal. 1991).  Wet season mortality. Wet season adult mortality was substantial and mainly due to causes other than predation. Proximate causes of mortality were not identified but starvation is unlikely here because food is abundant during the wet season. Marrow condition during the wet season suggests that many animals died in poor health, perhaps from pathogens that debilitate the animal over a long period of time before death occurs. The reverse is probably true for nonpredation carcasses that had high marrow fat content. Their deaths could result from virulent  101  pathogens that kill the animal within a short time period before exhausting their fat reserves. This is a subject for future research.  Predation. The above evidence suggests that predation plays only a minor role in limiting the wildebeest population size. First, predation on adult females constituted less that 3% of the total mortality and therefore, caused a minor effect on fecundity. More importantly, the Serengeti wildebeest reduces the impact of predators through long distance migration and birth synchronization (Maddock 1979, Fryxell & Sinclair 1988, Fryxell et al. 1988, Hilborn & Sinclair 1979). Migration creates a temporary refuge because predators have difficulty in adjusting their reproductive needs for denning sites to the mobility of their prey. Because of the temporary absence of migrating prey, the numerical response of predators is limited by the less numerous resident prey species. Birth synchronization and aggregation in open habitats by ungulates that give birth to extremely precocial young also act as a buffer against calf predation (Bergerud 1974, Estes 1976, Maddock 1979, Fryxell & Sinclair 1988). In the Serengeti wildebeest, predators are swamped with calves (up to several hundred thousand) which are born within a few weeks. Under such circumstances predators are able to take only a small proportion of the total calves born in a season.  Sex vulnerability to causes of mortality. Wildebeest territorial behavior (Kingdon 1982, Estes 1991) could contribute to high male mortality. Imagine this scenario: (f) male mortality is higher than that o f females (if) more males die from causes other than predation (Hi) most of these are in poor condition and, (iv) most are in their prime reproductive age (5-10 years old). These facts suggest a "postrutting reproductive cost" hypothesis. Males enter the dry season in poor body condition after the rutting season (May-July) (Sinclair 1977a). Regaining lost weight is difficult because food is in short supply during the dry season. Further weight loss makes them more vulnerable to subsequent starvation or other causes of mortality. Alternatively the "satellite male hypothesis " proposes that (f) males which fail to establish and defend territories are pushed into the peripheries. (if) Marginal habitats may fall short of quality food, (iii) Males in this category become more vulnerable to predation and  102  starvation during the next dry season (predator sensitive foraging (PSF) hypothesis) (Sinclair & Arcese 1995a). Finally there is the  '''solitary bull hypothesis.'''' From Figure 3.3 and 3.5 there  are indications that males in their prime reproductive ages (middle and old, 5-12 years) with high marrow fat scores, suffered higher predation while young adults (2-4) and very old (> 12) were least represented. Solitary bulls defending their territories away from the rest of the group may be easy targets for predators. The above discussion does not consider the possibility that the population age structure could determines the probability of predation. Nevertheless the degree o f skewness is not likely to affect reproduction and recruitment. A detailed study to explore the consequences of wildebeest male territorial behaviour is recommended.  Implications for conservation. The Serengeti wildebeest population has apparently reached its environmental carrying capacity under the present rainfall regime. Although illegal harvesting of this population has been a conservation concern since the 1970s (Dublin et al, 1990, Campbell & Hofer 1995, Mbano 1995), these results suggest that poaching off-take has played little or no role in limiting the population size. I investigate the magnitude of human off-take in Chapter 4. Thereafter, in Chapter 6,1 explore whether there is room for additional harvesting.  S U M M A R Y  1. I examined the patterns of wildebeest reproduction between 1960 and 1994. For the first time, there appear to be a delay in age of maturity and a decline of adult pregnancy rate. The most probable causes are reduced food quality and quantity associated with increased wildebeest population density. 2. I used the log likelihood and A>factor analysis to explore the wildebeest mortality patterns (1960-94). The results suggest that the amount of dry season rainfall sets the upper limit o f the wildebeest population size through intraspecific competition by determining available food resources during the dry season. This is consistent with previous studies. C a l f and adult mortality appear to be influenced by food limitation. Thus the data support the food limitation hypothesis and reject the predation hypothesis. 103  3. The process of population regulation suggested in Chapter 2 is most likely a result of the inverse relationship between per capita food availability and adult mortality shown above. While calf survival in the dry season appeared to be more sensitive to changes in food availability, patterns of pregnancy rates were better explained by changes in population density. 4. Neonatal mortality accounted for the highest proportional loss in the annual mortality rate. It was neither density dependent nor related to food availability. 5. C a l f mortality in the dry season was the "key factor" and, therefore, the most important stage in determining the year-to-year changes in the total mortality rate. This was related to dry season food availability but not density.  104  Chapter IV Is Wildebeest Poaching Mortality an Important Limiting Factor? A Preliminary Report  INTRODUCTION The harvesting of wild animals in the Serengeti region is presumed to be extensive and thought to be the major factor limiting the wildebeest population (Georgiadis 1988, Magombe & Campbell 1989, Dublin et al. 1990, Kajuni 1990, Hofer et al. 1993, Arcese et al. 1995, Campbell & Hofer 1995). This harvesting is conducted illegally by people living around the Park, and snaring is thought to be the predominant cause of poaching mortality. A detailed account of the extent of poaching mortality and areas affected is provided by Arcese et al. (1995) and Campbell & Hofer (1995). Arcese et al. (1995) demonstrated that wildebeest suffered the highest mortality because of their abundance rather than because of hunters' preference. In Chapter 3,1 described the causes and patterns of wildebeest natural mortality. I now ask: is poaching mortality the predominant limiting factor in the wildebeest population dynamics? T o do so, I discuss the dominant form of poaching in the Serengeti; hunting for meat using snares (Turner 1988, Campbell & Hofer 1995, Mbano et al. 1995). I specifically exclude the use of modern weapons and motorized hunting, which are now uncommon. I also consider other traditional hunting methods, e.g., bow and poisoned-tip arrows, spears and domestic dogs, where these were not combined with snaring. Snares could be thought of as ambush predators and in this study I explore their impact on the most dominant prey, the wildebeest. Unlike previous studies which have emphasized the dynamics of the neighboring human population, I focus on hunting tools to investigate the poaching off-take. In the next chapter, I test the consistency of poaching estimates by using a population dynamics model developed from wildebeest demographic data in Chapters 2 and 3.  105  MATERIALS AND METHODS  4.2.1. S O U R C E S O F D A T A  (i)  Daily patrol record cards. Since 1989, park rangers have been asked to fill in cards for each patrol made. The  relevant information recorded included: area surveyed, number of rangers, distance traveled, numbers of sighted poachers, arrested poachers, captured snares, species and count of animals killed by poachers, and, types and number of weapons confiscated. Some of these data have been analyzed and discussed elsewhere (Arcese et al. 1995, Campbell & Hofer 1995). (ii) Poachers arrest forms. In addition to patrol cards, park rangers have been asked to interview arrested hunters and complete forms that focus on individual poachers. The information provided includes name, age, home village, type and number of hunting tools, days spent hunting, size of hunting group, species and numbers of animals killed. These forms have been in use since November 1992. (iii) Monthly reports prepared by the Warden In-charge. The Warden responsible for antipoaching units compiles monthly reports that list the activities in each ranger post during the month. These include the number of poachers and weapons captured, and species and numbers of animals found in snares or poachers camps. Although these reports lack some details provided in the other data sources, they are more comprehensive in terms of anti-poaching accomplishments over the entire Park. (iv) Mark recapture method on snares. I used the Petersen mark-recapture technique (Krebs 1989) to estimate the abundance of snares in the Serengeti. Analogous to ambush predators, snares are mobile through human actions, and the basic procedure was to mark all snares found in the field using a shrouded permanent color spray over a short period of time. Marked snares M, were collapsed and left in the field for poachers to retrieve and translocate. The green mark was about 3 cm in the middle  106  of the snare. Un-retrieved snares were collected after two days and were deducted from the marked count. I checked whether color marks faded by using control snares. I allowed a period of one month for mixing and thereafter, all captured snares C , were scored for marked (R), or unmarked count so that the abundance of snares, N , s  could be estimated. I used the  unbiased estimator for analysis of abundance and 95% confidence limits.  N  s  =  (C + 1)(M-1) '-1 (R + l)  y  JK  4 1  Although the abundance of snares is likely to change because some are continuously being removed by rangers and others are destroyed through wear and tear, the available information suggests that these are being replaced within a short period of time. I therefore assumed a closed population. The exercise of marking snares was confined to the western corridor because of safety factors. Most poaching in this area is by snaring (Dublin et al.  1990,  Campbell & Hofer 1995, Arcese et al. 1995, Mbano et al. 1995).  (v) General information The descriptive information relating to poaching activities was gathered through discussions with wardens, rangers, arrested hunters and local people in neighboring villages. Additional information was obtained from office records maintained at the park headquarters.  RESULTS  4.3.1. D E S C R I P T I O N O F P O A C H I N G  Poaching in the Serengeti region is conducted by small organized groups of men (Table 4 . 1 a and b) often from the same village. However, there are occasional single poachers. Poachers set snares at strategic points where animals are likely to travel, such as along well used game trails, around watering points, or in thickets where animals seek food or shade. Occasionally, they construct brush fences with gaps where they place snares, or they may drive animals into thickets where they have placed snares (see also Sinclair 1977a, Turner 1988). Open areas with little cover are normally avoided. 107  Table 4.1.  The frequency distribution of poaching parameters summarized from the "arrest  forms" between November 1992 and June 1994.  Class interval (a)  Frequency  The data are based on poachers groups.  %  Mean  S.E.  3.81  0.42  2.28  0.23  13.85  2.40  1.77  0.19  Reported hunters per group 1-3  42  65.6  4-6  14  21.9  7-9  5  7.8  > 10  3  4.7  Total  64  100  (b) Arrested hunters per group 1-3  53  81.5  4-6  9  13.8  7-9  2  3.1  > 10  1  1.5  Total  65  100  (c) Number of snares per hunting group 1 - 10  19  29.2  11 - 2 0  8  12.3  21 - 3 0  3  4.6  >40  4  6.2  Total  34  52.3  31  47.7  65  100  1-3  57  87.7  4-6  5  7.7  7-9  3  4.6  65  100  Groups without snares Grand total (d) Days spent hunting  > 10 Total  108  Snares are manufactured locally by using a piece of twisted wire with a tensile strength that is sufficient to restrain a target animal. The weight and length of snares varies considerably. A random sample provided a mean weight o f 306.4 gm (+ 13.14 S.E., n = 100) and a mean length of 4.1 m ( ± 0 . 1 0 m S ' . £  )  w = 72). Snares are either made from worn out car  tires ( « 6 1 % ) , abandoned telephone lines ( « 2 5 % ) , industrial steel wire ( « 1 0 % ) , or a mixture o f other rare materials ( « 4 % ) . Sisal ropes are occasionally used for small ungulates (< 20 kg). The basic structure of a snare consists of a sliding loop at each end. One end is anchored around a solid object, normally a tree or bush trunk, and the other end forms a loose loop that entangles the animal around the neck or foot. The latter loop is strategically placed and held in place by thin pieces of grass string. A snare kills its prey by strangulation but poachers may use other tools, e.g., bow and poisoned-tip arrow, spear or machete to finish a restrained animal. Generally snares are non-selective and may kill a wide range of preferred prey (ungulates) and non-target species, such as predators (Table 4.2; see also Hofer et al. 1993). The distance traveled by poachers while searching for animals ranges from a few kilometers up to 50 km, occasionally more. A l l travelling is done on foot and I recognized three important forms, although their relative importance could not be established. (i) Short excursion: setting snares within a short walking distance (< 5 km) inside the periphery of protected areas. Snares are well camouflaged and are usually inspected on a daily basis but sometimes at three to four days interval. These are set by opportunistic poachers and, although their success rate is high during the few days when migratory animals are present, their overall offtake is presumed to be very low. (ii) Day excursions: Poachers in this category may travel long distances inside protected areas but will return home within a period of 36 hours. This form of poaching is normally conducted when it is possible to travel after dusk during moonlit nights. Poachers target areas with abundant wildlife, set snares before dawn and periodically inspect snares. Whether successful or not, they leave protected areas after dusk to avoid the risk o f arrest. (iii) Camping excursions involve setting up a camp in a secluded area for several days. While avoiding the risk of arrest, poachers may inspect snares during the day but will normally remain hidden, and check and move snares at night. 109  Table 4.2.  Carcasses recovered from poachers camps and snares as reported in the "arrest  forms" between November 1992 and June 1994. Figures in brackets represent percentages based on column total.  (2) Snare groups  (1)  Species recovered  (3) Non snare groups  Frequency (%) Frequency (%)  (4) Total Frequency (%)  Species recovered 1  Wildebeest  64 (73.6)  20 (35.7)  84 (58.7)  2  Zebra  (Connochaetes taurinus) (Equus burchelli)  11 (12.6)  6(10.7)  17(11.9)  3  Topi  (Damaliscus korrigum)  3 (3.4)  8 (14.3)  11 (7.7)  4  Kongoni  5  Impala  6  Thomson's gazelle  7  Buffalo  8  Waterbuck  9  Warthog  10  Reedbuck  11  Dikdik  12  Ratel  13  Lion  14  Hyaena  15  Black-backed jackal  (Alcelaphus buselaphus)  (Aepyceros melampus) (Gazella thomsoni)  (Syncerus coffer) (Kobus ellipsiprymnus)  (Phacochoerus aethiopicus) {Redunca redunca)  (Rhynchotragus kirkii)  (Melivora capensis) {Panthera leo) (Crocuta crocuta)  Total frequency Percent total  (Canis mesomelas)  2 (2.3) 1(1.1)  1(1.1) 1(1.1)  -  -  2(1.4)  7(12.5)  8 (5.6)  2(3.6)  2(1.4)  1 (1.8)  2(1.4)  -  1 (0.7)  3 (5.4)  3 (2.1)  2(3.6)  3(2.1)  -  4(7.1)  4 (2.8)  -  3 (5.4)  3(2.1)  1(1.1)  1(1.1)  -  1 (0.7)  1(1.1)  -  1 (0.7)  1(1.1)  -  1 (0.7)  87(100) 60.8  56(100) 39.2  143 (100) 100  110  If the snares have been successful, and the weight of the meat is more than the poachers can carry, one of them will return to their village, where porters will be enlisted to help carry the meat out. The porters receive a portion of meat for their service. Meat obtained from short and day excursions is carried back wet but the majority of that captured in camping excursions is processed and sun dried. Porters may remain in the hunting grounds helping with meat processing and learning from experienced hunters. The available data did not distinguish between hunters and porters. The age distribution of arrested hunters suggests a growing trend in the number o f poachers (Figure 4.1). The high frequency of arrested young aged individuals suggests that there is a substantial recruitment rate into the illegal activity. A small sample of interviewed poachers and local people living around the park suggested that most poachers are recruited in their teens and early twenties, but rarely after 30 years old. However, because the probability o f arrest was not considered, these results should be considered tentative since inexperienced poachers are more likely to be arrested, and hence, over-represented in this sample. The dynamics of poachers in response to law enforcement are not well understood. The general perception is that poachers modify their behaviour to avoid arrest while maximizing their catch. For example, with increased anti-poaching activities in the 1990s (Arcese et al. 1995), (f) the use of brush fences and pit hole traps became rare compared to the 1980s (if) hunting groups became smaller to avoid detection, and (iii) it is presumed that more poaching activities now occur at night. However, there is insufficient evidence to show that there is a significant change in either total off-take or the number of hunters.  4.3.2. DESCRIPTION OF ANTI-POACHING ACTIVITIES Anti-poaching activities are conducted primarily by National Parks and Wildlife Department Rangers. Most anti-poaching patrols are daylight trips, which originate from a ranger post and consist of several rangers  (x = 7.5, mode = 10, n  = 319 patrols) being driven to  likely areas for poachers, i.e., animal concentrations near bush. Areas thought suspicious as a result of clues and signs, are searched further on foot, or by vehicle where accessible.  Ill  r  ^ 5 0 - 5 9  'in S  40-49  %  30-39  o O)  20-29  w  <  <20  —i— 0  10  20  30  40  Frequency (%)  F i g u r e 4.1.  The age structure of 147 illegal hunters arrested between November 1992 and  June 1994 in the Serengeti National Park.  112  Rangers search for poachers, snares or poachers' camps. Snares and animals caught in snares are recovered. Sighted poachers are pursued and some are arrested. With sufficient signs o f poaching activities, night patrols may be conducted to facilitate arrest.  4.3.3. A N T I - P O A C H I N G  A C H I E V E M E N T S  The warden reports provide anti-poaching data dating as far back as 1957 (Figure 4.2). Prior to 1975 only two types of data were collected; numbers of arrested hunters and snares caught. In the subsequent years numbers of animals killed were recorded as well. Although the number of both illegal hunters, snares and wildebeest killed show an increasing trend from 1975 through the early 1990s, some essential parameters e.g., search effort, were not measured so that anti-poaching success and animal mortality rates could not be calculated. More recently (1991-92), Arcese et al. (1995) used patrol questionnaires to obtain standardized data on antipoaching activities. These provide some details of the history of the anti-poaching effort in the Serengeti and explored some possible effects of illegal hunting on ungulate populations. Although data have accumulated for almost three years following Arcese et al's. (1995) analysis, no significant changes have been detected so far.  4.3.4. A N A L Y S I S O F P O A C H E R S O F F - T A K E U S I N G " A R R E S T  F O R M S "  A total of 147 forms were completed from arrested meat hunters between November 1992 and June 1994. This covers 62.6% of arrested poachers according to the Warden Incharge reports. Reasons for the loss of the reports ( « 3 7 % ) are not known but could result from logistical and administrative problems. I assume the available information is representative o f the poaching activities especially for 1993 and 1994 which account for almost 85% of the completed arrest forms. These data, however, need to be treated cautiously. Arrested poachers sensibly hide information that could be used as proof of their guilt and probably determine the severity of their subsequent penalty. For example, poachers may not report undetected tools (snares, arrows, spears, etc.) or carcasses. They will also under-count days spent in the park hunting. Furthermore, poachers avoid implicating those who escaped arrest.  113  _ o o o  •a  12  84  Q) a ra o <0 0)  >_ ra c (/)  4H  nnpnnnpnlpWjMnnnnp  0 55  60  65  70  75  80  85  90  95  Year  Figure 4.2. Numbers of arrested hunters and snares captured  (bottom)  (top, squares),  wildebeest recorded  (top, circles),  obtained from Wardens' monthly reports and "patrol  cards." Search effort was not measured so that antipoaching success and animal mortality rates could not be estimated.  In most instances rangers search for clues and exhibits to complete the forms. Thus, the information provided here should be considered as conservative. The arrested poachers were organized in 64 hunting groups. Group size ranged from one to 18 individuals (x = 3.8 ± 0.42 S.E., n = 64 groups) based on the information provided by poachers. However, because some escaped, the average number of arrested poachers per group was 2.28 (+ 0.23 S.E., n = 64). Table 4.1 shows the frequency distribution of group sizes. Hunting tools are shared within a group, and some important parameters are better expressed on the basis of a group rather than individuals. Table 4.3 shows the distribution o f confiscated tools from each group. About 60% of all groups used snares as part of their hunting tools. Other tools, like machetes, knives, quivers and axes, were ignored here because they do not have the power of catching and killing in the sense of hunting large wild animals. The minor tools were fairly common in all groups including the 8 groups shown with no tools in Table 4.3. A total o f 143 animals belonging to 14 mammal species were recovered from illegal hunters (Table 4.2). Wildebeest featured most frequently in the kill (59%) followed by zebra (12%o). Snaring was the predominant cause of poaching mortality (60.8%) and accounted for 73.6%) of the total wildebeest killed. The importance of snaring mortality is consistent with previous studies (Arcese et al. 1995).  Estimating poachers off-take. In its simplest form, poachers off-take (catch) by snaring can be estimated using the following equation:  Catch = {snare success rate) x (abundance of snares)  (4.2)  (i) Snare success rate. I used the proportion of animals killed in 34 groups that used snares to estimate the capture success rate. These groups were caught with a total of 471 snares (x = 13.85 snares per group ± 2.40 S.E., n = 34; Table 4.1c). O n average each group spent 2.15 days hunting ( ± 0.33 S.E., n = 34) before it was arrested.  115  T a b l e 4.3. The frequency distribution of hunting tools summarized from poachers "arrest forms" between November 1992 and June 1994. The frequency is based on poachers groups. Note that 8 groups had neither of above hunting tools and these are excluded in last column.  H u n t i n g tools Snare + B o w & arrow  Frequency (%) 19 (29.2)  Snare  7 (10.8)  Snare + B o w & arrow + Spear  3 (4.6)  Snare + D o g  2(3.1)  Snare + Spear + D o g  2(3.1)  Snare + Spear Total groups with snares  52.3%  59.6%  34 8(12.3)  Dog  7 (10.8)  Spear + D o g  4 (6.2)  Spear  3 (4.6)  B o w & arrow + Spear  1 (1.5)  N o tools  8 (12.3)  Grand Total  Snares  .1 (1.5)  B o w & arrow  Total groups without snares  Combined %  Others 35.4%  40.4%  87.7%  100%  31 65 (100)  In estimating capture success rate I assumed that all animals recovered from groups that possessed snares were killed in snares. Thus, I divided the number of animals recovered (87) by the number of hunting days (73) and by the number of snares (471) which gives 0.0025 animals per day per snare. Since wildebeest constituted 0.736 of the snared animals (Table 4.2), its capture success rate was estimated to be 0.0019 wildebeest per snare per day (or simply 64 wildebeest / 73 days / 471 snares). Thus, the annual success rate was 0.924 animals per snare, or 0.679 wildebeest per snare.  (ii) Abundance of snares. I marked a total of 312 snares from December 1992 through April 1993. A l l but one of the marked snares were subsequently retrieved by hunters  (i.e., M=  311). I then inspected a  total of 2,728 snares captured by rangers between June and October 1993 A m o n g these only 38 were marked  (i.e.,  recaptured,  R=  (i.e., C -  2,728).  38). A l l captured snares were  destroyed after inspection. Using equation 4.1 (Seber's 1982 unbiased estimator) the abundance of snares was estimated to be 21,831 snares. The 95% lower and upper confidence limits were 16,282 and 31,176 respectively (Table 4.4)  (Poisson confidence  interval, Krebs  1989). Although snare marking was confined to the west, inspected snares came from the west, south and central parts of the park. The area north of Grumeti River where poaching occurs as well (Dublin et al. 1990, Campbell & Hofer 1995), was not represented in the estimate of snare abundance. To obtain a good estimate of snares in this zone I used the proportions of apprehended snares. Daily patrol records from 1979 through September 1994 showed, among others, the number of snares captured from different parts of the park. These were added annually into two main zones: (i) northern Serengeti, and (ii) the rest of the Park. The number of snares was weighted by the number of patrols in each zone. Then I employed equations 2.14-2.16 (Chapter 2) to estimate the ratio of snares apprehended in the north, x, compared to the rest of the Park, y. The number of years provided the sample size n. This gave a ratio of 25.06% snares ( ± 5.08% S.E., n = 15 years with a total of 42,188 snares). Thus, I assumed a 25% factor of the snares collected in the rest of the Park to estimate the number o f snares in the northern Serengeti (Table 4.4 a).  117  Table 4.4. (a) Estimates of snare abundance obtained by using Petersen's method of mark recapture technique, (b) Corresponding annual estimates of legal and illegal wildebeest offtake in the Serengeti region. Figures in parenthesis show percent of the total population (1.2 million).  (a) Abundance of snares West and central Serengeti North western Serengeti Total snares  95% lower limit  Estimate  95% upper limit  16,282  21,831  31,176  4,071  5,458  7,794  20,353  27,289  38,970  13,828 (1.2)  18,540 (1.5)  26,477 (2.2)  4,321 (0.4)  5,794 (0.5)  8,274  (0.7)  4,964 (0.4)  4,964 (0.4)  4,964  (0.4)  23,113 (1.9)  29,298 (2.4)  39,714  (3.3)  (b) Annual wildebeest off-take by humans Wildebeest killed illegally in snares Wildebeest killed illegally by other tools Wildebeest harvested legally Total wildebeest off-take by humans  118  Wildebeest offtake. I used equation 4.2 to estimate the annual wildebeest off-take and results are shown in Table 4.4 b. A total of 18,540 wildebeest (95% C.L.: 13,828 - 26,477) were killed in snares, about 1.5% of the total population (assuming 1.2 million wildebeest in 1992). The confidence limits are based on the abundance of snares.  4.3.5. O T H E R S O U R C E S O F H U M A N I N D U C E D M O R T A L I T Y .  (i) Illegal harvesting using tools other than snares. Table 4.2 shows the distribution of animal carcasses that were recovered from groups of poachers that possessed snares (60.8%; column 2) and those which did not possess snares (39.2%; column 3). More wildebeest than any other species were killed in non-snare groups as well (37.7%). If we assume that (i) the hunting success by using snares and by using other tools was constant (temporal and spatially), and (ii), that the proportion of snared animals to non-snared is a good measure of animals killed using other tools, then the non-snared wildebeest could be estimated as follows. The proportion of non-snared wildebeest was 35.7% which provides a ratio o f 0.312 for every wildebeest killed in a snare. Thus, the estimate of poached wildebeest using other hunting tools can be obtained as a ratio of wildebeest killed in snares (Table 4.4 b). This estimate was 5,794 wildebeest (95% CL. 4,321 - 8,274 based on the abundance o f snares) and adds up to 24,334 wildebeest killed illegally per year; about 2% of the total population and an average o f 67 wildebeest killed per day. (ii)  Legal harvesting.  I made a survey to quantify the number of wildebeest harvested legally in adjacent areas. Although data on success rates were not available, Table 4.5 provides a typical annual quota allocation. The law requires that only adult males are hunted.  119  Table 4.5. Types of legal harvesting programs in areas surrounding the Serengeti National Park showing a typical wildebeest quota allocated per year. ( S R C S and T A W I C O refers to the Serengeti Regional Conservation Strategy Project and Tanzania Wildlife Corporation respectively)  (z) Tourist sports hunting Number of tourist camps  8  Hunting season (weeks: July-December ) Wildebeest per group per week  26 3  Total  624  (if) S R C S Experimental Culling Program Number of villages  15  Hunting season (all year)  52  Carcasses per week per village  3 Total  2,340  (iii) Residents License Quota per season  1,000  (iv) T A W I C O Hunting quota Quota per season  1,000 Grand total  4,964  Proportion (1.2 million)  0.41%  120  (i) Tourist sport hunting is conducted inside Maswa Game Reserve in eight blocks (camps) between July and December. Typically a group of tourist hunters hunts for 3 weeks with an extra week allowed in between groups. O n average each group harvests 3 wildebeest per week giving a total of 624 wildebeest per hunting season per year. Hunting success is presumed to be very low since wildebeest are absent in the area for more than half of the hunting season. (ii)  Since the early 1990s, the Serengeti Regional Conservation Strategy ( S R C S ) program has been allowed to cull animals with the objective of assessing the role that meat from poaching plays in the local economy (Mbano et al. 1995). Hunting is conducted outside the western boundary of the Park and only 15 villages have been earmarked for this experiment. In theory each village is provided with three wildebeest carcasses per week. Although the migratory wildebeest are absent from the hunting grounds for at least 5 months in a year, I assume the theoretical upper value of 2,340 animals per annum.  (iii)  Resident's license in the four districts surrounding the western part of the park is allocated 1,000 wildebeest and,  (iv)  another 1,000 wildebeest are allocated to the Tanzania Wildlife Corporation ( T A W I C O ) cropping scheme.  Estimates of legal off-take provided in Table 4.5 are on the upper limit of the scale and they add up to a maximum of 4,964 wildebeest per year; approximately 0.4% of the total population before the severe drought in 1993. The total estimates of wildebeest harvested legally and illegally is about 20,000 - 40,000 each year (Table 4Ab).  DISCUSSION Is poaching mortality the predominant limiting factor? The available data do not support the hypothesis that poaching mortality was the predominant limiting factor for the Serengeti wildebeest population, at the least not between  121  1992-94. Instead, this study proposes that annual poaching mortality could be at most 39,700 wildebeest contrary to previous estimates o f 87,000 (Hofer et al. 1993), and 118,922 (Campbell & Hofer 1995). Estimates by Campbell & Hofer (1995) depend on the arbitrary assessment that there is one poacher per family in villages next to the park who make 5 trips per year and hunt for 5 days per trip with a success rate o f 8.95 per person per year. Other unpublished estimates range from 50,000 to 200,000 (A. Kajuni 1990 unpubl. ms., B . Mbano, pers. comm.). N o w I consider the rationale and validity for these estimates. The exploitation of wildlife to provide food for the pot and to supplement income has a long history, probably as old as mankind. In the Serengeti National Park, illegal hunting inside the protected area has been a persistent problem dating at least as far back as 1957 (Figure 4.2). Thus, poaching mortality should not be singled out and considered in isolation o f other population processes. The fundamental principle governing population change is based on a simple balance of births and deaths. Intuitive estimates of human off-take can be obtained by inspecting the difference between known inputs (reproduction and recruitment) and outputs (adult mortality). Details pertaining to the wildebeest population dynamics will be expounded in detail in Chapter 5, here I provide only a brief review. Records show that the wildebeest population increased exponentially from 0.23 million to about 1.4 million within a period o f 15 years (increase phase) and thereafter remained stable for the next 15 years (stable phase) (Figure 1.1 and Table 1.1). During the increase phase (1963 - 1977) the herd grew at an average rate of 10% per year. Since the annual recruitment rate was on average 13% (Table 2.7) and dry season adult mortality fluctuated around 2 - 4%, there was little room for human induced mortality. During the second phase (1978-1992) the population appeared to be stable within the limits of sampling error, implying a zero net increase. Indeed while the recruitment rate dropped slightly to about 12%, the dry season adult mortality rate increased dramatically to around 10% (excluding 1993). Thus, the unaccounted human off-take can only claim the difference, which is about 2%. M y results on annual human off-take (2.4%; 95% C.L. = 1.5%2.9%, or 29,300 with 95% C.L. = 23,000 - 39,700) are consistent with the overall population dynamics. 122  The alternative hypothesis is that, although the population appeared to be stable within the limits of sampling error, the gradual decline from 1.4 million in 1977 to 1.2 million in 1991 (census before drought) could have been real. Estimates of illegal off-take by Hofer et al. (1993) and Campbell & Hofer (1995) are within 1 S.E. of the census, making it difficult to detect using normal statistical methods. However, unless we assume poaching mortality increased dramatically in the 1990s, persistent annual off-takes above 70,000 would not have been sustained. A rapid increase of poaching activities is less likely especially in the late 1980s and early 1990s when the park's anti-poaching force was increasing and becoming more efficient (Arcese et al. 1995). Implications for  conservation  The supply of wildebeest meat estimated in this study is only 37.6% of the demand suggested by Campbell & Hofer (1995). This implies that dependence on wildlife meat may not have been as high as was initially thought. The next task is to find out what other sources of protein were available to the neighboring human population. Clearly, understanding these alternative sources is fundamentally important for the management of a sustainable quota and assessment of the economics of available options. If we assume the abundance of snares was fairly constant since the 1980s, then the park rangers removed less than 10% of the snares annually, except between 1989 - 1992. During this later period rangers were rewarded for each snare apprehended (Arcese et al. 1995). Rewards resulted in over 25% removal and in 1990 reached a peak with « 3 8 % removal (Figure 4.2). This suggests that: (i) snares could have been replaced at a rate which balanced removal, and (ii) although the necessity of reinstating the reward scheme can not be over-emphasized, efforts need to be extended to identify and incapacitate the source of snares. Warden's reports show that between 1957-94 over 93,000 snares were destroyed; x = 2,462.4 annually ( ± 737 95%) CL).  This study estimated the abundance of snares at about 25,000, and hence a crude  turn over rate could be around 12 % per year. Possible sources of error in estimates of human offtake and recommendations. A precise estimate of poaching off-take requires accurate measurements of; (i) the abundance of hunting tools, and (ii) the success rate of each hunting technique. The analysis 123  of poaching mortality in this chapter focused on snares hut lacked some important parameters that could have enabled accurate calibration of other hunting tools. Although snaring is the predominant cause of poaching mortality, other tools should not be ignored in future studies. The following sources of bias may have canceled each other; (z) the probable underreported hunting days, and (zz) the most likely undetected carcasses and snares that were not reported. While more hunting days would have lowered the capture success rate, unnoticed carcasses and tools could have increased the success rate. The estimates of snare abundance should be considered preliminary pending further testing o f (z) the reliability of the mark-recapture technique on snares and (zz) the variation in abundance between years. Future work should cover a wider area and use larger samples o f marked snares. Furthermore, the 1993 prolonged drought may have affected the estimates o f poaching offtake as well. Between October and November 1993 during the peak of the drought, animals wandered outside the protected areas in search of food and water. Many animals, including over 100,000 wildebeest were either killed by humans or starved outside the Park boundaries. Poachers may have used this opportunity to hunt outside the Park to reduce the risk of arrest. However, this is not likely to change my results radically. Although the resident wildebeest population in western Serengeti could be suffering a - proportionately higher poaching mortality than the migratory herd, its relative size is too small ( « 2 % ) to significantly change my results.  SUMMARY  1.  Poaching mortality is estimated from a study of snares, snares success rate, and poachers questionnaires. The best estimates of this mortality puts it in the region of 20,000 to 40,000 wildebeest per year.  2. This figure is consistent with the estimates of models for wildebeest population dynamics. It also suggests that previous estimates of poaching based on assumptions and extrapolations on villagers and their movements are overestimated by a factor of two at best.  124  3.  Although poaching mortality is not insignificant in the population dynamics of the migratory wildebeest it is not the predominant limiting factor. Natural mortality from food restrictions in the dry season appear more important.  4.  Efforts to contain poaching need improvements to effectively (/') discourage recruitment of poachers, and (ii) to initiate a system that will cut-off supply of snares.  5.  The data obtained from "arrest forms" provided useful information for estimating illegal off-take. This is yet another example that demonstrates how field personnel performing routine field work can be used to collect valuable scientific information.  125  Chapter V Estimating the Limits to Exploitation of Serengeti Wildebeest and Implications for its Management  INTRODUCTION Throughout the world, natural habitats are being lost at an accelerating rate as a direct result of human population increase (Sinclair & Wells 1989, Soule 1991, Geer 1992, Tolba et al. 1992, McNeely 1994, Sinclair et al. 1995). In the developing countries of the tropics human population expansion is increasing the exploitation of wild populations of indigenous species, particularly large mammals. Such exploitation applies to both herbivores for their meat and carnivores for their skins, claws, teeth and other parts. Clearly, increasing consumption, i f unregulated, will lead to over exploitation and extinction of such species (Caughley et al. 1990, Leader-Williams et al. 1990). In Africa, Dasmann & Mossman (1960), Dasmann (1964) and Mossman (1975) proposed that conservation of African ungulates would be ensured i f animals could be harvested economically. In particular, i f the meat could be sold at a profit to local people at prices they could afford, this would provide the incentive for those people to conserve their heritage (Talbot & Swift 1966). This idea has been expounded at length elsewhere (Field 1979,  Walker 1979, Eltringham 1984). It is favored particularly in southern Africa (Child &  Child 1987, Child 1990, Bothma 1989) and requires commercial "game cropping" operations using modern equipment, transport and hygiene regulations. However, there are problems in interpreting both the biological properties of indigenous flora and fauna (Walker 1976, 1979; Walker et al. 1987; Macnab 1991) and economic processes (Clark 1973 a, b, 1990; Caughley 1993). In eastern Africa, these schemes have all met with economic failure because overheads were too high and domestic species were more productive (Parker 1984, 1987; Macnab 1991). Exploitation of wildlife in the Serengeti ecosystem, Tanzania, is an exception to the above generalization. Local peoples have been hunting in this area, probably for centuries. 126  Although most of the harvesting is illegal after the Park was established in the 1950s, its existence is indisputable (see Chapter IV, also; Turner 1988, Arcese et al. 1995, Campbell & Hofer 1995). Instead of expensive modern equipment, hunters use traditional methods such as snares, pitfalls, and poison-tip arrows. The meat is dried and sold locally at prices affordable to the local community. Transport costs are minimal because the migrant herbivores, largely wildebeest, leave the Serengeti National Park and literally walk up to the village gates. During the wet season the animals return to the Serengeti plains, out o f reach o f the hunters, resulting in a natural "closed season". Thus, the system was sustainable at least until recently. However, as elsewhere in Africa, the human population has been increasing in the surrounding areas by 3% per year, and in some areas by as much as 15% per year, through immigration and reproduction (Campbell & Hofer 1995). The concern of the Tanzanian authorities is that the offtake, unregulated and illegal, could exceed biological capacity and result in a collapse of the wildebeest population and cause a major ecological change in the Serengeti ecosystem (Sinclair & Arcese 19956). M y study, therefore, investigated the current size of the hunting offtake and to estimate the harvest of wildebeest that could be tolerated under a regulated cropping regime. Previous harvesting schemes in eastern Africa have had only the most rudimentary census data with which to estimate offtake, with the exception of some elephant culling operations (Laws et al. 1975). This study uses thirty years of census, recruitment and mortality data to estimate harvest levels. It represents a case study, which could be employed as the basis for sustainable harvest of other systems employing traditional hunting methods. Hilborn & Sinclair (1979) explored models of the wildebeest and their predators to examine the likely impacts of different rainfall regimes. Neither legal nor illegal harvesting was a concern at that time, but the models used were essentially identical to those which can be used for determining the potential harvest. Hilborn and Sinclair (1979) argued that the data available at the time, which covered the period of exponential growth, combined with basic energetic knowledge of large ungulates, suggested that the wildebeest population would be food limited when the population size reached 1.5 million. This prediction was subsequently verified as the population did level off around 1.4 million animals (Fig 1.1).  127  Pascual and Hilborn (1995) explored harvest strategies under environmental fluctuations using a non age-structured model. They found that sustainable yields were on the order of 60,000 to 70,000 animals per year and that, to maximize yield, there would have to be significant year to year changes in harvest; in years of low rainfall harvest would have to be much lower than in years of high rainfall. In this Chapter, I expand the Pascual and Hilborn model by considering the interaction between legal and illegal harvests. I also add age structure, and consider in more detail the processes of birth, calf survival and adult mortality presented in Chapter II and III. These demographic data were estimated using well-established methods. Thereafter, I test the population model by using preliminary poaching estimates determined independently in Chapter IV. Finally, I consider the implementation and impediments to achieving a successful legalized harvesting programme.  MATERIALS AND METHODS  5.2.1. D A T A S O U R C E S  Analysis of the population dynamics and the potential harvest in the Serengeti wildebeest population used data collected since 1961. These data are given in Table 5.1a with their sources in Table 5.16. The data are (/') censuses of total wildebeest population conducted 15 times since 1961, (ii) estimates of yearling/adult ratio conducted 24 times since 1962, (iii) estimates of dry season adult mortality rate conducted 9 times since 1968, (iv) pregnancy rates collected by autopsy and analysis of hormone levels in fecal samples, (v) the relationship between rainfall and dry season grass production (in Sinclair 1979c Figure 4.4), and (vi) dry season rainfall measured from numerous stations throughout the Serengeti over the entire study period.  128  Table  5.1a. D a t a u s e d i n the m o d e l . J u l y to N o v e m b e r r a i n f a l l i n m m u s e d f o r this a n a l y s i s ,  t a k e n as the average f r o m N o r t h e r n Serengeti gauges 3,6,8,10 a n d 11 ( A p p e n d i x 8).  Year  Dry season rainfall (mm)  1961  38  1962  100  1963  104  1964  167  1965  167  1966  165  1967  79  1968  91  1969  77  1970  134  Wildebeest abundance (xlOOO) 263  Standard Proportion of Adult error monthly 12 months (xlOOO) calves mortality (%)  0.230  357  -  439  -  0.160 0.170 0.093 0.110  . 483  -  0.100 0.130  1.7 1.4  0.110  1971  192  693  28.8  0.139  0.8  1972  235  773  76.7  0.139  0.5  1973  159  1974  211  1975  257  1976  204  1977  300  1444  200  0.146  1978  187  1248  355  0.114  1979  84  1980  99  1337  80  0.094  1981  163 1208  272  0.145  2.7  0.103  2.1  1982  97  1983  228  1984  208  1985  83  1986  44  1987  112  1988  191  1989  202  0.097  0.140  1337  138  0.111  1146  134  0.109  1407  109  0.156  1221  177.  1990  127  1991  254  1992  153  0.173  4.0  1993  19  0.062  7.9  1994  227  917  173  0.073  1.0  n=  33  14  11  24  9  0.135  129  T a b l e 5.1 b. Sources of data used in the model as shown in Table 5.1 a.  Year  Wildebeest abundance  1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972  Sinclair (1973)  1973 1976 1977 1978 1980 1982 1983 1984 1986 1989 1990 1991 1992 1993 1994  Proportion of 12 months calves  Adult mortality  Watson (1967) Sinclair (1973)  Watson (1967) Watson (1967)  Sinclair (1973)  Watson (1967) Watson (1967)  Sinclair (1973)  Sinclair (1979c) Sinclair (1979c)  Sinclair (1979c) Sinclair (1979c)  Sinclair (1979c) Sinclair (1973)  Sinclair (1979c)  Sinclair (1979c)  Sinclair & Norton-Griffiths  Sinclair (1979c)  Sinclair (1979c)  (1982)  Sinclair (1979c) Sinclair (1979c) Sinclair & Norton-Griffiths  Sinclair (1979c)  Sinclair & Norton-Griffiths  Sinclair (unpubl)  Sinclair & Norton-Griffiths  Sinclair (unpubl)  Sinclair et al. (1985)  Sinclair (unpubl)  Sinclair et al. (1985)  Sinclair (unpubl)  Sinclair et al. (1985)  (1982) (1982) (1982)  Borner et al. (1987)  Sinclair (unpubl)  Sinclair (1987)  Sinclair (unpubl)  Campbell & Borner (1995)  Sinclair (unpubl) Sinclair (unpubl)  Campbell & Borner (1995)  Farm & Woodworth  (1994)  This study  This study  This study  This study  This study  This study  130  5.2.2. T H E P O P U L A T I O N DYNAMICS M O D E L  For convenience, all numbers of animals will refer to an arbitrary date of March 1, on which I assume that all calves are born. The following terms are defined as: G=  the amount of green grass growing per month in kg per ha in the dry-season in year y  y  F = the amount of food available per wildebeest in kg/mo in the dry-season in year y y  N =  the number of calves born in yearjy, sex  N =  the number of yearlings in year y, sex /  yj0  n  N  yi2  N = yii  = the  i (1  = females, 2 = males)  number of animals in year y, sex /* age 2  the number of animals in year y, sex /' age 3 and older  Y = the proportion of the total population that is yearlings T = the total wildebeest population summed over all ages and sexes y  V - the total wildebeest population weighted by relative vulnerability to snares v, .= the relative vulnerability of individuals of sex i and age j to snares.  s  •= the survival rate from natural mortality in yeaiy, sex  t  i,  age  j  m = the mortality rate per month of animals 1 year or older y  u ij= the survival rate from harvesting in year y, sex i, age j R = the dry-season (July-October) rainfall in mm averaged over the Serengeti woodlands y  Pj= the pregnancy rate of age j females a, b, c, d - parameters relating survival to food-per-animal C = the harvest in year y of all ages and sexes The amount of green grass growth is proportional to dry-season rainfall. Using Figure 4.4 of Sinclair 1979c, and later modified by Hilborn et al. (1994)  G = l.25R y  y  (5.1)  Where: Gy is the amount of grass produced measured in kilograms per hectare per month (kg/ha/mo); and, Ry the dry season (July - October) rainfall measured in m m and averaged over the northern Serengeti region.  131  A history of dry-season rainfall was given in Sinclair 1979c, but many of the gauges used in creating this sequence were discontinued, so I used a series of gauges that had complete histories (Appendix 8, C), to generate the sequence o f rainfall shown in Table 5.1a. The amount of food-per-animal is simply the total grass grown per month per ha, times the number of hectares utilized in the dry-season (approximately 0.5 10 ), divided by the total 6  number of wildebeest. G0.5xl0  6  y=^—?  (5-2)  F  y The number of births is the pregnancy rate of 3 year and older females times the number of 3 year and older females. It was assumed that 2 year old females have no successful reproduction, and that the pregnancy rates assumed were 0.85 for 3 year olds and older so the number of births is: (5.3)  N , =P N _ yJ 0  3  y  lXi  The survival rate of calves from birth to their first birthday is assumed to depend on grass per animal with survival reaching an asymptote:  aF,  The dry-season survival rate o f individuals 1 year or older is assumed to be proportional to grass per animal, which is converted to a monthly mortality rate. I implicitly assume that all adult mortality takes place during the four month dry-season. The same mortality is assumed for all ages older than 1 and all sexes:  " ^  d  +  y  (5.5)  F  = l-(^,)  a 2 5  Two of the constants used in the previous calculations, the 1.25 in the rain-to-grass relationship and the 500,000 ha of available dry-season habitat are of no importance, as the parameters b and d are also in units of food-per-animal. The only circumstance in which the  132  actual values of food-per-animal are important is i f one attempts to relate survival to a functional analysis of food availability. I allow for age/sex specific vulnerability to harvesting (v). Given a particular total harvest and age/sex specific vulnerability to harvest, the age/sex specific exploitation rates can be calculated by first computing the total population size weighted by age/sex specific vulnerability (V) and then computing the age/sex specific exploitation rates (u).  v  = y  y  N  y  i—ti—i^ (=1,2 >=1,3  v.  y,i,J I,J  (5-6)  v. C •j y y,U = — y  u  The number of yearlings is the number of calves born the previous year times the calf survival rate ^y,i,\  =  ^y-\,i,0 y-\fi(^~ y-\,i,o) S  ^  U  ^  The number of individuals age 2 is simply the number of yearlings the previous year times the adult survival rate. N ,  yJ 2  = N_ s_ y  w  y  (1 - u _ )  lAi  y  (5.8)  m  The number of age 3 and older is the sum of the number of age 3 and older and the number o f 2-year-olds alive the previous year times the adult survival rates. =(^-u,3  +N _ )s _ (l- , ) y  lA2  y  h2  Vl> 2  (5.9)  5.2.3. ESTIMATING HARVEST There are few reliable data on the total harvest o f wildebeest. The only published figures are those of Hofer et al. (1993) and Campbell & Hofer (1995) o f 87,000 and 118,922 per year respectively, estimated in the late 1980's. For my model I had to estimate the harvest each year. Although snaring of wildebeest and other animals has been going on for many years in the Serengeti, three recent changes may have affected the number of wildebeest taken by  133  snares. First, the wildebeest population has increased fivefold since the 1960's, and the number taken by snares would have increased because of higher abundance. Secondly, the human population adjacent to the Park has been growing at about 3% per year (Campbell & Hofer 1995), and this additional population pressure has certainly led to more snaring. Thirdly, while National Parks and the Tanzanian Wildlife Department have consistently had anti-poaching enforcement programs, a budget crisis in the Tanzania government from 1977 to about 1984, meant that anti-poaching posts were often totally without vehicles, fuel, and even staff. Antipoaching activities all but ceased during this period (Sinclair 1995, Arcese et al. 1995) and I presume there was a concomitant increase in numbers of wildebeest killed by snares. I have examined three possible ways to model the harvest of wildebeest. The first method assumes that the harvest has been proportional to the human population size and the size of the wildebeest herd. If I assume arbitrarily that the human population size in 1960 was 1.0, and grew at 3% per year (Campbell & Hofer 1995), then the human population size could be described as  H =l.03H y+l  (5.10)  y  The harvest of wildebeest is then  C =V H q y  y  (5.11)  y  where cy is a parameter representing the proportion of the vulnerable wildebeest population taken per unit of human population, and I estimate q. This approach accounts for the first two "facts" about poaching, namely that it has increased as human population has increased, and as the wildebeest herd has increased. The second approach assumes that poaching was insignificant until 1977, and has been constant since then. This is modeled by assuming that C = 0 prior to 1977 and that C is a y  y  constant to be estimated after 1977. The third approach is to modify the first approach by a year-specific factor reflecting the level of anti-poaching activity  C =V H qE y  y  y  y  (5.12)  134  where I will assume that E is 1 for all years before 1977 and after 1984, but is either a fixed y  constant, or a parameter to be estimated between 1977 and 1984.  5.3.4. F I T T I N G T H E M O D E L T O T H E D A T A  I used three sources of data in fitting the model; the aerial census of wildebeest numbers, the proportion of the population on the plains that is made up of yearlings, and estimates o f adult dry-season mortality. The data I used are shown in Table 5.1a. There are four free parameters relating calf and adult survival to food available per animal (a, b, c and d). Then, depending upon which harvest model is used, there are one or two additional parameters. M y basic approach is to find the values of these parameters which provide the best fit to the three available data sets.  Initial  conditions I assumed the population was exactly equal to the census in 1961, e.g., 263,000  animals, and that 10% were yearlings, 10% were 2 year olds and 80% were 3 years or older. I assumed that the sex ratio was 1:1.  Fitting method I fitted the model by simulating a trajectory of numbers and survivals from the starting conditions, known rainfall, and parameters a, b, c and d, and the harvest parameter(s). For any predicted values, a total goodness-of-fit was calculated by assuming that each observed type o f data was log normally distributed. A s is normal with maximum likelihood I used negative log likelihoods, the three components of which were calculated as follows (\n(T )-\n(T )f ohs  pre  y (ln(7^)-ln(^ y  4,  p r e  ))  2cri  2  (5.13)  -I (lnKJ-ln^))  2  y  2<£  135  Where the three L's are the likelihoods of the census of total abundance, the likelihood of the estimate of yearling percentage, and the likelihood of the estimate of adult dry-season mortality. TheCT'Sare estimated as follows. There are published estimates of the standard error o f censuses since the 1970s. These estimates are derived from normal distribution theory and the coefficient of variation (cv) of almost all estimates is about 0.2. I prefer the log normal model because most modern abundance estimates produce lognormal rather than normal estimates. I conducted runs of the model using the year by year cv's and a normal distribution and there was no appreciable difference in the results. N o standard errors have been published for the data on proportion of yearlings, although they are based upon very large samples so that estimates of cv's would be very small. I used 0.2 to allow for more uncertainty than the sample sizes would suggest. Sinclair et al. (1985) have published some variance estimates of the standard deviations of the mortality data for 1982 and 1983. The standard errors for these data are also quite low, with cv's less than 0.2. However, these data were given less weight (a cv o f 0.6) because the mortality rates were estimated in only a few places and a few years. These cv's were checked against the goodness-of-fit to the model, and the models fitted the data reasonably well with cv's of less than 0.2 for all types of data. It is more realistic, however, to keep the cv's higher for this analysis. Total negative log likelihood is therefore [ln(Z ) + ln(Z ) + ln(I )] r  y  m  (5.14)  RESULTS  5.3.1. F I T T I N G T H E M O D E L  A baseline fit in which no harvest is assumed depicts the data during the growth of the population in the sixties and seventies, the stability in the 80s, and the large decline in 1993 (Figure 5.1). Although the individual census estimates from 1977 to 1991 are not followed with any reliability, the major changes in population abundance are well represented. The data, and the fits to the data for components of the model are shown in Figure 5.2 for percent  136  yearlings and adult survival, and Figure 5.3 for the calf and adult survival as a function o f food availability. Harvest method I was then fitted by assuming that the total harvest was proportional to the human population size and the wildebeest herd size. The best fit to the data was obtained when vulnerable population q was very close to zero, indicating that the best estimate o f harvest was about 15,000 per year. Part of the reason for this is that from 1963 to 1977 the herd grew at 10% per year. Since yearlings during this period averaged 13% of the population and there was additional 2-4% adult mortality, any significant snaring mortality in the 1960's and 1970's makes it very difficult for the model to fit the observed rate of increase. The total negative log likelihood for this model was 21.6. Harvest method II produced almost identical estimates; the negative log likelihood was 21.5. The estimated harvest from 1977 onwards was 15,000 animals per year. Harvest method III, assuming an antipoaching factor set at 5 produced a fit slightly better with the total negative log likelihood at 21.2. The value of 5 was chosen arbitrarily to try to represent the major increase in poaching after 1977. The parameter q was chosen by the fitting procedure to maximize the likelihood. This fit estimated that the harvest was 30,000 - 40,000 from 1978 to 1984, but declined to a few thousand after 1984. The goodness-of-fit to the model was measured by the negative log likelihood, and none of these fits were significantly different from the others. I used the likelihood ratio test, and the Akaike Information criterion to test for best model. Both suggested that the no harvest alternative was the preferred model. This is because it has one less parameter, and the best fitting model, Harvest Model III, does not fit the data significantly better. However, the no harvest model could be ignored because I know there was a substantial harvest. Therefore, o f the three other models examined, harvest model III was the best fitting. However, the current illegal harvest is considerably greater than that predicted, and that there is little evidence to suggest that poaching was reduced after 1984. A l l of these models are equally consistent with the data presented here, but I preferred harvest model II based on my analysis of other data on poaching and antipoaching. A l l of the above models made similar predictions about sustainable yield, and so they did not affect my conclusions about the potential for a legalized harvest. 137  Figure 5.1. The data (squares) and best fit (line) population model with no harvesting.  0.3 -,  w cn |  ro  0.2  0)  >» 4-1  §  o  o.i  L-  0)  Q.  0.0  I  I  1  1  1  1  1  1960 1965 1970 1975 1980 1985 1990 1995  1o J  15  10  •a re >»  Z +J c o  5  0 1960 1965 1970 1975 1980 1985 1990 1995  Figure 5.2. yearlings  The data  (top)  (squares)  and best fit curve  (line) of the percentage  of population that is  and the adult mortality rate per month during the dry season  (bottom)  from  the model with no harvesting.  139  Food per animal (kg/mo)  Food per animal (kg/mo)  Figure 5 . 3 . The calf and adult survival rates plotted against food. The  squares are the  observed survivals plotted against the model fit of food per animal, and the  lines  are the  functional relationships fit from the model.  140  5.3.2. CONFIDENCE BOUNDS ON CURRENT HARVEST I used the likelihood ratio test to calculate confidence bounds on the harvest assuming harvest model II. This was done using the method of Likelihood Profile, in which the post-1977 harvest was set at different levels, and assessed how good a fit to the data could be obtained by searching over the other parameters, a, b, c and d. The 95% confidence interval for the parameter o f interest, harvest, occurred when the negative log likelihood was less than 1.96 units greater than its minimum estimate. Since the minimum estimate is 21.54, the 95% confidence interval for harvest is any value of harvest with a negative log likelihood under 23.52. Figure 5.4 (top) shows the results for this analysis. The negative log likelihood is quite flat from the region 0 to 40,000 animals per year, and the 95% confidence interval is roughly from 0 to 67,000.  5.3.3. L E V E L OF SUSTAINABLE HARVEST The sustainable harvest depends on the values of the parameters a, b, c and d, as well as the rainfall. The best estimate of the sustainable yield with a dry-season rainfall o f 150 m m is 66,000. Figure 5.4  (bottom)  shows the likelihood profile of the long term average yield. The  thin horizontal line is the 0.05 level so the 95% confidence interval is approximately 56,000 to 74,000. If the rainfall averages 200 mm, the sustainable yield would be 80,000. Pascual & Hilborn (1995) explored a wide range of harvest strategies when dealing with fluctuating rainfall, using a similar model that did not include much of the recent data.  141  28 -,  0  20  40  60  80  100  Harvest (x1000) 30 -.  50  60  70  80  Long term average yield (x1000)  Figure 5.4. The likelihood profile of total annual harvest in years 1977-94 (top) is flat in the region of up to 40,000 animals and the 95% upper confidence limit is ^63,000 wildebeest per year. The sustainable wildebeest harvest  (bottom) with 150 m m o f dry season rainfall is  about 65,000 animals per year (*57,000 - 73,000, 95% C.L). The negative log likelihood is shown as a solid line and the  dotted line represents the 0.05 confidence level.  142  DISCUSSION Wildebeest population  dynamics  The wildebeest population in the Serengeti ecosystem increased from about 0.25 million in the early 1960's to about 1.4 million in the late 1970's and it has remained at around 1.3 million until the drought of 1993. The evidence indicates that since the late 1970s the population is limited primarily by competition for dry-season food (Chapter III this thesis, Sinclair et al. 1985, Dublin et al. 1990, Sinclair & Arcese 1995a). M y estimates of the potential yield and the consequences of sustained harvesting depend on present environmental conditions continuing in the future. The most likely disruption is a reappearance of the exotic viral disease, rinderpest. In such an event, and any other shift in population dynamics, my present calculations would be invalid. M y estimates also depend on the assumption that the level of illegal harvest has been near constant for the last 15 years. If harvesting has expanded in the last 5 years, then the current level of illegal harvest could be greater than the sustainable level. A second likely event could be a major long-term drought. N o severe drought has occurred in the historical rainfall record (back to 1938); the 1993 dry-season had the lowest dry-season rainfall yet recorded. M y model predicted that the population level should have dropped to 850,000 animals and the census in 1994 counted 917,000 animals ( ± 18% 1 S.E.) (Farm & Woodworth 1994). Thus, verifying my predictions. Current estimates of illegal harvest M y above estimates of illegal harvest (0 - 40,000 wildebeest) are much lower than those of Hofer et al. (1993) and Campbell & Hofer (1995), and lower than most people working in the Serengeti believe. However, it is fairly consistent with the independent estimate of 29,298 wildebeest harvested legally and illegally per year (23,113 - 39,714, 95% C.L.; Table 4.4/3). The 95% upper limit of the selected model II was 67,000 wildebeest harvested per year (Figure 5.4 top).  143  While the model is complex, the basic calculations come from knowing only population size, calf recruitment and adult mortality. Given these figures the probable removals by harvesting can be estimated, and appear to be low. The likelihood profiles show that removals of up to 40,000 per year fits to the data well. However, removals of over 75,000 per year (as suggested by Hofer et al. (1993) and Campbell & Hofer (1995), are incompatible with the data. The census data and the yearling recruitment data are probably reliable. If there is a problem with data it must lie in the estimates of adult mortality rate. The most likely bias, however, is that adult mortality is actually higher than estimated, and therefore, that recent harvests are lower. Adult mortality could be higher for two reasons. First, I assumed no wetseason mortality, although I know it accounts for about 2 to 5% loss per year (Figure 3.8). Secondly, my transect method used to estimate mortality rates assumed that I found all carcasses in the surveyed area. This is almost certainly an underestimate.  The potentialfor legalized harvest The model indicates that the current estimated level of illegal harvest is roughly half of the potential harvest at average levels of rainfall. Thus, additional harvest is apparently available. However, any attempt to set a legal harvest above 40,000 would require a reduction in the illegal harvest. The calculations show that the population size that provides a maximum sustainable yield when dry-season rainfall averages 150 m m is about 800,000 wildebeest. The potential for a long-term legal harvest depends on the ability of management agencies to reduce the illegal harvest. The legal and illegal harvests are related. A legalized harvest could either aggravate or reduce the illegal harvest. I assume here that the illegal harvest could be reduced, and discuss how a legal harvest might be implemented.  Strategies and tactics for harvesting There are several alternative ways that a sustained harvest of wildebeest may be obtained. The annual harvest could be adjusted from year to year depending upon the size o f the wildebeest herd. Common harvesting strategies include taking a fixed proportion of the population, taking a constant number of individuals, or other more complex combinations. Tactics are the within-year regulations used to achieve the desired harvest. Tactics include quotas given to villages, harvesting seasons, and regulation of harvest areas. One can use 144  different types of tactics for different strategies: for example village quotas could be used to meet a proportional harvest strategy, or a "hunting season" could be used to keep a constant annual total kill.  Strategies I consider three types of strategy. These are (i) constant total catch, (ii) proportional catch, and (iii) "floor" strategies, that allow for a proportional catch above a specified "floor"; i f the population size drops below the floor, all harvesting is stopped. (i)  Constant catch policies have advantages for social and economic perspective.  The harvesters know what their future harvest will be, and there is no need for year-to-year adjustments in catch. The major drawback of a constant catch is that i f the population is subjected to year-to-year fluctuations in productivity (either survival or recruitment), then the yield that can be realized by a constant catch strategy is considerably lower than that obtainable with a proportional harvesting strategy. If a constant catch is set too high, and the population begins to decline, then the constant catch becomes an increasing proportion of the population and accelerates the decline. The catch would then have to be reduced or the population would be driven to extinction. Thus, unless one is very conservative in allocation of constant catches, the policy will fail to meet its two objectives of conservation and stability of harvest. (ii)  Proportional harvesting strategies have less stability in the harvest but are able  to adapt to population fluctuations. If the population declines due to poor environmental conditions or illegal harvesting, the legal harvest is reduced or eliminated. A proportional harvesting strategy requires annual estimates of abundance, which could come from either annual censuses, or less frequent censuses with extrapolated estimates of abundance in the years between census. (iii)  The safest type of harvesting strategy employs a  minimum population size (the  "floor") below which all harvesting would be stopped. Floor policies could also be combined with proportional harvesting or even with fixed total catch. Pascual & Hilborn (1995) evaluated a large number of alternative harvest strategies for Serengeti wildebeest and considered the impact of fluctuating rainfall. They present  145  detailed calculations of the trade-offs between average yield, variability of yield, and average population size.  Tactics In any year, the harvesting strategy would determine the total desired harvest. The tactics are the methods for achieving this harvest. One tactic would be village-based quotas in which each village would be given a proportion of the total desired harvest. Other tactics that are used in wildlife harvesting include season and area, but these may be too difficult to apply with villages on the border of the Serengeti. A n y form of village-based quota would require a social structure to monitor and administer the program, and there would be a high cost to the government to reliably measure the harvest. A program of a centralized harvesting, with profits going to villages, would be much easier to administer, but the costs of a centralized culling program might exceed the value of the meat produced. Impediments to implementing a legal harvest While a sustained harvest of wildebeest is theoretically possible, there are a number of concerns regarding the sustainability of a legal harvesting program. These concerns include: (i)  A  growing illegal harvest.  Roughly half of the sustainable harvest of wildebeest is  now taken in the illegal harvest. If the assumption of constant harvest over 15 years is wrong the current illegal harvest could be exceeding the sustainable yield. Also, i f the 1993 drought reduced the population as much as my model predicts, then there is little room to add a legal harvest to the illegal harvest There is only room for a substantial legal harvest i f the existing illegal harvest is reduced. However, it is possible that the addition of a legal harvest might aggravate, rather than reduce, the illegal harvest.  By  permitting legal possession of wildebeest meat and implements of harvesting (rifles, bow and arrow, snares), prevention of poaching may become considerably more difficult. If human population density on the perimeter of the Park continues to grow, I expect that poaching pressure would continue to increase and the potential for legal harvest would be very small indeed.  146  (ii)  Economic inefficiency of harvesting. Macnab (1991) has reviewed attempts at game cropping around the world and particularly in Africa. There are very few examples where game cropping has proved to be both cost effective and controlled. A major impediment to any legalized wildebeest harvest is finding a technology that is both cost effective and controllable. N o large scale legal harvesting should be undertaken until an economically viable method is shown to be effective.  (iii)  Inability to monitor. A n y harvesting strategy requires monitoring the levels of catch. This has proved to be difficult in most wildlife and fisheries harvesting schemes where the agency infrastructure and budgets are much larger than those available on the perimeter of Serengeti National Park. Once a legal harvest is in place, it could prove very difficult to determine and regulate.  (iv)  Inability to reduce harvest as necessary. Most of the harvesting strategies that might be adopted would require periodic adjustments in the quota. Such adjustments would from time to time mean reduction in quota. Experience in wildlife and fisheries around the world indicates that user groups are often very resistant to reductions in quota. It is quite possible that the government might be unable to implement a harvesting strategy that required harvest reductions.  Strategies for reduction in poaching. A sustained legal harvest of wildebeest requires a major reduction in the current illegal harvest. I believe that poaching should best be thought of as an economic activity. Individuals engage in poaching i f the expected benefits exceed the expected costs. The benefits of poaching are the acquisition of meat and/or money from the sale of meat. The costs of poaching are the time lost from other activities, any money spent on poaching equipment such as snares, and the expected probability of capture, arrest, and possible fine or imprisonment. The current Tanzania National Parks ( T A N A P A ) strategy for reducing poaching is based on increasing the expected costs by increasing the probability of capture. With enough enforcement officers and vehicles, the risk of capture or loss of snares would be so high that few people would poach. In contrast, the Serengeti Region Conservation Strategy (SRCS) which is a development project in the areas surrounding the Park, is based upon supplying meat 147  to a market at a price that would be below that associated with poached meat - specifically by providing meat without the risk of arrest. If villagers can legally obtain meat at a price they can afford, then the benefits to poach for meat would be reduced, and the market for illegally harvested meat would also be reduced. The T A N A P A and S R C S policies are complementary. Other studies in Africa conclude that a combination of both reduced benefit and increased cost is a better approach than either singly (Leader-Williams et al. 1990, Milner-Gulland & LeaderWilliams 1992, Wells  etal. 1992,  Newmark et al. 1993). The most cost-effective way to  reduce poaching could be by providing legal meat at a low price rather than by increasing the costs of poaching through anti-poaching patrols. Legal meat could come from legalized harvest o f wildebeest, or from subsidized imports of other sources of protein  (e.g.,  beef) from  other regions of Tanzania. However, wildebeest harvesting alone is not a long-term way to provide substantial benefits to the local population near the Serengeti. The value of meat harvested sustainably from the wildebeest population in the Serengeti could be as high as U S $ 3,000,000. Divided among the 150 villages on the perimeter of the Park, this could amount to about $20,000 per village per year, an enormous economic benefit to the individual villages. However, the cost of supervised harvesting and administration of harvest regulations would be substantial and might exceed the value of the wildebeest. For example, the Serengeti Regional Conservation Strategy (Mbano et al. 1995) has explored the economic feasibility of harvesting methods, and found serious impediments using either fire-arms or bow and arrows. The most cost effective method is the use o f snares, but because they are inhumane (cause suffering to snared-animal), and they are the tools of poachers, there is a strong reluctance to use this method. Also, any benefits of wildebeest harvesting would be diminished by human population growth. I believe, therefore, that wildebeest harvesting can perhaps be a useful addition to the regional economy, but not a major one. Given that growing human population and continued human encroachment on the Park are expected, it is dangerous for the local population to think of the wild animals in the Park as a potential food resource. Even i f poaching were reduced to allow for a legalized harvest, a breakdown o f anti-poaching programs could result in a major outbreak of poaching at some time in the future. A n y harvest poses the threat of population collapse i f the harvest 148  does not decline during times of reduced abundance. If the level of any form of harvest, legal or illegal, were to remain constant and the herd were to decline due to a drought or an outbreak of disease, such harvesting would accelerate the decline and potentially cause a population crash. Whether development assistance is legalized culling of wildebeest or direct financial assistance to villages, it is essential that such assistance is tied to reduction in poaching. Wells et al. (1992) have discussed many integrated development and conservation programs and shown that they almost always fail to tie development to conservation. This mistake must not be repeated in the Serengeti.  Monitoring and research needed to support such a program T w o types of data are essential for a legalized harvesting program: (z) estimates of wildebeest abundance, and (zz) estimates of both the total legal and illegal catches. The monitoring of abundance is by far the most important, and is currently in place as part of the Tanzanian Wildlife Conservation Monitoring ( T W C M ) . There is no systematic program in place to estimate the illegal harvest, yet such a program would be necessary both to determine the impact of harvesting on the wildebeest population in the future and to adjust local benefits in response to changes in poaching effort. A program to monitor the illegal harvest should consist of systematic searches for snares to estimate the total amount of snaring effort, and measurement of snaring success. Such a systematic survey could be integrated with a program to measure reductions in poaching effort as part of a benefits-for-conservation program. If a legalized harvest were implemented, it is essential that it be reliably monitored. If the legal harvest is determined on a village-by-village basis, monitoring the harvest could be as difficult as monitoring the illegal harvest. If quotas are allocated to villages, there will be economic pressure to exceed the quota illegally.  SUMMARY  1. A population dynamics model was developed that incorporates (z) intermittent sampling of the demographic parameters (population size, births, recruitment and dry season adult mortality) including their respective sampling errors, and (ii) the influence of dry season 149  food availability. Parameters not incorporated in the model include: (/) wet season adult mortality, and (//) human off-take. The model attempts to fit a curve that is most consistent with the census data by estimating the unknown human off-take. 2. The best estimates of human off-take range between 15,000 and 40,000 wildebeest per year. This estimate is consistent with that provided by independent estimates of legal and illegal harvesting in Chapter IV (20,000 - 40,000 wildebeest). 3. There is an opportunity for expanding the legal harvest i f the illegal harvest is reduced. B y providing a legalized harvest, the local population could benefit from the protected areas and the incentives for illegal harvest could be reduced, but considerable caution is required. 4. The long term conservation of the wildebeest population while exploiting its biological potential must meet the following conditions; (z) appropriate economics of harvesting, (ii) implementing appropriate harvesting strategies that recognizes the importance of environmental fluctuations on biological potential, and (///) an adequate monitoring and evaluation system is implemented that monitors the population and the harvest.  150  Chapter VI General Conclusions. Introduction In this concluding Chapter I summarize the key findings and highlight some of their management implications. The major purpose of this study was to describe the wildebeest population dynamics in order to estimate a sustainable harvest. This harvest required an understanding of the ongoing illegal human off-take. Although there were gaps in the data, and the dynamics were complex some conclusions were reached.  Population regulation (Chapter II) Both the decline in fertility rate and increasing adult mortality between 1960s and 1994 were found to be density dependent. The reduced reproductive output was a result of delayed age of maturity and declining pregnancy rate in adults. The proximate mechanisms causing these processes were not studied but were most probably associated with reduced nutritional well being. Overall the wildebeest population appeared to be regulated through density-dependent adult mortality in the dry season.  Resource limitation (Chapter III) Food limitation during the dry season provided the regulatory mechanism. This was shown by fluctuating dry season calf mortality and adult mortality. The proximate agents for the majority of wildebeest mortality are not yet well understood, but poor body condition at death suggests poor nutrition, diseases, or both. Predation appeared to play a less important role in the natural causes of wildebeest mortality ( « 2 5 % ) . Documented natural mortality (other than human induced causes) were largely sufficient to account for the fluctuations of the wildebeest population. Neonatal loss was the most severe mortality stage followed by dry season calf mortality. The latter was the most important stage determining population change. Relatively low adult mortality appeared to dampen population fluctuations. In general, for the 15 years  151  from 1977-92 the evidence suggests that the Serengeti wildebeest was maintained through resource restriction at levels near its environmental carrying capacity. The high juvenile and adult mortality in 1993 and the subsequent low census figure in 1994 are associated with the 1993 drought. The picture after 1994 is incomplete, in the absence of a recent census, but mortality dropped to levels seen in 1977-92.  Human predation (Chapter IV). Studies on poaching mortality are inherently difficult to conduct. However, I believe we are now in a better position to estimate poaching mortality in the Serengeti ecosystem than before. Preliminary estimates suggest that the illegal off-take ranges between 1.6 - 3% per year; i.e., much lower than was previously thought. The total human off-take from both legal and illegal sources is < 3.5%  (i.e., 40,000 wildebeest per year). This estimate is consistent with  the overall population dynamics model. Until now human predation has never been the predominant limiting factor of the wildebeest population. Had it been so, (i) it would have prevented the wildebeest population explosion following the eradication of rinderpest disease. More recently (ii) i f there was any other mortality factor that had been more important than the measured natural mortality, a significant population decline would have been inevitable unless our methods are wrong. Additional data on poaching activities are required to verify or modify my interpretation. Essentially, human off-take is part of the total population output and must be consistent with the general pattern of the population dynamics; it should not be considered in isolation. These results should not underestimate the potential of illegal human offtake to affect the ecosystem. Unlike historical times (prior to the 1950s), I believe that human predation can cause a collapse of the wildebeest population, and those of other large mammal species, in the absence o f penalties for poaching, such as arrest and imprisonment. This potential calls for improved anti-poaching techniques to raise the costs for poaching and a broad based system o f alternative economic options for local residents.  Sustainable harvesting (Chapter V) The wildebeest population dynamics model estimates the current human off-take to be in the region of 0 to 40,000 wildebeest per year. This estimate is consistent with the 152  independent estimates o f legal and illegal harvest which was noted to be around 20,000 40,000 wildebeest (Chapter IV). The synthesis of wildebeest population models discussed suggest that there is a potential for expanding the sustained legal harvest that could provide benefits to the neighboring human population. This was estimated to be around 5% of the population  (i.e.,  60,000 wildebeest) if illegal harvesting could be substantially reduced. This  off-take should cause the herd size to stabilize at around 0.8 million. However, before the benefits of exploiting wildebeest can be realized, there are a number o f impediments to the proposed legalized harvesting programme. These include: (i) the possibility of a growing illegal harvest, (//') the economic inefficiency o f legal harvesting methods, (iii) the inability of authorities to monitor a legalized harvest, and (iv) the difficulty in reducing harvest quotas in the event of population declines. It is important to record that any level o f sustainable harvesting would be, at best, a useful supplement to the regional economy but not a major one. M o n i t o r i n g a n d research A l l man-made interventions in the Parks' natural resources must be regarded as experimental and should be implemented through scientific hypothesis testing (Sinclair & Norton-Griffiths 1979, Sinclair & Arcese 19956). Although the switch from illegal subsistence harvesting to legalized hunting may not necessarily alter the dynamics of the herd, a program to monitor the key elements of the wildebeest population is essential and must be tied to the harvesting program. The present data collection should be continued to ensure that changing patterns of reproduction and mortality are adequately documented  (i.e.,  aerial censuses,  poaching data including patrol and arrest records, age and sex sample counts, and mortality surveys). Similar methods should be expanded to include other large animal species. Our knowledge of the population dynamics and ecology of the wildebeest is unusually complete in comparison to other populations; this record is a good example o f long-term monitoring. Other good long-term data sets are those on moose (Peterson 1996 and earlier reports) and on elk  (Alces alces)  (Cervus elephus)  on Isle Royale  in Yellowstone (Houston  1982). However, with wildebeest there are still significant gaps in knowledge that are essential for the management of the herd. For example, (i) research is needed to understand causes o f  153  neonatal mortality and the influence of diseases in the population dynamics; (ii) we need to know to what extent does the migratory animals use unprotected areas in the ecosystem. Another interesting question concerns (iii) the distinction between the absolute food limitation and the relative food limitation hypotheses as proposed by Smith et al. (1988) and Royama (1992). Relative limitation implies some factors other than direct starvation, e.g., poor quality of food or lack of accessibility due to avoidance of predators. Findings from this study may provide insights to the understanding of the community ecology of the Serengeti ecosystem. So far we have limited our focus largely to the species level. General remarks Perhaps the greatest threat to the long term viability of the wildebeest population in the Serengeti, and the viability of the entire ecosystem is the loss of habitat caused by encroachment of human settlements (Sinclair & Arcese 19956). The movements of large animals (including wildebeest) outside the Park are likely to be density dependent. A s the human population expands into areas that were previously used by wildlife, wild animal populations are likely to decrease in size. Since the protected areas do not include the entire ecosystem, the danger of losing the ecosystem, and most probably the migration, is imminent. Our next important challenge is how to protect the integrity of the system in the face o f increasing human-wildlife conflicts. Because Serengeti can not be isolated from the problems facing a larger part of the world, my hope is in finding effective ways that will integrate wildlife management with community development. 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Progesterone levels (ng/gm) measured from wildebeest fecal samples collected  between 1992 and 1994.  (1)  (2)  SN  Male (1993)  (3)  Yearling (1993-94)  1  (4)  (5)  (6)  (7)  (8)  Autopsy nonpregnant (1994)  Autopsy pregnant (1994)  For pregnancy test 1992  For pregnancy test 1993  For pregnancy test 1994  5.92  5.76  6.05  8.14  0.98  2.22  1.34  2  1.05  3.09  3.32  8.23  6.01  6.11  8.36  3  1.05  3.26  6.08  9.56  6.53  6.47  8.46  4  1.05  3.83  7.23  10.07  7.48  7.14  8.94  5  1.34  8.94  7.25  10.80  7.72  7.99  8.94  7.56  8.94  6  1.48  11.65  7.84  8.04  7  3.67  12.31  8.02  8.04  8.97  8  4.83  19.55  8.89  8.06  9.01  9  9.21  8.16  9.34  10  9.54  8.20  9.36  11  9.69  8.31  9.65  12  9.82  8.50  9.76  13  10.00  8.73  11.36  14  10.83  8.82  11.63  15  14.72  9.17  17.56  16  14.79  9.34  18.05  17  15.03  9.41  18.45  18  15.07  9.61  21.20  19  15.18  9.61  20  15.80  9.81  ... continued next page.  165  Appendix 1.  Continued...  (1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  SN  Male (1993)  Yearling (1993-94)  Observed lactating, (Mar 1993)  Autopsy nonpregnant (1994)  Autopsy pregnant (1994)  For pregnancy test 1992  For pregnancy test 1993  For pregnancy test 1994  21  16.09  9^91  22  16.66  9.96  23  18.95  10.06  24  19.45  10.27  25  20.89  10.37  26  21.01  10.57  27  21.69  10.73  28  21.91  11.55  29  24.15  11.98  30  24.41  13.12  31  25.61  13.23  32  27.46  15.73  33  28.03  15.98  34  32.21  16.13  35  35.83  16.34  36  17.09  37  17.98  38  18.40  39  24.89  40  26.52  41  30.79  42  35.17  43 44  ~  42.06 • -  47.60  166  Appendix  2. Observed and estimated ratios of wildebeest calves per female between 1962  and  Year  1994.  1965  1966  1971  1972  1973  1984  1992  -  -  1993  1994  -  1373  8094  -  2676  2211  -  7149  5943  625  3674  2473  3822  3700  10862  Sample size (calves + adult females) -  January  4125  2130  February  4605  1727  5074  6271  2989  March  8040  772  9777  12806  4764  2177  April  608  1764  14208  2985  2603  3733  May  1875  4879  1892  7490  June  2649  1829  July  1175  -  August  1914  October  789  -  November  1555  -  September  December  -  -  3462  -  1663  8268  -  -  4249  4022  2724  2186  2272  1367  3733  3411  5288 3479  3458  1864  -  2395  1731  3795  5796  2886  2097  571  3245  2314  3113  1102  1301  -  -  389  1412  5294  -  516  708  2875  1489  273  -  Total  27336  15288  48970  47537  19879  17238  5835  27272  55202  n (# of months)  10  7  8  10  6  6  5  12  12  Observed calves:adult female ratio -  0.004  0.291  0.457  -  0.235  0.119  0.352  0.805  -  0.708  0.257  0.405  0.428  0.690  -  0.447  0.192  0.352  0.437  0.368  -  0.536  0.258  0.214  -  0.482  -  0.690  -  0.521  0.260  0.293  0.391  0.312  0.482  0.332  0.523  0.258  -  0.473  -  0.529  0.413  0.431  0.306  0.292  0.360  0.376  0.298  0.257  0.268  -  -  -  0.375  0.286  0.158  January  0.193  0.038  -  0.165  -  February  0.454  0.065  0.467  0.469  March  0.386  0.329  0.548  0.398  April  0.274  0.341  0.516  May  0.284  0.334  June  0.297  July  0.214  August  0.203  October  0.221  -  November  0.225  -  0.253  0.278  -  -  0.323  0.063  0.125  December  -  0.263  0.250  0.301  -  -  -  0.187  0.147  September  -  167  Appendix 2. Year  Continued .  1965  1966  1971  1972  1973  1984  1992  1993  1994  Estimated calves;adult female ratio January February March  0.355  0.360  0.576  0.444  0.384  0.77  -  0.578  0.263  April  0.314  0.321  0.464  0.441  0.376  0.73  -  0.581  0.263  May  0.278  0.287  0.374  0.438  0.368  0.69  -  0.584  0.263  June  0.245  0.256  0.302  0.435  0.360  0.65  -  0.587  0.263  July  0.238  0.254  0.292  0.407  0.333  0.55  0.379  0.453  0.238  August  0.231  0.253  0.283  0.380  0.308  0.46  0.373  0.349  0.215  September  0.225  0.252  0.274  0.355  0.285  0.38  0.368  0.269  0.195  October  0.218  0.251  0.265  0.332  0.264  0.32  0.362  0.208  0.177  November  0.212  0.249  0.257  0.312  0.244  0.27  0.357  0.160  0.160  December  0.206  0.248  0.249  0.292  0.226  0.22  0.351  0.123  0.145  168  Appendix 3.  Observed and estimated ratios of wildebeest yearlings per adult.  Month Sample size  1963  1971  1992  January  -  -  February  1760  7687  March  -  -  May  1780  2358  June  -  5907  -  -  April  July  5613  August  -  September  3977  October November  -  December  Total  13130  2031 2533  1993  1994  1911  9729  2804  4954  4855  7468  565  6841  2930  5348  4320  14527  4266 671 '  8020 4421  1633  1774  617  1811  6995  774  950  4639  2360  511  29217  77221  -  0.162  0.076  0.276  0.070  0.160  0.058  0.308  0.039  0.146  0.048  0.141  0.056  0.099  0.185  0.062  0.111  0.107  0.097  -  0.191  0.096  0.070  0.128  0.084  0.046  7113  -  23065  7588  3768  Observed ratio January  -  -  February  0.304  0.069  March April  -  -  May  0.309  0.124  June  -  0.101  July  0.282  August  -  -  September  0.230  October November  -  0.055  0.109  0.042  0.038  December  -  -  -  0.349  0.065  0.207  0.065  0.203  0.063  0.199  0.061  0.195  0.060  0.190  0.058  0.186  0.057  Estimated ratio January  -  -  February  0.307  0.096  March  0.307  0.095  April  0.307  0.095  May  0.307  0.095  June  0.307  0.095  -  July  0.279  0.085  0.148  0.145  0.057  August  0.254  0.076  0.141  0.113  0.056  September  0.231  0.068  0.134  0.088  0.056  October  0.210  0.061  0.128  0.068  0.056  November  0.191  0.055  0.122  0.053  0.056  December  0.174  0.049  0.117  0.041  0.056  169  Appendix 4. Wildebeest carcass data recorded between July 1992 and December 1994 and accumulated for each transect. These data sets were imported in the program  DISTANCE ®  and used to estimate the effective sighting width and carcass densities. Note: column 4 refers to cumulative transect distances and column 6 the frequencies of surveys per transect.  (1)  (2)  (3)  (4)  (5)  (6)  Total  Frequency  Number of carcasses per sighting distance class Straturn  Transect #  Distance (km)  West  1  510.2  33  20  9  3  2  2  69  26  West  2  630.0  26  14  0  3  3  3  49  28  West  3  528.0  25  16  8  1  1  1  52  24  West  4  340.0  15  14  5  2  1  2  39  17  Plain  6  1080.0  34  25  19  6  4  3  91  28  North  7  424.5  10  16  8  0  2  3  39  13  Central  11  238.0  5  2  4  0  0  0  11  9  Central  12  131.7  5  5  2  3  3  5  23  6  153  112  55  18  16  19  373  151  Total  3882.4  0-100 101-200 201-300 301-400 401-500 > 500 (m) (m) (m) (m) (m) (m)  170  Appendix 5 . Adult wildebeest mortality rates shown at different time scales between July 1992 and December 1994.  Month  Average daily mortality (%)  Monthly mortality (%)  Jul.-92  0.061  1.87  Aug.-92  0.021  0.64  Sept.-92  0.059  1.75  Dry  Oct.-92  0.270  8.03  15.14  Nov.-92  0.062  1.85  Dec.-92  0.061  1.87  Jan.-93  0.038  1.17  Feb.-93  0.031  0.87  Mar.-93  0.033  1.01  Wet  Apr.-93  0.157  4.61  11.58  May-93  0.089  2.73  Jun.-93  0.059  1.74  1993  M.-93  0.027  0.83  36.44  Aug.-93  0.119  3.63  Sept.-93  0.250  7.23  Dry  Oct.-93  0.252  7.52  28.12  Nov.-93  0.338  9.65  Dec.-93  0.097  2.96  Jan.-94  0.012  0.38  Feb.-94  0.030  0.82  Mar.-94  0.005  0.15  Wet  Apr.-94  0.013  0.40  2.68  May-94  0.018  0.54  Jun.-94  0.014  0.41  1994  M.-94  0.023  0.71  6.37  Aug.-94  0.038  1.16  Sept.-94  0.025  0.74  Dry  Oct.-94  0.014  0.45  3.79  Nov.-94  0.027  0.79  Dec.-94  0.000  0.00  Seasonal mortality (%)  Annual mortality (%)  Appendix 6. Steps for estimating wildebeest life table entries (Appendix 7). I made the following assumptions in constructing the life table: (i) all censuses were conducted in March and does not include the number of neonates, (ii) estimates of potential pregnancy rate refer to June which is the end of the rutting season, and (iii) estimates of realized (measured) pregnancy rates refer to March which is the end of the calving season. I also assume that all calves are born in March. The following terms are defined as: N  c  N  y  N  ad  . = the number of calves (<1 year) in month mi and year yi.  m  .= the number of yearlings in month mi and year yi.  m  m  .= the number of adults (>2 years) in month mi and year vi. . = the number of potentially pregnant adult (>2 years) females in year yi.  N N  . = the number of pregnant females in year yi.  C  . = the proportion of the population that is calves (< 1 year) in month mi and year yi as  op  mi  shown in Table 2.7 and estimates from the seasonal lognormal model. Y  mi  ,= the proportion of the population that is yearlings (1 < 2 years) in month mi and year yi as shown in Table 2.9 and estimates from the seasonal lognormal model.  T j = the total wildebeest population in March, from censuses and interpolation. m  . = the adult annual mortality rate (<2 years) in year yi.  s  . = the adult monthly survival rate in year yi.  a  m  p  p  . = the potential pregnancy rate which refers to all adult (>2 years) females in year vi. I assumed that adult females constituted 45% and 58% before 1990 and after 1990 respectively (Figure 2.4).  p  a  . = the adult pregnancy rate in year yi (Table 2.4).  Steps (columns indicated below refer to those in Appendix 7) 1. Where census was not conducted, I used smoothing curve interpolation to estimate the population size in March (Ty)(Co\. 3). 2. The number of calves recruited into the adult population was obtained by multiplying the total population size by the proportion of last years' calves,  N,  y yi  =T C yr  _,  Dec<y  A.1  172  3. Thus the number of adults (> 2 years) is obtained by subtracting last years' yearlings from the total population size (Note: total population size does not include young of the year). N ,  = T -N ,  ad yi  y  A.2.  y<y  4. The annual adult mortality rate is the difference between the number of adults in consecutive years divided by initial population size, _  a,yi  ( ad,yi  ~  N  -  m  ad,y-\)  N  A  N  -  "  3  5. The monthly adult survival rate is therefore,  s , ,= p-™ J x  m y  A.4.  a  Thus the adult monthly population size is reduced by monthly survival rate (assuming equal mortality). The estimated survival rate covers the period from March through February. 6. From the estimated adult population size in June, the number of potentially pregnant females (Col. 8) in year yi is given by N  = N -p  myi  adyi  A.5.  pyi  7. and the realized pregnancy and hence calves born in March (Col. 9) of year yi is N ,  = N  op yi  p  adjyr  A.6.  oyi  8. Estimates of calves alive in June and December (Col. 11 & 12) were obtained by multiplying the proportion of calves in June and December by the adult population size in those months. N  c,m,yi  = C  mi,yi  • N  ad,m,yi  A 7 '  '  9. The numbers of yearlings in January, June and December (Col. 5, 6 & 7 respectively) were obtained by multiplying the proportion of yearlings in January, June and December by the number of adults their respective months. ^  ,m, i  y  y  ^tni, i y  ^ad, i y  A.  8.  173  Appendix  7. Wildebeest life-table showing population estimates used in k-value analysis.  Figures in bold face represent census results in March, while others are fitted by interpolation. With the exception of interpolated adult survival, estimates for other demographic parameters were measured independently. page.  174  Appendix 7. Wildebeest life-table continued . (2) (3) (1) Year Population in March Census January estimates (Adults + Recruits) 1959 1960 1961 1962  234,227  -  (4) Adult population (December)  212,220  203,597  232,368  224,884  263,362 306,789  -  (5) Yearlings (January)  (6) (7) Yearlings Yearlings (June) (December)  -  -  -  108,053  -  -  1963  361,302  356,124  342,784  111,028  1964  405,800  402,916  -  1965  445,266  439,124  373,725 423,431  -  -  1966  464,616  461,219  -  -  -  1967  488,476  483,292  436,962 471,749  1968  522,480  519,959  502,006  -  -  -  1969  574,188  570,299  550,451  -  -  -  1970  633,805  629,506  694,914  1972  777,474  692,777 773,014  619,780  1971 1973  897,250  897,156  672,266  66,364  -  65,295  772,592  -  853,204  -  -  59,473  -  32,941  -  1975  1,222,212  1,057,890 1,221,879  1,170,854  1976  1,346,779  1,335,785  -  -  1977  1,455,723  1,149,711  -  -  -  1978  1,303,652  1,440,000 1,248,934  1,262,060  -  1,170,912  -  -  -  1979  1,310,003  1,293,457  1,197,204  -  1981  1,106,276  -  1,144,925  -  1,227,856 1,139,468  -  -  -  1,357,933  1,337,979  1,198,561  1980  1,050,777  -  1,061,649  -  1,099,598  -  -  -  -  1974  -  -  1,302,201  1,273,345  1982  1,242,225  1,208,711  1983  1,328,740  1,315,111  1984  1,356,328  1,337,879  1985  1,254,186  1,214,961  1986  1,179,166  1,146,340  1987  1,179,230  1,161,429  1,059,453  1988  1,197,716  1,176,517  1,073,085  1989  1,213,106  1,191,606  1,059,224  1990  1,233,699  1,206,694  1991  1,245,399  1,221,783  1,092,463  -  -  -  1992  1,240,779  1,215,627  1,050,209  170,972  122,626  1993  1,242,517  1,209,471  936,808  244,677  43,952  1994  967,457  917,204  208,280  876,746  76,178  63,641  58,906  1995  continued... 175  Appendix 7.Wildebeest (1) Year  1959 1960 1961 1962 1963  life-table continued .  (8) Potential pregnant females 91,619  -  1964  168,176  1965  190,544  1966 1967 1968 1969  -  (9) Calves born(JanFeb) 87,038  -  (10) Calves (March) -  (11) Calves (June) 41,372  -  (12) Calves (December) 17,991 _  64,864  77,357  54,845  74,659  63,533  168,176  70,224  54,229  39,379  181,017  74,759  58,435  48,940  76,706  47,175  97,642  65,261  -  -  95,813  -  1970  278,901  87,675  68,176  1971  302,520  278,901  179,477  120,028  266,217  154,355  154,575  107,390  155,044  144,691  82,761  204,787  170,945  1982  - -  93,445  1972  1983  539,352  1973 1974 1975 1976 1977 1978 1979 1980 1981  1984 1985 1986 1987 1988 1989 1990  -  -  1991  660,892  1992  609,451  544,643  1993  615,757  509,522  1994  614,483  551,952  1995  466,105  -  -  446,099  -  -  147,895 143,875  -  108,073  -  169,782 123,452 132,890  -  120,584  -  178,608 165,761  -  222,252  181,784  386,938  235,768  65,822  178,366  147,557  77,340  501,333  176  Appendix 8. Selected rain gauges with a relatively long term record of monthly rainfall shown in relation to wildebeest migration zones. Rain gauge numbers refer to the T W C M / S W R C recording system.  Zone / Location A  B  C  Rain Gauge # Serengeti plains; wet season ranges  % data available  1  Lake Lagarja  23  90.8  2  Serengeti M a i n Gate  24  92.8  3  Naabi  25  90.0  4  Simba Kopje  29  94.8  5  G o l Kopje  34  92.8  6  Lake Magadi  55  92.8  7  Loliondo Kopje  58  94.0  8  Moru  61  86.8  9  S.E. Kopje  71  92.4  10  Zebra Kopje  77  94.0  Central woodlands; transition zone 1  Kimarishe  18  87.2  2  SWRC  35.  85.6  3  Banagi  36  93.2  4  Nyaruswiga S.  65  88.0  5  Seronera (Simba)  72  89.2  6  Seronera South  73  90.8  Northern Sereneeti; drv season ranges 1  Kogatende  3  86.0  2  Bologonja  6  91.2  3  Klein's Camp  8  92.0  4  Lobo  10  91.2  5  Togoro  11  93.6  D Western Sereneeti; earlv dry season ranges Insufficient record 21  Total  Average  90.9  177  


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