‘ . .llV .3 1.5.7.. J i... 3 :G. L i. .1. .v 1 Jr?! . .....t . it!...l...:: , ’3. .5: a..¢.$l.§atl:s . 37.131 311 a! ‘ .. .. . u. , V .33.. I: u! . to 3.5.4 V3.21? . , .c . A 3.1.3.... ‘ V. e I K 22.71 :x . 411:... r... v. 5..»- :23 5 ‘ .21....- . . .u f e .OI:|;.. :21... . 1.. .2; .1 t o .. .15. : 3.21 12I to n . 4... 3“ 221.3. y.‘ . If I t 23;: ..v..}..- .z . .:. ‘1"x' ‘ t": I,..J1-.o F ‘W LIBRARY Hickman State University L .J This is to certify that the dissertation entitled POPULATION DYNAMICS AND MANAGEMENT OF THE IEEEEEEEEEEEEEEEEE OKAVANGO RIVER CROCODILES IN BOTSWANA presented by Goran Ernst Daniel Blomberg has been accepted towards fulfillment of the requirements for Doctor of Philosophy degree in Wildlife Biology Date K. 25““ 2' I? 20 MSU is an Affirmative Action /’Equal Opportunity Institution Major professor HIGAN STATE EEEEEEEE EEEEEEEEEEEEEEEEEEEEEEEEEEI 293 00906 3672 0-12771 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE IE EMS! QQQ 1' M80 In An Affirmletive ActiorVqu-_—uel Opportunity Institution cmmS-DJ POPULATION DYNAMICS AND MANAGEMENT OF THE OKAVANGO RIVER CROCODILES IN BOTSWANA By Goran Ernst Daniel Blomberg A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Fisheries and Wildlife 1990 ABSTRACT POPULATION DYNAMICS AND MANAGEMENT OF THE OKAVANGO RIVER CROCODILES IN BOTSWANA By Goran Ernst Daniel Blomberg Behavior of the Crocodylus niloticus population in the Okavango River and its upper delta was modeled, to guide conservation practice. Background knowledge and data were acquired in Botswana, 1974 through mid-1976. In preliminary simulations the population, when undis- turbed, equilibrated at 21,000, in 130-140 years. Four consecutive years of severe floods every 20 years caused noticeable decreases, though the population recovered quickly. Droughts on the same schedule had less severe effects. Simulated hunting of animals 120- 190 cm long lowered the population to l,400-2,000. Following correc- tions and alterations, data were varied for several parameters, to gauge the model's response. The population curve varied with changes in initial population size, initial age structure, age-specific per- centages of nesting females, and age-specific clutch sizes. Sensi- tivity was also ascertained from changed data for age-specific survival rates, including arbitrarily lowered rates for juveniles; their rates are believed to be reduced by adults' aggression, in nature. Growth rates of crocodiles were expressed in age spans cannibalized, initial ages of cannibalistic behavior, initial age of egg laying, and age spans subjected to hunting (which superseded, up to a point, natural mortality). Response to altered data was considerable for all but the first of these parameters, and for certain combinations. Replacement of the present data with field data thus appears worthwhile (l Goran Ernst Daniel Blomberg exception), and should make the model more reliable. Raising the first value for age-specific survival rates from 42.3 to 100.0 raised the population's equilibrium from 26,500 to 65,900. The latter population size might have allowed a total harvest of 40,000 during 1958-69. Uncertainty regarding original population size makes postponement of proposed hunting, of 1,000-1,400 crocodiles annually, until the popu- lation approaches or attains equilibrium phase, seem wise. Ranching (dependent on eggs or young from the wild), and more moderate hunting by local people, appear workable as commercial management schemes, how- ever. If ranches become farms (dependent on captive breeders), the latter scheme may remain an incentive for conserving the wild popula- tion, and the model could predict allowable hunting rates. Dedicated to my mother, Mrs. Karin J. Blomberg, whose knowledge of and interest in biology nurtured my interest therein, from early childhood. Her interest and encouragement proved invaluable when serious studies were undertaken. Her tenacity, in circumstances that would have daunted many, has been, and remains, an inspiration. ii ACKNOWLEDGMENTS The U.S. Peace Corps and the Smithsonian Institution made possible the field work which is the basis for this study. Botswana Department of Wildlife and Tourism, the Department of Fisheries, and Botswana Game Industries (Pty.) Ltd. (BGI) provided the supplies. Mr. S. Bakani and Mr. E. Balson hunted the crocodiles for BGI. Dr. W. Von Richter super- vised the field work. Mr. A. D. Graham helped to supervise, and lent invaluable aid. Mr. A. P. Ziegler, Mr. I. S. C. Parker, Dr. L. Patterson, Ms. U. Wilmot, and Ms. S. Waterhouse assisted at various times. Mr. P. A. Smith, Mr. T. Mfiller, Mrs. B. Gibbs-Rossel, and Mr. M. Biegel got me acquainted with the plant life of the Okavango Delta. Particular thanks are due to Mr. P. Blignaut, Mr. T. Nicolle, Mr. and Mrs. B. J. Pryce, Mr. and Mrs. T. Liversedge, and Game Scouts Mr. D. D. Diau and Mr. F. Mokgwaphe. Mr. and Mrs. B. Truthe and Mr. and Mrs. T. Liversedge helped make my stay pleasant; Tim's knowledge of the area's natural history was very much appreciated. The prototype of the model resulted largely from the work and expertise of fellow students Mr. K. D. Smith, Mr. S. M. Caddell, Mr. S. R. Pett, and especially Mr. B. C. St. Pierre. Dr. W. E. Cooper of the Department of Zoology and Dr. E. D. Goodman, then with the Department of Electrical Engineering and Systems Science, supervised the develop- ment of the model and critically read the original manuscript. The latter kindly subsidized some further development of the model, as did the Department of Fisheries and Wildlife. iii Much of my understanding of the FORTRAN computer language I owe to Mr. J. E. Underwood, formerly at Lansing Community College. His inter- est and donated time were indispensable. Dr. W. E. Magnusson, Departado de Ecologia, INPA, C.P. 478, Manaus, AM, Brazil, offered invaluable advice on further development of the model. This develop- ment, and testing, would have been impossible without frequent advice from consultants at the MSU Computer Center, notably Mr. P. Pirozzo, Mr. M. Riordan, Mr. R. Wiggins, and Mr. C. Severance. Dr. D. McGroarty at Lansing Community College and Dr. M. Taylor, formerly with the Department of Fisheries and Wildlife, are thanked for advice that moti- vated further scrutiny of the computer program, which in turn revealed the need for an important correction. Dr. G. A. Petrides, Professor Emeritus, Department of Fisheries and Wildlife, is thanked for having been chairperson of my Student Guidance Committee for some years. Dr. M. M. Hensley, Professor Emeritus of the Department of Zoology, is thanked for having served on the same Committee. I thank Dr. H. H. Prince for being chair- person of my Student Guidance Committee, and I thank Dr. N. R. Revern, Department Chairperson, Dr. W. W. Taylor of the same Department, and Dr. W. E. Cooper, for serving on the Committee; all are thanked for critically reading the manuscript. iv TABLE OF CONTENTS Page 'LIST OF TABLES ................................................... vii LIST OF FIGURES .................................................. xi CHAPTER 1: INTRODUCTION ......................................... 1 CHAPTER 2: REVIEW OF LITERATURE ................................. 5 CHAPTER 3: MATERIALS AND METHODS ................................ l7 POPULATION MODEL ............................................... l7 ALTERATIONS .................................................... 38 SENSITIVITY TESTING ............................................ 43 Initial Population Size ...................................... 44 Initial Age Structure ........................................ 45 Age-specific Percentages of Females Nesting in a Given Year .. 46 Age-specific Clutch Sizes .................................... 46 Age-specific Survival Rates .................................. 51 ngor Portions 2: Curve 2: Survival Rates .................. 51 Constraint gg_Juvenile Survival ............................ 55 Growth Rates of Crocodiles ................................... 56 Age §pans Cannibalized ..................................... 56 Initial Aggg 9f Cannibalistic Behavior ............... ...... 58 Initial Agg gf Egg Laying .................................. 58 ,Agg,§pans Being Hunted ..................................... 62 CHAPTER 4: RESULTS .............................................. 65 PRELIMINARY SIMULATIONS ........................................ 65 Normal Conditions ............................................ 65 Extreme Water Levels ......................................... 65 Hunting ...................................................... 68 SENSITIVITY TESTING ............................................ 68 Initial Population Size ...................................... 77 Initial Age Structure ........................................ 78 Age-specific Percentages of Females Nesting in a Given Year .. 83 v TABLE OF CONTENTS (cont'd.) liege Age-specific Clutch Sizes .................................... 86 Age-specific Survival Rates .................................. 89 M312; Portions 2: Curve 2; Survival Rates .................. 89 Constraint‘gg_Juvenile Survival ............................ 92 Growth Rates of Crocodiles ................................... 95 Relation £2 Cannibalism .................................... 95 Relation g2 Initial Age 2; Egg Laying ...................... 96 Relation 52 Age Spans Being Hunted ......................... 101 CHAPTER 5: DISCUSSION ........................................... 109 PRELIMINARY SIMULATIONS ........................................ 109 Normal Conditions ............................................ 109 Extreme Water Levels ......................................... 110 Hunting ...................................................... 110 Management Implications ...................................... 111 PRELIMINARY CONCLUSIONS ........................................ 112 SENSITIVITY TESTING ............................................ 113 Initial Population Size ...................................... 116 Initial Age Structure ........................................ 116 Age-Specific Percentages of Females Nesting in a Given Year .. 117 Age-Specific Clutch Sizes .................................... 118 Age-Specific Survival Rates .................................. 118 Major Portions 2; Curve 2; Survival Rates .................. 118 Constraint g§_Juvenile Survival ............................ 119 Growth Rates of Crocodiles ................................... 123 Relation £2 Cannibalism .................................... 123 Relation Eg_Initial'Agg_g§ Egg Laying ...................... 124 Relation £2 Age Spans Being Hunted ......................... 125 CHAPTER 6: SUMMARY AND RECOMMENDATIONS .......................... 130 SUMMARY ........................................................ 130 RECOMMENDATIONS ................................................ 137 APPENDIX A: COMPUTER PROGRAM .................................... 143 APPENDIX B: VARIABLES IN PROGRAM ................................ 149 APPENDIX C: YEARLY VALUES FOR POPULATION SIZE ................... 160 LITERATURE CITED ................................................. 190 Table 10 11 LIST OF TABLES 382. Various initial age structures entered into the model, with initial population size held constant. Numerical values are numbers of females, i.e., data for variable FPOP .................................................... 47 Smoothed values, original and from selected simulated years, for probability of survival to given age class (PSURV). Individuals' probabilities are given in parentheses ............................................. 53 Ages of crocodiles for parameters affected by differ- ent growth rates ........................................ 57 Values for PERBRD and CLUTCH in response to varied initial age of egg laying, due to differing growth rates ................................................... 59 Harvests of crocodiles under tested hunting schemes ..... 69 Summary of response of population curve to changed data in selected parameters ............................. 73 Effects of hunting different age spans on means of huntable male cohort (HMPOP), huntable female cohort (HFPOP), and harvest (HUNT), and on number of years of no hunting .............................................. 105 Effects of different growth rates, simultaneously expressed in age spans cannibalized, initial ages of cannibalism, initial age of egg laying, and age spans hunted, on means of huntable male cohort (HMPOP), huntable female cohort (HFPOP), and harvest (HUNT), and on number of years of no hunting .................... 107 Hunting history of crocodiles on the Okavango River, with a large harvest by B. Wilmot assumed ............... 115 Incidence of injuries, attributable to intraspecific aggression, from the 1974 crocodile harvest on the Okavango River .......................................... 122 List of variables in program CROC ....................... 149 vii Table 12 13 14 15 16 17 18 19 2O 21 22 23 24 25 26 27 28 29 LIST OF TABLES (cont'd.) Page. List of variables in function subprogram TABLIE ......... 155 List of variables in function subprogram TABEXE ......... 156 List of variables in subroutine HUNCRl .................. 157 List of variables in subroutine HUNCR2 .................. 158 List of variables in subroutine HUNCR3 .................. 159 Values for population size at original values for all parameters (Figure 13) .................................. 160 Values for population size at low estimate of initial size (Figure 13) ........................................ 161 Values for population size at high estimate of initial size (Figure 13) ........................................ 162 Values for population size at initial age structure as a narrow pyramid (Figure 14) ............................ 163 Values for population size at even initial age struc- ture (Figure 14) ........................................ 164 Values for population size at inverted initial age structure (Figure 14) ................................... 165 Values for population size at PERBRD increased by 15% (Figure 15) ............................................. 166 Values for population size at PERBRD decreased by 15% (Figure 15) ............................................. 167 Values for population size at CLUTCH increased by 15% (Figure 16) ............................................. 168 Values for population size at CLUTCH decreased by 15% (Figure 16) ............................................. 169 Values for population size at raised PSURV values for the first 20 years of life (Figure 17a) ................. 170 Values for population size at lowered PSURV values for the first 20 years of life (Figure 17a) ................. 171 Values for population size at asymptotic PSURV values lowered to 953 (Figure 17b) ............................. 172 viii Table 30 31 32 33 34 35 36 37 '38 39 4O 41 42 43 LIST OF TABLES (cont'd.) Values for population size at asymptotic PSURV values lowered to 93% (Figure 17b) ............................ Values for population size at asymptotic PSURV values lowered to 92% (Figure 17b) ............................ Values for population size at original values for all parameters, but PSURV(1) raised to 100.0 (Figures 12 and 18) ................................................ Values for population size at constrained juvenile vival, and PSURV(1) raised to 100.0 (Figure 18) ........ Values for population size at initial ages of canni- balism of 11 for males and 18 for females (growth rates of Graham (1976)) (Figure 19) .................... Values for population size at initial ages of canni- balism of 35 for males and 46 for females (growth rates of Graham (1968)) (Figure 19) .................... Values for population size at initial age of egg lay- ing of 10 (Figure 20a) ................................. Values for population size at initial age of egg lay- ing of 13 (growth rates of Graham (1976)) (Figure 20a) Values for population size at initial age of egg lay- ing of 18 (growth rates of Graham (1968)) (Figure 20a) Values for population size at age spans cannibalized, initial ages of cannibalism, and initial age of egg laying at growth rates of Graham (1976) (Figure 20b) .... Values for population size at age spans cannibalized, initial ages of cannibalism, and initial age of egg laying at growth rates of Graham (1968) (Figure 20b) .... Values for population size at age spans hunted at original growth rates (Figure 21a) ..................... Values for population size at age spans hunted at growth rates of Graham (1976) (Figure 21a) ............. Values for population size at age spans hunted at growth rates of Graham (1968) (Figure 21a) ............. ix Pag_e_ . 173 . 174 . 176 . 177 . 178 . 179 . 180 . 181 182 183 . 184 . 185 . 186 LIST OF TABLES (cont'd.) Table 3&82. 44 Values for population size at original age spans can- nibalized, initial ages of cannibalism, initial age of egg laying, and age spans hunted (Figure 21b) ........... 187 45 Values for population size at age spans cannibalized, initial ages of cannibalism, initial age of egg lay- ing, and age spans hunted, at growth rates of Graham (1976) (Figure 21b) ..................................... 188 46 Values for population size at age spans cannibalized, initial ages of cannibalism, initial age of egg lay- ing, and age spans hunted, at growth rates of Graham (1968) (Figure 21b) ..................................... 189 LIST OF FIGURES Figgre ngg, 1 Condensed flow chart of the computer model. Because of the assumed sex ratio of 1:1 and emphasis on the female cohort, separate calculation of the size of the male cohort takes place only during hunting (CRHUNT set at .TRUE.), and then because age spans of hunted males and of hunted females differ. TPOP and FPOP (in second comment) represent size of population and of female cohort, respectively. Each iteration of the main do loop represents a year. FLAG is a water level index dependent on a random number, and can have a value of 2, 1, or 0, each of which corresponds to premature flood conditions, drought (hence low water levels), and normal water levels, respectively. In case of flood, function subprogram TABLIE is called to determine a value for F1. If FLAG is 1 or 0, F1 is 0. HATCH represents the number of successfully hatching eggs. F3M1 is the multiplier function, either equal to 1 (normal water levels), or to a value determined by function subprogram TABLIE, on the rate of canni- balism on 0-2-year old crocodiles. M2 is a density index of 0-2-year old crocodiles, and equals 0, 1, or 3. NORPRED is the assumed constant rate of cannibal- ism ..................................................... 19 2 Curve of survival rates for Okavango crocodiles (PSURV), based on the assigned age structure of the 1974 kill and hypothetical points ....................... 24 3 Percent of female cohort nesting as a function of age (PERBRD)' ................................................ 25 4 Relation of cube root of clutch size to age of female (CLUTCH) ................................................ 27 5 water levels generated by random numbers. The normal water level is designated by 0 .......................... 28 6 Relation of percent egg loss to flood level (F1) ........ 30 7 Relation of percent egg loss by monitor lizard preda- tion to number of nests available (F2) .................. 31 xi LIST OF FIGURES (cont'd.) Figure Page 8 Multiplier function for the cannibalism rate on young crocodiles, in relation to water level (F3M1). The normal water level is designated by 0, where the mul- tiplier equals 1 ........................................ 34 9 Curves representing various survival rates entered into the model .......................................... 52 10 Trend of population size without unusual environmen- tal disturbance, and response to various levels of hunting efficiency at a minimum of 300 harvestable crocodiles .............................................. 66 11 Response of population size to 4 consecutive years of droughts and floods every 20 years ...................... 67 12 Main method of presentation of output from the model. With unchanged data for all parameters (except that PSURV(1) - 100.0) and no simulation of hunting, the equilibrium phase averages 66,000 individuals; it is reached in 78 years ..................................... 72 13 Response of population size to varied estimates of its initial size. The age structure at year 0 is held constant ........................................... 80 14 Response of population size to varied initial age structure. The size at year 0 is held constant ......... 82 15 Response of population size to different sets of age- specific percentages of females nesting in a given year .................................................... 85 16 Response of population size to different sets of age- specific clutch sizes ................................... 88 17 Response of population size to (a) sets of changed survival rates in the first 21 age classes, and (b) sets of survival rates lowered from 99.0% in the asymptotic portion (age classes 22-51) of the curve of survival rates ....................................... 91 18 Response of population size to arbitrarily lowered survival rates of juveniles (ages 5-10, 1.5-2.5 m long). (PSURV(1) was in this comparison set at 100.0.) Lowered survival of juveniles is believed to result from aggression by adults ........................ 94 xii LIST OF FIGURES (cont'd.) Figure Page 19 Response of population size to changed growth rates, as expressed in initial ages of cannibalistic behav- ior. The curve labeled ”MALES 11, FEMALES 18" results from suggested growth rates of Graham (1976); that labeled "MALES 35, FEMALES 46' results from the low growth rates in Lake Turkana, Kenya (Graham 1968) ....... 98 20 Response of population size to changed growth rates, as expressed in initial age of egg laying, (a) singly, and (b) in combination with age spans canni- balized and initial ages of cannibalistic behavior. Initial ages of laying of 13 and 18 correspond with suggested growth rates of Graham (1976), and low growth rates in Lake Turkana, Kenya (Graham 1968), respectively. The curves labeled "10 YEARS” and "M 19, F 37; 10 YR” are identical .......................... 100 21 Response of population size to changed growth rates, as expressed in age spans vulnerable to hunting, (a) singly, and (b) in combination with age spans canni- balized, initial ages of cannibalism, and initial age of egg laying. The curves labeled "MALES 4-7, FEMALES 5-9' and "M 4-7, F 5-9; M 11, F 18; 13 YR“ result from the suggested growth rates of Graham (1976). Those labeled "MALES 11-19, FEMALES 11-20' and "M 11-19, F 11-20; M 35, F 46; 18 YR" result from the low growth rates in Lake Turkana, Kenya (Graham 1968) .............. 104 xiii CHAPTER 1 INTRODUCTION This work reports on a model of the behavior of the Nile croco- dile (Crocodylus niloticus) population in the Okavango River and its upper delta, in Botswana, Africa. Its purpose is to provide manage- ment implications, by which to conserve the crocodile population on a biologically sound basis. Sensitivity analyses are performed on the population simulation model for a number of parameters. Much of the original data are based on extrapolations, estimations, or are obtained from the literature. The parameters are (1) initial (1975) pOpulation size, (2) initial age structure, (3) age-specific percentages of nesting females in a given year ("PERBRD”), (4) age-specific clutch sizes ("CLUTCH"), (5) age-specific survival rates (”PSURV"), and (6) growth rates of crocodiles. Sensitivity to changed data for these parameters, as reflected in behavior of the population curve, provides a more reliable guide to biologically sound management of the crocodile population. The biological background for this computer model, and some data supporting it, were gained in Botswana, in a position of Peace Corps Volunteer/Crocodile Biologist, from 1974 through mid-1976. The pro- ject began in connection with a concession, bought by Botswana Game Industries (Pty.) Ltd. (hereafter BGI) of Francistown, to hunt 500 crocodiles a year in the Okavango panhandle and upper delta. This concession, intended to last 3 years (Taylor 1973), was abandoned after the second season. Unable to meet their quota then, BGI l 2 reported a financial loss, and forfeited further crocodile hunting. At the same time P. Becker (1974, pers. comm.), executive director of BGI, recommended a lO-year ban on commercial hunting. Crocodiles and their relatives constitute a distinct group of reptiles, worthy of study and protection. They are the only survi- vors of the Archosaurian stock of the reptile age, over 100,000,000 years ago. They are of exceptional scientific importance, as they can provide indirect information on several aspects of the biology of reptiles long extinct (Cott 1961). Crocodilians furthermore deserve study because of their poten- tial economic importance. The commercial value of the skins of many species is generally acknowledged (Cott 1954, 1961; Chabreck 1966, 1967a; Graham 1968; Bustard 1970; Downes 1970; Parker and Watson 1970; Yangprapakorn et al. 1971; Puffet 1972, 1973; Pooley 1973a; and Blake 1974), and needs no elaboration. They also have value as a tourist attraction (Cott 1961, Pooley 1973a). Crocodilians appear to have ecological value. Cott (1961) and Pooley (1962) believed that crocodiles help control predators on fish esteemed by man. Kellogg (1929) expressed the same belief regarding the American alligator (Alligator mississipiensis). Improved angling following the introduction of crocodiles into the Zambezi River above Victoria Falls has been claimed, according to Child (1974). Fittkau (1970) hypothesized a direct relationship between caiman populations and yield of fish in the oligotrophic mouth—lakes of certain tribu- taries to the Amazon River, in Brazil. In a follow-up he (Fittkau 1973) considered the nutrients excreted by the caimans, assumed primarily of allochthonous origin, to significantly increase the 3 primary productivity in the electrolyte-poor Central Amazonian waters. Pooley (1962, 1969a) reported 2 adult Nile crocodiles to burrow under Ficus gycamorus roots on the Mkuzi River (Zululand, Natal, R.S.A.) during a drought. The pool thus formed in the dry river bed lasted until the rains again filled the river (over 2 months), and was important to small game mammals, birds, amphibians, fish, and insects. Kolipinski and Higer (1966) stated that the holes made by American alligators, in many tree islands, are vital refuges for fish and other wildlife in the dry season, and are therefore essential to the biological survival of the Everglades. The world-wide decline in numbers of crocodilians is widely documented (Cott 1961; Chabreck 1966, 1967a; Graham 1968; Pooley 1969b, 1969c, 1970, 1971, 1973a; Bustard 1970; Charnock-Wilson 1970; Parker and Watson 1970; Lekagul et al. 1971; Joanen and McNease 1971, 1974; Ogden 1973), and is cause for concern. In light of the present status of crocodilians, studies of general biology, artificial hatching, reproductive behavior, effects on fisheries following drastic crocodile reduction, and population surveys to determine breeding stocks and recruitment rates, have been urged by Cott (1961), Fitter (1970), Parker and Watson (1970), and Pooley (1973a). Blake and Loveridge (1975) stressed the need for assessment of mortality patterns in a natural population, in connection with the 5% replacement rate of 1 m long crocodiles from eggs collected for captive rearing. The "vulnerable” status (IUCN 1982) of the Nile crocodile calls for management intended to prevent slippage to "endangered" status, or possibly even extinction, in the future. It is far better to a practice preventive maintenance of the crocodile population now, than to frantically and probably at great expense try to save it from extinction some decades later. Commercial utilization of the crocodile, on a sustained-yield basis, will motivate conservation of the Nile crocodile; human sentiment alone is not believed suf- ficient (Blake and Loveridge 1975). Graham (1976, 1977) believed that if the Okavango crocodiles are not harvested commercially, they will be viewed merely as pests, and will therefore be eli- minated, passively and actively, by the local people. CHAPTER 2 REVIEW OF LITERATURE The scope of this chapter is to summarize modelling of croco- dilian populations, and the models' relation to sustained-yield commercial utilization. It is additionally intended to report on commercial utilization, and on potentially useable populations, in relation to conservation of crocodilians. Bustard (1970) stated that commercial use of wild crocodilians is the best way to conserve them. Crocodilian skins can be the basis for a sustained-yield industry that will make people accept crocodile conservation as sensible, practicable, and profitable. Essentially the same rationale for sustained-yield utilization, of several species, was given by Bustard (1972) Downes (1973, 1975), Blake and Loveridge (1975), Graham (1976, 1977), Whitaker and Whitaker (1979), Bustard and Choudhury (1980), Jenkins (1980, 1982), Whitaker (1980, 1982a), Ross (1984), and Webb (1985). Bustard (1970) and Blake and Loveridge (1975) maintained that public sympathy for crocodilians, as a motivating force in conservation, would be difficult to arouse. A computer model of any wildlife population is intended to logically and mathematically mimic the dynmamics of the population, and the external forces that act upon it. In the case of commercial utilization, the chief purpose of a model is to optimize sustained cropping (Graham 1976, 1977, Nichols 1976). A computer model is also useful in suggesting management strategies, monitoring progress, and directing research (Graham 1976, 1977). An advan- tage of trying to model a population is that its biological 5 6 characteristics that are in greatest need of being researched are highlighted, e.g., improvement of age criteria and age-specific mortality rates. Simultaneously the characteristics of no direct relevance to management become obvious (Graham 1977). Experimental harvest manipulations are potentially more dangerous to populations of alligators than to those of many other wildlife species, due to high vulnerability to hunting, also to the long time to reach sexual maturity (typically 9 years in Louisiana), and the drastic effects on the populations of certain natural phenomena, e.g., hurricanes, drought, and severe freezes (Nichols 1976; Nichols, Viehman, Chabreck, and Fenderson 1976). Nichols (1976) considered these facts as reason for simulating experimental harvests that in practice could do lasting damage to the population. He further stated that computer models make available immediate predictions of effects on population growth of certain management practices. Lastly, Nichols (1976) mentioned the large number of management options available for alligators, i.e., restocking programs, various combinations of size- and sex-specific harvest rates, and various methods of harvest. Graham (1976, 1977) reported a model, largely dependent on data on the structure of 2 annual harvests of Nile crocodiles, also on the known size and age structure of nesting females, in the Okavango River. Various population sizes can be tested until 1 containing these observed segments emerges. The model thus circumvents the extreme difficulty, or great expense, or both, of estimating the size of the population in the field. A logic diagram is presented in Graham (1977). Graham (1976, 1977) stated that though simulated 7 population size will initially be rough, it will improve with more accurate measurements of the model's parameters, also that even a rough estimate will enable preliminary cropping to avoid dangerously large or unnecessarily small numbers. The next step is to use the model to simulate population growth over possibly 20 years, at various cropping rates. Finally it would be used to optimize yields from any given situation (Graham 1976, 1977). The model of Nichols, Viehman, Chabreck, and Fenderson (1976) was constructed to simulate the dynamics of a commercially harvested alligator population inhabiting privately owned coastal marshland of Cameron and Vermillion parishes in Louisiana. Nesting effort, nest flooding, dessication mortality, and predation on eggs and young were all determined as functions of monthly water depth averages. Cannibalism was considered the major density-dependent factor operating on the population, and was determined as a function of population density and water depth. A freeze mortality based on minimum winter temperatures was included, as was a harvest option. Harvest regulations were designed to protect mature females and animals under 1.2 m in length. The model contained the possibly erroneous assumption that hunting mortality of alligator popu- lations is entirely additive to natural mortality. Simulated hunting therefore had maximal detrimental effects on the popula- tion. The management plan for the Okavango crocodiles, which centers on Graham's (1976, 1977) model rests on 2 assumptions: (1) that the crocodiles, if not exploited, become “pests" regardless of legal status, and (2) that planned and monitored exploitation turns the 8 animals to economic advantage and produces information that confers ability to manage the crocodiles for preservation, exploitation, or a combination of both. Prerequisites for a successful management plan are: (1) values for certain population biology parameters that are accessible to monitoring, (2) the offer of a reasonable and predictable return to Botswana's government and to the crapper, and (3) adequate conservation safeguards that can be observed and enforced. Use of a model to compile information gained from research, cropping and monitoring makes possible more rapid accumulation of knowledge and skill in management, and forestal- ling drastic mistakes (Graham 1977). The model of Nichols, Viehman, Chabreck, and Fenderson (1976) was used to examine the alligator population's response to various differential harvest rates in which age- and sex-specific propor- tions of animals were similar to those observed in the 1972 and 1973 hunting seasons in Louisiana. These simulations demonstrated that a base population of 100,000 animals, under existing habitat conditions, should be maintained for a minimum of 20 years when subjected to an annual differential harvest rate of slightly greater than 5%. Simulations were conducted in which animals were taken in proportion to their abundance in the population. Effects of propor- tional harvests, compared with those of differential harvests, indicated that the former can give increased yields of hides. In further work on the above model, Nichols, Chabreck, and Conley (1976) examined potential use of restocking programs to reduce or eliminate effects of harvests on population growth, while main- taining harvest yields. Population growth rates and harvest yields 9 were examined for various simulated restocking quotas. The authors proposed, as a result, that harvesters be required to collect eggs, for rearing and release of young after 2 years, in proportion to the number of female alligators killed in the preceding season. Crocodilians may, in addition to, or in lieu of, hunting, be raised on farms or ranches (the latter sometimes are termed "rearing stations“), for their skins. The term “farm“ denotes a self- sufficient establishment in which eggs come from captive breeders (Chabreck 1967b, 1971, 1973; Pooley 1973a; Blake 1974; Blake and Loveridge 1975). Farming does not directly relate to conservation, and receives only brief mention in this work. A ranch is usually defined as an establishment dependent on wild-caught young, or young hatched in captivity from eggs collected in the wild (Pooley 1973a, Blake 1974, Blake and Loveridge 1975). Magnusson (1984) reported that Papua New Guinea, Zimbabwe, and the U.S.A. are the only countries with extensive farming and ranching operations. The last, though significantly dependent on farmed alligators, produces most of its skins via controlled hunting in Louisiana. The other 2 countries have limited farming, and produce most of their skins by ranching. Magnusson (1984) concluded that (1) in no country are crocodilians produced in commerical quantities by captive propagation (farming), and (2) projects that most effectively help in maintaining wild stock and its habitat involve hunting of adults, or collecting of eggs or hatchlings by local land owners. The government of Papua New Guinea, after uncontrolled hunting and depletion of estuarine and New Guinea crocodiles (Crocodylus 10 porosus and g, novaeguinea, respectively), eased the hunting pressure by organizing a network of village rearing pens and com- mercial ranches (Downes 1971a, 1971b, 1975; Puffet 1972; Montague 1981a). This also gave native people, even if in isolated areas, a chance to earn money, and a vested interest in conserving wild populations (Montague 1981a, Magnusson 1984). Downes (1975) stated that the rearing of wild-caught young is the way to conserve Papua New Guinea's crocodile populations, if it is established and con- trolled for national benefit. There are legally set maximum and minimum belly widths for the harvested crocodiles, namely 51 cm (20') (total length being about 180 cm) and 18 cm (7”) (total length being about 90 cm). The former protects the breeding stock; the latter ensures growth to economic size (Bustard 1970, Lever 1975a, Montague 1981a, Kwapena and Bolton 1982). Downes (1975) and Bustard and Choudhury (1980) stated that the industry in Papua New Guinea could have a major impact on conservation of crocodiles. Puffet (1972) stated that the future of the industry is in the hands of the native people, and that management would be unworkable without their cooperation. He and.Montague (1981a) commented on the people's interest in raising crocodiles. The Department of National Parks and Wildlife Management in Zimbabwe agreed in 1966 to establishment of private rearing stations for young Nile crocodiles. Permission to capture young crocodiles (later prohibited), or collect eggs, was granted on condition that a 10% (but currently 5%) equivalent of young be released to the wild at an age to be determined by the Department (Blake 1974). Blake and Loveridge (1975) stated that wild breeding populations now have ll substantial value as basis for rearing stations, a fact not to be underestimated as a motive for crocodile conservation. They also considered juveniles of rearing stations a valuable resource for supplementing wild recruitment and restocking suitable habitat. Ferrar (1974) and Nathan (1977) also pointed out the conserving effect of Zimbabwe's 3 ranches. The purpose of the commercial management is to achieve maximum sustained annual harvest (Zimbabwe Department of National Parks and Wildlife Management 1974). Blake and Loveridge (1975) and Loveridge (1980) reported that repeated egg collections, since 1967, have not adversely affected the new large and stable crocodile population in Zimbabwe. Ferrar (1974), Zimbabwe Department of National Parks and Wildlife Management (1974) and Nathan (1977) discussed farming of crocodiles in the future. It now takes place concurrently with ranching at Spencer Creek Crocodile Ranch in Victoria Falls (Blake 1974, Medem 1981). Magnusson (1984) pointed out that if ranches turn into farms, the incentive to maintain wild crocodile populations will be reduced, which would put the Department in a difficult situation. The possibility of sustained hunting of crocodiles has been considered, but would be actively discouraged until the populations could withstand it (Zimbabwe Department of National Parks and Wildlife Management 1974). In the U.S.A., Louisiana's alligator management program resulted from research begun in 1958. Legislation to set up the basic framework for hunting seasons in 3 parishes was enacted in 1970 (Palmisano et a1. 1973). Chabreck (1971) recommended establishment of size limits to protect breeders, designing regulations so as to 12 harvest surplus males, also use of a population's size, composition, annual production, and annual mortality as basis for harvest regula- tions. Palmisano et a1. (1973) considered the management program an excellent example of modern, goal-oriented wildlife research, enforcement, and management. The first hunt took place in 1972 in a parish judged to have the largest coast-wide population. Hunting was allowed gradual expansion, to become state-wide in 1981 (Joanen and McNease 1982). Joanen and McNease (1972) and McNease and Joanen (1978) expressed eagerness to initiate wild harvests of alligators, because this motivates land owners to maintain, rather than drain, wetlands, to benefit other wildlife as well. Recovery of depleted alligator populations in the U.S.A., in response to management, is reported by Chabreck (1967a, 1971), Palmisano et a1. (1973) Core (1978), Brazaitis (1984), and Niering (1985). Abercrombie et a1. (1980) believed that Morelet's crocodile (g, moreleti) in Belize, after a 5-10-year cessation of hunting, needed a carefully monitored harvest program. They felt that the population here, unlike those in many other developing countries, still had a capacity for rapid recovery. Abercrombie et al. (1982) felt, however, that production should be on a small scale, to prevent establishment of a large tannery requiring enormous numbers of skins. The possibility of restoring the American and Guban crocodiles g. m and g. rhombifer, respectively) to levels at which they perform normally in Cuba's ecosystems, has been mentioned. It would be followed by a careful harvest program for the international hide market, and meat for local people (IUCN 1978). Graham (1968) discussed a possible commercial management plan 13 for the Nile crocodile in Lake Turkana, Kenya. He considered cropping of younger age classes, possibly supplemented by arti- ficial rearing of young. For Uganda, Cott (1954) mentioned the need to give thought to the breeding stock of the Nile crocodile, if the skin industry were to be saved. He (Cott 1961) also recommended for Uganda and Zambia, effective conservation measures with regard to modern hunting procedures and to the animals' slow growth rate. Medem (1981) recommended that the Okavango crocodiles be managed by farming or by rearing stations. He stated that the rural people would benefit thereby. In the face of pressure for land development in Mozambique, Whitaker (1981) recommended ranching projects at 2 locations. Examination of other locations for utilization of the Nile crocodile should follow. Bustard and Choudhury (1980) and Whitaker (1982a) recommended well-managed commercial utilization of the estuarine crocodile in India, as a conservation measure. The marsh crocodile (g, palustris) responds rapidly to effective management, making substantial economic returns possible (de Waard 1978, Whitaker 1979). A described scheme allows for establishment of a large number of village pens to be used for raising juveniles. Local people would get increased income and employment opportunities (de Waard 1978). Without incentive, based on governmental guidelines for large-scale rearing, the marsh crocodile will never again be plentiful, according to de Waard (1978). He believed that, with large-scale rearing, the gharial (Gavialis.gangeticus) in India might respond to effective management, l4 and that substantial economic returns are possible. Whitaker and Daniel (1978) stated that important populations of the estuarine crocodile exist on Little Andaman and Nicobar Islands, and that they could support a forest-based industry to benefit indigenous tribes. For Nepal Whitaker (1982a) stated that survival of the marsh crocodile and gharial, outside Royal Chitwan National Park, might depend on developing controlled commercial interest among river dwellers and fishermen. Seed stock would come from the rearing scheme of Chitwan. For Bangla Desh, Whitaker (1982a) stated that development of crocodiles as economic and ecologic resource appears to be the best option. He alluded to the estuarine species, which appears not uncommon in the Sunderbans (Ganges delta). For the estuarine crocodile in Sri Lanka, Whitaker (1979, 1982a) recommended farming and wild propagation for economic return, outside of national parks. He (Whitaker 1982a) recommended the same for the marsh crocodile. Whitaker and Whitaker (1979) recommended cropping quotas, upper size limits, and publicity to ensure the con- tinued existence of the latter species. Whitaker (1982a, 1982b) reported interest in Burma, in rearing young estuarine crocodiles. This was on the village level, as in Papua New Guinea. In Malaysia there is recent history of small rearing stations, so controlled harvest of young crocodiles (presumably meaning estuarine) would be a logical approach (Whitaker 1982a). Some states are interested in conservation and management, and initial 15 surveys have been drafted. Whitaker (1982a) suggested, for Indonesia, a crocodile manage- ment program like Papua New Guinea's network. He reported a similar recommendation, specifically for Irian Jaya (which is not surprising), by an unnamed FAO consultant surveying the crocodile industry. Controlled exploitation, in the Philippines, will probably be the key to obtaining significant official involvement in crocodile conservation (Whitaker 1982a). The government would be interested in how crocodiles can benefit people, not in conservation of a non- commercial resource (Ross 1984). The Agusan River drainage could be a sanctuary for the estuarine species if local inhabitants and political dissidents were convinced that they could ranch or crop on a sustained-yield basis (Ross 1984). For the estuarine crocodile in Australia, Bustard (1972) and Jenkins (1980) believed commercial use, after population recovery, would offer an excellent conservation solution. According to Jenkins (1982) and Webb (1985) the subadult segment could be har- vested without adverse effect, once the populations reached equilibrium. Webb (1984) stated that strictly controlled commer- cial use of Johnson's crocodile (Q, jghnggni) is now possible, and can play a positive role in its conservation, granted that its hide is less valuable than that of the estuarine species (Jenkins and Forbes 1983). Webb (1984) stated that if crocodilians are of commercial value, their wetland habitat will be an asset, and destruction thereof would be a liability. For Papua New Guinea's island provinces, i.e., Manus, New 16 Ireland, East New Britain, West New Britain, and the North Solomons, Whitaker (1980) mentioned status, needs, and commercial possibilities of the estuarine crocodile populations. He stated that proving and sustaining economic value of crocodiles as a resource may be the only way to guarantee survival. The estuarine crocodile in the Solomon Islands is partly protected (Whitaker 1982a, 1982b). It could become a valuable resource to villagers interested in rearing or capturing young for sale to a commercial farm (presumably meaning 'ranch'), according to Whitaker (1982a). He added that tourist viewing of wild croco- diles could provide an additional source of income to local villagers. CHAPTER 3 MATERIALS AND METHODS POPULATION MODEL The model, written in FORTRAN IV, represented a first attempt at describing the behavior of the crocodile population. It projected population growth from 1975, and incorporated simulated hunting as an option. The program "CROC”, in updated form, with its function sub~ programs and subroutines, is in Appendix A. The reader may wish to refer to it frequently in relation this chapter. Figure 1 shows a condensed flow chart. The model began by naming and dimensioning a number of variables, and providing numerical values for some, including the number of females in each of 66 age classes ('FPOP(K)'). Then it initialized the population (“TPOP") for year 0 (1975) and the variable for hunting kill of males ('MHKIL') and of females('FHKIL"). Next it calculated the population size, and the number of females by age class. The initial population estimate (for 1975) was made as follows. It was first assumed that BGI's kill of sexually mature females (1974- 75) was not intense enough to get the more remote nesting portion, but only that portion which did not nest and which numbered 11. An unbiased sampling of the sexually mature females would have numbered 33, assuming that 2/3 of the mature females nested that year. Scanty field observations suggest that this is so. Thirty-three sexually mature females would increment the entire female kill, by 22, to 220, of which these 33 females constitute 15.0%. It is then assumed that there were 123 sexually mature females in the population (2/3 of which 17 Figure 1. 18 Condensed flow chart of the computer model. Because of the assumed sex ratio of 1:1 and emphasis on the female cohort, separate calculation of the size of the male cohort takes place only during hunting (CRHUNT set at .TRUE.), and then because age spans of hunted males and of hunted females dif- fer. TPOP and FPOP (in second comment) represent size of population and of female cohort, respectively. Each itera- tion of the main do loop represents a year. FLAG is a water level index dependent on a random number, and can have a value of 2, 1, or 0, each of which corresponds to premature flood conditions, drought (hence low water levels), and normal water levels, respectively. In case of flood, func- tion subprogram TABLIE is called to determine a value for F1. If FLAG is 1 or 0, F1 is 0. HATCH represents the number of successfully hatching eggs. F3M1 is the multi- plier function, either equal to 1 (normal water levels), or to a value determined by function subprogram TABLIE, on the rate of cannibalism on O-2—year old crocodiles. M2 is a density index of O-Z-year old crocodiles, and equals 0, 1, or 3. NORPRED is the assumed constant rate of cannibalism. 19 éflflifib C INITIALIZE THE POPULATION FOR START AT YRS - O. C PRINT RESULTS AT THIS TIME. TPOP, FPOP. C INITIALIZE‘iARAMETERS. SPECIFY AND CALCULATE VARIOUS PARAMETERS C EXECUTION PHASE FOR 300 YEARS. (Main do loop) M - 1 YES M - 300? M - M + 1 NO [CRHUNT - .FALSET] C RANDOM WATER LEVEL VARIABLE ASSIGNED A VALUE. - ICALL FUNCTION SUBPROGR. TABLIE TO DETERMINE EGG MORT. FROM FLOOD (F1) s C NUMBER OF EGGS FIGURED. NO. secs - N0. MATURE 99 x z BREEDING (PERBRD) x CLUTCH SIZE (CLUTCH) (BY AGE CLASSES) CALL FUNCTION SUBPROGR. TABEXE TO DETERMINE MONITOR PRED. ON EGGS (F2) l C TOTAL HATCH MINUS MORTALITY. HATCH REDUCED BY F1, F2, MINOR EXTRINSIC MORTALITY (0.072), INTRINSIC MORTALITY (0.236) A A Figure l. 20 8 d'HATCH - g HATCH - HATCH/2 C EACH ACE CLASS IS NOW ADVANCED 1 YEAR. YES ICALL SUBROUTINE HUNCRl TO ADVANCE EACH AGE CLASS OF d'd' 1 YEAR ADVANCE EACH ACE CLASS OF 99 1 YEAR BY ARRAY INTERCHANGE ALGORITHM CRHUNT YES CALL SUBROUTINE HUNCRZ TO FIGURE TRUE? KILL, AND PARTITION IT BY SEX AND BY AGE CLASS NO CALL FUNCTION SUBPROGR. TABLIE TO DETERMINE MORT. OF 0-2- YR. OLD CROCODILES (F3M1>1 OR <1) C CANNIBALISMdeCURED ON THE O-Z-YEAR OLD CROCODILES. PREDATION - (NO. CANNIBALS x F3Ml x M2 x NORPRED (0.06))/2 \D FIGURE AGE-SPE- CIFIC SURVIVAL, 0-2-YR. OLD g NO CRHUN YES TRUE? FIGURE AGE-SPE- CIFIC SURVIVAL, 3-65-YR. OLD 99 IV 9 HUNTING EACH 0' ACE CLASS - RE- SPECTIVE 9 AGE CLASS Fi I,( d ) " ."'_n" E: 0‘ § -14 '2 S s . . u o 2 4 6 8 10 RANDOM NUMBER (KK) Figure 5. Water levels generated by random numbers. The normal water level is designated by 0. 29 Function Fl (Figure 6) estimated the percentage of egg mor- tality due to prematurely high water levels. Its shape is justified by the fact that 68% of the nests will be between 0.8 and 1.8 m above water in normal seasons (mean 3 standard deviation - 1.3 i_0.5), as determined by 40 measurements in the field. If the value of the subscript were smaller, representing drought (FLAG - l), or water levels were normal (FLAG - 0), the number of eggs ('TEGGS,‘ under comment “NUMBER OF EGGS FIGURED.") was calculated at F1 - 0, for each age class of females. The calculation involved variables PERBRD and CLUTCH above. The average clutch size ("ACLUTCH") was then obtained by dividing TEGGS by the number of nesting females. ACLUTCH was used in calculating the number of nests “NNEST", based on the value of F1 (0 or positive). NNEST was 1 of the arguments used in obtaining the decimating factor on eggs, "F2” (Figure 7) due to Nile monitor predation. Function F2 estimated the percent of egg loss caused by monitor predation. The shape of the function is based solely on 2 data points: apparent lack of predation with 40 nests in 1974 and predation on 23% of 82 nests in 1975 (Blomberg 1977). The difference in nest numbers for the 2 seasons was real. Additional justification for the general shape of the function was the density-dependent nature of predation in general (Emmel 1973). The predation rate for 1975 may have been somewhat lower if visits to nests could have been very brief or not undertaken. The reason is that females tend to leave the nests unguarded if human visits last about 30 min (Graham et a1. 1976). The maximum predation rate was set at 28%, which seems reasonable, con- sidering that 20% of nests were robbed at Ndumu, Zululand, R. S. A., 30 100 « 80- 60- 40‘ Z EGG MORTALITY 20- FLOOD LEVEL (m) Figure 6. Relation of percent egg loss (F1) to flood level. 31 .mfiomawm>m name: no human: ou Ammv coaumumud_u0uacoe he mmoH mwu ucmuumd mo :oaumamm .n muswam Salome; 31.3" .2: T 8 . pm . 3 . cm. as Nb .2 m . w. W ZN M 32 where density was low (Pooley 1969b), and 33.8% (Pooley 1969b) and 49.4% (Pooley 1973b) at Lake St. Lucia (Zululand) where nest density is high. Nest density was low along the Okavango River. F2 was calculated by calling function subprogram TABEXE. Thus the program let premature flooding, if it occurred, take its toll prior to predation by monitor lizards. This seems realistic, as F1 is an independent variable inversely proportional to F2. Next (under comment “TOTAL HATCH MINUS MORTALITY.") the number of hatching eggs, ”HATCH," was obtained by subtracting from TEGGS the proportions due to F1 and F2. Also subtracted were proportions due to intrinsic mortality, due mostly to infertility, also to embryonic death ("IEM" - 0.236, Blomberg (1977)), and due to a minor extrinsic mortality factor which summed up effects of occasional heavy rain, abandonment of nest and death of the female ("MEEG' - 0.072, Blomberg (1977)). These were all observed in the field. The simulated hatch was divided by 2, to produce equal numbers of female and male hatch- lings ("FHATCH' and 'MHATCH", respectively). When hunting was simu- lated, MHATCH was used in calculating the size of the male cohort as age classes of hunted males differed somewhat from those of hunted females due to greater growth rates in males (Graham 1968, 1976, 1977). After that (under comment "EACH AGE CLASS 18 NOW ADVANCED ONE YEAR.') each age class, beginning with the previous year's hatchlings, was advanced 1 year, to add the present year's hatchlings into the population. This was done only with age classes of females (FPOP(K)) when hunting was not simulated. At this point, if hunting were opted for, the program added up and printed the number of 4- to 7-year old 33 females, and the number of 3- to 5-year old males. The total hunted cohort was obtained by adding the huntable males and females. Hunting was simulated on males and females separately, after which the total hunt was figured and printed. Cannibalism on the young crocodiles (Cott 1961, Pooley 1969b) was assumed significant in the first 3 years of life. Graham (1968) implied that nearly all young around North and Central Islands in Lake Turkana, Kenya, might be cannibalized, due to virtual lack of shelter. While field data on rates of cannibalism and knowledge of its impact on the crocodile population on the Okavango River were lacking, it was believed that at low water levels the young crocodiles would be forced into the main channels. There large numbers would fall prey to older individuals. During floods it was believed that the cannibalism rate will markedly decrease due to formation of extensive sheltered areas. An entirely hypothetical approach was used, namely "F3Ml" (Figure 8). It was a simplified adaptation from Nichols, Viehman, Chabreck, and Fenderson (1976), which computed from a given water level a corres- ponding multiplier effect on the assumed normal cannibalism rate of 6%. These authors' value of 4.65 was used in severe drought, in diagramming F3Ml, though for a water level of -1.3 m. Therefore the slope of F3Ml is only half that of their multiplier function. A multiplier function of some type seemed justified in view of the density-dependent nature of predation (Emmel 1973). If the water level index (FLAG) were not 0, i.e., drought or premature flood occurred, the value of the multiplier that affected cannibalism, F3Ml, exceeded or fell below 1, respectively. The actual value of F3Ml was obtained by again calling function subprogram TABLIE. 34 IVIJLTIPLIER Figure 8. Multiplier function for the cannibalism rate on young croco- diles, in relation to water level (F3M1). The normal water level is designated by 0, where the multiplier equals 1. 35 If FLAG equalled 0, however, F3Ml equalled 1, and TABLIE was bypassed. The 0- to 2-year old crocodiles were subjected to cannibalism by 19- to 65-year old males and 37- to 65-year old females (under comment 'CANNIBALISM FIGURED ON THE 0-2-YEAR OLD CROCODILES”). The age dif- ference was due to the males' greater growth rate, yielding an average length of 1.12 times the length of the females in any given age class (see Graham (1968) for probable age classes). In this model, 19-year old males and 37-year old females had attained a length of 290 cm. This was chosen as a minimum length of canni- bals, because Cott (1961) recorded only 2 of 17 cannibals as under 300 cm long. The total kill of young crocodiles, 'TOTKIL', was obtained by use of the size of the cannibalistic cohort ('PREDPOP'), F3Ml, a variable ”M2“ equal to 0 (if the 0-2-year old crocodiles numbered under 500) or 1 (if they numbered at least 500) or 3 (if the number of nesting females reached 1,360, which was thought at first to saturate the nesting areas), and the assumed constant cannibalism rate (“NORPRED") of 0.06. The result was divided by 2, as the program was primarily tracking females. Sixty percent of the value of TOTKIL was assigned to the 0-year old females, 30% to the l-year old females, and 10% to the 2-year old females in figuring the cannibalism on the 0-2-year old cohort. When hunting was simulated the number of cannibalized males were set equal to that of cannibalized females, and the same rates of TOTKIL were applied separately, to the respective age classes of males. Figuring the size of the cannibalized cohort involved multiplying the original size of each age class by its respective PSURV, subtracting the 36 portion resulting from the appropriate value of TOTKIL, and sub- tracting the hunting kill (always 0 in cannibalized age classes). The cohort size of females not cannibalized was calculated in the same way, by age class, but without any percentage of TOTKIL. Next the population size for the year was figured by adding the female and male cohorts. During simulated hunting (under comment "FIGURE TOTAL POPULATION FOR THE YEAR.'), the size of the 0- to 2-year old male cohort, and of the non-cannibalized cohort, were figured in the same way as their respective female counterparts. Then the popula- tion size for the year was obtained by adding all the male and female age classes. Toward the end of the main do loop (under comment “PRINT INFORMATION AND RESULTS FOR.YEAR PROCESSED.') much of the infor- mation that was acquired for the year was printed. In case of simulated hunting, the annual harvest was printed. Then, the following information was printed if needed: number of females in each age class; number of nesting females; total number of croco- diles; values for KK, FLAG, F1, F2, F3M1, M2, and WLEV; and values for the total number of eggs, hatch of females, total number of 0- to 2-year old crocodiles, number of cannibalistic crocodiles, and the kill of 0- to 2-year old crocodiles. At this point 1 iteration of the main do loop was complete. When the 300 iterations were completed, the population size ('ATPOP') and the number of nesting females ('ANNFEM”) were listed for each year. Then the program terminated. TABLIE, the function subprogram sometimes called for 37 determining the value for F1 (the percent egg mortality owing to premature flooding) and the value for F3Ml (the multiplier affecting cannibalism on 0- to 2-year old crocodiles) operated by interpolation from an array (dummy argument) of numerical values. Two such arrays were entered in the beginning of the main program as 'VALl' (used in obtaining F1) and 'VAL3' (used in obtaining F3Ml). Given a numerical value for "VAL”, the dummy variable in TABLIE corresponding to VALl and VAL3 in program CROC, TABLIE inter- polated to find a corresponding value for F1 and F3M1. An essential feature of TABLIE was that it did not extrapolate beyond the range of the values given to VAL. The rationale was that there must be limits to VAL, as neither flooding of eggs nor canni- balism on 0- to 2-year old animals can exceed 100%. Furthermore, in the latter case, a fixed ratio of rate of cannibalism to rate of production of adults was assumed. TABEXE, the function subprogram called in determining a value for F2 (percent egg mortality due to predation by monitors) also operated by interpolation from an array (dummy argument) of numerical values. This array was entered in the beginning of the main program as 'VAL2.” Given a numerical value for VAL, the dummy variable in TABEXE corresponding to VAL2 in program CROC, TABEXE interpolated to find a corresponding value for F2. Unlike TABLIE, TABEXE extrapolated beyond the range of values given to VAL when necessary, before interpolating. The rationale was the assumption that the Nile monitor population can expand without bound relative to the number of crocodile nests or eggs. They must find other sustenance during the many months that few or no 38 crocodiles nest. A working model was produced, and the population size, resulting from no environmental disturbance, was graphed. Also, the effects of 2 sources of disturbance on the population were studied. The first was consecutive years of extreme water levels, and the second was different intensities of hunting. To simulate consecutive years of extreme water levels, 4 con- secutive years of droughts every 50 years were induced, for the duration of the program. Inter-drought intervals of 20 years were also simulated. Finally, the population was subjected to premature floods on the same schedules. Population sizes resulting from the latter 2 simulations were also graphed. Several simulations, to test harvesting strategies consisting of minimum numbers of 300 and 500 at 3 different efficiencies, 0.3, 0.4, and 0.5 were made. Resultant population sizes were graphed with that resulting from no environmental disturbance. Simulated hunting took males and females according to their relative proportions in the 120-190 cm length range, as it is impossible to sex these animals without cloacal inspection (Graham 1976, 1977). The hunting kill was at this time additive to natural mortality. ALTERATIONS A number of alterations were made following the above simulations, but prior to testing of the simulation for sensitivity to altered data for specified parameters. It was felt that these alterations produced a more realistically operating model. The statements effecting simulated hunting, originally on 7 sets 39 of cards, inserted correctly in the deck, were consolidated into 3 subroutines, "HUNCRl', 'HUNCR2", and ”HUNCRB". The first printed out the year number and advanced each age class of males 1 year. The second printed the size of the huntable cohorts of both sexes, added these numbers, and multiplied the sum by EFFIC. The product was "HUNT“, the actual numbers killed, which was also printed. HUNT was partitioned into numbers of each sex, and lastly numbers in each age class of males and females. This subroutine omitted hunting if the size of the huntable cohort did not exceed a specified minimum number (300), 'NONHUNT' (which replaced MINHUNT, mentioned earlier, on the cards), and omitted hunting of either sex if its huntable cohort size did not exceed 0. The last subroutine, HUNCRB, set the number of cannibalized males equal to that of cannibalized females, by age class. Then it subtracted the number cannibalized and the number killed by hunting from respective age classes of the male cohort. The sub- routines were accessed by the logical parameter 'CRHUNT”. In the process above, 2 variables were eliminated from sub- routine HUNCR2, i.e., 'FTIAGG” (proved unnecessary), and THUNT (redundant of HUNT), printed at the end. The 2 remaining statements in this last set, "IF(M.LE.10) GO TO ...' and "IF (M/50*50.NE.M) GO TO I..', were incorporated in program CROC a few lines below comment “PRINT INFORMATION AND RESULTS FOR YEAR PROCESSED.” to be accessed during simulated hunting (CRHUNT - .TRUE.). The model was run at this point with and without.simulated hunting (CRHUNT - .FALSE.), and the resulting population sizes and numbers of nesting females were identical, respectively, to those of prior simulations. Another logical parameter, 'INPRINT', was inserted into the 40 program, under comment 'INITIALIZE PARAMETERS.'. Its purpose was simply to include (set at 'TRUE'), or exclude (set at 'FALSE”), all statements beginning with 205, and ending with 305, which governed the printing of number of females in each age class, number of nesting females, etc., mentioned earlier, which often constituted a cumbersome amount of information. The population size remained identical in both test runs, and to population sizes in previous simulations‘without‘hunting. Next, 3 statements making possible the postponement of hunting for 10 years (or any number of years desired) were added directly below the first statement in the main do loop. First "CRHUNT - .TRUE." was moved there followed by 'IF(CRHUNT) 103,104" and "103 IF (M.LE.10) CRHUNT - .FALSE.'. The reason was the 10-year ban on hunting crocodiles, proposed by BGI (P. Becker 1974, pers. comm.), which began in January 1975. Again test runs with and without simulated hunting were made, and the resultant population size and number of nesting females were identical to those from previous runs without hunting, and reasonable if different from those of previous runs with simulated hunting. Next, hunting mortality was made to supersede natural mortality, up to a point. This alteration is based on Errington's (1945) threshold of security hypothesis, as elaborated upon by Romesburg (1981) and other authors. In case hunting mortality (FHKIL(K) in program CROC,'MHUNKL(K)” in subroutine HUNCR3) were less than natural mortality ('FPOP(K) * 'NATMORT(K)" in program CROC, "MCOHORT(K)' * 'NATUMOR(K)" in subroutine HUNCR3), hunting mortality was made entirely supersessive of natural mortality. A 41 simple, mathematically correct treatment would be to set FHKIL(K) and MHUNKL(K) equal to 0, as if no hunting had taken place. How- ever, this would make the model logically self-contradictory at these points, so a set of 3 replacement statements were written, to more realistically model what happens. The first of these replace- ment statements calculated an increased value for PSURV(K) and its counterpart ”CHANSRV(K)“, in subroutine HUNCR3, as survivors of the hunting efforts, in each hunted age class, would have a higher probability of survival to the next age class if hunting mortality were supersessive. The second replacement statement used the resultant enhanced survival rates in calculating a higher value for the sizes of the hunted age classes, FPOP(K) and MCOHORT(K). From these the number cannibalized (if any), and the harvest, were sub- tracted. The last replacement statement used the new values for PSURV(K) and FPOP(K), and CHANSRV(K) and.MCOHORT(K), to restore the original values of PSURV(K) and CHANSRV(K) respectively. This would prevent cumulative error in the values for these variables. The replacement statements were preceded by descriptive comments, placed below statement 112 in program CROC and below statement 123 in sub- routine HUNCR3. In case hunting mortality equaled or exceeded natural mortality, it was made to supersede 95% of the natural mortality. Beyond that, hunting mortality was additive. This was done by calculating enhanced values for PSURV(K) and CHANSRV(K), though in a different way from that above, in program CROC and subroutine HUNCR3, respec- tively. Next, values for FPOP(K) and MCOHORT(K) were calculated, based on enhanced values for PSURV(K) and CHANSRV(K), respectively, 42 from which numbers cannibalized (if any), and numbers harvested, are subtracted. Thereafter the original values of PSURV(K) and CHANSRV(K) are reinstated. These replacement statements were preceded by descriptive comments, placed below the previously described sets of 3 replacement statements. A short test run without hunting (CRHUNT - .FALSE.), with 50 iterations ("'IRNLGTH' - 50'), was then done, which gave values for population size and number of nesting females identical to those of any previous run with no hunting. Then CRHUNT was set at .TRUE., and IRNLGTH at 300, for a full test run. The population size and number of nesting females became greater with supersessive hunting mortality, in the long run. The value of PERBRD for age class 17 (16-year old crocodiles) was originally and erroneously 1; it was changed to 9 in keeping with the trend of the data set. No change in the values for the population size and number of nesting females resulted. Experimentally, the first numerical value of PSURV (i.e., "PSURV(1)') was raised from 42.3 to 100.0 in the beginning of the program. The resulting population curve was used to show the main method of presenting results, and to make comparison with a curve resulting from lowering survival rates of juveniles (Figures 12 and 18, respectively). The value of PSURV(l) is the probability of sur- vival to the hatchling stage (0-year old crocodiles). Because all known mortality factors involved here were applied prior to the hatch, keeping a value of less than 100.0 for PSURV(l) is not realistic; it implies influence of mortality factors that do not exist. In other words, the hatch must equal the number of 0-year 43 old crocodiles in the population. (It is the value for PSURV(2) that gives the probability of survival to age 1, and so forth.) Time did not permit experimentation with the value of 100.0 for any other simulations. When hunting was not simulated, the number of males in the population remained at initialized values. This error was corrected by inserting do loop 114, which set the number of males in each age class equal to their female counterparts, toward the end of each simulated year. The entire program is presented in Appendix A. Lists of variables in program CROC, in function subprograms TABLIE and TABEKE, and in subroutines HUNCRl, HUNCR2, and HUNCR3 are in Appendix B (Tables 11-16). SENSITIVITY TESTING The present numerical values for some parameters in the program are general estimates, which should be replaced with data obtained in the field. The parameters are initial population size, initial age structure, age-specific percentages of females nesting in a given year (PERBRD), age-specific clutch sizes (CLUTCH), age-specific survival rates (PSURV) beyond age class 6, and growth rates of crocodiles, (which do not appear directly in the model, but are expressed in age spans cannibalized, initial ages of cannibalistic behavior, initial age of egg laying, and age spans hunted). Acqui- sition of field data requires that the model proves sensitive to altered hypothetical data, for each of the mentioned arrays. Time, money, and energy should not be allocated for obtaining field data to which the model is unresponsive. With demonstrated sensitivity, 44 the entry of field data would make the model a more realistic, and a more reliable guide regarding management of the Okavango crocodile population. The population size resulting from each sensitivity test was graphed against time in years. This was done via library program 'EZGRAPH', at the Computer Center, Michigan State University. Initial Population Size The initial (1975) population size, entered as 9,730 in the model may well be an overestimate. Therefore it was felt necessary to use a lower estimate, of 7,858 and test for sensitivity of the model. This estimate was based on a somewhat larger estimate of the proportion of sexually mature females in the 1974-75 hunting kill (0.184), made in an attempt to lower the population size suffici- ently to obtain a number of hatchlings closer to the estimate from the field, of 2,730 (Blomberg 1977). Also an estimate higher than 9,730 by the same percentage (19.2), i.e., 11,598, was used. These population estimates were halved to get 3,929 and 5,799, respectively, as totals for the numerical values of variable FPOP (the female por- tion of the population). The age structure of the population remained unchanged. In calculating and adding the number of individuals in each age class, the total for FPOP for the lower population estimate actually became 3,920, a deviation of -0.2% from 3,929. In the same way the total for FPOP for the higher population estimate actually became 5,807, a deviation of +0.1% from 5,799. The resultant output of population size was graphed with that resulting from the originally used FPOP, which totaled 4,865 (half of 9,730). 45 Initial Age Structure Another parameter to which sensitivity to altered data was investigated was the initial population's age structure. During this testing the size of the initial population was held constant. Alterations of the poulation's age structure were effected on the data for variable FPOP. Alterations were: (1) an age structure in.which the number of individuals in different age classes was somewhat intermediate between the the original one and a perfectly even structure. In the original structure roughly 98% of all indi- viduals were in the 14 youngest age classes (ages 0-13), while in the present one this percentage was spread out into the 28 youngest age classes (ages 0-27). The total number of individuals was 4,857, a deviation of -0.2% from the original 4,865 for FPOP. (2) An even structure; each age class contained virtually the same number of individuals (i.e., 47 of the age classes each contained 74 indi- viduals, and were evenly interspersed among the remaining 19, each of which contained 73 individuals; the total number of individuals was, as originally, 4,865); and (3) an inverted structure in which the 28 youngest age classes contained either 0 or 5 individuals (in 15 of these age classes) and the remaining 38 age classes held individuals, amounting to 98.5% of the total, at progressively greater numbers with age (the total number was 4,868, a deviation of +0.06% from the original 4,865). A number of inverted age structures had been tried prior to the one used. Some such stuctures resulted in seemingly negligible response in the curve for population size, and several (one being the exact reversal of the original structure) resulted 46 in error messages (”indefinite operand”) on the computer terminal, indicating that there were too few reproducing individuals to maintain the population. Another less radically top-heavy structure (the exact reverse of that having about 98% of individuals in the first 28 age classes) produced such a low population curve that the cursor failed to complete graphing on the terminal screen. All the input data for this sensitivity test are listed in Table l. Age-specific Percentages of Females Nesting in a Given Year The percentage of females nesting in each age class (PERBRD) should, if the program is realistic, affect the simulated repro- ductive rate. It was believed that females begin laying eggs at age 10, on the Okavango River, and this was the initial age in the model. Four sensitivity analyses of the model to changed values of PERBRD were tested for by entering (l) the original values in the program, but increasing from 66.8% to 80.0% beginning at age 37; (2) the original values, but with a decrease from 66.8% to 0.0%, beginning in age class 51 (as there may be a decrease of ovulation in the oldest females (Graham et a1. 1976)); (3) values higher by 15% than the original ones; and values lower by 15% than the original ones . Age-specific Clutch Sizes The next procedure was to test the model's sensitivity to changes in age-specific clutch size. The data for variable CLUTCH is given in the program as the cube root of clutch size. The cubed numerical values were increased, and decreased by 15%, to form 2 new data sets. Thereafter the cube roots were obtained for the values of 47 Table 1. Various initial age structures entered into the model, with initial population size held constant. Numerical values are numbers of females, i.e., data for variable FPOP. FPOP Age Original Other nor- a Even Inverted class structure mal structure structure structure 0 2,465 1,972 74 5 1 1,043 1,015 73 0 2 525 575 74 0 3 280 349 74 5 4 216 266 74 0 5 56 133 74 0 6 34 101 73 0 7 ' 26 69 74 5 8 12 71 73 O 9 12 49 74 5 10 15 24 74 O 11 4 13 74 5 12 4 12 74 O 13 15 15 73 5 14 7 16 74 O 15 4 10 73 5 l6 . 7 11 74 5 l7 4 7 74 5 18 4 8 74 0 l9 4 11 74 5 20 4 10 73 O 48 Table 1 (cont'd.). FPOP Age Original Other nor- Even Inverted class structure mal structure structure structure 21 4 4 74 5 22 4 4 73 0 23 4 4 74 5 24 4 4 74 0 25 4 4 74 5 26 4 4 74 5 27 4 4 73 5 28 4 4 74 6 29 4 4 73 7 30 4 4 74 6 31 4 4 74 6 32 4 4 74 7 33 4 4 74 6 34 0 0 73 6 35 4 4 74 7 36 4 4 73 6 37 4 4 74 12 38 4 4 74 17 39 4 4 74 36 40 4 4 74 41 41 0 0 73 45 42 4 4 74 37 49 Table 1 (cont'd.). FPOP Age Original Other nor- Even Inverted class structure mal structure structure structure 43 0 0 73 37 44 4 4 74 49 45 0 0 74 39 46 4 4 74 46 47 O 0 74 53 48 4 4 73 55 49 4 4 74 54 50 4 4 73 75 51 0 0 74 53 52 4 4 74 68 53 0 0 74 75 54 4 4 74 113 55 0 0 73 89 56 4 4 74 135 57 0 0 73 156 58 4 4 74 212 59 0 0 74 200 60 0 0 74 254 61 O 0 74 296 62 4 4 73 396 63 0 0 74 478 64 0 0 73 688 50 Table l (cont'd.). FPOP Age Original Other nor- a Even Inverted class structure mal structure structure structure 65 4 4 74 927 Totals: 4,865 4,857 4,865 4,868 a In this structure approximately 98% of the individuals are stretched into the first 28 age classes (ages 0—27), in contrast to being only in the first 14 age classes (ages 0-13) in the original structure. 51 these data sets, and entered into the model. The population sizes for different clutch sizes were graphed with those resulting from the original clutch sizes. Age-specific Survival Rates (PSURV) for the various age classes were calculated for several simulated years, from printout showing the population's age structure from the program. The percentages were plotted, and curves were fitted to the points. Percentages based on fewer than 30 indi- viduals in an age class were discarded. Some value sets had enough age classes indicating a 0% chance of survival to make any reasonable curve unobtainable. For the first tests with altered data for PSURV, only the rates through age 20 were changed. Figure 9 shows the curves that were obtained and found workable, and Table 2 gives values from these curves and the individual's probability of survival to a given age. The survival rates for simulated year 50, somewhat higher than those of the original PSURV (listed in program CROC), and with an individual probability of survival to age 20 of 4.5% (Table 2) were entered. Blake and Loveridge (1975) believed an individual's chance of survival to reproductive age to be from 1% to 5%. Values inter- mediate between those for simulated years 70 and 80 were calculated and graphed, and entered into the model. The probability of an individual's chance of survival to age 20 was 0.5%. Later, asymptotic values for PSURV (age classes 21-50, see Figure 9) were changed from 99.0% to 95.0% and 90.0% and entered, 52 mm om _ .Hoooa ecu coca voumuco mommy Hm>a>usm msoaum> wcaucomoudou mm>uso m3 mm om we oe mm om mu om mu _ _ _ _ _ _ _ _ _ n: _ m _ wm4_zm>:fi zo Pz~uon can no Essasaa a as aocowu«umo wedges: mo m~o>o~ aneuue> Ou oncoqoou one .ooconuauuwo Heucoecouw>co Assess: usozufiz ouae coausasdoe mo vocab m pom . 1omm com oma cod om o o «mflmuuflnuafluflu. ....l.....u.. nu...” mun." wind ”1...... and 4.44.13.13.43... h0.1.1.11”. .4114... .1... 1 a W Am.o 1.1. .s.o....- .m.o----- ".uHaamv uzsazsx .w . a 1 . ca zoaesozou n ommmsemsozs . O N 000'I X 3ZIS NOIlVWHdOd .o~ shaman 67 .eueoa om >uo>o moooau use munwsouv no cues» o>qusoomcoo q ou ouwe coauaasmoo mo uncommom .~_ ouswqm Em; oom omm oom oma 03 cm 0 o a .. IO .. 0 a? .4 u no mood . .. . _m Is .. . fl OH W a I . m ... ... s w .... 112.25 H. vs. . . . . .. . . X s. . — I as, \\ r T— .o o s. . co ‘ C II 0 \ t r a a . . . . a x . .uN mw . a . a. . . a, s r 0 s a . . . < a s. . .. . fl an \ o a c U \ o . o s .2 . .. s 1 s ass '1. 68 cohort appeared unaffected by the drought and flood conditions. The water level simulations showed that the population size was more responsive to floods than to droughts. Premature floods caused extensive destruction of the eggs, but had little other effect. Droughts, however, should mainly affect juveniles by inducing intensi- fied cannibalism and other predation. Although predation may be significant, the number of juvenile crocodiles lost during drought was small compared to the number of eggs lost during severe floods. Thus, the model indicates that factors affecting eggs effect greater changes in the population. Hunting At a minimum of 300 harvestable crocodiles (120-190 cm long), the population size reacted similarly at all 3 hunting efficiencies (Figure 10). Smaller oscillations occurred with increasing efficiency, but all 3 tended toward a level of 1,400 animals. At a minimum of 500 harvest- able crocodiles the population fluctuated around 2,000. The best yearly hunt was realized at an efficiency of 0.3, at the 300 minimum, which also gave the fewest years without hunting (Table 5). SENSITIVITY TESTING The model's reliability and accuracy as a management guide should increase with entry of field data for a number of parameters. Pre- requisite to the entry of field data, however, is to ascertain that the model is sufficiently responsive to altered hypothetical data, for the parameters, to justify the time and expense of the field work. The response of the model to changed hypothetical data was tested 69 Table 5. Harvests of crocodiles under tested hunting schemes. Minimum number of Total Mean Number of huntable a harvest annual years of crocodiles Efficiency (300 yr.) harvest no hunting 500 0.30 24,700 82 164 500 0.40 23,700 79 192 500 0.50 23,200 77 223 300 0.30 26,000 87 85 300 0.40 24,500 82 137 300 0.50 23,800 79 180 a Total length = 120-190 cm. 70 following the alterations described in the previous chapter. The results of the testing follow. Two groups of parameters can be recognized, according to whether they indirectly or directly affect the number of young produced, and the number surviving to the first reproductive age and beyond. The first group changed the time of attainment of equilibrium phase, but had negligible effect on the mean value of that phase, of the popu- lation curve. Parameters in this group were initial population size, initial age structure, age-specific percentages of females nesting in a given year (PERBRD), and initial age of egg laying (an expression of individual crocodiles’ growth rates). The second group noticeably changed the time of attainment of equilibrium phase (1 exception) and the mean value of the equilibrium phase. In some cases, however, the survival rates were so low that the population curve dropped and remained below initial population size. This group included age- specific clutch sizes (CLUTCH, which in effect mimics survival rates), age-specific survival rates (PSURV), initial ages of cannibalistic behavior (time of attainment virtually unaffected) and age spans hunted (the last 2 being expressions of individual crocodiles' growth rates). Figure 12 exemplifies the primary way of analyzing the model's output. This curve results from no changes in the data (other than the alterations described in the preceding chapter, including PSURV(l) set at 100.0), and no simulated hunting. The mean height of the equi- librium phase (65,900) and the year of attainment (78) are indicated on the axes. With PSURV(l) set at 42.3, as in most simulations, the equilibrium values averaged 26,500, and the year of attainment was 96. Table 6 summarizes effects of varied data for the mentioned 71 Figure 12. Main method of presentation of output from the model. With unchanged data for all parameters (except that PSURV(l) = 100.0) and no simulation of hunting, the equilibrium phase averages 66,000 individuals; it is reached in 78 years. 72' com omN cow p _ m and _ oo— om o on ON on ow on on Oh .Ns ssasaa 000'I X 3218 NOIlVTHdOd 73 Table 6. Summary of response of population curve to changed data in selected parameters. Timing of Level of equilibrium equilibrium Measure of Papulation Measure of Parameter Treatment Year sensitivity size sensitivity Initial popu- 7,858 110 0.76 26,400 0.02 lation size a 9,730 96 -- 26,500 -- 11,598 90 0.33 26,600 0.02 Initial age wide pyramid a 96 -- 26,500 -- structure ' Narrow pyramid 87 -- 26,700 -- Even 9 -- 26,000 -- Inverted pyra- 88 -- 26,700 -- mid Age-specific Maximum: 56.8 122 1.81 26,200 0.08 percentages a of nesting Maximum: 66.8 96 -- 26,500 -- females (PERBRD) Maximum: 76.8 85 0.76 27,000 0.13 Age-specific Range: 23-55 h 120 1.67 22,100 1.11 clutCh size a (CLUTCH) Range: 27-65 96 -- 26,500 -- Range: 31-75 h 89 0.49 31,100 1.16 Age-specific survival rates (PSURV) - First 21 Lower c -- -- 1,000 14.4 age classes a Unchanged 96 -- 26,500 -- Higher ° 64 8.15 36,600 9.32 - Asymptotic d 95% -- -— 2,600 22.3 (age classes 22-51) 93% -- -- 1,800 15.4 Table 6 (cont'd.). 74 Timing of Level of equilibrium equilibrium Measure of Pepulation Measure of Parameter Treatment Year sensitivity size sensitivity - Age classes Unchanged a e 78 -- 65,900 -- 5-10 mean: 89.3 Lowered -- -- 6,600 3.97 mean: 69.1 Growth rates of crocodiles f - Initial ages M 11, F 18 100 0.09 22,500 0.32 of cannibal- a istic behav- M 19, F 37 96 -- 26,500 -- ior f M 35, F 46 96 0.00 30,800 0.30 - Initial age 18 236 1.82 25,600 0.04 of egg laying 13 123 0.94 25,500 0.13 10 a 96 -- 26,500 -- - Combined can- 0-10; M 35, 237 -- 27,300 -- nibalism and F 46; 18 initial age of egg laying 0-3; M 11, 158 -- 23,400 -- F 18; 13 0-2; M 19, a 96 -- 26,500 -- F 37; 10 - Age spans M 2-4, F 3-6 a -- -- 1,800 -- hunted M 4-7, F 5-9 -- -- 2,700 -- M 11-19, F 11- -- -- 2,700 -- 20 - Combined can- 0-2; M 19, a -- -- 1.800 -- nibalism, F 37; 10; initial age M 2-4, F 3-6 of egg lay- ing, and age 0b3; M 11, -- -- 2,600 -- spans hunted F 18; 13; M 4-7, F 5-9 75 Table 6 (cont'd.). Timing of Level of equilibrium equilibrium Measure of Population Measure of Parameter Treatment Year sensitivity size sensitivity 0-10; M 35, -- -- 2,400 -- F 46; 18; > F 11-20 a Values in original simulation. b Values changed by 152 from the original ones. c Means of deviations, from original values, for lower and higher rates, were 6.72 and 4.12, respectively. dThe original value was 992. e PSURV(I) was raised from 42.3 to 100.0. Unweighted means of males' and females' deviations, from original values, for higher (Graham 1976) and lower growth rates (Graham 1968), were 46.82 and 54.22, respectively. 76 parameters. The decimal fractions by which year of attainment of equilibrium phase, and the mean value of the equilibrium phase, differ due to altered data, from their counterparts resulting from original data, were calculated whenever feasible. Likewise, the decimal frac- tions by which altered input data for each parameter differ from the original data were calculated, whenever quantification was possible. For all sensitivity tests in which both fractions were obtainable, the former fraction was divided by the latter to obtain a measure of sensitivity (Johnson and Sargeant 1977). A feature common to all population curves, except that resulting from an even age structure (i.e., 73 or 74 individuals in each age class, Figure 14), is a dip that begins immediately and lasts 24-123 years. Its depth, 1,800-3,800, is well below initial population size. Its main cause may be the low number of sexually mature individuals in the population's age structure for year 0. Fourteen (25%) of the 56 age classes of sexually mature females contained no individuals, and only 2 of the 42 remaining age classes held more than 9 individuals. Also relevant to the initial dips may be that in most simulations only 7% of the females survive to age 10, and only a fraction of these lay eggs. This percentage of survival is close to the hypothesized span of 1-5% (Blake and Loveridge 1975). When the largest (reproductive) animals are harvested first, followed by progressively smaller indi- viduals, as has happened on the Okavango River and in other areas of Africa (Cott 1961, Graham 1976, Loveridge 1980), an initial dip might well occur before reproduction can begin to surpass natural mortality. Possibly such a dip occurred in the Okavango crocodile population shortly before or after 1969, when the late B. Wilmot abandoned his 77 destructive 12-year hunting concession (Taylor 1973, Graham 1976, Loveridge 1980). Graham (1976) stated that the cohort of breeding females has steadily increased during 1974-76. Therefore any such dip admittedly coincides poorly with those in the diagrams that follow. The initially low number of reproductive individuals also appears to be a factor in the very delayed equilibrium phase; at 78-237 years it exceeds the turnover time of roughly 60 years. (Within a given species, the percentage by which attainment of equilibrium exceeds, or falls short of, the turnover time might be a useful indicator of the relative size of the breeding cohort.) Exceptions are in Figures 14 and 17a, and they seem to rule out any unexplained artefact of the computer program. The rather gradual increase relative to age, in percentage of nesting females, is another factor delaying attainment of equilibrium phase. This can be inferred from Figure 2, and the factor is well established in Cott (1961:255), where percentage of nesting females increases directly with size, and therefore, presum- ably with age. In every diagram that follows, the solid curve results from unchanged data for each parameter. The solid curve is in any case the standard of comparison for each test of the model's sensitivity. Numerical data for all curves are in Appendix C (Tables 17-46). Values for consecutive years are found by reading down a column. Initial Population Size A population estimate of 7,858 for year 0 in the model, which is possibly more accurate than the originally used value (9,730), was used to ascertain response of the simulation. Likewise an estimate 78 higher by the same percentage (19.2), 11,598, was used. Age structure of the population remained the same with each estimate of size. The higher estimate of population size resulted in earlier attainment of equilibrium phase, by 6% (from year 96 to year 90), and the measure of sensitivity is 0.33. The lower estimate of population size delayed this attainment by 15% (year 110), effecting a measure of sensitivity of 0.76. Regardless of estimate, the equilibrium phases of the curves appear virtually identical (Figure 13). Numerical values for popula- tion size at the original, the lower, and higher estimates of initial size, are in Tables 17, 18, and 19, respectively. Initial Age Structure Equilibrium phases of resultant population curves seem virtually identical, but noticeable differences in initial growth resulted from change in the population's age structure at year 0, with size held constant (Figure 14). In the unchanged age structure, which forms a wide pyramid, roughly 98% of all crocodiles were in the 14 youngest age classes (ages 0-13). A narrower pyramid, resulting from redistri- bution of this percentage into the 28 youngest age classes (ages 0-27) resulted in an earlier attainment by 9% (year 87) of equilibrium. The curve resulting from the even age structure resulted in earlier attainment of the equilibrium phase by 91% (year 9), attributable to a larger proportion of females of reproductive age. The inverted age structure (97% of crocodiles concentrated in the 28 oldest age classes) caused the population curve to reach equilibrium phase earlier by 8% (year 88). It is believed that the model would respond markedly to increased concentration of individuals in the very oldest 79 Figure 13. Response of population size to varied estimates of its ini- tial size. The age structure at year 0 is held constant. 80 m . 2 muswfim 8m emu cow cm: 2: cm 0 _ _ _ _ e _ o . a . [IN V. . “ml _ m sea: 1:: ,.,. __ e was; ..... _a. . d 3:528 02.4.. I 4... _...~ .. w . n .., .4 . a S m .. .l e. .n. u. s . 0 3 . . N u w u‘ ...q 1. Wu S _u ..... .2 ms . u i a - W“. X l _ .o. N I. ON ”IL __ a.“ l 0 _ m w . l . _e 1 mm _ . . .: at . . r om 81 Figure 14. Response of population size to varied initial age structure. The size at year 0 is held constant. 82 35 D # H z < a: >- — D. A C CD 0—0 L” D LLJ z (D H D: g z Z 3 < g 1— >- I U Q. U >- D z D. a: D :5 I'- LIJ v: m 1— O C! _ LL] 0: z LIJ D C! LIJ > - H < > Z 3 2 1.1.1 H e 1 1 I I ‘ I I l 'E:E-‘- i'uadl‘“: A . —--—:‘~£4JI ~“\ ' .-.—-—- ~ ‘ ___,-_-'uv ‘ a ' ~w— .----- _.-—%=$-U—- .u... ' «=1 ‘~~-- \ ms-w ”7" A T--- A 7C- ‘23115 —-—‘.fi--. .. m'?.:.— 0'8 ~ “=.-—-—-"'- «a: ---:-.-...,-—--_,,..—-3:“- a. “-4'? ‘— ,’ . :‘—-_-- _ : ‘ ’ l l D to D IO D ID a) N N F‘ "" 000'1 X 3218 NOIlV'lfldOd 300 250 200 150 100 50 YEAR Figure 14. 83 age classes, as the computer prematurely terminated several runs, due to prompt depletion of most reproductive females. It is believed, however, that a more intermediate inverted structure would instead simply delay, markedly, attainment of equilibrium. Numerical data on population size, resulting from age structures describable as a narrow pyramid, an even structure, and an inverted pyramid, are in Tables 20, 21, and 22, respectively. Age-specific Percentages of Females Nesting in a Given Year Because possibly only 2/3 of the sexually mature females appear to nest in any given year on the Okavango River, percentages of females in the model that did nest were assigned to each age class, beginning with 0.42 for those 10 years old, and gradually increasing to a maximum of 66.8 for those at least 37 years old, in construction of the model. These figures are adapted from the S-curve in Cott (1961:255), which relates percent nesting to length. For testing the model's sensitivity, the original set of data (PERBRD) was treated as follows: (1) an increase from 66.8% to 80% beginning at age 37, (2) a decrease from 66.8% to 0.0%, beginning in age class 51, (3) an increase of, and (4) a decrease of, 15%. The last 2 data sets thus had maxima of 76.8 and 56.8, respectively. The first 2 data sets resulted in little change in the population curve. The last 2 data sets effected population curves with very simi- lar values in the equilibrium phase, but with exponential phases markedly separated in time (Figure 15). Earlier attainments of equi- librium phase, by 11% (year 85), with the maximal percentages being 76.8, and delayed attainment, by 27% (year 122), with the maximal 84 Figure 15. Response of population size to different sets of age- specific percentages of females nesting in a given year. 85 MAXIMUM = 66.8% MAXIMUM = 76.8% 35 MAXIMUM = 56.8% -‘..---:::.3 .0... ‘— h.‘?~ -'.':£'§;alma‘ 3;.- -.-.;::: ~~ ~-~... \. “-f“? 7_“ .g" . f k' l T I l l D ID 0 1.0 D ID (0 N N v-d c-a OOO’I X 3ZIS NOIlVTHdOd 300 250 200 150 100 50 YEAR Figure 15. 86 percentages being 56.8 resulted. Respective measures of sensitivity of 0.76 and 1.81 were obtained. The numerical values for population size resulting from the maximal percentages of nesting females being 76.8 and 56.8 are in Tables 23 and 24, respectively. Age-specific Clutch Sizes Responsiveness to altered data on age-specific clutch sizes (CLUTCH) was gauged. Data for this parameter are derived from the cube root of clutch size, being linearly related to age of the croco- dile. This is an adaptation from Cott (1961) and Graham (1968). Comparison was made of the population curve resulting from unchanged data with those resulting from increasing, and decreasing, these values by 15%. The 2 data sets so derived, ranging from 30.8 (10- year old females) to 75.0 (GS-year old females), and from 22.8 (10- year old females) to 55.4 (65-year old females) markedly raised and lowered, respectively, both exponential and equilibrium phases of the population curves (Figure 16). As indicated, this is the result of a parameter that directly affects the number of young that in time reach maturity. The curve resulting from greater clutch sizes reached equilibrium phase earlier by a possibly negligible 7% (year 89), resulting in a measure of sensitivity of 0.49, while the curve resulting from the smaller clutch sizes delayed equilibrium by 25% (year 120), resulting in a measure of sensitivity of 1.67. The curve resulting from greater clutch sizes averaged 31,100 at equilibrium. This is an increase of 17% resulting in a measure of sensitivity of 1.16. The mean for the curve resulting from smaller clutch sizes is 22,100, a decrease of 17% resulting in a measure of sensitivity of 87 Figure 16. Response of population size to different sets of age— .specific clutch sizes. 88 :C.-‘.--.-.-‘ v_ .. — ‘ ' m ..---- - _ -~~fi-_- ~:::::: " ‘ ' H -..._ '7 Cd- _n.: _ .. *- E:::3'.- "._:=-." *“zzzzazzz'; ‘- m _ o—e ¢:§-.-:: . ' ..=’;£. ‘ u u . u . .--- :Sissh ' - —- - $2.}: 0 r I ' ‘ '—*~ ' _a-.- 7.23.1.1-..“ , , hon-'- --- - m 5.. ‘-:- D- <‘\ 93:22:1127' I ' ‘::::” 'TT?.?: vv~——— . '?--—- ."'----- A ‘ n m m Ln .-.-::.-.-.- - m, _- - -.=m— “3 '7 “9 ""‘se------- \.-",,, .— N m N con-'08:... . ‘fl ‘ . II II II '.-- — “moon-1'. “tun-- I.” “J LU w... _ . fl 2 z Z .--.‘ —-—-‘—.-l '1‘ o... “A~‘..,I— <<§ Inn-03:8: “—t —-.-—- m x W:.-.--. - 4m- c - - ‘ ..... --»- .. elm-7 . ' “-5.”.--3 "" ' '- -— ' ' —.“ I . ‘------.--- -‘- m,'_- - _ ___ _ . I 9:339!“ ‘ -~ ='-"' ..-.0---- ---T’ .I-------- 7”! I ‘ ”Ah-— <-—r‘% -‘ - ‘0 #:211111st * .Em ~--~----‘--~- - --.. , ~.-.--— .I .I : ‘UI :5332..- .3.” “Patna..- - --’ 3"" .‘-- § o.... \‘ ...~. g \ , "' 9:." Va: .‘-9~ ‘ o. ’ .‘ -1 I I j 1 ID 0 ID 0 ID N N .-o C-I 000’I X 3218 NOIlV'lfldOd 135 3C) 3C") 25“) ZEN) 1150 1130 St) YEAR Figure 16. 89 1.11, respectively. Numerical values for population size, resulting from increasing and decreasing the original values for clutch size by 15%, are in Tables 25 and 26, respectively. Age-specific Survival Rates .nggr Portions g; 92233.2; Survival Rates.--The model's response to varied age-specific survival rates (PSURV) for the first 20 years of life was tested. A set of high survival rates was obtained from the age structure in the 50th simulated year; a set of low survival rates consisted of values intermediate between those of the age structures in the 70th and 80th years. The higher survival rates, which on the average deviated from those originally used by 4%, resulted in a population curve that reached equilibrium phase earlier by 33% (year 64), effecting a measure of sensitivity of 8.15. The curve averaged 36,600 in the equilibrium phase and is thus 38% higher than that resulting from the originally used rates. The measure of sensitivity is 9.32. The popu- lation curve resulting from the lower set of survival rates, which on the average deviated from those originally used by 7%, soon dropped, to level off at 103 years. It is lower by 96%, i.e., 1,000, resulting in a measure of sensitivity of 14.4 (Figure 17a). Numerical values for population sizes derived from the age structure of the 50th simulated year, and from the age structure intermediate between that of the 70th and 80th simulated years, are in Tables 27 and 28, respectively. Investigation of the model's response to age-specific survival rates (PSURV) lower than 99.0% (i.e., 95%, 93%, 92%, and 90%) in the asymptotic portion (age classes 22-51) of the curve of survival rates 90 Figure 17. Response of population size to (a) sets of changed survival rates in the first 21 age classes, and (b) sets of survival rates lowered from 99.02 in the asymptotic portion (age classes 22—51) of the curve of survival rates. 91 JP.-. .lu uuuuuu sun 1. 1 mm manna: .. lg ' 00"""00’00 00 I? T ..... IIIIIIIII ‘50." IIIIIII 0". -0. fl IIIIIIII 0‘? ls. ............. I 0"... ............ 00‘ t 4 ll (I. .- lfllfli‘lltllflf" b33301 ..‘I. *0“. .0"'...... o 00000 H ‘~‘K.l~.~.~ ‘0 (lull| IIIIIII ’e. . -’ ’ I. ”OUEII’I‘ so IJHHMMKNNNHC sflFIOHl-I II . 11...)? .mmum.....- IV. I a..." 0‘3! .uaaauuuu f ocuhw uuuuuu nouns-amuse... iammfl-: Until? ”nunnmun-.. cdhflliflflysu oauummmmmmu... "'”"- 15...: II 0“. ”MI. 0 O IIIIN’ IIIIIII 0" .I...‘ ‘00....h: I III ’00; """I.'..- 300 -— WCHANGED RATES ----- HIGHER RATES -— LOWER RATES ASYMPTOTE . 95.02 YEAR ‘ ‘~ -OM-uom C'. l. 00 O "5 0.: 00 l 32 O 99 l I I I S O C O ----- ASYMPTOTE --- ASYIPTOTE d ooo.~ x mN_w zo_e<3=aoa 6000 5000 a 4000 3000 a \ mN_m zo_h<4=mom 300 250 J -}f‘r‘nf-"uzfif\r'zq 'f "",'}.,-"“~.. 4 200 150 YEAR 100 50 1000 Figure 17. 92 was also made. With the last value set the population size ultimately declined to below 10, and the result was not graphed. The curve for population size resulting from asymptotic values of 92.0% shows a continuing downward trend. The curves resulting from asymptotic values of 95% and 93%, which are respective deviations of 4% and 6%, stay level after an early decline, at 2,600 and 1,800 respectively. The changes represent decreases in the population level, of 90%, resulting in a measure of sensitivity of 22.3, and of 93%, resulting in a measure of sensitivity of 15.4, respectively (Figure 17b). Numerical values for population sizes resulting from lowering the asymptotic survival rates to 95.0%, 93.0%, and 92.0% are in Tables 29, 30, and 31, respectively. Constraint 29_Juvenile Survival.--As stated, Magnusson (1984, pers. comm.), from observation of the smooth-fronted caiman, and Messel et a1. (1982, 1984), reporting on the estuarine crocodile, hypothesized that survival of juveniles is reduced by aggression of adults. Therefore, lowered survival rates (PSURV) for 6 age classes of crocodiles (being 5-10 years old, hence 1.5-2.5 m long) were entered into the model, to further gauge its response. These lowered survival rates were chosen arbitrarily; their mean (69.05) deviated 23% from that (89.32) of the original values, and reduced the population size by 90%, to 6,600 (Figure 18). (For this simulation PSURV(l) was set at 100.0.) The measure of sensitivity is thus 3.97. Numerical values for population size with unchanged data (PSURV(l) - 100.0), and with lowered juvenile survival, are in Tables 32 and 33, respectively. 93 Figure 18. Response of population size to arbitrarily lowered survival rates of juveniles (ages 5-10, 1.5-2.5 m long). (PSURV(I) was in this comparison set at 100.0.) Lowered survival of juveniles is believed to result from aggression by adults. 94 m . 2 madman Dom cmN DON om“ On: 31m mmw< .mmSE 3533 .1-.. M mm._.<~_ .22530 I M .1 V H 0 N .8. Z 3 X ...... 0 _I 0 3 8 0 i 8 __ .‘ 95 Growth Rates of Crocodiles Relation §2_Cannibalism.--The differing growth rates of croco- diles in different populations should have a bearing on the age spans that are subject to cannibalism. A given variable ”TOTKIL", representing the number of cannibalized crocodiles, was originally spread over the first 3 age classes. Sensitivity of the model was tested by spreading this number over 4 age classes (ages 0-3) and over 11 age classes (ages 0-10), in accord with suggested growth rates of Graham (1976) and with low growth rates in Lake Turkana, Kenya (Graham 1968), respectively. They would, at any of these growth rates, be under 120 cm in length. Responses of the population curve ranged from 0% to slightly under 5%; sensitivity (its measures ranging from 0 to 0.1) to changes in this parameter is considered negligible. It is believed that cannibalistic behavior begins in older age classes in populations where crocodiles grow more slowly, based on Cott's (1961) data. Responsiveness of the model to changed initial ages was tested. Specifically, initial ages of 11 and 18 (males and females, respectively) in accord with Graham's (1976) suggested growth rates, and of 35 and 46, respectively, with the low growth rates in Lake Turkana, Kenya (Graham 1968) were entered, for comparison with the originally used ages of 19 and 37, respectively. At these growth rates the crocodiles would have just reached 290 cm in length at the stated ages. Simulation of earlier ages of cannibalistic behavior resulted in only slightly lower values for the exponential phase, and therefore delayed attainment of equilibrium phase by only 4% (year 100, the 96 measure of sensitivity being 0.09). No change in attainment resulted from entry of later initial ages. The mean for the equilibrium phase of the curve resulting from earlier initial ages was 22,500, a decrease of 15%, resulting in a measure of sensitivity of 0.32. Simulation of later initial ages of cannibalistic behavior resulted in an equilibrium phase averaging 30,800, an increase of 16%, resulting in a measure of sensitivity of 0.30 (Figure 19). (The changes in initial age of males and females were averaged, resulting in -46.8% and 54.2% for growth rates of Graham (1976) and of Graham (1968), respectively.) The numeri- cal values for population size at early and delayed initial ages of cannibalistic behavior are in Tables 34 and 35, respectively. Relation 22 Initial Age 2; Egg Lgyigg.--Initial age of egg laying is believed to vary inversely with growth rates of crocodiles. Initial ages of 13 (an increase of 30%) in accord with suggested growth rates of Graham (1976) and of 18 (an increase of 80%) in accord with Lake Turkana's low growth rates (Graham 1968) were entered and compared with the effect of the originally used age of 10, to gauge sensitivity of the model. With initial age of egg laying delayed to 18, attainment of equilibrium phase was delayed by 146% (year 236), resulting in a measure of sensitivity of 1.82. A delay to 13 years postponed attain- ment of equilibrium phase by 28% (year 123), resulting in a measure of sensitivity of 0.94 (Figure 20a). Respective population levels with these delays averaged 25,600 and 25,500, decreases of 3% and 4%, which, like the measures of sensitivity, may be considered negligible. This is the response of a parameter that only indirectly influences the num- ber of hatchlings and their survival rates. (The equilibrium phase representing age 10 (Figure 20a), and that representing the original Figure 19. 97 Response of population size to changed growth rates, as expressed in initial ages of cannibalistic behavior. The curve labeled "MALES 11, FEMALES 18" results from suggested growth rates of Graham (1976); that labeled "MALES 35, FEMALES 46” results from the low growth rates in Lake Turkana, Kenya (Graham 1968). 98 "IP-—- ‘3 0"-.- ‘fi‘.. ‘1 "h w- ‘fl'~._ '- HF," - ~ ’ "” -~‘ ‘1’..- “an... ‘I' .- -~d~- . ~-~ -.= — ‘3 ~ - ‘ “' Q‘“ I I “.4- ----- -- ---“ con-0:.- (23%-‘— g-..“ at... k -'-' . ,s.—-..E . - -_.___. . ::...'-. .3 ‘ 0-: :3. -mr W'I“—_.._.-.o 1 ‘-fi '1 -, '0.- ‘-—-—d . _-‘- .v’— .‘fg-‘_";‘,-Ia “‘“Q ~- 1““ --.- .Q‘--.-‘.“ C- -‘ ‘:=:::----0.,.' ‘-‘- ‘JuuafipO. —-.- ““ 'b—g— & ' _& 4— - g...‘.. ’~-~ :O’- s""- - LT" “” 3‘..- P. ‘~.‘w -_' Q---~ ~-_‘ “P I I a ._ - .——-; :kxy "" ' __. Um...- -—.‘ u:------:.‘ ’ ‘.-——- -~m3---“ * ..1 e ”‘7 3. 1 m .“_ ‘_. __.. J .--- r~00 COFH (DUO LUUU _J_J EEE UUUJ u.u. O O Chrd q—u—a U7U) UJUJ —J_J ESE 1 a I I -— MALES 35, FEMALES 45 35 “D C: “a C: N N ,_. d 000'I X 3213 NOIlVTRdOd 300 l 250 1 200 l 150 I 100 50 1'0 YEAR Figure 19. Figure 20. 99 Response of population size to changed growth rates, as expressed in initial age of egg laying, (a) singly, and (b) in combination with age spans cannibalized and initial ages of cannibalistic behavior. Initial ages of laying of 13 and 18 correspond with suggested growth rates of Graham (1976), and low growth rates in Lake Turkana, Kenya (Graham 1968), respectively. The curves labeled "10 YEARS" and "M 19, F 37; 10 YR" are identical. 100 200 250 300 YEAR 150 100 o o 11 .0 I 3 Q . 111 .116 so 1 1. . 1 "".. . Iouuuumllo 1D,, (In?! I. 0 1 In if."‘ - 1. 1 1 1 - . -H. van... 1.1 -. 5 .W11- ....n.1-1 1 1 O'- 555 I111 lllllll ai'lhll E“ u 0 ill I 'l '0 YY Y - II ”0%.. 03 8 1"”16 I9 9 ’00 0’0 11 1 DAN-I... l, o u. all. . . 0 ......... “J R R R I, r O I o ’0'...l" ..... A Y Y Y If: . . has..- ,0 -. 1. 1 . _ 2 14.86.11»... 0 as 0' “UL” . I10. 5..., 0| 1 11 ‘0'“ ’0'"””.... ‘d? O. C, I. a! v 41195661 c 7 8 6 .‘P I, 0". ’0’ 3 1 ‘ I lllll . 0‘0 o o ‘lltuuflltlu .. 4 0. Hunt“)... F. F F 1 - 1. .I. 0 m .- 11 mm 11.1“." I. O .. hi: I 6 if 0 0 1 101.50“? 11 Y .1 ...-.¢¢ Caustic-“finds! In a" ‘0‘".0 u I -‘E‘... 'N"I‘."J' ‘flflh'W‘ . IICM'O'."O an" n — 1 .- 11.11 0.4". .. 1.11....»91511111 haw.” ” . IIIII I. ’0'. IIIIIIIIIIIII debt"? 0 - J‘Iv OH-~QWIIIHIO 0”“... sthWflu‘ [fill 00 I ..... 0' CCIIUCUIHH. O “-111ui1daahnns1111ah\ 0 Y I F 1' o PIII-‘--O b. 1 .3: a.- .I 0 6 . J a a a 0 _ a a . a . 0 6 0 5 o 5 o s o s o 6 o 5 3 2 2 1. l 3 3 2 2 I I 08% x mum 2251.28 000% x MN; 20:53.5; Figure 20. 101 population size in previous diagrams, prior to rounding off mean values, differ by a mere 0.03% from reducing the number of laying age classes from 56 to 48, for valid comparison with the 2 other data sets.) Values for population curves resulting from initial age of laying at 10, 13, and 18 are in Tables 36, 37, and 38, respectively. It was felt that certain combinations of parameters pertaining to growth rates of crocodiles should also be run. Age spans canni- balized, initial ages of cannibalistic behavior, and initial age of egg laying were varied simultaneously, according to suggested growth rates of Graham (1976) and according to the low growth rates in Lake Turkana, Kenya (Graham 1968), to again test the model's response. There were again lowered exponential phases of the population curves, hence delay in attainment of equilibrium phase with the growth rates of Graham (1976) by 65% (year 158), and with the low growth rates in Lake Turkana, Kenya (Graham 1968) a delay of 147% (year 237). The former growth rates lowered the equilibrium phase to 23,400, a change of 12%, while the latter rates raised the equilibrium phase to 27,300, a negligible change of 3% (Figure 20b). The numerical values for population size resulting from the combination of age spans cannibal- ized, initial age of cannibalistic behavior, and initial age of egg laying, at the growth rates of Graham (1976), and the growth rates of Graham (1968), are in Tables 39 and 40, respectively. Relation g2 Ag; §p§§§ figiggiflunggg.--Prior to testing the model for sensitivity to changed age spans vulnerable to hunting, several alterations were made. Hunting was postponed 10 years, which had little impact on the population curve. Hunting mortality was also made to supersede natural mortality, up to a point, and this visibly 102 raised the population curve. Lower growth rates of crocodiles would delay the initial ages of vulnerability to hunting, and increase the number of years crocodiles remained vulnerable. The lower and upper length limits would be 120 cm and 190 cm, respectively. These length limits were reached at the age spans in Table 3. Hunting at the original growth rates made the population level stabilize (year 105) well below the initial popula- tion size, i.e., 1,800, a change of 93%. The effects of postponing and expanding age spans subject to hunting for both of the lowered growth rates, is a population size, averageing 2,700 when stabilized, an increase of 50% from that above (Figure 21a). Numerical values for population size resulting from age spans subject to hunting at the original growth rates, and those of Graham (1976) and of Graham (1968) are in Tables 41, 42, and 43, respectively. Smaller means for the huntable male cohort, and the harvest, but apparently not the huntable female cohort, result from lower growth rates (Table 7). If the averages of the 2 huntable cohorts are added for each set of age spans, however, a progressive decrease is evident. There is an increase in number of years during which no hunting takes place. A combination of the 4 parameters pertinent to growth rates of crocodiles was also used to test the model for sensitivity. Simul- taneous alterations of data for all 4 parameters, in accord with sug- gested growth rates of Graham (1976), and with the low growth rates in Lake Turkana, Kenya (Graham 1968), were made and entered. Where level, the curve for the growth rates of Graham (1976) averages 4% lower than its counterpart in Figure 21a, and that for growth rates of Graham Figure 21. 103 Response of population size to changed growth rates, as expressed in age spans vulnerable to hunting, (a) singly, and (b) in combination with age spans cannibalized, initial ages of cannibalism, and initial age of egg laying. The curves labeled "MALES 4-7, FEMALES 5—9" and "M 4—7, F 5-9; M 11, F 18; 13 YR" result from the suggested growth rates of Graham (1976). Those labeled ”MALES 11-19, FEMALES 11- 20" and "M 11-19, F 11-20; M 35, F 46; 18 YR" result from the low growth rates in Lake Turkana, Kenya (Graham 1968). 104 10 8 - O O O .4 x 6 - . DJ 2 —— MALES 2-4, FEMALES 3-6 m ----- MALES 4-7, FEMALES 5-9 2 1 --- MALES 11-19, FEMALES 11-20 9 4 1- " 1 5 . l ' 1‘ = E / - 9.4 :1!“ 0“ O- . a O '0 : H 0 I o .a E {‘1'} 1! 1‘. .9, z ' kl, ‘. “2:59"! 5.. 4‘15)" '11 V 2-1’1' ‘11.:11. '- 7 ' 1 “f, " 1 ' N ' ‘1 1 1 0 1 1 1 1 I 0 so 100 150 200 250 300 a YEAR 10 8 - O C) O .1 x 6 1.1.) E (I) z -— n 2.4. F 3-6; 1119, F 37; 10 m E’- ---- 11 4.7. F 5-9; 1111. F 18: 13 m 3 4 —-— M 11-19. F 11-20; M 35, r 46; 18 m a . 010.0. ”,0 E I." g: I 0‘ h on. a: 0.0"" - " .' ‘ . I1 ,1}, 11"!” 'd‘ 2 1 ' ’ r a ' . ‘ f " 1 1 1'; 1 1.? 1’ ‘ \ H 1 ,1 1 " o I 1 t 1 1 0 50 100 150 200 250 300 b YEAR Figure 21 105 Table 7. Effects of hunting different age spans on means of huntable male cohort (HMPOP), huntable female cohort (HFPOP), and harvest (HUNT), and on number of years of no hunting. Years of no hunting b Mean of a Mean of a Mean of Age spans HMPOP HFPOP HUNT No. 2 Males, 2-4 c 223 140 83 79 27 Females, 3-6 Males, 4-7 d 185 165 79 87 30 Females, 5-9 Males, 11-19 6 134 143 28 217 75 Females, 11-20 a Means are based on a sample of 59 years, beginning with year 11, then year 15, and every 5th year thereafter. b Based on all 290 years during which hunting was simulated. c Age spans at original growth rates. Age spans based on Graham's (1976) suggested growth rates for Okavango crocodiles. e Age spans based on growth rates reported by Graham (1968) for croco- diles in Lake Turkana, Kenya. 106 (1968) thus averages 11% lower (Figure 21b). The changed growth rates caused respective population levels of 2,600 and 2,400, respective increases of 44% and 33% from that resulting from the original values. The curve resulting from growth rates of Graham (1976) averages slightly higher (8%) than that from growth rates of Graham (1968) in Figure 21b, unlike the the situation in Figure 21a. Apparently, in the long run, inclusion of changed data for the first 3 parameters depresses the population curve more, negligibly in the first case, but by a considerable percentage in the second, than hunting alone can do. It appears from Figure 21 that hunting the youngest age classes lowers the population curve the most. The curve for population size labeled ”M 2-4, F 3-6; M 19, F 37; 10 YR” is nearly the same as that resulting from hunting alone in Figure 21a (labeled ”MALES 2-4, FEMALES 3-6'). (Prior to rounding the mean off to 1,800, it deviated from its counterpart in Figure 21a by -0.7%, due to reduction of the number of egg laying age classes, from 56 to 48, as in the other 2 data sets, for valid comparison.) Numerical values for population size at originally used growth rates, and at growth rates of Graham (1976) and Graham (1968), as expressed in the 4 parameters combined (48 egg laying age classes in each case) are in Tables 44, 45, and 46, respectively. The huntable male cohort and the harvest again diminish with lower growth rates, while the mean of the huntable female cohort does not (Table 8). As before, a progressive decrease becomes apparent if the means of the huntable male cohort and the huntable female cohort are added for each growth rate. The 3 values above, for growth rates of Graham (1976), are noticeably lower in the present table, as is the mean for harvest at growth rates of Graham (1968). The number of 107 Table 8. Effects of different growth rates, simultaneously expressed in age spans cannibalized, initial ages of cannibalism, initial age of egg laying, and age spans hunted, on means of huntable male cohort (HMPOP), huntable female cohort (HFPOP), and harvest (HUNT), and on number of years of no hunting. Years of no hunting b Mean of a Mean of a Mean of Growth rates HMPOP HFPOP HUNT No. 2 Original 223 140 83 79 27 According to C 165 151 58 141 49 Graham (1976) According to d 134 145 16 252 87 Graham (1968) a Means are based on a sample of 59 years, beginning with year 11, then year 15, and every 5th year thereafter. b Based on all 290 years during which hunting was simulated. c Suggested rates for Okavango crocodiles. Reported rates for Lake Turkana, Kenya. 108 years of no hunting increases, though at a somewhat greater rate than in Table 7. CHAPTER 5 DISCUSSION PRELIMINARY SIMULATIONS Normal Conditions The population level of roughly 21,000 is comparable to an earlier estimated prehunting population of 28,400, obtained by adding the initial population estimate (9,730) to the kills in Table 9. It was initially assumed that Wilmot took an estimated 14,400 crocodiles, instead of the present entry, making the total kill only 18,640. If Wilmot took about 10,000 crocodiles, as believed by Graham (1976, 1977), the prehunting estimate would be just below 24,000. Crocodiles 0-3 years old normally comprised 50-85% of the entire population; they have a high mortality rate (Blake and Loveridge 1975, Graham 1968). This high mortality in any 1 year causes drastic declines in population size. Losses of hatchlings, which generally comprised 20-45% of the population, would certainly cause severe year- to-year fluctuations in population size. Another important factor causing population fluctuations is the hatching rate of eggs. Two simulated phenomena, weather and predation by monitors, play a major role in determining this rate. Inclement weather, resulting in floods, can cause extensive destruétion of eggs, sometimes eliminating the entire year's production (Pooley 1969b). Minor predation on eggs over many years is at least as destructive as mortality due to occasional floods. 109 110 Extreme Water Levels The severe drought and flood simulations generated for the Okavango area are probably unrealistic. That the crocodile popula- tion placed under these unusually harsh conditions maintained itself at close to undisturbed (normal) levels over 300 years implies that the population is relatively insensitive to extreme water levels. The ability of female crocodiles to reproduce from ages 10 to 65 forms a population structure well buffered against recurring large losses of eggs and young. Hunting The larger population size obtained at a minimum of 500 huntable crocodiles might be explained by the roughly 36% fewer years of hunt- ing when figures in Table 5 are averaged for both minimum numbers. That the ratio of nesting females to total population should be greater (5:100) at a minimum of 500 huntable crocodiles than at a minimum of 300 (3.75:100) is noteworthy. The difference might be an artefact of the program, changeable by raising the value for the number of females originally thought to saturate the nesting grounds (CCAP) above 1,360. It is also possible that fewer years of hunting enhances survival rates of females to a greater extent than survival rates of males. Because the females grow more slowly, their vulnerability to hunting lasts 1 year longer than that for the males. There is little difference between total harvest averages over 300 years (roughly 4% less at the 500 minimum, Table 5). The best yearly hunt was realized at an efficiency of 0.3 at the 300 minimum, which also gave the fewest years without hunting. 111 However, according to Graham (1976, 1977), at least 200 crocodiles per hunting month are needed to make a profit. Hunting would be done from August to perhaps February (5-7 months) when the water level is low, so the crocodiles concentrate in the main channels. This means an annual harvest of 1,000-1,400 crocodiles, which far exceeds the simu- lated harvests (77-87 crocodiles per year, Table 5), and therefore appears unfeasible. Furthermore, such annual cropping rates approxi- mate the destructive ones of 1958-1969, assuming B. Wilmot's total harvest was roughly 10,000-14,000. Management Implications Egg collection appeared more acceptable than hunting as a method of utilizing the crocodiles on the Okavango River. Commercial utili- zation of the crocodiles, on a sustained-yield basis, will motivate conservation; human sentiment alone is not likely to suffice (Bustard 1970, Blake and Loveridge 1975). Graham (1976, 1977) believed that without commercial harvesting, the Okavango crocodiles would be treated as pests and be eliminated. Egg collection, followed by incubation and captive rearing, is the method of harvesting crocodiles in Zimbabwe (Blake and Loveridge 1975). The crocodiles are kept for 3 years, after which most are killed and skinned. The rest, representing 5% of the number of col- lected eggs, are released to maintain wild breeding stock. This percentage is believed to compensate adequately for lost natural recruitment to the population (Blake and Loveridge 1975). Nearly 80% of the collected eggs can be expected to hatch and about 50% of the hatchlings should reach age 3. In the wild, survival to that age is 112 much less. Egg collection allows more production from the p0pulation because the high mortality of young is circumvented, and crocodiles of age 3 in a rearing station are nearly twice as long as those in the wild (Blake and Loveridge 1975). If well fed, crocodiles released at this age can be expected to have a high survival rate. Blake and Loveridge (1975) suggested that at most 1,500 eggs be collected per rearing station annually in Zimbabwe. 0n the Okavango River, because of the average clutch size of 60.8 (Blomberg 1977), only about 25 nests would have to be robbed. For this reason and the believed adequacy of the 5% release, egg collection, and release of juveniles were not incorporated into the model. Greater numbers had lower hatching rates, probably because the rearing stations had more clutches than could be carefully managed at hatching time. PRELIMINARY CONCLUSIONS Commercial use of the Okavango crocodiles, on a sustained-yield basis, is viewed as a motivating force in conservation. On the basis of the described computer model, hunting could only play a minor role. It was concluded at this point that commercial use should take the form of captive rearing for the valuable skins, and that it should include the release of the number of 3-year old animals that represent perhaps 5% of the number of eggs collected. To increase income from the rearing scheme, there should be guided public tours of the rearing station. The computer model should, at this point, be viewed only as a first approximation of the behavior of the crocodile population in the Okavango River. Discussion of results of further work, to make a 113 second and presumably better approximation, follows. SENSITIVITY TESTING Results have been presented primarily in the form of curves representing size of the entire population. The model also produces numbers of nesting females for each year. Their curves are not presented, because of being artificially constrained by variable CCAP, set at 1,360. The population size of 65,900 at equilibrium (Figures 12, 18), resulting from setting PSURV(l) at 100.0, merits some discussion. It should approximate the population size prior to the large-scale commer- cial hunting initiated in 1957. A pre-l957 population size of roughly 66,000 seems conceivable at this point, so an attempt was made to relate this population size to a reported harvest by the late B. Wilmot, significantly greater than the earlier reasoned estimate of 14,400. A. C. Campbell, former director of the Department of Wildlife and Tourism in Gaborone, Botswana, stated in a letter to R. I. G. Atwell of the Department of National Parks and Wildlife Management in Causeway, Zimbabwe, on August 9, 1973, that B. Wilmot (with whom he was acquainted) had killed an estimated 40,000 crocodiles. If it can be shown that this harvest is conceivable, then a pre-l957 population size of 66,000 must be conceivable. Regardless of total harvest, B. Wilmot was instrumental in depleting the population. That means that the pre- 1957 population was probably in the tens of thousands. A lower order of magnitude appears impossible, and a population size of a higher order should have experienced little or no effect from the hunting. A harvest of 40,000 crocodiles is incongruous with Graham's 114 (1976, pers. comm.) report that B. Wilmot hunted for 12 years with an annual quota of 2,000, which those who worked for him say he seldom filled. I have never seen whatever authentic records of B. Wilmot's harvests might exist; no one in the Department of Wildlife and Tourism in Gaborone mentioned such records. A. C. Campbell used the term “estimate” for the harvest in his letter, as indicated, and further stated that B. Wilmot operated in an estimated 1/6 of the Okavango Delta (which should roughly coincide with the present study area). If B. Wilmot indeed killed roughly 40,000 crocodiles, despite seldom meeting his annual quota of 2,000, possibly his team shot far more crocodiles than they actually gaffed and loaded into the boats. A shot crocodile sinks and is lost if not gaffed within 5-10 seconds. An alternative explanation appears implicit in A. C. Campbell's letter, namely that the annual quota of 2,000 (to be reduced by 500 annually) was not imposed until 1967. This allows for an annual harvest of far more than 2,000 crocodiles prior to 1967, and there- fore a total harvest of possibly 40,000. If B. Wilmot killed 40,000 crocodiles, his and other harvests total 44,240 (in contrast to the previous estimate of 18,640), as shown in Table 9. The estimated pre-l957 population then becomes 44,240 + 9,730, or 53,970. The calculated mean population size of 65,900 at equilibrium exceeds this estimate by 22% when the model is run without hunting. As a kill of 40,000 crocodiles is conceivable, a pre-l957 population of roughly 66,000 is also conceivable. 115 Table 9. Hunting history of crocodiles on the Okavango River, with a large harvest by B. Wilmot assumed. Year Harvest Enterprise Source 1957 2,000 8. M. Lurie and Co. (Pty.) S. M. Lurie Ltd., Bulawayo, Zimbabwe (1975, pers. comm.) 1958 800 " " 1959 500 " " 1958-1969 40, 000 a B. Wilmot Assumed 1973 500 BGI, Francistown, Botswana Taylor (1973) 1974 440 " Blomberg and BGI Total: 44,240 a This number is an estimate. The information from different sources varies. B. Wilmot may have had a quota of 2,000 crocodiles per year; at any rate it was seldom filled (Graham 1976, pers. comm.), though it may have been raised the last few years. This makes 40,000 crocodiles seem incredibly high, unless many of those killed were not harvested. An alternative explanation is that the annual quota of 2,000 (lowered by 500 per year) was not applied until 1967 (Campbell 1973, in litt.). This allows for more than 2,000 crocodiles in each earlier year, hence for the possibility of a total kill of about 40,000. 116 Initial Population Size The change in attainment of equilibrium phase with change in initial population size (age structure held constant) is evident in Figure 13, and shows desirable sensitivity. The measures thereof are 0.33 and 0.76 for the higher and lower estimates of population size, respectively. It is a positive feature of the model that the curves representing population size level off at seemingly identical values. Initial population size should not be a determinant of ultimate popu- lation size, so for this parameter the model seems to operate realis- tically. Initial Age Structure Response to changed'initial age structure has been ascertained. It indicates that the model can be made a more reliable management guide for the Okavango crocodile population, if and when new field data can be collected for this parameter. The somewhat earlier attainment of equilibrium phase, of the curve in Figure 14 resulting from the other normal population struc- ture (narrow pyramid), can be attributed to a larger proportion of the females being of reproductive age. This also holds true for the curves resulting from the even age structure, in.which the proportion of reproductive females is significantly greater than that in the previous data set, i.e., 84.9% vs. 5.5%, respectively. The curves resulting from the inverted age structure reached equilibrium phase at roughly the same time as the curves resulting from normal age structures, though one might guess that it should happen very quickly as with the previously discussed structure. The 117 reason is probably that a large proportion of reproductive females died too soon to effect an almost immediate attainment of equilibrium phase for population size. The oldest 5 age classes contained 57.2% of all individuals; the oldest 10 contained 76.9%. It is a positive feature of the model that varied age structures, with initial popula- tion size held constant, also resulted in seemingly identical values for the equilibrium phase. An even age structure in a wild population would seem improbable at best, and then transitory, and the value of it in this analysis lies only in testing for sensitivity. The same may be generally true of an age structure that forms an inverted pyramid. As mentioned, however, Graham (1968) implied such structures around the unsheltered islands in Lake Turkana, Kenya, resulting from cannibalism exacerbated by a near-lack of sheltering emergent vegetation for the young. These populations were apparently maintained by recruitment of adults from the lake's shore, instead of by reproduction. Also, Watson et a1. (1971) reported another population of crocodiles in the Grumeti River, Tanzania, that consisted apparently of little more than adult males that had moved in from Lake Victoria to avoid harassment by hunters. Age-specific Percentages of Females Nesting in a Given Year Conspicuous change in time of attainment of equilibrium phase, for population size (Figure 15) resulted from variation in the per- centage of sexually mature females that nest in any given year. Good sensitivity of the model to variation in PERBRD is demonstrated, the measures thereof being 1.81 and 0.76, respectively, for maximal per- centages of 56.8 and 76.8. Scanty observations in the field suggest 118 that roughly 2/3 of the sexually mature females nest in a given season. This fraction probably rises somewhat above that, with increasing age (see Cott 1961:255). It seems a strength of the model that the equilibrium values for population size, resulting from dif- ferent values for PERBRD, differ very little (see Figure 15). This parameter should not be a determinant of ultimate population size. Age-specific Clutch Sizes Desirable responsiveness to clutch sizes that, though changed, remain well within the actual range of sizes found in nature (roughly 23 to 75 due to the described changes), has been demonstrated. There- fore acquisition of age-specific clutch sizes from the Okavango River for entry into the model appears worthwhile. It is noteworthy in Figure 16 that the time of attainment of equilibrium is delayed by smaller clutch size, and that equilibrium phases of the curves vary directly with clutch size. The measures of sensitivity for time of attainment were 1.67 and 0.49, for smaller and larger clutch sizes, respectively, and those for level of equilibrium were 1.11 and 1.16, respectively. Change in equilibrium level makes sense, as variation in this parameter mimics variation in PSURV (i.e., varying PSURV has the same effect as varying the survival rate of the eggs or young, or both), which is a limiting factor on ultimate popu- lation size. Age-specific Survival Rates ngor Portions 2; Curve gf_Survival Rates.--Several tests of response to changed values for PSURV, for the first 20 years of life, and for the asymptotic values (see Figure 17) were run. Very 119 noticeable changes in population size resulted. For the higher rates of survival in the first 20 years the measure of sensitivity was 8.15 in time of attaining equilibrium phase and 9.32 in the level of equi- librium. At lower rates of survival the measure was 14.4 in the level of equilibrium. For the asymptotic survival rates (ages 22-51) the measures of sensitivity were 22.3 at 95.0% and 15.4 at 93.0%. Good response to variation in this most important parameter is thus demonstrated. It appears very worthwhile to obtain data from the Okavango crocodiles, on age-specific survival, for entry into the model. Possibly males and females of any particular age class have differing survival rates. Any field study of survival rates should include sexing by the only known way, i.e., cloacal inspection (Graham 1976, 1977), of all animals possible. This will prove difficult at best, with very small crocodiles, however (Blomberg 1975). PSURV is a key parameter in this model, in determination of a realistic population size at equilibrium phase, and in a realistic number of years for attainment thereof. Age-specific survival rates are intrinsically important to science, and are badly needed for sound management of crocodile populations (Graham 1968, 1976, 1977; Blake and Loveridge 1975). Constraint 29_Juvenile Survival.--The preceding tests of sensi- tivity, involving altered data for various values of PSURV, signifi- cantly affected population size. Therefore the drastically lowered curve in Figure 18 can be expected. The measure of sensitivity for change in equilibrium phase was 3.97. It is not known what might be reasonable survival values for age groups 5-10; those used, as men- tioned, were arbitrary due to lack of any field data. It therefore 120 seems pointless to enter other hypothetical sets of survival data for these age groups. The purpose of this test, as indicated previously, was merely to ascertain the efficacy of varying juveniles' survival rates in regulating the the average height of the equilibrium phase. Such regulation might prove useful if a more reliable estimate of the population size prior to 1957, that is well below 54,000 (total in Table 9 + 9,730), can ever be reasoned out. If field data on low survivorship of juveniles is obtained and incorporated into the model, enhancement of survival rates of crocodiles 3-4 years old, or increase of age-specific clutch sizes, or some other adjustment, may become necessary for maintaining roughly 66,000 individuals, or whatever number seems correct, at equilibrium. The rationale for hypothesizing a survival bottleneck for juveniles (Magnusson 1984, pers. comm.), as mentioned previously, is that when the crocodiles reach “medium length“ (normally about 1.5 m in Crocodylus niloticus), they visually resemble adults enough to pose a territorial threat, or a sexual threat, or both, to them. The adults then might well attempt to kill the juveniles, or at least drive them to less suitable habitat, where mortality should be higher (Messel et a1. 1982, 1984). Magnusson furthermore reasoned that large K-selected animals should produce few but large young (few small young, with more intense and protracted maternal care than is actually the case, is also conceivable), but that crocodilians instead produce many small young because the environment is unpredictable for the medium- sized individuals. The environment is normally saturated with large crocodiles, and room for a younger crocodile would usually exist only where an older conspecific has died. 121 In addition to his own evidence from Paleosuchus trigonatus, Magnusson (1984, pers. comm.) mentioned data from Webb and Messel (1977) that show increased scarring beginning at a snout-vent length of roughly 70 cm (roughly a total length of 1.4 m) in Crocodylus .porosus in northern Australia. Cott (1961) reported similar results with Q. niloticus. He and Webb and.Messel (1977) suggested that the reason is either attempted cannibalism or other social interaction. Messel et al. (1984) stated that many juvenile C. porosus grow to about 1.5 m, but do not enter the adult segment of the population. Cott's (1961) statement that cannibalism in Q. niloticus is acquired with age (which is written into the model) may also be relevant. The incidence of injuries in the 1974-75 harvest from the Okavango River also increases toward greater length classes (Table 10). The small percentage of individuals at least 290 cm long, i.e., 1.7% of 241, suggests that most injuries resulted from aggression among juveniles, however. The proportion of injuries resulting from such aggression, and that resulting from adults attacking juveniles, probably vary with the proportion of adults in the population. Increased incidence of injuries toward greater length classes may be ambiguous evidence of intolerance for juveniles by adults. Assuming the described constraint on juvenile survival, and supersessive hunting moratlity, it appears that hunting, within the previously mentioned length limits (120-190 cm), should not be post- poned until the population attains equilibrium (although lO-lS—year moratoria have been recommended in certain situations (e.g., Cott 1961; Becker 1974, pers. comm.)). Because skins are best within the mentioned length limits, and due to the constraint on survival, this 122 Table 10. Incidence of injuries,a attributable to intraspecific aggression, from the 1974 crocodile harvest on the Okavango River. Incidence Length class (cm) No. examined No. % 25-124.5 48 4 8.3 125-149.5 78 5 6.4 ISO-174.5 47 7 14.9 175-325 b 68 13 19.1 a They consisted largely of amputations of portions of limbs and tails, and scarring. b Individuals at least 250 cm long numbered 7 (10%), and individuals at least 225 cm long numbered 21 (31%) of this class. 123 would be the most economical stage in life to hunt crocodiles. It follows that the crocodile population that produces the greatest number of huntable individuals is at equilibrium. The greatest sus- tained yield is not from the population that has reached only about 50$ of saturation (Magnusson 1983, pers. comm.). Growth Rates of Crocodiles Relation to Cannibalism.--The means of the population curves resulting from spreading TOTKIL (index of number of cannibalized croco- diles) over 4 age classes (ages 0-3), and over 11 age classes (ages 0- 10), differed little from that due to spreading TOTKIL over 3 age classes (ages 0-2). Therefore only a slight sensitivity to variation in the number of age classes subject to cannibalism was ascertained. However, no data were collected from the Okavango River, and no smaller crocodiles were found in the stomachs of any of the 240 Okavango croco- diles dissected. The explanation may be that only 4 (1.7%) of these were over 290 cm long; 172 (71.7%) were under 175 cm long. Therefore cannibalism probably had negligible effect on the.0kavango River croco- dile population. Other studies, e.g., Cott (1961) and Messel et a1. (1984), have reported cannibalism. Cannibalism on young, as programmed in this model, is highly speculative. Degree of sensitivity to changed data for this parameter is therefore of small significance, and this portion of the program should be rewritten, preferably following a detailed field study incorporating cannibalism. Thus the model points out a useful line of research. Even without a field study, cannibalism could well be rewritten to supersede natural mortality, but become additive to 124 whatever extent it might surpass it. It would thus operate as hunting does in the model. Figure 19 shows marked differences in equilibrium phases of the curves representing population size, due to variation in initial ages of cannibalistic behavior by large crocodiles (the measures of sensi- tivity for the growth rates of Graham (1976) and Graham (1968) being 0.32 and 0.30, respectively). This is viewed as a strength of the model. (The change in time of attainment of equilibrium was slight, however, measures of sensitivity being negligible for growth rates of Graham (1976) and 0 for those of Graham (1968).) It is believed that cannibalism is a potentially important, density-dependent, limiting factor on the population (Emmel 1973). In this context it is note- worthy that Graham (1968) reported possibly 100% cannibalism on young crocodiles around the unsheltered islands of Lake Turkana, Kenya, which indicates that the populations are maintained by recruitment of larger animals from the mainland (as mentioned). attainment of equilibrium phase, with measures of sensitivity being 0.94 and 1.82, and resulting from delaying initial age of egg laying to 13 and 18, respectively, and negligible differences in equilibrium phases, seem realistic. This parameter should not limit ultimate population size. It is apparent from Figure 20a that populations which differ in the initial age of egg laying have different time spans for recovery from any catastrophic event, e.g., overhunting. This age should be ascertained beforehand, preferably in tandem with age-specific percentages of nesting females and age-specific clutch sizes, for each Nile crocodile population in Africa that could become 125 subject to commercial hunting in the future. Generally, variation of data for initial age of egg laying, combined with appropriately varied data for age spans cannibalized and initial ages of cannibalistic behavior, has noticebly changed the curves representing population size (Figure 20b) from what they were in the test solely of the first, and of the last (Figure 20a), parameter. Again, desirable sensitivity of the model to altered growth rates is demonstrated. Relation to Age §p§g§ ggigg,flunggg.--Sensitivity of the model to changed growth rates, expressed in age spans subject to hunting, has been demonstrated in Figure 21a and in Table 7. It again appears worthwhile to obtain data on growth of wild crocodiles, for entry into the model. In Table 7 it may be noteworthy that the mean for the huntable female cohort is less than that for the huntable male cohort by 36% for the original age spans, but only by 11% for the age spans based on Graham (1976), and is more by 8% for the age spans based on Graham (1968). This progression seems attributable in part to the increasing degree of overlap of male age classes with female age classes, as one reads down the table. Lower means for the female cohort in the first and second growth rates are probably due to the females' longer age span of vulner- ability to hunting, due to lesser growth rates (Cott 1961; Graham 1968, 1976, 1977). Beause the sexes are indistinguishable without cloacal inspection (Graham 1976, 1977), a somewhat greater harvest of females than of males may be unavoidable with anenforced upper length limit. If so, the proportion of females in the harvest, averaged over the 126 years, may be an important factor in limiting the extent of allowable hunting, even at the low annual rates in Table 7. The hunting rates in Table 7 are far below those of 1,000-1,400 implied by Graham (1976, 1977) to be minimal for economic profit. It should be realized that his rates are economical for the western style of hunting. Possibly, as suggested by W. E. Magnusson (1983, pers. comm.), and considered by Graham (1976), a local hunter network could harvest a far smaller number. This might approximate the hunting kill in the 3d column of Table 7, and be determined each year by a legal quota or limited number of hunting licenses. Some few additional licenses might also be sold, at higher prices, to tourists. If skins were then properly treated and sold to a reliable buyer, local hunters might still profit economically from an animal they otherwise would like to eliminate. This should result in a more positive attitude toward crocodiles among the local people (Graham 1976; Magnusson 1983, pers. comm.) than would ranching. Ranching would provide employment, though in Maun (Medem 1981), at least a day's journey by road from the Okavango River and upper delta. The local people might therefore, and because it would be European-owned, view the ranching as an enterprise in which they have too little influence. Especially difficult to under- stand or appreciate would be any legislation protecting crocodiles in their area, seemingly or actually for the mere benefit of an enterprise in Haun (Magnusson 1983, pers. comm.). The attitude of the local people is very important in long-term maintenance of the crocodile population. A local hunter network, once well organized, might be an alternative management scheme to crocodile ranching (which involves large overhead costs, and 10-12 years to recover the initial monetary 127 outlay (Magnusson 1984)). Perhaps the most efficient way to exploit the crocodile resource, however, is to carry out both management schemes simultaneously. Because Medem (1981) recommended that rearing stations (i.e., ranches, which depend on eggs or young collected in the wild) be turned into farms (which, by definition, depend on captive breeding stock), and because Magnusson (1984) stated that farming would reduce the incentive to maintain wild populations, a local hunter network might in the long run maintain this incentive (Magnusson 1983, pers. comm.). The local hunter network therefore should be seriously considered as a management tool for the Okavango crocodiles. This model might then prove useful in predicting allowable hunting rates. The proposed hunting rates of 1,000-1,400 per year (Graham 1976, 1977) constitute 30-42% of B. Wilmot's destructive annual kill of 3,300, assuming he killed roughly 40,000 in 12 years. If this west- ern style of hunting is used, it seems wise not to apply Graham's proposed rates before the population approaches or reaches equilibrium phase, resulting in.maxima1 annual recruitment of huntable young. If, as suggested by Graham (1976, 1977), the comparatively dense human population along the Okavango River never again allows the crocodile population to reach its natural equilibrium, annually harvesting 1,000-1,400 crocodiles might well deplete the population. If Wilmot's total kill was only about 14,000, however, i.e., an annual mean of 1,200 in 12 years, Graham's proposed rates would, as stated earlier, certainly be unacceptable. A response is evident, from Figure 21b, when all 4 parameters pertinent to growth are varied in accordance with the different growth 128 rates. Desirable sensitivity to different growth rates is again demonstrated. In Figure 21b the equilibrium phase for population size resulting from Graham's (1976) growth rates averages slightly higher than that resulting from Graham's (1968) growth rates. One might expect the reverse, as the latter (lower) rates would result in fewer years of no hunting, however. Small differences in means of huntable male and female cohorts, and of harvest, between Table 8 and Table 7, were obtained for origi- nal growth rates, prior to rounding off. The differences are meaning- less, as the values in Table 8 result from reduction of number of egg-laying age classes from 56 to 48, as discussed. Generally, Table 8 reflects a more depressed trend in numbers of crocodiles, resulting from including the effects of varying all parameters, than what results from hunting alone. Again, sensitivity of the model to changed growth rates is demonstrated. It may be noteworthy that the mean for the huntable female cohort deviates from that for the hunt- able male cohort by -36% at the original growth rates. For the growth rates of Graham (1976) and Graham (1968) this mean deviates from that for the huntable male cohort by -11% and by +8%, respectively. This progressive increase in the ratio of females to males, like that in Table 7, would be attributable partly to the increasing overlap of huntable male age classes and huntable female age classes at lower growth rates. It is felt, as an afterthought, that the efficiency of the hunter (EFFIC, subroutine HUNCRZ) should be lowered from 0.3 to 0.12. The reason is that Messel et a1. (1981, cited by Montague (l981b)) suggested that roughly 60% of the crocodiles present (and presumably 129 of any cohort thereof) are seen at night, when most hunting takes place. It is then assumed that the hunter succeeds in killing roughly 20% of these. A comment, in closing, regarding exceptionally low growth rates may be in order. Populations of stunted Nile crocodiles (at most 1.5- 1.8 m long) exist in the Aswa, Ketchi, and other rivers in northern Uganda (Pitman 1952, Cott 1961). The arid environment forces the animals to estivate several months of the year (Pitman 1952), thus markedly limiting their food intake. It would be a positive feature of the model, were more of these populations' dynamics known, if entry of their growth rates effected successful execution. CHAPTER 6 SUMMARY AND RECOMMENDATIONS SUMMARY Prior to certain alterations of the model, and tests of its sensitivity to changed data for several important parameters, the population leveled off at roughly 21,000. Achievement of this population size resulted from reducing the maximum rate of predation on eggs to 28%. Imposition of 4 consecutive droughts every 20 years seemed not to significantly affect population size. However, this regimen of premature floods, severe enough to inundate a year's entire crop of eggs, often caused a noticeable decrease in population size every 20 years, though recovery was rapid. These simulations of drought and flood are believed unrealistically harsh, and the population's maintaining itself at close to normal levels over 300 years implies that it is relatively insensitive to extreme water levels. While drought intensified the rate of cannibalism on young, the loss to the population was less than that resulting from total flooding of eggs. With 300 harvestable crocodiles (120-190 cm long) as minimal for allowing hunting, regardless of the hunter's efficiency (0.3-0.5), the population size leveled at roughly 1,400. At all efficiencies, the mean annual harvest was in the 70's to 80's; the highest averaged harvest was 87, with a minimal number of 300 and an efficiency of 0.3. Fewer years of hunting appeared to enhance survival of females more than that of males; the former had 1 additional year of vulner- ability to hunting, due to lower growth rates. For economic profit, 130 131 at least 200 crocodiles must be taken for each of 5-7 hunting months (Graham 1976, 1977). The resulting annual harvests of 1,000-1,400 far exceed the simulated harvests and approach the clearly destruc- tive rates of 1958-69, assuming the latter totaled 10,000-14,000. Captive rearing from eggs collected in the wild (ranching) was con- sidered a more acceptable alternative of commercial utilization. Enhancement of the usefulness and reliability of the model is a desirable goal. Some needed changes of certain numerical values, and corrections and alterations in structure were made. Former Director of Botswana's Department of Wildlife and National Parks, A. C. Campbell, estimated that B. Wilmot, with whom he was acquainted, had during 1958-69 harvested 40,000 crocodiles. This number was judged conceivable, and compatible with an equilibrium phase of 65,900 cro- codiles, resulting from a correction in the program. In addition, the response of the model to changed data sets, for a number of para- meters, was tested, in order to determine the usefulness of obtaining and entering field data. When possible, a measure of sensitivity was calculated to quantitatively gauge the model's response. All population curves except 1 were characterized by a dip well below initial size, over the first 24-123 years, reaching minima of 1,800-3,800 individuals. This may be attributed to the low number of sexually mature females at year 0 (1975) and rather low survival rates to age 10, at which fewer than 1% of the females lay eggs. These factors also postpone the time that equilibrium phase is reached. Input of varied data sets for population size at year 0 (age structure held constant), for age structure at year 0 (population size held constant), for age-specific percentages of nesting females, and 132 initial age of egg laying (treated later under growth rates) resulted in similar population sizes at equilibrium phase, i.e., 26,000- 27,000. Lower (7,858) and higher (11,598) initial population sizes than that used originally (9,730), postponed (to year 110; measure of sensitivity - 0.76) and hastened (to year 90; measure of sensitivity - 0.33), respectively, attainment of equilibrium phase (originally year 96). Alteration of the population's age structure to a narrower pyramid than that originally used, to an even structure (diagram- matically rectangular), and to an inverted pyramid, hastened attain- ment of equilibrium phase to years 87, 9, and 88, respectively. Lowering and raising the maximal age-specific percentages (56.8 and 76.8, respectively, from 66.8) of females nesting in a given year post- poned (year 122) and hastened (year 85), respectively, the attainment of equilibrium phase. (Respective measures of sensitivity were 1.81 and 0.76.) Appreciable sensitivity of the model to altered data for the preceding parameters was demonstrated, in terms of times of attain- ment of equilibrium phase. The similarity in equilibrium levels sug- gests realistic operation, as data for these parameters should not determine ultimate population size. For the remaining parameters, namely age-specific clutch sizes, age-specific survival rates, and growth rates of crocodiles (with exception of initial age of egg laying), input of varied data sets usually resulted in changed years of attainment of equilibrium phase and in changed level thereof. The latter change can be expected from a parameter that directly affects the number of young that in time reach maturity. Age-specific clutch sizes, lowered and raised 15% from originally used values (27 in lO-year old females to 65 in 133 65-year old females), postponed (to year 120; measure of sensitivity - 1.67) and hastened (to year 89; measure of sensitivity - 0.49), respectively, attainment of equilibrium phase. Respective equi- librium levels were 22,100 (measure of sensitivity - 1.11) and 31,100 (measure of sensitivity - 1.16). Lowered values for age-specific survival rates in the first 21 age classes (ages 0-20) simply caused the population to drop off at 1,000 (measure of sensitivity - 14.4), i.e., well below population size in year 0. Raised rates for these age classes hastened attain- ment of equilibrium phase to year 64 (measure of sensitivity - 8.15) and the equilibrium level to 36,600 (measure of sensitivity - 9.32). The lowering of the asymptotic survival rates (age classes 22-51 insofar as possible), from 99.0% to 95.0% and 93.0%, again made the population curves level off well below the initial population size, i.e., 2,600 (measure of sensitivity - 22.3) and 1,800 (measure of sensitivity - 15.4), respectively. When these survival rates were lowered to 92.0% the population curve declined over the entire time span. Good response to changes in age-specific survival rates is apparent. Survival rates of crocodiles aged 5-10 (1.5-2.5 m long), were lowered by 23% on the average, based on the hypothesis of increased aggression by adults toward juveniles. The response of the population curve was to level off well below the initial population size, at 6,600 (measure of sensitivity - 3.97), a decrease of 90% from the equilibrium of 65,900 used in this test. Evidence for this aggression as cause of lowered survival rates of juveniles is presented. Increased incidence of injuries with age of young crocodidles seems to be ambiguous evidence of such 134 aggression, however. Growth rates of crocodiles were expressed through the following parameters: age spans cannibalized, initial ages of cannibalistic behavior, initial age of egg laying, and age spans being hunted. Effects of changed data, representing the higher growth rates sug- gested by Graham (1976) and the lower growth rates of Lake Turkana, Kenya (Graham 1968) were noted for each parameter separately, and for certain combinations of these parameters.‘ The population curve under- went only slight change from increasing the number of age classes vul- nerable to cannibalism from 3 (ages 0-2) to 4 and 11 (ages 0-3 and 0-10, respectively). These crocodiles would be under 120 cm long. No data on cannibalism were obtained from killed crocodiles on the Oka- vango River, perhaps because only a small percentage of these were over 290 cm long. Growth rates resulting in initial ages of cannibalistic feeding (lengths being 290 cm) in males at age 11 and in females at age 18 (due to faster growth in males) postponed attainment of equilibrium phase, perhaps negligibly, to year 100; the equilibrium phase was lowered to 22,500 (measure of sensitivity - 0.32). At the low growth rates, in which males became cannibalistic at age 35 and females at age 46, the year of attainment of equilibrium phase remained 96, but the population leveled off at 30,800 (measure of sensitivity - 0.30). Sensitivity to changes of initial ages of cannibalistic behavior is viewed as a strength of the model, as cannibalism is a potentially important limiting factor on a crocodile population. Initial age of egg laying, delayed from the originally used 10 to 13 (Graham 1976), postponed the year the population reached 135 equilibrium phase to 123 (measure of sensitivity - 0.94) and lowered the equilibrium phase to 25,500, a probably negligible 4%. A delay to age 18, corresponding to the low growth rates (Graham 1968) delayed attainment of equilibrium phase to year 236 (measure of sensitivity - 1.82), but lowered the equilibrium level insignificantly (by 3%). The response of the population curve appears typical for a parameter that does not directly affect survival rates, hence ultimate p0pu- lation size. Initial age of egg laying has a bearing on a crocodile population's recovery time after a catastrophic event, such as over- hunting. Age spans cannibalized, and initial ages of cannibalistic behav- ior and of egg laying, in combination, delayed attainment of equilibrium phase to year 158, and lowered the equilibrium phase to 23,400, at Graham's (1976) suggested growth rates. The lat- ter change is 11%. At the low growth rates of Graham (1968) the equilibrium phase was reached in year 237, but was higher than that resulting from originally used.values, by merely 3%. Hunting at the originally used growth rates, at which males were aged 2-4 and females 3-6 (120-190 cm long), held the population well below its initial size, at 1,800, a change of 93% from 26,500. Post- poning and expanding the age spans to 4-7 for males and 5-9 for females (Graham's (1976) suggested growth rates), and to 11-19 for males and ll-20 for females (low growth rates of Graham (1968)), the length span remaining constant, raised the population level to 2,700. Lower growth rates resulted in a progressive decrease in averages of the huntable cohort and an increase in the number of years when no hunting can take place. 136 Simultaneous alteration of data in all 4 parameters, for each growth rate, resulted in depressed population curves much like those resulting from varying age spans hunted only. The curve resulting from growth rates of Graham (1976) was lowered to 2,600 (a negligible 4%), that resulting from growth rates of Graham (1968) to 2,400 (11%). It appears that hunting the youngest (and shortest) age spans lowers the population curve the most. The trend in averages of the huntable cohort and in the number of years of no hunting is similar. The model has responded noticeably to changed data for nearly all parameters tested. It should therefore have potential as a management tool. Further manipulation of it may be desired, and should include (1) redoing all simulations with PSURV(l) set at 100.0, (2) thoughtful rewriting of cannibalism on young in relation to growth rates, (3) experimenting with values of maximum numbers of nesting females in the population (CCAP) greater than 1,360, and (4) reducing the efficiency of hunting to 0.12. Input of field data for all para- meters possible should increase the usefulness and reliability of the model as a guide to conserving the Okavango crocodile popula- tion. In reality, however, shortage of equipment, funds, and trained personnel might limit the acquisition of much of the desired field data. Some unanticipated changes in the model's mode of operation might become necessary, and ultimately the model will be outmoded. Nevertheless, it is felt to constitute an important step in the right direction, and that its implications should be applied as soon as possible. 137 RECOMMENDATIONS It is assumed that commercial utilization of the Okavango crocodiles, on a sustained-yield basis, for the valuable skins, will motivate conservation. Prior to various corrections, alterations, and sensitivity testing of the model, it appeared that hunting at least 200 crocodiles per hunting month (1,000-1,400 annually) would again deplete the population, and that the method of utilization should therefore be captive rearing of young from eggs collected in the wild (i.e., ranching). This method is more efficient, relative to population size, because much natural mortality of young is elimi- nated. It appeared that hunting could only play a minor role in utiliza- tion of the crocodile population. Ranching should include release of 3-year old animals constituting perhaps 5% of the number of eggs collected, and guided public tours to increase monetary income from the rearing scheme. Because the egg collection, with subsequent release, was assumed to have no adverse effect on the population, it was not incorporated into the model. Appreciable change in time of attainment of equilibrium phase, which itself changed immaterially from 26,500, from changed data for population size and for age structure in year 0, and for age-specific percentages nesting in a given year, suggests a realistically ope- rating computer model. The value of reasonably accurate estimates of the crocodile population's size and age structure is potentially accurate prediction of the time of attainment of equilibrium phase. Seasonal monitoring of the number, and of at least approximate 138 lengths, of nesting females, followed by estimation of the population's size and age structure, should make the field data on the last of the above parameters available. Censusing the popula- tion by airplane is unworkable on the Okavango River; night counts by helicopter might work well, but could prove cost-prohibitive (Graham 1976, 1977). A marking scheme, described later, might be useful in estimation of population size. Collection of field data for the last parameter, for entry into the model, would be desirable. Appreciable change in time of attainment of, and level of, equi- librium phase resulted from data on age-specific clutch sizes, changed within the range found in nature. Entry of field data should therefore be desirable for the model. Use of an approximate length- age relationship of aerially photographed females, each with its own clutch size (Graham et a1. 1976), should provide data on age-specific clutch sizes. Appreciable change in the population curves resulted from chang- ing the first 21 age classes, and the asymptotic portion, of the curve of age-specific survival rates. This indicates that it is worthwhile to obtain data in the field, for this most important parameter, for entry into the model. Because males and females in a given age class might well have differing rates of survival, animals captured and marked in a field study should be sexed (difficult at best with very small animals (Blomberg 1975)). A large-scale program of capturing, individually marking, and recapturing the following year, would be needed. Animals should be measured for snout-vent length at least. Animals of all lengths that can be safely handled (up to roughly 240 cm) by 2 trained persons should be captured. From the 139 recapture program, the following year, data would be obtained on growth, from which an approximate age-length relationship can be derived. A new marker, perhaps a collar differently colored from that used in the previous season, should then be secured onto each animal. The observed ratio of old to new markers should then be used to estimate the total number surviving of those captured in the previous year, to reduce the overestimate of mortality resulting from the impossibility of recapturing all survivors. Age-specific survival rates is perhaps the most important parameter in establishing the model's credibility and reliability. Acquisition of the data, though expensive in terms of time, money, and energy, is urged. Acquisition might well be repeated, possibly every 5 years, as long as the population is recovering from the earlier, destructive, hunt- ing rates. There is evidence, in other crocodilian populations, of markedly lowered survival of juveniles, resulting from aggression by adults. For this reason, and the assumption of supersessive hunting mor- tality, it is felt that allowable hunting (lengths being 120-190 cm) not be postponed until the population has reached equilibrium phase. Such postponement means foregoing economic gain. Restriction of hunting to juveniles results in skins of optimal condition (Magnusson 1983, pers. comm.). It also protects the breeders, and it follows that the greatest sustained hunting yield will come from a population at equilibrium phase. The effect of cannibalism on young in the model is highly speculative, as no data from the Okavango River were obtained. It is felt that this portion of the computer program should be 140 rewritten, preferably supplemented by a telemetry study of survival of the youngest animals, before and after a substantial proportion of adults has come about. Thus the model points out a useful line of research. A study of incidence of cannibalism by various length classes of adults, to determine initial age, may never again become feasible, unless it is restricted to stomach analysis of killed nuisance crocodiles. These will increase in number if the population is allowed to approach or reach its pre-l957 size. A more expensive alternative would be to extract stomach contents of live, restrained, and possibly tranquilized, crocodiles. This has been done by Taylor et a1. (1978) with Crocodylus porosus, of 28-180 cm total length, to date. Because initial age of egg laying has a bearing on time spans of recovery from a catastrophe, it, preferably in tandem with age-specific percentages of nesting females and age-specific clutch sizes, should be ascertained for all Nile crocodile populations that might be subjected to hunting in the future. The initial age would come from derivation of an approximate age-length relationship from growth rates (mentioned earlier), and from aerial photogrammetry, of nesting females, as recommended by Graham et a1. (1976). The females' lower growth rates will likely result in somewhat greater harvest of females than of males, with enforcement of an upper length limit. This seems unavoidable, as crocodiles generally cannot be sexed without cloacal inspection. The proportion of females in the harvest, averaged over the years, may become an important factor in setting the legal limit on the size of the harvest. 141 Sensitivity to changed data for growth rates, as expressed in initial ages of cannibalistic behavior and egglaying, and age spans vulnerable to hunting, has been ascertained. It therefore appears worthwhile to obtain data in the field on these 3 parameters for entry into the model. Allowable annual hunting rates indicated by the model are far below the 1,000-1,400 implied to be needed for economic profit in the western style of hunting (Graham 1976, 1977). An alternative might be a well-organized local hunter network (Graham 1976; Magnusson 1983, pers. comm.), with provision for a limited number of hunting licenses for tourists, to harvest an approximation of what the model indicates to be allowable. A more favorable attitude by the resident people toward crocodiles would thus result, which is needed to help ensure the crocodile population's long-term survival. Ranching (rearing from eggs or young collected in the wild) as a simultaneous way of commercial utilization is also recommended. A likely shortcoming that must be considered, however, is that the employment it provides will be at least a day's journey (i.e., Maun (Medem 1981)) from where the crocodiles are, and people living along the Okavango River itself might not be involved. Other short- comings (Magnusson 1984) are (1) large overhead costs, (2) 10-12 years to recover the initial monetary outlay, and (3) likely conversion to farming (dependent on captive breeding stock, and therefore reduces the incentive to maintain wild stock). Well before this conversion is completed, the local hunting network should be organized and active. If farming largely or entirely replaces ranching, the incentive for long-term maintenance of the wild population might remain 142 sustained by hunting. The model could well before then prove useful in predicting allowable hunting rates. However long ranching lasts, it should be done simultaneously with hunting, to bring about the most efficient commercial utilization of crocodiles. It is far better to initiate ranching and organization of a local hunter network, to provide incentives for conserving the crocodile population now, than to frantically, and at great expense and difficulty, try to save it from extinction some decades later. Assuming B. Wilmot harvested approximately 40,000 crocodiles dur- ing 1958-1969, which would make the prehunting population of roughly 66,000 (produced after certain necessary changes in the model) seem likely, the proposed western style of hunting 1,000-1,400 annually, would constitute 30-42% of Wilmot's destructive harvest, each year. Use of this style of hunting might be unwise prior to the crocodile population's attainment of the above equilibrium phase. If the com- paratively dense human population never again allows the crocodile population to reach its natural equilibrium level, taking 1,000- 1,400 annually might well deplete the population. APPENDICES APPENDIX A: COMPUTER PROGRAM COMPUTER PROGRAM APPENDIX A 9 G [O 9 o 0 \I 1 s 6 9 l. 6 3 9 o 9 l. H 720 S 09 e G 9 n. 99 G) .l 90 9 E1 S 9 cc 1 E 29 O 9‘ N .95 )V MI: 9.1. 6.5.. 59 9 6L 9 930 (H ) L .6 9 s H 6 T. 072 c 9 (a K 8 02 TI) l\ 88 9 U.U T 9 990 L... R 2 o 9 o C‘ 0 M 01.9 3 M 8 02 9L .l 9 88 9 )A A 0 I90 \I/DV N E 6 9 o 96 9 R .86 ll 9 \I P 7 03 p10) 6 R 87 9 PR3 6 0 I90 A81 l\ N 3 9 0 TR‘ 1. .63 9.L2\IT.T 9 7 04 BPLOKRZ 7.7 9 AIHOL I90 _L 9V4MMA 1 9 s P) ( 9TH .30 3.5 T67E6NOT679 9(2F6 NNrgo TPlN‘ 9 R0 9 o U0(NLH9P.77 FFT.AT.C.1N_D e5 TFL KTLISE9 U A IHAA 9 640 0 9V)FHMT“ 9 o 9) U9HRN074 T691).0U0s6 U6946 9NH55 9 P(6(6P R190 NV6P‘09C390 IR‘OPPM9pol (ULPOMEEZ 07 CSITP IU459 OPKAM9 9.5/90 R L9AV9s CNNNNIGVRIS OOOOKE Us? MIIIIHEL549 ASSSSMMAPGJG RNNNN C 9s GEEEELLIASS 79991002913029160392101 0495608958059590796009962019 .9280092160956.934o926o92912o915o92*4o915 9 4 00’40’00’40’00’40’0013*‘90’009409009409009 925 02“ 8 0.3395 9 935 989 0 I42 05 05 09.38 39532 99 97 969 O 522 .23 9 .639. 9 733 976 0 I49 .6 02 .936 3330 99 95 966 o 29.9 .33 O .637 I 631. 971.. U 946 07 09 0034 3339 99 93 953 e 926 043 0 .735 I 439 970 0 933 08 are 0139. 3437 99 91 950 e 62!. 053 1 0833 I 237 977 0 930 08 .3 0230 3535 99 IO) 957 o 31.0 .53 2 .931. I 135 97.4 0 937 09 .0 0238 3633 98 I7 954. o 9t 9 998935 96.... 06 :4 9 e o 939 or.» 3 I04 6627 .337. 4. as 0 .6 I631. 98 002 90 9 Us 951 o 1. I9 .49 .1“ .73 9 o 00 920 0037 I 094 s 6 9* 32 968 5* 9° .60 931 00 67 012 01¢. 0935/ “10,35,739 985 2 Ian 96H: 998 9C1}. .732 P7 98 09T .136 I0 I 03R7 O I 0R3 0U31 965 s P. .4624...» 938 01‘. F4 up 9.6C9. 0‘ 33 9 I e 3 9 837 982 A no.“ s3A1 945 OMMMMAAGT o8/.T7 9Tb. .T18 .830 .mIIIIEECAZ 90:» I .4523} .134. Ind FUCDDRRLDQoU so .40 96039 962 s e + 9 + + 09 9690+. ca. .5 =0. INITIALIZE THE POPULATION FOR START AT YRS C Us OP(K)¢MPOP(K) POP(JJ)=TPOP S ANNFEM(JJ)=82.0 2F: 3 1P 2 0T K:K\I :OEKOA \I K KPU .- T.K1(o TNS): 2(aal— : 6212K . .1P131P1irT12xl nu Kn..UN .L: OoLuHPh2rofi¥1J DMHErTP=ICDSAJ 1 1a .5 5 2 .1 11 2 1 1 1 PRINT RESULTS AT THIS TIME. TPOP,FPOP. C N f... S E A r»: r. L V At 6 I .A .L \I A 0 K Pt t O C Is E C K’R H 0 E 0 IA T R H Cir.» C TI TI oVI N D .L L N RET E A I ARA H T. ERH T O S YUT E T. r. C B L LC” 9 1 A01 5 9 D M E o O RTE L o C OHC I a 0 NGA D 1 R UL O F C AOP C 9 9. 0 i .L TDK R L A 0 C pr. A HAO R NI. T TI E E E T .L H F SAD A NHO Mu E F. ATO E R 0) E L F E I NSF. H T, N t T. D] 0AA 9 U! E o t T... GMT. 0 9 S o T A 8 0 A 1” F 0 "C L T 9 4. 0T. A0 I.) F \1 IR UTS t 9 I TF 0 N If... a) I AAA ) ELA JR. * 9 L 9: RE A9PR . ‘1 UI s GUM I 20AM * Pan H AG \IEIPEO H ON 1 LE2 IR 9TYI 1 PA I‘. F (E. T 0| HI 0 60 PH 9......“ 0 AS 3 ART. OTDSAAL 3 OT 1 9L 6 PtNRtU 1 90 9 9FL 6 Fly 99: 9 *8 t 0 A 9 t to t 1 0 .AU 9. I .909: O 0* 5.0.!0062 O‘ROl‘OI‘ 9EOI 2 E2 3 s 2 OTAITATAOATUITAtTA Tan :NHRNMNH 9LN2.NH NHNM‘H SIR IRIR’FI IIRFIRIIR RROORCROs RoanuCRnu R0 TPFGFFPF ORPDIUFF PFSFF. 9 9+ .+ + O 7 0 21 3 . 6 C 9 O 00 O U 2 2 3 22 2 2 INITIALIZE PARAMETERS. C 0.07 VAL1(3)=0.039 S VAL1(4) 143 0 2 e o 0 3.377600 00 2 .. 2 : 03:6 0.. H12 .203 :‘l TTLLD err—111 NGAA:0R : Ln! RLMHG:PP L1 PNRR—LMRA AL NROOEEOC HA- IINNHINC SM 144 O 30 .31 2: 8: O) 0) 02 02 =1 89.. . (L (L 02.4 1‘ 2 LV LV IA A 4 V... V.) l. 238 $8 I. 2 9 J5 . 9.. V260 TO .1: :- 3 :l 0) 01 21.. «I. 21 )1 0" 7‘ 372 (1 2 (\L 02 7.. .2 2’5 00) )0 0:0 6.1. 029.1 ((0) 6l\ 1.1.1.2 (a... LL2( 2L A422 LA VVFLAV FAV SC:LV s D s 4)=l.0 2 2VAA $6 2 .2 . 33 02 e2 2) ..)\IO 3261 F(‘( .7333 ILLL DAAA vvv 55 S 588 71$ 552 $8.. 19 O 02 .5 O 0 003 01* 0” 1..” .III ell-.1. réuH (Rn. V87.- RRU6 UEL625 6SPC I . e e .9 o .0 o Oznéep 2 29.9.16LL1L 00.11.54.002 9.5 e . 92))...1 . 9H“ 9H 2 2 2.. 2 2) . 2 2 21.11.111.222 28.. )\I2\l))32\l))2Il\l‘ T)..))..) 5921. 591.31.59.1(0H3on 1115.1... ((Ll\ (((L‘I\I\ VRC10( (( l\ .1le 222L3331RBT1SHV2VV3V LLAA LLLRLLL URU TE EE E RAM A‘AHAAAOC—ELO‘ LCLLAUL VVSu. VVVSVVVDPPCDNHOHUOH 13 1 .375 LEV(7)=0. .6875 .FALSE. + MALLI§OIFFI.K19ULEV(KK)) ls ‘ PSURV(I) -l) )=H V(I'1) + .2.) GO To 4 VALlos NE ( UA 2 KK .FA NRG(I\OI\T RANDOM WEATHER VARIABLE ASSIGNED A VALUE. EXECUTION PHASE FOR 300 YEARS. NUMBER OF EGGS FIGURED. A» K LFF1.F 1. RKFIIFIF C C : RBRO(67-K)*CLUTCH(67-K) ) T S E N .0 N \I 9 K 9. - K 7. 9 6 2 I. F D F R T. £8 0 I 9 e E5 \a 1. 2 )P K F. L K 90 . l— .)T 7. s A 7K 6 HM 6 . 0 (TSCST. (75 SOGT 90 p6) GTGUZT 01.? G/ELL . PPA ESTCA F. FOCI. +G(AV: c7o:Pku.E .36.:(l L5)F.:U GESD ) A9K(E3R GTGLEJ . FI.+LHT8E=GOXJ 0 .277... .ITHEHEI .. .:K60T$: :CT:8H .SOéc (YLU F2USTL.TA¢L G: USS :T3UTGUDSTF GTL GT(:L GLLE...N ECAOGCFzAOECCNZN T9LVDF?11HVG§2§HNSK~ 4 58 1 EH + MEEG * F2 + F1)) -(HATCH * H31) -(TEGGS * (I HATCH=(HATCH CH=HATCH/2. S T H=TEGG VALUE) CH=FHA EACH AGE CLASS IS NOH ADVANCED 1 YEAR. TOTAL HATCH MINUS MORTALITY. C C 145 ) P 0 P ) Mn \1 0. K \a P K H O ( C D. V T F. E A o. L H L “I M T. I 9 K 3 D. H K 0 Mn. I P o 3 M L F. ' I F S K T. R H 0 VI o F I ‘0 l\ 3 : 5 L IN 2 L RC R0 A C..- CT H NA N s UH UC I HF H6 3 ) L L a . L) A L0 H... L 0 V A. C A0 ( CT)T6)E C o LIAGKV E F. .I .(H 9(A )N I THPFZPSDT o L NCO: 202LNG a UTPIKPIOUA .TA HAFl FKHHL... RH:(5:(:RF:O= CFEPIDPECIITI ((VO LOV( M M FFAPOOPAFF303 IISFDHFSIIFGF T 5 6 1 CANNIBALISH FIGURED ON THE O-Z-YEAR OLO CROCODILES. .) GO TO 13 NORPRED)/2. I 2:0 2:1 2. I K MM" .V. :00 FPOP(K) K ( K)¢PSURV(K)-FHKIL(K) MPOP(K) OCKS+FPOP(K)*MPOP(K) ecaocxs 09 + AFPOP a a 3 s 3 1 c p Q .GE.(FPOP(K)*NATMORT(K)}) GO TO 117 ZLGPLLL PD. 1 0 001113. 0 PepobP-JRP SSEKKK 9.19. E 6 o I 6 p 6 p 7 8 6 3 0 I0 OOOCHIKKRTTTIKF o .1 I910. 0K. P3POP13AECCPOOO:((5° ThF-.F5:( F3F2M: 2 ..UOO(TTTKP:32EN= 2K22KL A2A2AK$PLRR2222 0)....)UUK... )2 I :K:K: KOACCL)))5PK KNH KAK 6K P gr DkuCDLXUR¥L19§2OF(;U(T:K“(IéInle 0809010DC((K((I\1(PTPTCIPIPT1F PPPRE TLLL (0 ON(00 C MEErOMfizLRFELrOTI$£UFDhXPOFhEEOPhqu flUAOADBPIIITKKKCIFGFCIDFOHGDI 3R..J4 4.24 11..I1 1. 1 11. 11.. 78901.2 111 CCCCCC - FHKIL(K))/((FPOP(K) HKIL(K))/FPOP(K)) T. T I A.‘ —L N M" Y. t). )K 5K5 KH 9‘9 I." .V . V I R RL 0U. UT. 5. SK ‘0?) P I KiK 9V ()1! IR RPbSIlDIL UOUN 0L SDLSOfiflPA .FFDLLDFBL 7 6 8 1.. 1. 1 1. I .3 FIGURE TOTAL POPULATION FOR THE YEAR. C 146 9POP(K) + FPOP(K) + 1,66 p PRINT INFORMATION AND RESULTS FOR YEAR PROCESSED. C I O t BIB S F 9 D E G OE IFOE L N. .U 90CH A E I EL C OT M H 9 T UA 9RR E S T S S LV BECN F R G E A F8 0 9 A D G N VE 9MR 9 ENN ) E ) H 9 UEL X YYIA I I S ET NDL 6 T ( N ( E H9 5 LI 9 ID .3 L 0 L L ) T9 ) ALOK 9 LCDG A A A 2 99 2 HA N AOEN V N V .M I I0 . TFL D TLCI 9 D 9 E 9 9. 5 ROOA I RFUL F I. F F 9 09) FLAT T T 0 DH F TR F */O 9912.. R0 A MNOC I AA I E S ,9. 9KYEET L IRT O DE D R A I34 T H8 U T PA ) / EY / U “I I or. SOSTME p N o H F \I R \I T 07. ATI.UH O ERS F F PN F A R .F H H9NT P CAGE I F E F M A 3 9S 9T 9 9 a REGH D I DU I E F9A RP 0L: 9 EYET . D RI O y: Y r H AOR9A9 9 P I 9 AG 9 L .S EPO9TO ) NFT K ) Z ) ) L S A2 YDF/O9 9 J REOC 3 ( 1 IY Y 1 A I SHH E 9T: 9 J OV E Y T . LN M . U H A SRSD I I 9 FIRE M A I A M I X T UZF IPG.EI 9 1 GEF M O C R U C E FO H GBHO 9 : S BA U L T ON 0 T S R G T9EFT. G I EAM O F A TI 1 A 0 AFE S 998 N U UL 9 9 0 I K 0 9 F2LOU RKF99F I 9 LRNL K ) L NS 9 )L 9 HF L CEO 9’ T ) A0 I 9 D F 0T F KF G R EA F0 809 S I ) VFEH F . . MS F 9. . E9EUV RRA9 E)( )J H F O M E I )M 6 BIHL LCEU 9S NIHIJJ ELTY . I 9 U EN 0 EU 0 F MMTAE EBB IA 9/EOJ9 TE TS D L D T 9 .D 0 9 U3 VH V. NH 9") 9 IF 9 91. AVTIE 9 L 9. AF L It... 1 9 NFF T E9UCO O XINTI: LECLL L A 9 L0 L 99 I OE. LHNT.G. 9.NF:I ULEAI L H ) U A F) 0 E M 9 H 9 C ASN.8 9HA 9.... 9 C FTD A S ) CR H F) 6T 9 R 02ET9 RTLHFUF 9 I X 9) LRFRO H . I LE 5 II 3 J E OFU90 EAA 9O 9 L( 97)I AEAOC S Y . ( AB 9 O( 1.0 mi D. N L9t TNT—Liv: A7.) 9I( CT “no 9 H L C" L [L 06 G 9 )0 A 9A. 9.).AFOL T I04..." AL R L H A U In "A 030 )SE9P RIVO/KH TASES OX(.PE LULSC A U V LN V UV IIT) IRR 9T F 9 9K 9 "AHA T69702- L II v.10 A _ L (I D. 9 9 M (YE E E 93(ESEEHTH 9 IOFPN IEUHD (.31. K) IE 3 9) 210 . D. 9H. 9 H IH/ .VHGHF . 9.19. 9TH UH. TL E1... 21. UH EILOI OnGE OTT9S TGT97ETGT SNS X.TXAA TY O I(XFI9 .T X(L.9 11 N6 POtDRK9A93FL9E9LEOE 2HA2(( N TS LLAF I N ELAII 9: .6 FT I .YK 9L 9 .9 H T 9AL L 91:. 9))... ONIRR BAMI)( ON BAM(( ))DO 9 9 4 9 F 97 t 9 TIGI 9 ( 9110 IOLAA AVADIL I0 AVSIL TTISI 990F990 IDES 90 9OODND .09. 44 9 T AEE T I/9A T T .XA NN.9: 14993396.9A4959TOI06 99109337 CGTYY NIHKV CG NYAV RUEOI OO(9OO(O(9HO(O( CYCOE3I94I99F NNR . NONU.‘ NN NOMM( PHLS 22 23 3 3 3 EOEO2U3 93 89( UIOT2 OIIOQ: UI OIM(: NR./5 TR T TSI T THRRR N T T((T FDMH ISM9EEN FD ISUOEN ICMMOITTAATTATAAHTATATCPCTITA9TAEEA N GO TNAO.IR N TNDNXR ‘(((2 . NNHENNMNM H3NMNH 9 NTNM 9NMTTM SESUN CE: .ILU SE CE :IEU IIIRYIIRIR FIRIR9YSYINIR/IRIIRO IPIOA NHHI(8TD IP NMMMBTO FFFFO..RRG RRDROI RDRO9BE8RORO 9RORRON HEHR . UIU..FAEN HE UIU:AEN IIIICJPPFNPFFFFEFFFPFDALA PCFF 9PFulu-FE TDTDI FCDIITRE TU FDDITRE 9 99 9999 9 . 21 6 5 4 3 6 4 5 O 9 O 1 «do 3 0 0 nu 0 0 0 0 3 4 6. II I 2 2 3 3 3 3 I 3 3 3 CCCCC CC HHEN HUNTING OF CRCCO- NUMBER AND ADVANCES 147 EACH AGE CLASS OF MALES 1 YEAR. R O E T. HE U v. Dr. TS QTTNML . Au IIDHCIT F L FEUEHEGA S 0.6 OYE RDU SA F EBF EFEDOEIL URFIU GYCOHAHH . I E N NNX T TTR D 6 GBDNS IAEGOD E.E 6 NMEAE T N NN IBDN ( IUZCS NNTI A0» MEI T . I TNI S UIOT. ITUTA R U .U N LRA H NNDDTNNNT IO .. . UEAEL G U ECU UB TH P 8 HHBBC NNSHDTAHSHO R0 0 F TIM EIE ENRNI 0C P I N NUE HTOSEIF HXE HM M I 9 ESNNG "NUTCR STER U9 H U HTA A U IXPLE SA CI 2 . S HECE DHTHE AV N6 P 7 . 9 I S HE E R0 EHI .HX I6 0 F nu 0 D FTV LSO TRIGDCE TI. 9. 9 2 2 S ETC I LTHOOAC EAS RT F 9 I I E LS ST AIOSN ESTE 0R H 7 7 L LRRTC I CMCL SDIN H Ho 2 l. l. I AIECE P C ASE HIFC 0H 3 P L L D CFBAP I S E EZATROA co 0 K K 0 MRS P. 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I3M.:I.F.:I Ia TEIY IOOD949.0(K0(L LEFIE ERB IOU20KF MIIMPQ 3IPP.4.P.3IHTKKGHTKKE2* LL30 TICZIBIPCT CTO SIHI LMTBAH TIHT: HIHI H0(.(4H00(109(4(N (G(N (U4( SIA N USM T TIHRSHRHN IDTCFBUEMPU USMNP2:1: T=PLOL TP:L:P=L :UTLA:U6LN TN IDB9A 0N TATAD...OI202R 0 EIASKU N 0N UUIPIPTAPHK2K02FTKGHTKOTHIKLTHIKITAR OIS RELNMNHMEHIDHEU SCTP T CNN RELHPIDIDNMDTNTNTTHNNGHNNTNHINFNFINTNMU SCNED BMAIRIRCVD LOVTD TOASXNEA RE BHANH P PIRPIUNU NIUUA(UU U( U(U( UNIRTD IONLE UIEROROFACOOCAEN HRH EUHRLUH UIECTDFOMROHFHUHOUFHHLFHHOHFDHFHFDHDROEN HRAAZ SCRDFFFISHDHHSRE TCTASHTBATT SDRN CHDHPFTIFHMGHIFFFIHHGHIDHIFIDFCPFRE TCCHI 6 3 5 2 I 2 O I 2 73 63 I D Q I I I I 2 1 I 13 II 2 2 a I I n I A. A. a. II I“ A. I. “- CCCCCCCCCCC CCCCC 148 THE MALE COHORT. C 9. 1 0 1. T 1 1 0 G 0 TI I I o R 0 9 GI GI T MIA- IK L U6 9" o T( 0L I3 AT .K K1 NH TN ( I0 LU L0 TH 9H KT R0 I" N 0C K. U0 HM (I HG 09 LK M. C) Kl‘ I MI: NN - I I6 UN I L... R HA IK KL 0 MK Kl. NK M .M (R UN U I. N0 HU T KI NM “H A (I AU [M N NK KT N9) 9 N‘ MA NI6T AV N A66R KR .t KIb‘O MS I '(RH .N IK VNOO IA I‘ RNHC IH KT SAUM KC (R NKYn 9 (I v0 .A QAL VI RH HINK RK so CID 9N SI. NC (IOIU NT AH (6H AR HI. 3V6" H0 C 0 RR‘ 9 III CH 2E CSNN 1.23 *0 I6 NNNN (1!... IC K o UAAA NNMI. KM o (I HHKKIb NNNZI!‘ 0 TK CMM6.AAA9T2 2 5R( r. 9 IOKKKlRI I IOL NNNNI: .- 2 2 20K3K 3HK IOON:)IIIKH(2(E:ON TIIAKK123 OTITUKCU USSK (C((3CR RN MH CNN 0NNNN9.M.000T.1.(M REELINNNN1(HTHT1(( BHM: AAAA (0 ON UIIECKKKKOFCOCCOFF SDCRDMMMMDIHGMCDII 33 1.2 19.2 10 cracccc .T(KI) L(KII/( I I/MCOHOR MHUNKL(K - MHUNK ) I I K . IK ( Kl. LI(R KKVO NtRM UNSU NNT .KHN CCC 95 * NATUMOR(KI HANSRV(KI - HKANN(KI - MHUNKL(K) 95 * NATUMOR(KI 0c. +£- III KKK (15‘ VTV RRR SOS NHN AOA ”CH 9 CHC O 966 =HCOHORT(K)tCHANSRV(K)-HHUNKL(K) 6 I III \I SOSOOIZOR NHNTHTIHU ADA 0” AUTO HCHOCOOCEN CMCGMCUHRE 051 2 11 1 13 APPENDIX B: VARIABLES IN PROGRAM APPENDIX B: VARIABLES IN PROGRAM Table 11. List of variables in program CROC. Name Definition ACLUTCH Average clutch size per nesting female (TEGGS/TOT). AFPOP Size of cohort of cannibalistic female crocodiles (ages 37-65). AMPOP Size of cohort of cannibalistic male crocodiles (ages l9-65). ANNFEM Number of nesting females, subscripted by JJ (below). It gets each year's value from TOT (below) before TOT is reset to O in the main do loop, so that the number can be printed outside the main do loop. ATPOP Population size, subscripted by JJ (below). It gets each year's value from TPOP (below) before TPOP is reset to 0 in the main do loop, so that the number can be printed outside the main do loop. BABY A minimum number of crocodiles (constant at 500) of ages 0-2, which if not met sets a density factor (K2), hence the rate of cannibalism, at O. BCROCKS Number of 0-2-year old crocodiles, which are subject to cannibalism. CCAP Number of females at first believed to saturate the nesting grounds (constant at 1,360). CLUTCH Cube root of clutch size (age-specific). It is cubed prior to use in the main do loop. CRHUNT Logical parameter with which to opt for simulated hunting (set at ”.TRUE.” or '.EALSE."). DIFFl One of several factors (constant at 0.25) to gene- rate a value for F1 (below). It is the argument for dummy variable DIFF in function subprogram TABLIE. DIFFZ One of several factors (constant at 10.) to generate a value for F2 (below). It is the argument for dummy variable DIFF in function subprogram TABEXE. 149 150 Table 11 (cont'd.). Name Definition DIFF3 EGGS F1 F2 F3Ml FHKIL FLAG FPOP FHATCH HATCH HOLD One of several factors (constant at 0.5) to generate a value for F3Ml (below). It is the argument for dummy variable DIFF in function subprogram TABLIE. Number of eggs produced by a given age class of females, dependent on survival and clutch size for the age class. Percentage egg mortality due to premature flood. Its value, except when 0, is obtained via function subprogram TABLIE. Percent egg mortality relative to number of nests, due to monitor lizard predation. Its value is obtained via function subprogram TABEXE. Multiplier of cannibalism rate, dependent on water level. Its value is obtained via function sub- program TABLIE, except during normal weather ("FLAG - 1') when it is 1. Number of females killed by hunting, by age class. It is the argument for dummy variable FHUNKL in subroutine HUNCRZ. Variable assigned a value of 0 in case of normal weather, 1 in case of drought, and 2 in case of flood. These values depend in turn on the value of KK (below) which originates from generation of a random number. Size of female portion of population. It is the argument for dummy variable FCOHORT in subroutine HUNCRZ. Number of female hatchlings, i.e., HATCH/2. Number of hatchlings produced (TEGGS - (TEGGS * (IEM + MEEG + F2 + F1))). Dummy variable standing for: (1) total number of eggs - percentage lost to premature flood (TEGGS - TEGGS * Fl)), also (2) number of females in any given age class (FPOP(K)) except the first, later assigned to dummy variable SAVE, when advancing each 151 Table 11 (cont'd.). Name Definition IEM INPRINT IRNLGTH JJ K1 K2 K3 KIL age class one year. Subscript used in designating ages of crocodiles and categories of other variables prior (mostly) to the main do loop. Intrinsic egg mortality (constant at 0.236). Logical parameter, making optional the printing of certain information toward the end of each iteration of the main do loop. Number of iterations (usually 300) in the main do loop, representing number of years. Subscript designating an age class 1 year younger than I (above), i.e., J - I - 1. Counter for each year simulated by the model, used as a subscript for ATPOP and ANNFEM (above). Subscript used in designating age classes of crocodiles, and certain.variables pertaining to age classes. One of several factors (constant at 11) to generate a value for F1 (above). It is the argument for dummy variable X in function subprogram TABLIE. One of several factors (constant at 12) to generate a value for F2 (above). It is the argument for dummy variable K in function subprogram TABEXE. One of several factors (constant at 9) to generate a value for F3Ml (above). It is the argument for dummy variable X in function subprogram TABLIE. Number of 0-2-year old female crocodiles cannibalized; it differs with age class (TOTKIL * .6, * .3, * .1, respectively). It is the argument for dummy variable KANN in subroutine HUNCR3. Random number, used each year to determine a value for FLAG (above), which determines weather 152 Table 11 (cont'd.). Name Definition M2 M3 MEEG MHATCH HHKIL MPOP NATHORT NNEST NORMALl conditions. It is also a subscript for WLEV (below), and turns RANNUM (below) into a random num- ber from 1 to 11. Index for the main do loop, designating the number of years simulated. Its highest value is IRNLCTH. Density~dependent factor influencing rate of cannibalism on 0-2-year old crocodiles; possible values are 0 if the crocodiles number fewer than 500, and 1 if a least 500. A.value of 3 is assigned if the number of nesting females exceeds the arbitrary carrying capacity (CCAP) of 1,360. Factor used in decrementing the hatch by 0.1 when the number of nesting females exceeds the arbitrary carrying capacity (CCAP) of 1,360. Minor extrinsic egg mortality (constant at 0.072). Number of male hatchlings, i.e., HATCH/2. It is the argument for dummy variable NPIP in subroutine HUNCRl. Number of males killed by hunting, by age class. It is the argument for dummy variable HHUNKL in sub- routines HUNCRZ and HUNCR3. Size of male portion of population. It is the argument for dummy variable NCOHORT in subroutines HUNCRl, HUNCR2, and HUNCR3. Natural mortality by age class, equal to 1.0 - PSURV (below). It is the argument for dummy variable NATUMOR in subroutine HUNCR3. Number of surviving nests, obtained by number of eggs surviving flood, divided, by average clutch size (HOLD/ACLUTCH). It is one of several variables used to generate a value for F2 (above), and is the argument for dummy variable DUMMY in function subprogram TABEXE. Criterion (constant at 5) for random number KR; if 153 Table 11 (cont'd.). Name Definition NORMALZ NORPRED PERBRD PREDPOP PSURV RANF(0) SAVE SMALLl SMALLZ SMALLB TEGGS KR is less, FLAG (above) - 1, which means drought. Criterion (constant at 7) for random number KK; if KK is greater, FTAC (above) - 2, which means premature flood. Normal cannibalism rate on 0-2-year old crocodiles (constant at 0.06). Percent of sexually mature females that are nesting, by age class. Size of cannibalistic cohort of the population (ANPOP + AFPOP, see above). Probability of survival to a given age class. It is the argument for dummy variable CHANSRV in subroutine HUNCR3. Random number generator, intrinsic to FORTRAN. Random number obtained by use of RANF(O) (above). Dummy variable used to save the numerical value of the first age class of females (FPOP(1)), later set equal to HOLD (above) when advancing a given age class of females (FPOP(K)) to the next age class (FPOP(K + 1)). One of several factors (constant at 0.) to generate a value for F1 (above). It is the argument for dummy variable SMALL in function subprogram TABLIE. One of several factors (constant at 20.) to generate a value for F2 (above). It is the argument for dummy variable SMALL in function subprogram TABEXE. One of several factors (constant at -1.5) to gener- ate a value for F3M1 (above). It is the argument for dummy variable SHALL in function subprogram TABLIE. Cumulative number of eggs for the year, resulting from production by each age class producing eggs. 154 Table 11 (cont'd.). Name Definition TOT TOTKIL TPOP VALl VAL2 VAL3 VALUE YRS Number of sexually mature females nesting (TOT + (FPOP(67 - K) * PERBRD(67 - K))), accumulated by year classes. This variable is within the main do loop, and gets reinitialized at 0 with every iteration, and therefore lacks a subscript. Index of total number of 0-2-year old crocodiles cannibalized ((PREDPOP * F3Ml * M2 * NORPRED)/2). It is partitioned by differing proportions into different age classes (see KIL above). Size of population (TPOP - MPOP(K) + FPOP(K)), accumulated by year class. This variable is within the main do loop, and gets reinitialized at O with every iteration, and therefore lacks a subscript. An array from which a value for F1 (above) is obtained by interpolation. It is the argument for dummy variable VAL in function subprogram TABLIE. An array from which a value for F2 (above) is obtained by interpolation or extrapolation. It is the argument for dummy variable VAL in function subprogram TABEXE. An array from which a value for F3M1 (above) is obtained by interpolation. It is the argument for dummy variable VAL in function subprogram TABLIE. Logical parameter, set at '.FALSE.", but reset at '.TRUE.' if the accumulated number of nesting females exceeds 1,360 (i.e., CCAP, above), and if so it effects decrementation of HATCH (above) by 0.1 and effects (via M2 - 3) a higher value for TOTKIL (above). A water level index, and array of values used to generate a value for F1 and F3M1 from function subprogram TABLIE. It is then subscripted by KK (above), and is the argument for dummy variable DUMMY in TABLIE. Counter for each iteration (representing a year) of the main do loop; it is one less than JJ (above). Table 12. 155 List of variables in function subprogram TABLIE. Name Definition AMAXI AMINl DIFF DUM DUMMY FLOAT SMALL VAL A function, intrinsic to FORTRAN, that returns a real maximum value of 2-500 arguments in an array of real numbers. A function, intrinsic to FORTRAN, that returns a real minimum value of 2-500 arguments in an array of real numbers. Dummy variable for arguments DIFFl and DIFF3 in program CROC, being the difference between adjacent elements in DUMMY (below). It is an element in generating a value for VAL (below). Dummy variable that temporarily holds a value. It is the amount by which the DUMMY (below) argument is larger than SMALL (below), and it is converted to 0 if it is less than SMALL. Dummy variable for argument WLEV(KK) in program CROC, and the array that is the basis for interpolation in generating a value for VAL (below). A function, intrinsic to FORTRAN, that transforms an integer to a real value. The interval within which the DUMMY argument is found. Dummy variable for arguments K1 and K3 in program CROC, and the number of intervals between elements in DUMMY (above). It is an element in generating a value for VAL (below). Dummy variable for arguments SMALLl and SMALL3 in program CROC, and the smallest element in DUMMY (above). It is an element in generating a value for VAL (below). Dummy variable for arguments VALl and VAL3 in program CROC, and the array from which a value is returned to F1 and F3MI, respectively, in program CROC. Table 13. 156 List of variables in function subprogram TABEXE. Name Definition DIFF DUM DUMMY FLOAT MAXI MINO SMALL VAL Dummy variable for argument DIFF2 in program CROC, being the difference between adjacent elements in DUMMY (below). It is an element in generating a value for VAL (below). Dummy variable that temporarily holds a value. It is the difference between the DUMMY (below) argument and the minimum of the argument array, SMALL (below). Dummy variable for argument NNEST in program CROC, and the array that is the basis for interpolation in generating a value for VAL (below). A function, intrinsic to FORTRAN, that transforms an integer to a real value. The interval within which the DUMMY argument is found. It is held within the limits of 1 and K (below). Dummy variable for argument K2 in program CROC, and the number of intervals between elemets in DUMMY (above). It is an element in generating a value for VAL (below). A function, intrinsic to FORTRAN, that returns as an integer result the largest value of 2-500 arguments in an array of real numbers. A function, intrinsic to FORTRAN, that returns as an integer the smallest value of 2-500 arguments in an array of integer numbers. Dummy variable for argument SMALL2 in program CROC, and the smallest element in DUMMY (above). It is an element in generating a value for VAL (below). Dummy variable for argument VAL2 in program CROC, and the array from which a value is returned to F2 in program CROC. Table 14. 157 List of variables in subroutine HUNCRl. Name Definition HOLD MCOHORT MPIP SAVE YARS Dummy variable standing for number of males in a given age class (MCOHORT(K)) except the first, later assigned to dummy variable SAVE, when advancing each age class one year. Size of male portion of population. It is the dummy variable for argument MPOP in program CROC. Number of male hatchlings. It is the dummy variable for argument MHATCH in program CROC. Dummy variable used to save the numerical value of the first age class of males (MCOHORT(1)), later set equal to HOLD (see above) when advancing a given age class of males (MCOHORT(R)) to the next age class (MCOHORT(K + 1)). Counter for each iteration (representing a year) of the main do loop in the calling program, CROC (within which all subroutines are called). It is the dummy variable for argument YRS in program CROC. 158 Table 15. List of variables in subroutine HUNCR2. Name Definition EFFIC Efficiency of hunter (constant at 0.3). FCOHORT Size of female portion of population. It is the dummy variable for argument FPOP in program CROC. FHUNKL Number of females killed by hunting, by age class. It is the dummy variable for argument FHKIL in program CROC. FHUNT Female fraction of population actually hunted ((HFPOP/THPOP) * HUNT). FLAGG Variable initialized at 0, but set at 1 whenever HFPOP (below) equals 0, so as to avoid simulated hunting of females. HFPOP Huntable portion of female cohort (3-6 years old, 120-190 cm long). HMPOP Huntable portion of male cohort (2-4 years old, 120-190 cm long). HUNT Harvest, i.e., huntable cohort of population times efficiency (THPOP * EFFIC). MCOHORT Size of male portion of population. It is the dummy variable for argument MPOP in program CROC. MHUNKL Number of males killed by hunting, by age class. It is the dummy variable for argument MHKIL in program CROC. MHUNT Male fraction of population actually hunted ((HMPOP/THPOP) * HUNT). NONHUNT The number (constant at 300) which must be exceeded by the huntable cohort (THPOP, below) if hunting is to take place in any one year. THPOP Total huntable cohort of the population (HMPOP + HFPOP). 159 Table 16. List of variables in subroutine HUNCR3. Name Definition CHANSRV Probability of survival to a given age class. It is the dummy variable for argument PSURV in program CROC. KANN Number of 0-2-year old female crocodiles cannibal- ized. It is the dummy variable for argument KIL in program CROC. MCOHORT Size of male portion of the population. It is the dummy variable for argument MPOP in program CROC. MHUNKL Number of males killed by hunting, by age class. It is the dummy variable for argument MHKIL in pro- gram CROC. MKANN Number of O-2-year old male crocodiles cannibalized; each age class is set equal to the corresponding age class of MANN (see above). NATUMOR Natural mortality by age class. It is the dummy variable for argument NATMORT in program CROC. APPENDIX C: YEARLY VALUES FOR POPULATION SIZE APPENDIX C: YEARLY VALUES FOR POPULATION SIZE Table 17. Values for population size at original values for all para- meters (Figure 13). 9730. 6009. 7016. 27672. 26076. 26193. 26002. 0260. 9320. 20379. 20031. 20372. 19170. 3930. 6027. 20230. 23707. 23090. 20319. 3030. 0039. 16331. 22030. 27223. 27320. 3733. 6320. 22977. 21701.. 20930. 29301. 3399. 7972. 17379. 20200. 29076. 20999. 3313. 6023. 10030. 26030. 30163. 23736. 3006. 7791. 13303. 27200. 30370. 27003. 3393. 0392. 20001. 23673. 32036. 29101. 3320. 9070. 20361.- 26060. 31073. 30100. 3233. 9330. 20006. 20331. 20060. 29777. 2706. 9721. 23913. 20000. 32312. 30729. 2991. 10193. 20773. 10270. 31203. 31273. 3793. 10717. 10232. 20313. 31013. 27070. 3197. 11209. 22001. 27003. 31720. 23961. 3319. 11600. 23067. 19316. 29766. 20767. 3397. 11971. 17916. 13037. 22311. 29076. 2633. 12309. 13010. 23061. 27023. 30330. 2267. 12901. 22033. 26676. 26000. 21091. 3360. 9219. 23610. 27133. 20609. 26703. 2616. 11061. 26239. 26000. [233009 20220. 3736. 12761. 26630. 20320. 29230. 17030. 0033. 10320. 27727. 29010. 30007. 20663. 3137. 10910. 20032. 29667. 27917. 27120. 2371. 13062. 20063. 30093. 26900. 20232. 0020. 10097. 23039. 30333. 29110. 20360. 3290. 10060. 27106. 20310. 21392. 23103. 3970. 16293. 20230. 29003. 23302. 26303. 6163. 17316. 23600. 30169. 20603. 20703. 0233. 12229. 23001.. 30720. 26200. 30011. 3090. 13330. 26393. 29320. 29033. 21677. 6090. 17660. 19636. 21730. 26023. 26007. 0763. 12322. 20273. 23300. 26699. 27139. 3703. 16007. 27063. 20096. 29031. 20990. 6190. 10100. 20705. 20790. 26911. 29170. 7011. 10697. 20911. 20923. 20737. 20066. 3136. 20119. 17163. 27071. 27669. 21331. 3993. 20750. 13276. 27699. 20616. 26020. 6631. 21600. 22309. 20730. 23701. 20003. 7001. 22103. 23302. 23003. 27300. 20973.- 3002. 23033. 10700. 19622. 23101. 30133. 7610. 16279. 13301. 23091. 20020. 20362. 0730. 20319. 13026. 23060. 23060. 20131. 9030. 23039. 22000. 20062. 20729. 26621. 9903. 20306. 16702. 23331. 10790.. 29033. 12200. 20367. 23630. 27900. 23002. 21603. 10133. 20322. 26766. 26007. 26209. 27011. 10710. 23930. 19002. 20301. 26006. 23910. 11079. 23763. 20120. 29379. 23769. 27673. 11290. 27990. 23000. 29969. 22700. 29636. 160 161 Table 18. Values for population size at low estimate of initial size (Figure 13). 7090. 5300. 6069. 22000. 26023. 25072. 26123. 39,1. 7723. 23061. 23065. 29300. 19225. 3191. 5653. 16,90. 23509. 23615. 29350. 3097. 7020. 13317. 22070. 27060. 27597. 3099. 5295. 10909. 21959. 20937. 29321. 2900. 6620. 19520. 20227. 29323. 21039. 2075. 5003. 12263. 26327. 29936. 25771. 2093. 6900. 10996. 27003. 30136. 27021. 2039. 7150. 10766. 25056. 30611. 29201. 2090. 7559. 22795. 26579. 31227. 30129. 2096. 7931. 29673. 29692. 20639. 29095. 2299. 0001. 25923. 20090. 30131. 30030. 2616. 0961. 25071. 10361. 31315. 31910. 2692. 0090. 11009. 29661. 31003. 27603. 2751. 9205. 21516. 27067. 31670. 25719. 2019. 9667. 23057. 19009. 29111. 20795. 2020. 9001. 17209. 15020. 22979. 29959. 2197. 10399. 19263. 23292. 27309. 00967. 1092. 10626. 21157. 26191. 26990. 21972. 2753. 1599. 29570. 27016. 20650. 26000. 2155. 9931. 23361. 26151. 25999. 20319. 3063. 10993. 25706. 20030. 29201. 17103. 3500. 11771. 26697. 29292. 31122. 20306. 2501. 12261. 27795. 29629. 20206. 27129. 2109. 12711. 19912. 30119. 27167. 20003. 3599. 0965. 29999. 30570. 29293. 20509. 9305. 11900. 26102. 20356. ZLSOS. 25290. 9062. 13900. 19350. 29903. 25151. 26909. 5017. 19920. 23005. ' 30161. 20770. 20530. 3955. 10071. 20631. 30666. 26352. 29715. 9012. 12019. 25039. 29015. 29133. 21559. 5633. 19060. 19070. 21699. 26120. 26011. 3095. 10325. 23695. 25170. 26709. 27219. 3069. 13607. 26967. 20270. 29109. 29076. 5070. 19903. 20360. 20952. 27173. 29262. 6003. 15995. 20520. 20072. 29305. 20960. 9192. 16627. 16756. 27302. 27995. 21376. 3200. 17155. 19079. 27929. 20700. 26159. 5959. 17933. 21013. 20503. 25059. 20009. 6999. 10350. 25199. 25590. 27960. 20029. 0902. 19073. 10530. 19600. 25169. 30067. 6209. 13963. 15279. 23233. 29066. 20900. 7230. 16975. 13610. 25015. 25001. 20079. 7011. 19077. 21573. 23007. 29720. 26551. 0210. 20275. 16060. 25106. 10010. 20901. 0005. 20159. 23126. 27522. 23910. 21502. 0392. 20209. 25761. 26203. 26100. 26951. 0059. 21951. 10972. 20023. 26500. 25071. 9160. 21301. 23373. 29202. 23939. 27631. 9301. 22901. 29690. 29617. 22022. 29623. Table 19. (Figure 13). 162 Values for population size at high estimate of initial size 1161.. 7617. 503.. .538. .318. .179. 3982. 38.9. 375.. 3706. 3665. 362.. 3081. 3390. 3538. 370.. 3880. 3989. 3072. 2633. 3951. 3060. ..23. 5193. 3707. 3007. 519.. 6223. 7021. 7227. .956. 6893. 8050. 8337. .36.. 7201. 8603. 5932. .6.2. 7685. 9125. 6307. 8817. 10131. 10937. 11.96. 11802. 117.1. 12388. 12800. 130.1. 902.. 107.3. 7868. 9719. 7273. 91.1. 6921. 89.0. 9867. 10..2. 10989. 11229. 11803. 12.32. 13023. 13596. 13935. 1.615. 13027. 10726. 13339. 1.850. 16670. 173.8. 1797.. 12662. 16796. 18910. 20321. 1.187. 1802.. 20.57. 1.309. 1908.. 20992. 21626. 2326.. 23989. 25067. 256.6. 26682. 18825. 23728. 26666. 283.2. 28186. 28369. 30009. 28831. 292.1. 28875. 29366. 21.59. 17621. 223.2. 1783.. 1580.. 1.13.. 21969. 28.83. 28.59. 2.398. 25..1. 19010. 22551. 2.627. 18662. 13752. 2289.. 26397. 27179. 27.88. 28319. 29622. 218.6. 2608.. 27839. 20809. 23955.’ 23798. 26.62. 19839. 2..6.. 2771.. 2958.. 21.52. 178.2. 18871. 22773. 288... 19082. 15722. 13977. 22005. 16758. 23869. 26.28. 18783. 23897. 25098. 26530. 2.386. 23987. 22819. 222.1. 2.687. 26335. 27607. 25681. 26602. 2.623. 2.726. 18.29. 2..39. 26867. 19.70. 15869. 229.5. 26807. 26976. 26765. 28226. 29312. 30252. 30369. 30659. 28353. 29.13. 301... 30679. 29452. 21729. 25393. 28637. 28958. 29197. 27795. 27517. 28685. 25673. 197.8. 233.2. 25.10. 2.180. 25198. 27976. 26169. 28095. 29528. 29.71. 26868. 2.613. ' 23.21. 27112. 28988. 29553. 302... 30.17. 30873. 31.50. 28850. 30299. 31176. 31766. 31659. 30.02. 22809. 2753.. 26318. 20720. 288... 292.3. 3117.. 28270. 27220. 29288. 21715. 25157. 28732. 26295. 2908.. 26071. 26697. 29031. 27108. 29203. 27827. 20726. 257.0. 27327. 25036. 239.8. 2.968. 2.61.. 18753. 233.6. 26127. 25911. 23631. 22609. ‘25961. 19112. 2.253. 27.70. 28673. 20690. 25221. 27195. 29119. 30110. 29862. 30869. 31.51. 27637. 25753. 28786. 30005. 30513. 21971. 26889. 20289. 17064. 2.325. 27037. 27983. 20425. 25136. 26288. 28751. 29951. 21617. 25920. 27088. 28878. 290.5. 29901. 21571. 26825. 29277. 29026. 3003.. 29000. 282.2. 2719.. 29210. 21782. 26967. 288.8. 27987. 30968. 163 Table 20. Values for p0pulation size at initial age structure as a nar- row pyramid (Figure 14). 9722. 6620. 550‘. 26665. 26963. 26166. 26096. ‘757. 11207. 29727. 23936. 2‘561. 19190. “67. 6301. 21792. 23626. 23919. 2‘32’. ‘320. 10266. 11961. 22‘9‘. 27277. 27531. ‘160. 7762. 2276‘. 21976. 29020. 29366. 3900. 966‘. 162‘9. 2“3‘. 296‘6. 21045. 3669. 1‘96. 15015. 26061. 30226. 25‘00. 379‘. 9669. 1‘569. 27366. 30‘12. 27293. 3773. 109‘9. 22‘9’. 25“3. 3067‘. 29175. 37590 1166‘. 26962. 26570. 31‘66. 301‘6. 3765. 12321. 26690. 2“00. 26636. 29632. 3172. 12629. 2506‘. 2‘50‘. 30272. 3079‘. 36‘7. 1031‘. 256‘1. 16270. 31152. 31350. 3679. 1‘055. 1,267. 2‘265. 31755. 275‘1. ‘1“. 1‘7‘9. 23136. 26696. 31665. 26037. “‘9. 15‘13. 2‘606. 1’3‘3. 30‘17. 26666. ‘632. 15796. 16666. 15166. 22637. 29992. 3‘92. 16351. 16962. 22921. 27575. 30‘61. 2953. 17007. 23563. 26560. 26560. 21063. ‘613. 12096. 266‘6. 27073. 20762. 26633. 3509. 1602‘. 27691. 26650. 25597. 20275. 5167. 16695. 27366. 2631‘. 29306. 17066. 611‘. 16701. 26629. 29‘35. 30556. 2‘715. ‘30‘. 19‘23. 2"02. 29706. 2796‘. 27160. 3‘5‘. 20075. 21666. 30165. 270‘0. 26263. 5999. 1‘1‘2. 26273. 30566. 29161. 2060‘. 7190. 16660. 26101. 263“. 216‘7. 25230. 6093. 20962. 20950. . 29‘33. 26112. 26357. 6313. 22502. 2‘0“. 30161. 26729. 26637. 6665. 15730. 2360‘. 30703. 26320. 3006‘. 769‘. 1,912. 26,,6. 29‘61. 2,1‘0. 21713. 9207. 2256‘. 2009‘. 21712. 2610‘. 260‘6. 63‘6. 16023. 2‘977. 256‘6. 26776. 27201. ‘976. 21009. 26311. 26651. 2913‘. 2903‘. 617‘. 23076. 2,‘66. 266‘0. 26992. 29207. 9731. 23761. 21396. 290‘0. 26619. 26666. 6711. 255‘6. 17507. 2761‘. 271.5. 21356. 5250. 2633‘. 15536. 27616. 20676. 26650. 8621. 2761‘. 23110. 20797. 2661‘. 26909. 1020'. 26151. 2576,. 25563. 21‘53. 26966. 7065. 29261. 16001. 19666. 25161. 30130. 9627. 20667. 15616. 231‘3. 2‘072. 26527. 112‘6. 23613. 13652. 25‘95. 25113. 26112. 1206‘. 26567. 21‘70. 2‘076. 2‘772. 26561. 12616. 27952. 16‘17. 725630. 16635. 29011. 126‘6. 216‘2. 23191. 2793‘. 23‘71. 21625. 12657. 276‘9. 26136. 25992. 26260.} 26976. 13193. 267‘9. 16579. 26510. 26072. 26661. 13‘61. 26‘03. 23362. 29552. 23766. 27635. 13613. 29315. 2“93. 29":. 2275‘. 2,617. 164 Table 21. Values for population size at even initial age structure (Figure 14). 9730. 10935. 21005. 30761. 12966. 25011. 3171‘. 17727. 20031. 23207. 20017. 23023. 19199. 22“6. 10020. 23‘9‘. 21115. 255‘2. 19020. 21972. 19‘17. 16600. 23201. 2‘9‘9. 15209. 2‘575. 269“. 23606. 26703. 26200. 27510. 27‘10. 27“5. 26952. 10550. 2‘905. 2597‘. 29152. 26007. 26250. 26077. 20700. 19709. 27327. 2970‘. 23100. 20262. 3090‘. 25017. 27072. 279‘3. 10970. 19530. 20070. 15905. 1551‘. 26201. 23616. 22163. 19602. 2700‘. 16650. 2“05. 27953. 2209‘. 26790. 20105. 2‘205. 20770. 209‘9. 17990. 25613. 296‘9. 1‘100. 2“29. 21523. 20937. 10690. 26152. 23550. 2‘01‘. 27061. 25503. 270‘0. 20773._ 250‘2. 20533. 2‘396. 10906. 20603. 2379‘. 23977. 23351. 26751. 27273. 27202. 19922. 19516. 20026. 2‘735. 15756. 253‘5. 27976. 22093. 25231. 29750. 2“53. 27253. 21‘07. 10075. 29002. 17509. 1‘922. 27733. 15500. 21529. 29207. 22565. 23106. 27970. 2569‘. 17337. 29702. 10979. 2293‘. 21750. 156‘0. 25‘75. 2‘03‘. 13927. 26730. 203‘7. 22097. 27396. 30001. 16019. 26119. 30127. 23650. 27213. 30225. 26692. 20520. 3120‘. 10970. 29260. 31221. 23001. 2973‘. 31509. 250‘0. 265‘0. 2“5‘. 2‘129. 23010. 22‘6‘. 2“22. 2635‘. 27113. 25535. 263‘5. 2“6‘. 29425. 10273. 20500. 27035. 19551. 15910. 23206. 26105. 27070. 2625‘. 20237. 295‘9. 29091. 30371. 30026. 27095. 29327.7 30239. 30040. 29632. 21795. 25260. 203‘2. 20066. 29191. 27703. 27‘01. 20629. 25553. 1965‘. 2317‘. 25563. 2‘152. 25070. 27760. 259‘9. 29535. 2959‘. 29900. 26230. 2‘620. 23913. 27229. 209‘6. 29‘0‘. 30023. 30192. 30625. 31212. 20611. 3069‘. 31269. 31755. 31502. 30320. 22700. 27‘07. 26‘71. 20690. 25512. 29195. 31102. 207‘1. 27‘27. 29397. 21709. 25211. 20007. 26359. 29150. 26109. 26776. 29123. 26900. 2001‘. 277‘2. 20606. 25009. 27“‘. 25152. 2‘050. 25009. 29720. 10023. 23‘37. 26221. 2600‘. 23696. 22700. 26000. 19107. 2‘332. 27531. 29360. 210‘2. 25307. 27267. 291‘3. 30111. 29090. 30910. 31510. 27700. 25019. 20057. 30077. 30507. 22030. 26907. 203‘2. 17115. 2936‘. 2700‘. 20032. 20‘70. 25100. 26335. 20000. 29995. 21655. 25956. 27093. 2091‘. 29005. 20776. 21272. 267‘3. 20792. 200‘6. 30005. 20‘0‘. 27992. 27095. 2920‘. 21711. 26906. 25070. 27623. 29603. 165 Table 22. Values for population size at inverted initial age structure (Figure 14). 9736. 12013. 9530. 29‘06. 26009. 26193. 26092. 6966. 12169. 29037. 2‘630. 2‘73‘. 19200. 09‘0. 0029. 21005. 2‘20‘. 235‘2. 2‘36‘. 9520. 11072. 17097. 22966. 27239. 27590. 9527. 0602. 22706. 22372. 29107. 20793. 0967. 11576. 10135. 2‘702. 29652. 20773. 0562. 0350. 15722. 26‘01. 30335. 25311. 0202. 10902. 1‘310. 2763‘. 30‘07. 2720‘. 70“. 11092. 22190. 2560‘. 30933. 29203. 7‘01. 12172. 2570‘. 26765. 31‘97. 3010‘. 6070. 12307. 25665. 2‘0‘2. 20092. 29963. ‘902. 12001. 2‘791. 2‘770. 30335. 30903. 5207. 12207. 25560. 10‘70. 31205. 3156‘. 51‘5. 12‘05. 19075. 2‘305. 31700. 27750. ‘925. 12600. 22551. 27390. 3167‘. 25060. ‘700. 12037. 2‘523. 197‘3. 30‘17. 20906. ‘399. 12933. 10619. 16026. 22020. 30126. 3‘70. 13366. 15739. 22956. 2753‘. 30631. 3003. 13610. 22071. 26‘7‘. 26513. 22056. 3‘00. 99‘2. 25036. 26923. 20717. 26900. 29‘6. 12137. 2699‘. 26663. 25527. 20365. 3‘77. 13‘39. 26950. 20099. 29197. 17130. 37‘0. 15057. 2056‘. 29200. 31095. 2“11. 3036. 15729. 29351. 30100. 207‘9. 27131. 2656. 16393. 21“0. 30339. 27‘37. 20000. 3051. 11696. 25090. 30636. 293‘9. 20‘97. “31. 15623. 27605. 2035‘. 21763. 25210. 50‘3. 17720. 20770. 29‘53. 25‘30. 26366. 5360. 19235. 23900. 30230. 20036. 20029. 3003. 13977. 23090.. 30790. 26332. 30025. 5‘61. 17‘10. 26703. 29597. 29007. 21673. 6522. 20010. 20023. 21020. 2606‘. 25973. ‘595. 1‘150. 2‘057. 25320. 2660‘. 27109. 3602. 19000. 20292. 20‘35. 29011. 20926. 6276. 21139. 29550. 20900. 27093. 29097. 7665. 21923. 21527. 2932‘. 29193. 20709. 5200. 23750. 17660. 27‘05. 27023. 21201. ‘1‘0. 2‘622. 15710. 27‘15. 20736. 26706. 7157. 2502‘. 23203. 20635. 2576‘. 29239. 0655. 26‘0‘. 26533. 257“. 27366. 29020. 5922. 27561. 19‘91. 19779. 25005. 30050. 0‘91. 19336. 15996. 23067. 2‘010. 29026. 9002. 2“62. 1‘107. 25337. 250‘5. 20270. 10761. 2751‘. 21099. 2‘199. 2‘690. 27235. 1130‘. 29230. 16767. ‘25265. 1001‘. 29260. 117‘3. 29021. 23921. 2006‘. 23“‘. 21703. 117‘0. 29155. 26919. 26250. 262‘9. 27020. 12590. 30705. 19061. 20196. 26030.‘ 25909. 13163. 29‘75. 23070. 29629. 237‘0. 276‘2. 13730. 290‘3. 25301. 29566. 22721. 299‘1. A 166 Table 23. Values for population size at PERBRD increased by 15% (Figure 15). 9738. 6‘78. .283. 28778. 265‘.. 26287. 27159. ‘26:. 11388. 38188. 2‘358. 2‘671. 18776. 385‘. 8218. 28193. 2‘119. 2‘28}. 2‘723. 3818. 8833’. 18329. 23132. 27622. 28856. 3718. 7666. 23283. 22‘91. 29513. 292‘8. 3563. 8936. 18618. 2‘912. 39895. 21082. 3‘62. 7‘1‘. 16285. 26“2. 387“. 258‘3. 339‘. ’88,. 1‘888. 2778‘. 30787. 28156. 3351. 18998. 22781. 28655. 31836. 38858. 3321. 117“. 26161. 26899. 31882. 3885‘. 3288. 12‘2‘. 26‘81. 2‘826. 2899‘. 38239. 27‘7. 12776. 25‘86. 2‘682. 31139. 31967. 3127. 13‘62. 25788. 18‘32. 31589. 31868. 3821. 1‘289. 18‘13. 2“5‘. 32159. 28388. 3518. 1‘932. 23188. 27587. 3218‘. 26612. 3721. 85632. 25387. 18853. 30795. 29312. 3832. 16868. 182‘7. 16137. 23139. 30‘68. 2888. 16838. 162‘7. 23339. 2778‘. 31288. 2‘28. 8737‘. 23666. 27873. 26772. 22‘8‘. 3693. 12862. 27‘... 27516. 28966. 27‘97. 2826. 15338. 28132. 27138. 25858. 28728. ‘168. 17117. 28371. 28‘68. 29738. 17‘2‘. ‘926. 18886. 28326. 28718. 31663. 2‘58‘. 3‘69. 28215. 38‘88. 289“. 28615. 2717‘. 2783. 21876. 221.5. 38338. 27837. 28‘97. ‘925. 1‘696. 265‘7. 38967. 29836. 28888. 5866. 88683. 28783. 287“. 21788. 26838. 6751. 22283. 21‘89. 29761. 23363. 27211. 6891. 2‘852. 2‘55’. 38515. 2907‘. 293.5. ‘788. 166‘5. 2‘281. 3128‘. 26385. 38511. 666‘. 81‘78. 27‘86. 29‘21. 29227. 22959. 7827. 2‘581. 28331. 21785. 25975. 267‘1. 53‘8. 17816. 23171. 25622. 26965. 27895. ‘16‘. 22873. 28268. 28552. 29“7. 29671. 7885. 23531. 38818. 28395. 268“. 29729. 8“8. 26328. 21783. 28691. 29022. 38115. 576‘. 26885. 17686. 288‘7. 28527. 22117. “72. 26288. 156“. 278‘3. 21129. 273“. 7897. 27286. 28983. 299‘2. 26178. 29856. 9899. 86829. 26382. 26877. 276‘2. 29296. 6217. 88893. 192‘8. 28836. 25308. 38677. 8887. 28288. 15786. 23637. 2‘257. 29035. 18218. 23873. 1‘883. 23628. 25231. 285‘1. 11886. 26889. 2229‘. 2‘513. 2‘916. 2766‘. 11783. 28138. 16919. 28961. 18968. 2975’. 12853. 2818’. 2338‘. 28328. 23883. 22138. 11981. 28172. 26988. 26781. 26183. 27‘96. 127“. 28333. 19875. 2’1‘2. 26298. 25613. 13218. 2887:. 2‘15}. 38°68. 2‘276. 27776. 33‘88. 28859. 35292. 38293. 23219. 38381. Table 24. 15). 167 Values for population size at PERBRD decreased by 152 (Figure 9730. 6‘7‘. ‘260. 3865. 3706. 3610. 3‘61. 3368. 331‘. 329‘. 3280. 3217. 2‘58. 291‘. 3009. 3101. 3215. 32“. 25‘2. 2202. 3122. 2‘76. 3‘31. 3961. 2903. 2‘62. 3970. ‘683. 525‘. 5‘1‘. 3762. 5176. 6019. ‘216. 3353. 5399. 6‘09. “77. 35“. 5763. 6778. ‘738. ‘5‘7. 7505. 8065. 8‘77. 86‘3. 8588. 90‘7. 9302. 9‘08. 6557. 7735. 569‘. 6882. 519‘. 6“9. ‘921. 6210. 6797. 7136. 7‘58. 7552. 788‘. 8252. 0595. 8920. 90‘5. 9‘10. 961‘. 6973. 8568. 0‘76. 1056‘. 10901. 1125‘. 00“. 10572. 118‘2. 12692. 895‘. 11229. 12701. 9096. 1183‘. 12911. 18268. 1‘187. 1‘5‘2. 15181. 15‘55. 1601!. 11‘17. 1‘158. 15839. 16762. 16595. 16611. 17‘76. 17275. 18009. 18302. 1867‘. 13‘68. 10951. 1‘990. 11606. 9878. 8902. 1‘593. 17523. 18865. 19683. 20632. 1‘589. 38860. 21225. 15197. 1226‘. 18903. 22270. 22985. 2“87. 25795. 2686‘. 18815. 23995. 25561. 18500. 26306. 27131. 19‘57. 2‘031. 27750. 29808. 21101. 16926. 1‘858. 21‘37. 2‘601. 181“. 1‘980. 133‘8. 20566. 1586‘. 2213‘. 2‘930. 17965. 227‘9. 23808. 25035. 23136. 22727. 21801. 21011. 23682. 25562. 26971. 25051. 25917. 23“‘. 23822. 17969. 237‘8. 20656. 19315. 15753. 23198. 26272. 27127. 26285. 28089. 28835. 29523. 30039. 30‘28. 27896. 29‘3‘. 30160. 30707. 29167. 21‘17. 2‘739. 2780‘. 28323. 28571. 26938. 26895. 20091. 2‘628. 189‘7. 2225‘. 2‘578. 23‘16. 2““. 26961. 25381. 27682. 287‘6. 28975. 25507. 2‘052. 23025. 26629. 28097. 28563. 29317. 29‘78. 30‘95. 30786. 28022. 3001‘. 30695. 31298. 31265. 29536. 22277. 27062. 26066. 20379. 25135. 28700. 30‘06. 28039. 26780. 28823. 21375. 2‘501. 28215. 25731. 28512. 25637. 26107. 2838‘. 26019. 28059. 27232. 20268. 2‘8‘2. 26770. 2‘620. 23‘11. 2‘8‘0. 2‘198. 18‘08. 22951. 25257. 25417. 23588. 22061. 25687. 18839. 23733. 2671‘. 283‘9. 20386. 2‘990. 27009. 28958. 299‘5. 29313. 29997. 30571. 268‘7. 25008. 28005. 29‘00. 30077. 21602. 26506. 19957. 1676‘. 2399‘. 26‘11. 27‘75. 20051. 2‘760. 26016. 27879. 28895. 2096‘. 25222. 26373. 28289. 28“9. 28262. 2085‘. 26073. 281‘1. 28012. 29505. 28080. 276‘9. 26532. 28789. 21370. 26553. 2‘93‘. 27023. 28813. 168 Table 25. Values for population size at CLUTCH increased by 15% (Fig- ure 16). 9730. 6608. 9‘38. 03181. 305“. 30‘65. 31085. ‘328. 11‘35. 3‘089. 28055. 28619. 22673. ‘067. 8320. 2‘861. 2785‘. 27037. 28301. 3992. 10538. 20‘11. 26718. 315‘5. 32103. 39‘8. 7806. 26155. 26027. 33990. 33‘5‘. 3830. 10057. 20831. 28792. 3‘0‘9. 2‘1‘9. 3759. 7512. 18096. 3056‘. 35183. 29633. 3703. 99‘3. 1652‘. 32058. 35‘62. 32318. 3658. 11082. 25626. 29719. 36770. 3‘5‘1. 3588. 11790. 2961‘. 31221. 36861. 35507. 3526. 12‘37. 29360. 28709. 33‘80. 3‘8‘8. 2902. 1275‘. 288‘6. 28‘38. 35913. 358“. 3237. 13‘1‘. 29502. 21267. 36‘59. 36719. 3371. 1‘136. 22079. 28166. 37195. 32622. 3‘95. 1‘827. 26609. 31633. 37156. 30677. 3638. 15505. 285‘3. 22819. 35628. 33811. 37“. 15966. 21670. 18535. 267‘9. 35165. 2862. 16781. 18316. 26730. 32115. 36136. 2‘37. 17329. 27223. 30901. 30995. 259‘7. 3702. 122‘2. 30812. 32186. 2‘251. 31717. 28“. 15337. 32176. 31318. 299‘5. 23896. ‘176. 171‘7. 31985. 32611. 3“35. 20079. ‘9“. 19355. 33681. 33932. 35881. 283‘7. 3‘93. 20287. 3‘3‘2. 35262. 32809. 313‘0. 2810. 21119. 250‘2. 35368. 31170. 328520 ‘96‘. 1‘728. 29895. 35625. 3363‘. 23975. 6016. 19720. 325‘8. 329‘1. 25068. 30006. 6821. 22331. 2‘289. 3‘901. 29“2. 31362. 1031. 240... 2.245. ' 3523.. 33795. 33.1.. ‘779. 16675. 27231. 3579‘. 30707. 351‘2. 6755. 21‘87. 30893. 3‘580. 33987. 259060 79‘2. 2‘512. 23116. 25‘6‘. 30222. 30831. 5‘27. 17232. 28713. 29531. 3063‘. 321‘7. ‘226. 22969. 32‘10. 33“6. 33833. 3‘16‘. 71“. 25‘97. 3‘576. 3‘2‘3. 3097‘. 3‘202. 861‘. 26333. 25017. 3“29. 33535. 3‘615. 587‘. 28‘88. 20‘15. 32850. 32615. 25‘3‘. ‘553. 29559. 18091. 32‘35. 2‘20‘. 31‘08. 7719. 01001. 26875. 2‘328. 29990. 3“‘6. 9257. 31886. 29876. 30251. 31661. 3‘111. 6325. 332‘6. 22050. 23225. 28968. 35‘66. 896‘. 23228. 181“. 27289. 277‘9. 3‘2‘0. 10359. 27016. 16106. 29539. 28862. 33252. 11228. 3006‘. 0‘852. 282‘1. 28‘33. 32056. 118‘2. 31585. 1903‘. 29917. 21683. 3‘377. 12219. 3136‘. 267“. 32653. 27151. 25633. 12168. 315‘9. 302‘7. 30809. 30622. 317‘3. 1289‘. 327‘5. 2152‘. 3366‘. 30‘05. 29555. 13388. 32333. 27560. 3‘765. 27891. 32032. 13721. 33‘65. 29006. 35081. 26592. 3‘928. 169 Table 26. Values for population size at CLUTCH decreased by 15% (Fig- ure 16). 9730. 6371. 632‘. 17292. 21393. 21667. 21797. ‘205. 1‘09. X7627. 19‘17. 20069. 16000. 379‘. 5‘62. 12729. 1,265. 19‘33. 20‘60. 362‘. 6550. 1:360. 13519. 22663. 22636. 3:23. ‘92:. 1‘138. 178‘6. 23993. 2‘162. 3368. 6’25. 10963. 23105. 2“27. 17315. 3268. ‘692. ,3‘0. 22002. 25098. 21235. 3:90. 590‘. 0‘23. 22915. 2525‘. 2300‘. 3125. 6‘29. 13806. 21366. 25765. 2‘662. 3651. 6737. 16530. 22:39. 26215. 25‘96. 2979. 7:39. 17772. 20052. 23932. 2‘953. 2:10. 7127. 18537. 202‘7. 25:80. 25529. 27‘5. 7‘51. 1,‘30. 15193. 2650‘. 26012. 2319. 7010. 13762. 23‘37. 26622. 225‘6. 29cc. 51‘2. 17719. 22568. 26612. 21263. 3090. 9‘61. 20009. 16235. 25135. 23822. 3050. 9611. 1‘335. 13225. 1893‘. 25002. 2‘08. 9000. 11520. 191‘9. 23006. 25513. 2099. 020‘. 11310. 22022. 22158. 15375. 3020. 6671. 21111. 22630. 1731‘. 22535. 2350. 5220. 2177‘. 21956. 21365. 1697‘. 3339. 910’. 23119. 23‘1‘. 2‘397. 1‘262. 3061. 10165. 23202. 2‘352. 25859. 20390. 2825. 18‘95. 23‘39. 2‘916. 23252. 22‘35. 2333. 13821. 16720. 25‘00. 22736. 23350. 3852. 7121. 20366. 25606. 2‘5!‘. 170‘?. ‘586. 1015‘. 21767. 23‘52. 18163. 210‘7. 515‘. 11367. 160‘!. 2‘663. 20310. 22161. 5311. 12175. 1,302.. 25319. 23961. 23691. 3701. 3538. 19756. 25505. 21037. 2‘568. 5067. 10732. 21‘63. 2‘336. 2‘131. 17525. 5690. 32130. 15797. 17916. 21735. 21‘52. ‘120. 570‘. 19666. 23875. izcal. 2291‘. 5273. 1:306. 2223’. 23‘65. Z‘CO‘. 2385‘. 5280. 12310. 23‘65. 23972. 22301. 2‘080. 6260. 12657. 169‘2. 2‘139. 2373‘. 23977. ‘37.. 13536. 13611. 229‘8. 230“. 11690. 3‘56. 13062. 122‘9. 22913. 17159. 221‘9. 5593. 1“29. 10:03. 11019. 21038. 23926. 6532. 1‘670. 20695. 20975. 22580. 2‘08‘. ‘60‘. 15190. 15236. 16153. 200‘7. 2‘712. 6353. :06‘2. 12530. 15027. 19822. 23707. 7239. 13‘31. 11216. 20757. 21036. 23‘36. 7805. 15001. 1733‘. 19,03. 20‘92. 22535. 8175. 1585‘. 13369. 29055. 15532. 2“B‘. 33‘3. 1571‘. 1.615. 23060. 19‘I1. 16153. 829‘. 151.3. 2119,. 21721. 21837. 22593. 67‘2. 16526. 15206. 23‘02. 21783. 21226. 3959. :63‘6. 10263. 2“82. 20015. 2391‘. 9076. 1705‘. 20045. 2“67. 187‘0. 2‘5‘3. Table 27. 170 first 20 years of life (Figure 17a). Values for population size at raised PSURV values for the 9730. 7157. 5273. 5000. Q977. Q097. Q791. Q750. Q721. Q699. Q666. Q637. Q090. QQ31. Q595. Q70Q. 500Q. 5239. Q363. 3930. 5520. Q525. 6313. 7Q73. 57Q9. Q970. 0059. 9667. 11190. 11023. 0092. 12009. 13992. 10503. 0002. 13Q00. 1501Q. 11092. 10000. 15160. 17705. 13QQ9. 10111. 2000Q. 22752. 2QQ63. 25061. 265Q2. 20551. 3020Q. 31093. 2QQ93. 29112. 23206. 20Q7Q. 22003. 20560. 23067. 29Q67. 32096. 33070. 30000. 33017. 3Q67Q. 36635. 30073. 39265. 37Q27. 30Q33. 36670. 3069Q. 35673. 30103. 3999Q. 35657. 3QQ21. 29696. 36Q62. 30129. Q0010. 330Q7. 33960. 30007. 319Q2. 3763Q. 35661. 39171. Q0536. 30200. Q0603. 30903. Q1Q99. 3Q363. 35703. 39591. Q2217. Q30Q2. QQ376. Q5027. Q5705. Q601Q. QQQ13. Q5035. 375Q3. 33300. 3Q091. 311QQ. 209Q2. 27Q36. 36590. 39673. 37960. 3Q059. 3Q290. 29006. 32Q77. 3Q113. 20Q07. 25553. 33660. 36977. 30033. 30570. Q0015. Q2070. 33693. 37939. Q066Q. 33227. 3Q099.‘ 32509. 37237. 30757. 36Q17. 39063. Q0761. 331Q2. 29QQO. 27205. 3Q335. 37150. 30506. 27271. 25395. 32Q72. 27Q32. 3Q361. 37761. 30277. 35650. 3Q635. 37920. 33555. 32650. 30337. 27Q05. 31969. 35Q50. 360QQ. 3267Q. 3Q035. 30331. 29300. 25112. 32032. 36236. 20906. 25602. 33962. 37000. 36330. 35Q13. 37052. Q0191. Q2051. Q3320. Q2076. 3005Q. Q0701. Q2622. Q266Q. Q0750. 33507. 35000. Q05Q6. Q0392. Q10Q9. 37QQ7. 37502. 31371. 36510. 3076Q. 33Q03. 35675. 32357. 33939. 37Q72. 33017. 37031. 39271. Q0016. 35320. 31Q7Q. 29097. 3Q50Q. 37791. 391Q0. 39020. Q1023. Q26Q7. QQ1Q2. 303Q5. Q1Q51. Q3107. Q3607. QQ750. Q0073. 3Q562. 30559. 3Q665. 30Q00. 35206. 30909. Q1Q66. 36030. 33922. 30500. 31Q99. 33070. 303Q0. 32352. 36672. 319Q2. 32239. 35097. 33058. 36Q09. 3Q777. 20550. 33606. 36250. 31303. 20792. 30020. 2092Q. 2Q6Q9. 29060. 31270. 31619. 27126. 253Q5. 30500. 2Q605. 3070Q. 3Q19Q. 36736. 20937. 3Q3Q5. 35729. 30Q97. 30060. 30102. Q0707. Q2290. 36Q32. 33Q53. 37935. QOQ17. Q0700. 323.1. 303Q5. 31339. 27011. 35556. 3069Q. 39057. 31700. 36195. 37001. Q0399. Q2Q21. 3Q157. 39071. 39769. Q2107. Q2711. Q25Q0. 35069. Q0092. Q2906. Q1021. Q3620. Q0607. 39976. 36903. 39036. 33669. 39906. 35037. 30115. Q1170. Table 28. 171 first 20 years of life (Figure 17a). Values for population size at lowered PSURV values for the 9730. 6139. 3739. 3273. 29Q1. 2721. 2520. 2Q07. 23Q1. 2303. 225Q. 2150. 1599. 100Q. 193Q. 1971. 2009. 1960. 1332. 1032. 1572. 1099. 1507. 1000. 1359. 1162. 1712. 1905. 2070. 2071. 13Q6. 1061. 2112. 1355. 1177. 1002. 2059. 1Q50.. 1052. 1732. 1907. 1QQ2. 1093. 2090. 2185. 2235. 2227. 217Q. 2229. 2237. 221Q. 1376. 1727. 1220. 1590. 1103. 1Q35. 911. 1276. 1Q09. 1Q65. 1501. 1Q95. 151Q. 1532. 15Q2. 15Q9. 1535. 15Q5. 1535. 10Q9. 1293. 1Q00. 1Q95. 1510. 1539. 966. 1329. 1Q79. 1561. 1059. 13Q0. 1Q91. 929. 1302. 1Q30. 1Q09. 1561. 150Q. 1610. 162Q. 16Q7. 111Q. 1300. 1525. 1507. 1570. 1573. 1605. 1571. 1590. 1579. 1570. 1059. 015. 1137. 01Q. 663. 501. 1017. 1216. 1300. 1360. 1QOQ. 9Q6. 121Q. 1336. 907. 631. 1060. 1257. 1303. 1370. 1Q10. 1QQO. 969. 1233. 1305. 091. 1163.7 1271. 1305. 611. 1090. 1252. 1326. 017. 502. Q56. 077. 109Q. 7Q2. 51Q. Q69. 071. 61Q. 933. 1076. 720. 970. 1076. 1096. 1110. 1131. 1126. 1117. 1095. 1119. 113Q. 1120. 1139. 1131. 1137. 709. 952. 10Q0. 652. Q67. 790. 92Q. 902. 1010. 1039. 1056. 1065. 1060. 1066. 10Q5. 10Q6. 10Q5. 10Q2. 1027. 696. 050. 93Q. 962. 975. 971. 972. 661. 033. 537. 762. 060. 912. 95Q. 99Q. 1000. 10Q1. 106Q. 10Q7. 105Q. 1060. 1062. 1005. 1095. 1065. 1003. 105Q. 1069. 1072. 105Q. 1056. 1053. 10Q7. 1011. 1013. 6Q0. 0Q2. 912. 579. 009. 915. 97Q. 992. 100Q. 996. 62Q. 0Q0. 939. 965. 999. 997. 1010. 1029. 102Q. 10Q1. 10Q2. 70Q. 090. 967. 900. 999. 1022. 1032. 699. 091. 900. 1012. 1020. 1035. 1060. 713. 900. 903. 1021. 63Q. 023. 927. 977. 1002. 1011. 1021. 1023. 100Q. 993. 1005. 1000. 1011. 633. 033. 530. 397. 707. 012. 09Q. 605. 000. 093. 9Q6. 976. 655. BQ3. 919. 966. 900. 1001. 619. 035. 921. 95Q. 976. 901. 90Q. 979. 990. 616. 016. 079. 910. 991. Table 29. 172 Values for population size at to 95% (Figure 17b). asymptotic PSURV values lowered 9730. 6979. 9299. 3079. 3710. 3599. 3921. 3291. 3199. 3137. 3009. 3090. 2971. 2739. 2019. 2020. 2015. 2759. 2120. 1009. 2960. 1921. 2593. 2939. 2105. 1695. 2717. 3197. 3950. 3965. 2300. 3192. 3552. 2962. 1923. 2950. 3916. 2371. 1050. 2039. 3253. 2313. 3013. 3335. 3997. 3500. 3590. 3999. 3603. 3655. 3676. 2500. 3000. 2307. 2769. 2290. 2611. 1959. 2923. 2606. 2690. 2760. 2799. 2012. 2000. 2939. 2970. 2973. 3033. 3035. 2305. 2691. 2009. 3037. 3073. 3096. 2205. 2765. 3012. 3150. 2363. 2739. 2906. 2192. 2679. 2066. 2090. 3033. 3060. 3127. 3131. 3102. 2906. 2707. 3020. 3129. 3055. 3019. 3125. 3056. 3152. 3163. 3100. 2999. 2076. 2597. 2093. 1099. 1696. 2377. 2690. 2016. 2070. 2937. 2205. 2619. 2099. 2161. 1602. 2910. 2762. 2707. 2909. 3000. 3069. 2203. 2609. 2770. 2161. 2553. 2715.. 2735. 1962. 2393. 2652. 2792. 1979. 1575. 1369. 1909. 2367. 1066. 1937. 1391. 2019. 1651. 2130. 2360. 1009. 2209. 2366. 2379. 2927. 2971. 2979. 2970. 2950. 2530. 2500. 2563. 2505. 2552. 2560. 1033. 2299. 2939. 1759. 1915. 1903. 2299. 2396. 2377. 2930. 2969. 2990. 2520. 2537. 2503. 2537. 2560. 2576. 2556. 1995. 2265. 2935. 2500. 2531. 2521. 2539. 1909. 2291. 1699. 2117. 2325. 2307. 2956. 2535. 2539. 2613. 2666. 2599. 2606. 2619. 2629. 2709. 2797. 2669. 2730. 2673. 2793. 2776. 2797. 2779. 2796. 2009. 2721. 2790. 1999. 2909. 2551. 1079. 2326. 2563. 2605. 2697. 2711. 2679. 1930. 2300. 2629. 2670. 2779. 2752. 2795. 2069. 2095. 2907. 2919. 2297. 2605. 2775. 2799. 2002. 2099. 2061. 2220. 2572. 2750. 2031. 2026. 2029. 2903. 2299. 2603. 2790. 2097. 2066. 2910. 2679. 2029. 2093. 2910. 2962. 2905. 2929. 2911. 2977. 3012. 3039. 2375.. 2630. 1962. 1629. 2332. 2520. 2721. 2095. 2507. 2695. 2032. 2900. 2209. 2596. 2769. 2097. 2999. 2901. 2109. 2607. 2037. 2916. 2971. 2970. 2970. 2950. 3003. 2190. 2609. 2750. 2059. 2919. 173 Table 30. Values for population size at asymptotic PSURV values lowered to 932 (Figure 17b). 973'. “73. 1‘9‘. 20“. 15.9. 1818. 2027. ‘237. 19". 2099. 1‘27. 1827. 15.7. 3843. 133.. 15‘3. 1‘59. 183‘. 17“. 3‘59. 19“. 129?. 1‘7‘. 1875. 1932. 3520. 1‘35. 1‘58. 1‘81. 1900. 2005. 3328. 1739. 1319.‘ 1‘70. 1580. 139‘. 317‘. 12“. 1137. 1712. 1911. 1‘92. 305‘. 1‘38. 103.. 17‘3. 1893. 137'. 2962. 179.. 150‘. 1739. 1921. 19‘3. 2882. 1‘39. 172‘. 17‘5. 193‘. 200‘. 2511. 19.2. 181‘. 172‘. 1925. 202‘. 22“. 19.1. 135‘. 1723. 19‘2. 203‘. 2“‘. 1933. 139‘. 120‘. 1952. 2971. 252‘. 19“. 1392. 1‘7‘. 1959. 20“. 255‘. 19". 1‘1‘. 1599. 1923. 20“. 2577. 20“. 1.25. 1135. 193‘. 2079. 2‘91. 20“. 13‘1. ‘99. 137‘. 2099. 1877. 2°29. 1032. 1271. 1‘77. 211‘. 155‘. 2.27. 131‘. 1“3. 179‘. 1‘02. 2033. 151‘. 17". 151‘. 1287. 1‘11. 157‘. 17“. 1‘11. 15‘3. 1‘17. 1322. 20“. 1l‘9. 1‘72. 158.. 1735. 1072. 22‘1. 1993. 1923. 1‘09. 1871. 15... 17‘0. 2.1.. 1959. 1‘33. 1891. 17“. 1‘95. 2019. 1‘30. 1.60. 1906. 1.35. 2089. 1‘11. 1709. 1‘82. 1910. 139‘. 23.9. 17‘3. 1‘09. 1‘90. 133‘. 1700. 2“9. 192.. 133‘. 17". 1“3. 18‘2. 2‘38. 29.3. 1‘3‘. 1735. 183‘. 193‘. 1‘31. 1‘.‘. 1’59. 1757. 18“. 19.3. 21". 19“. 1‘99. 175‘. 19“. 1‘55. 2372. 19.1. 125‘. 1299. 19‘2. 17". 1‘52. 1337. 1550. 1339. 1971. 1300. 1‘57. 1‘95. 173‘. 1‘71. 2010. 19“. 1930. 183‘. 1820. 172‘. 2005. 20". 2195. 1‘9‘. 125‘. 1750. 20‘.. 2027. 1‘93. 19.5. 97‘. 1732. 20‘7. 139‘. 127‘. 19.3. ‘3'. 17‘2. 1520. 1'53. 181‘. 2.2.. 13.1. 13.1. 1797. 1917. 20.3. 2.29. 15“. 155‘. 1929. 19.1. 1591. 203.. 1153. 1125. 19“. 2919. 192‘. 152‘. ‘7‘. 1“3. 1915. 2.23. 20“. 1793. ‘9‘. 139‘. 2°33. 203‘. 2173. 19“. 1211. 1‘55. 2913. 203.. 2221. 201‘. 9“. 1701. 1501. 295‘. 2223. 2913. 13.5. 1145. 1713. 1‘39. 2239. 2012. 1511. 1755. 1912. 19‘1. 22.2. 205‘. 1100. 179‘. 1979. 18.2. 23.9. 29‘1. 1‘93. 1.30. 1979. 1935. 2325. 29.1. 153‘. 181‘. 1933. 199‘. 174 Table 31. Values for population size at asymptotic PSURV values lowered to 921 (Figure 17b). 973°. “7‘. 1392. 133°. 791. "59. 5‘3. ‘231. 1‘52. 1380. 309. ‘61. ‘31. 382‘. 1271. 1021. ‘22. ‘61. 51‘. 3‘32. 1519. 3‘1. 82‘. ‘71. 53‘. 3‘82. 1112. 1072. 822. ‘77. 31‘. 3277. 1‘00. 3‘1. 80‘. 6‘3. 39‘. 310‘. 1021. 725. ‘19. ‘72. ‘7‘. 29“. 1290. ‘51. 827. ‘59. 529. 2355. 1392. 955. ‘20. ‘6‘. 53‘. 2757. 1‘35. 1092. ‘15. ‘68. 5‘2. 2‘7‘. 1“3. 11‘5. ‘00. “1. 5“. 21“. 1‘58. 11“. 793. ‘52. $71. 231‘. 1‘19. 1191. 55‘. 6‘2. 512. 2358. 1503. 8“. ‘73. ‘60. 5“. 231‘. 1522. 19‘3. 121. “3. 572. 2379. 153‘. 1135. 51‘. “‘. 575. 2357. 153‘. ‘3‘. ‘07. ‘57. 577. 17“. 15“. ‘31. 5‘5. 558. 379. 1‘29. 15‘1. 92‘. ‘3‘. ‘0‘. ‘0‘. 185‘. 1152. 1911. “1. ‘30. ‘9'. 1‘2‘. 13“. 109‘. “O. 537. 357. 152‘. 1‘37. 1132. “0. 5‘3. 2“. 19“. 1519. 1159. “8. ‘12. ‘22. 1570. 1531. 1195. ‘9‘. ‘15. “5. 135‘. 1332. 0‘9. 102. ‘13. ‘99. 1309. 13‘2. 1005. 70‘. ‘13. 3“. 19“. 1319. 19‘9. 703. ‘27. “‘. 2977. 1‘29. 1‘3. 711. 53‘. ‘8‘. 2962. 1“2. 93‘. 719. 591. 50‘. 1‘18. 1059. 19.1. 72‘. ‘02. 51‘. 179‘. 127‘. 101‘. 718. ‘17. 375. 199‘. 1381. 707. 531. ‘13. ‘52. 1377. 9“. ‘55. ‘37. ‘20. ‘89. 1209. 121‘. 95‘. ‘80. ‘30. 507. 1‘53. 1312. 99‘. ‘93. ‘2‘. 517. 1857. 13‘2. ‘89. ‘97. ‘32. 323. 1‘0‘. 1392. 53‘. ‘92. ‘32. 359. 10“. 1‘00. ‘52. ‘90. “5. “7. 1587. 1‘19. ‘92. 512. 551. ‘0‘. 133‘. 1‘29. 820. ‘0‘. 590. 50.. 1357. 1‘32. ‘99. ‘3‘. 59‘. 5.5. 1732. 1053. ‘59. 5‘2. 593. 30‘. 1901. 12‘1. ‘21. ‘17. 59‘. 51.. 1979. 133‘. ‘10. ‘29. 598. 50‘. 2013. 1379. 515. 6.0. “3. 50'. 2012. 1363. ‘95. ‘51. 527. 35‘. 1989. 1335. T79. ‘31. 5“. ‘2‘. 2013. 1379. 5‘1. “‘. 57‘. “2. 2022. 13“. 71‘. ‘73. 575. ‘75. 2.23. 1385. 717. “0. 57‘. ‘00. Table 32. 175 meters, but PSURV(I) raised to 100.0 (Figures 12 and 18). Values for population size at original values for all para- 9738. 1559. ‘812. 5178. 5‘52. 5‘61. 5788. 57‘7. 5779. 379‘. 5759. 57‘1. “92. 5238. 5‘87. 5915. ‘2‘8. ‘58‘. ‘788. 3815. ‘51‘. ‘71‘. 7‘88. 9589. ‘387. ‘818. 9783. 12359. 1‘329. 1‘982. 9‘35. 1“29. 1766‘. 11531. 8‘15. 16269. 283‘8. 13229. 982‘. 18528. 23171. 15188. 22798. 27847. 29853. 32871. 33925. 3‘07). 36868. 3919‘. ‘1357. 27589. 3‘812. 252“. 35882. 25217. 3‘231. 25588. 37989. “355. ‘8731. 52558. 85373. 35888. 57528. 58981. 59761. 88685. ‘8227. 59585. ‘2559. 51983. 5‘538. ‘1322. 59252. 583“. ‘292‘. 87285. ‘273‘. “25‘. ‘1557. 5‘5‘9. 6‘2‘1. ‘7119. ‘88‘3. ‘13‘8. ‘39‘8. ‘9815. “8‘3. 71639. ‘9‘91. 71717. 82928. ‘1833. 71137. "538. 7‘883. 75353. 78171. 788‘7. 7818‘. 7171‘. 885‘8. 59“8. ‘92‘8. ‘1235. ‘9‘58. ‘335‘. 39781. 51‘88. ‘1‘65. “378. 6113‘. “788. ‘8811. 59‘63.- “3‘8. ‘82“. ‘83‘2. 5979‘. ‘17‘1. ‘9‘2‘. ‘8‘23. 71‘29. 7“‘9. 53965. ‘888‘. ‘92‘2. 51551. 8823‘. 58213. “29‘. 0922‘. ‘2527. ‘1878. 11“‘. 5195‘. ‘2578. 37818. 8‘799. ‘251‘. “223. 381‘1. 33958. 82119. ‘812‘. 57577. 52552. “981. 5718‘. 68828. 5388‘. 59687. 589‘8. 5837‘. 5:658. ‘8883. “‘33. ‘1588. ‘137‘. ‘5553. 59998. 58581. “118. 591“. “895. ‘E783. 38339. 55“‘. ‘5815. ‘382'. ‘51‘8. ‘18‘8. 71293. 1‘9‘3. 73829. 75‘E8. ‘98“. 7‘738. 73872. 7‘81‘. 72938. 5359‘. ‘278‘. 7182‘. 71518. 73138. 7116‘. ‘91‘2. 51671. ‘25“. ‘8382. 5‘92‘. ‘2827. 5856‘. ‘2783. 78188. ‘7119. 7335‘. 7‘7‘5. 1‘927. ‘1‘8‘. ‘1181. 5981‘. ‘9125. 7‘819. 75‘59. 78312. 78193. 8896‘. 19523. 7259‘. 78355. 1‘1‘1. 79298. 19593. 76759. 57721. ‘8822. ‘783‘. 32‘69. ‘5321. 72872. 77‘21. ‘8“2. “887. ‘91‘1. 52322. 599‘3. ‘828‘. ‘877‘. 71829. 63931. “983. 71551. ‘7123. 73‘89. 11982. 52712. ‘581‘. 71135. ‘2283. 578‘9. ‘1‘6‘. 58273. ‘51“. 55619. $3315. “5‘7. 5887‘. 5“9‘. ‘5‘51. ‘76‘9. 59283. ‘77‘8. ‘9292. 58189. 59598. “1“. ‘9281. 7‘28‘. 78187. 71317. 72219. ‘6888. “573. 71898. 73361. 7‘6‘8. 33‘52. ‘725‘. 58121. ‘1771. 598‘8. ‘5‘38. 78185. 55“5. 63711. “592. ‘9538. 73882. 528‘8. 63832. ‘72‘8. 78971. 72573. 7‘278. 5‘893. 67288. 72912. 72625. 1“33. 7‘178. 73598. ‘8‘35. 7868‘. 533‘2. “928. 62931. “23‘. 73119. 176 Table 33. Values for population size at constrained juvenile survival, and PSURV(I) raised to 100.0 (Figure 18). 0030. 030‘. 30‘0. 0031. 00‘3. 0‘33. 103.1. 0003. 0033. ‘003. 0133. 0000. ‘301. 03.0. 3333. 0303. 0330. 0000. 003.. 0‘3‘. 0303. 3300. ‘300. 0033. 000.- 030‘. 3103. 0“.. 0300. 0100. 00‘3. 0001. 0300. 33.0. 0100. 00‘0. 30.0. 0000. 3303. 3303. 0300. 0030. 0‘00. 0003. 300‘. 300‘. ‘003. 0‘00. 00.3. 033‘. 030‘. 0100. ‘313. 0000. .003. 033.. 0“3. 0103. 0303. 0000. 10030. 0000. 000‘. 3000. 0000. 0001. .10300. 3000. 0.03. 0033. “01. 0111. 10333. 3030. 00.3. ‘301. 0003. 0100. 10.33. 0013. 00‘1. 0131. 000‘. 0103. 103.3. 0130. 3113. 0001. 0113. 0‘00. 103‘3. 033‘. 3133. ‘103. 3010. 00‘0. 10.00. 03.3. 3130. 3010. 3000. 00‘0. 100.0. 3“3. 0300. 3300. 0000. ‘313. 1000‘. 3000. 0330. 0030. 0000. 0310. “31. 3311. 3‘33. 0000. 0000. 0031. 0003. 3031. 0330. 3030. ‘01.. 0313. 3303. 33‘.. 0330. ‘33‘. ‘30.. 03‘0. 3030. 3000. 30‘1. ‘030. ‘003. 700‘. 03‘3. 3013. 03‘3. ‘001. 0303. 01‘3. 0003. 330‘. 0000. 0300. 0‘33. 0010. 0‘30. 301.. 3303. 0000. 0‘30. .103. 3013. 0300. 0‘00. ‘003. ‘3‘0. 00‘0. 0‘01. 000‘. 0330. 3003. 0303. 0000. 00... 0000. 3‘00. 0300. 0‘00. 003‘. 10000. 3030. 3030. 0133. 0‘10. .301. 11130. 0333. 0001. 0100. 0300. 0003. ‘0... 30.0. 0330. 3000. 0300. 0033. 03.0. 30.0. 3300. 0031. 3003. 0000. 10300. 33‘3. 003.. 010‘. 0030. 0133. 11331. 033‘. 001‘. ‘300. 0300. 0100. 11330. 313‘. 00‘0. 3030. ‘300. 03‘3. 1100‘. 3331. 3033. 3‘03. .003. 0030. 0330. 0100. 0003. 3000. 03‘0. 0000. 0033. 0330. 0303. 0003. 0303. '00.. 11033. 0310. ‘30.. 0300. 3330. 0“3. 11313. 3303. 0331. 3300. 3003. 000‘. 110‘3. 0030. 0333. 3333. 3103. 0100. 11000. 0‘03. 0030. 1030. 0000. 0000. 13103. 00.0. 0003. 0333. 0330. 0000. 1331‘. ‘1... ‘30.. 3003. “‘3. 0003. 133“. 0303. ‘131. 0.0.. 003‘. 00.1. 09500 ‘003. ‘030. 0‘1‘. 0301. 0133. 10033. ‘30.. ‘003. 3‘03. 0310. 0‘13. 11033. ‘30.. ‘103. 3130. 0030. 00“. 113.0. ‘001.' ‘000. 0000. 0010. 0000. 1103‘. 177 Table 34. Values for population size at initial ages of cannibalism of 11 for males and 18 for females (growth rates of Graham (1976)) (Figure 19). 9039. 6002. 0209. 23001. 20009. 20209. 31116. 0263. 8591. 20060. 10001. 10306. 13031. 3926. 6301. 10306. 19303. 1600‘. 20036. 3003. 0603. 13003. 10010. 21309. 23269. 3012. 3030. 19110. 16669. 23310. 23103. 3530. 0215. 10030. 20033. 30009. 10063. 30.0. 3.00. 12303. 32030. 25000. 32230. 3302. 6968. 11230. 30000. 26101. 30000. 3323. 0300. 10200. 21211. 26098. 33003. 3210. 7802. 33330. 22300. 20060. 26933. 3000. 0208. 20013. 10213. 23000. 36630. 2306. 0103. 31360. 19133. 26000. 30602. 2839. 0010. 20061. 10336. 20000. 30303. 2100. 9310. 13310. 30666. 30990. 33933. 3830. 9036. 10300. 23100. 20231. 31030. 3056. 10310. 10030. 16330. 23030. 33000. 2930. 10300. 10003. 13111. 10230. 36000. 3330. 10000. 13360. 20330. 30000. 30300. 2060. 11215. 10300. 33302. 22132. 10003. 3163. 0030. 22003. 33006. 10100. 33030. 2030. 10233. 30000. 32036. 31000. 10300. 3319. 11306. 33300. 33101. 23000. 10303. 0060. 13005. 33063. 36000. 20060. 21000. 2933. 13100. 2300’. 36030. 33001. 33003. 3300. 13303. 10060. 26002. 33303. 303000 0331. 0332. 33633. 30333. 33000. 10006. 0930. 13030. 30663. 20030. 10100. 31600. 3633. 10360. 10033.' 36003. 30300. 32130. 3390. 13033. 20000. 30100. 20303. 30303. 0021. 10000. 10333. 30011. 30610. 33300. 5606. 13001. 23000. 33801. 20100. 10130. 6600. 13020. 16060. 10000. 10002. 31000. 0533. 11100. 23100. 31003. 30333. 32303. 3309. 10000. 30910. 30903. 33102. 30660. 3033. 13032. 36330. 23030. 20036. 30030. 7003. 16300. 10001. 33033. 33303. 30100. 0060. 10006. 13360. 22060. 33033. 10031. 3003. 10133. 13006. 32000. 16130. 33030. 6331. 1000‘. 30601. 16000. 30010. 30006. 0063. 19306. 33300. 21603. 33001. 30033. 3109. 30030. 10002. 16003. 10066. 33030. 0226. 10130. 13000. 10316. 10203. 33003. 0301. 10500. 13300. 30133. 10030. 33031. 8003. 19000. 10003. -10663. 10061. 30903. 0303. 2112.. 10961. 10331. 13602. 30302. 0305. 21060. 31030. 33031. 10300. 10013. 9301. 31310. 30333. 30013. 20600. 33031. 10031. 23310. 10102. 33000. 30000. 30300. 10360. 32100. 31023. 30363. 10031. 32033. 10301. 33190. 33010. 33003. 16030. 30000. 178 Table 35. Values for population size at initial ages of cannibalism of 35 for males and 46 for females (growth rates of Graham (1968)) (Figure 19). 9730. 6090. 0067. 30291. 29300. 32903. 32500. 0271. 9691. 31070. 28133. 32278. 20077. 3933. 7090. 22170. 28311. 32302. 29076. 3020. 0066. 17081. 20190. 30093. 32010. 3750. 6612. 23009. 28161. 35250. 30000. 3636. 0307. 10556. 20022. 35019. 25180. 3553. 6300. 15057. 30522. 35007. 29651. 3002. 01,3. 10315. 31066. 30903. 323113 3022. 9111. 22135. 30019. 35756. 30092. 3353. 9690. 25003. 31002. 36295. 30060. 3301. 10163. 27039. 29620. 30.16. 30509. 2739. 10097. 27002. 29909. 36191. 35176. 3023. 10907. 20390. 22387. 36252. 35501. 3159. 11037. 20750. 20205. 36520. 33055. 3266. 11933. 25218. 31150. 35912. 31000. 3377. 12031. 27.07. 22005. 35517. 335.6. 3527. 12909. 20719. 10700. 27091. 30350. 2717. 13000. 17230. 26210. 31007. 35311. 2326. 10001. 20037. 29050. 32220. 260,1. 3029. 9972. 20135. 30529. 25270. 31010. 2671. 12219. 2.506. 30509. 30252. 20193. 3370. 13532. 29009. 32232. 33696. 20616. 0606. 15201. 30056. 32793. 35500. 20230. 3283. 16120. 31916. 33507. 33520. 30700. 2659. 16822. 23271. 300,7. 32605. 31366. 0516. 11021. 20395. 33807. 33537. 23800. 5501. 15059. 2,733. 3239’. 25500. 29213. 6213. 17001. 22379.. 33030. 30350. 31156. 6330. 10650. 27038. 30106. 33610. 33159. 0357. 13067. 2.682. 30757. 32135. 30111. 6090. 16706. 29807. 33751. 3051.. 25159. 7080. 10860. 22326. 25113. 32622. 30201. 0099. 13010. 26769. 29535. 32091. 32021. 3050. 17570. 30265. 32076. 30290. 30003. 6333. 19560. 31612. 32816. 33215. 30036. 7605. 20011. 23322. 33101. 30670. 30552. 5207. 21536. 10200. 32513. 30501. 25603. 0100. 22010. 17229. 32006. 25960. 30951. 6750. 23331. 20560. 20690. 31100. 33532. 0130. 20003. 27050. 29562. 33219. 30271. 5610. 20906. 20925. 23000. 32121. 30613. 7023. 17600. 17000. 27683. 31561. 30010. 0900. 22355. 15501. 30526. 32750. 30115. 0706. 25015. 23606. -30007. 32161. 330,1. 10200. 26560. 10370. 31790. 20616. 30030. 10521. 26360. 23339. 33270. 29291. 25030. 10038. 26516. 20609. 32025. 31,60. 30105. 11026. 20135. 20601. 30099. 32701. 31151. 11010. 2793.. 26276. 35119. 31578. 33106. 11605. 2906,. 20025. 30059. 30200. 30126. Table 36. (Figure 20a). 179 Values for population size at initial age of egg laying of 10 0730. 6461. 4254. 3014. 3705. 3724. 3501. 3506. 3441. 3330. 3316. 3240. 2702. 2097. 3091. 3103. 3315. 3303. 2631. 2264. 3356. 2613. 3751. 4307. 3153. 2567. 4414. 5206. 5060. 6154. 4227. 5000. 6007. 4756. 3737. 6103. 7306. 5000. 3000. 6610. 7067. 5433. 7605. 0743. 0441. 0025. 10106. 10136. 10600. 11057. 11270. 7000. 0302. 6011. 043‘. 6300. 7036. 6003. 7746. 0532. 0025. 0405. 0605. 10160. 10602. 11173. 11651. 11034. 12511. 12063. 0101. 11430. 12726. 14200. 14075. 15410. 15065. 14424. 16250. 17466. 12103. 15501. 17500. 12400. 16435. 15000. 10626. 20036. 20661. 21500. 22003. 22054. 16211. 20440. 22062. 24305. 24263. 24423. 25022. 25645. 26071. 21544. 20240. 20163. 16276. 22060. 17403. 14760. 13244. 20604. 24245. 24625. 23035. 24730. 10212. 22014. 23704. 17064. 14071. 22351. 25500. 26502. 26756. 27724. 20774. 20033. 25371. 27000. 20177. 23613. 23706. 26200. 10571. 24676. 27607. 20436. 21270. 17360. 15411. 22646. 26057. 10161. 15754. 14003. 22064. 16031. 23600. 26764. 10041. 24110. 25374. 26456. 24020. 23650. 22303. 21605. 24216. 26403. 27250. 25625. 26404. 24464. 24423. 10244. 24470. 27017. 10507. 15050. 23072. 26601. 27153. 26145. 20012. 20315. 20654. 30150. 30655. 27704. 20212. 30127. 30750. 20577. 21740. 25374. 20500. 20056. 20020. 27560. 27700. 20764. 25403. 10600. 23051. 25377. 23036. 25302. 27700. 25062. 20340. 20332. 20731. 25000. 24300. 23606. 27530. 20073. 20317. 20030. 30110. 30563. 31175. 20504. 30677. 31252. 31722. 31534. 30246. 22735. 27410. 26305. 20640. 25425. 20110. 31020. 20634. 27310. 20203. 21720. 25410. 20056. 26374. 20130. 26076. 26720. 20061. 27143. 20200. 27000. 20774. 25022. 27425. 25136. 24021. 25021. 24644. 10700. 23356. 26111. 26450. 23063. 22763. 26076. 10106. 24305. 27400. 20202. 21015. 25737. 27304. 20150. 30000. 20046. 30044. 31407. 27602. 25716. 20746. 20062. 30460. 21065. 26030. 20206. 17005. 24333. 27050. 20006. 20454. 25103. 26324. 20006. 30020. 21670. 25005. 27126. 20044. 20105. 20010. 21203. 26750. 20700. 20067. 30022. 20412. 27005. 27075. 20173. 21603. 26001. 25067. 27613. 20502. Table 37. 180 (growth rates of Graham (1976)) (Figure 20). Values for population size at initial age of egg laying of 13 9730. 6016. 0231. 3000. 3606. 3009. 3030. 3336. 3270. 3207. 3210. 3190. 2621. 2929. 2900. 3030. 3070. 3013. 2016. 2120. 2709. 2209. 3002. 3069. 2621. 2216. 3610. 0290. 0096. 0116. 3072. 0990. 0002. 0000. 3233. 0333. 6307. 0019. 3071. 0011. 6902. 0766. 6602. 7602. 0270. 0669. 0026. 8111; 9160. 9000. 9077. 6093. 7676. 0660. 6700. 0101. 6166. 0760. 0006. 6313. 6090. 6060. 6009. 7173. 7096. 7703. 0070. 0100. 0003. 0723. 6309. 7913. 0013. 0099. 10200. 10690. 7620. 10207. 11001. 12000. 0709. 11003. 12073. 0932. 11792. 12703. 13110. 10000. 1.300. 10936. 10100. 10603. 11100. 13702. 10311. 16170. 10972. 10096. 16093. 16303. 16900. 17000. 17300. 12601. 10290. 13020. 10797. 9202. 0309. 13033. 16007. 17290. 10073. 10909. 13076. 17021. 19601. 10100. 11021. 17700. 20962. 21690. 23200. 20600. 20736. 17909. 23109. 20710. 17790. 23213. 26309. 10000. 23290. 26091. 20722. 20330. 16201. 10260. 21010. 26070. 10720. 10100. 13276. 20313. 10639. 21006. 20170. 17000. 22002. 23179. 20010. 22307. 22301. 21170. 20797. 23106. 20023. 26107. 20307. 20201. 22006. 22699. 17203. 23009. 20072. 10093. 10203. 22169. 20000. 20906. 20611. 27169. 27766. 20002. 29206. 29170. 26076. 20170. 29007. 29601. 20200. 20700. 20231. 27101. 27620. 27766. 26217. 26393. 19603. 20232. 10006. 21700. 23907. 22730. 23629. 26101. 20600. 26000. 27070. 20067. 20703. 23160. 22032. 20662. 27023. 27019. 20030. 20300. 29260. 29997. 27100. 20700. 29717. 30010. 30090. 20760. 21603. 26130. 20107. 19690. 20263. 27030. 29093. 27277. 26010. 20000. 20763. 20112. 27367. 20017. 27691. 20906. 20030. 27090. 20710. 27392. 26079. 19720. 20097. 20922. 23003. 22760. 23770. 23390. 17022. 22222. 20067. 20710. 22606. 21132. 20700. 10193. 23130. 26261. 27000. 19907. 20003. 20909. 27790. 20900. 20603. 29072. 29036. 26190. 20603. 27203. 20300. 29200. 20900. 20000. 19200. 16231. 23320. 20612. 26030. 19392. 20030. 20200. 27006. 20106. 20020. 20010. 20002. 27710. 27630. 27009. 20073. 20279. 27060. 27301. 20370. 27391. 26730. 20700. 27001. 20602. 20676. 20012. 26290. 20397. Table 38. 181 (growth rates of Graham (1968)) (Figure 20a). Values for population size at initial age of egg laying of 18 9733. 3333. 9233. 3395. 3971. 3333. 3133. 3399. 2935. 2921. 2333. 2331. 2333. 2322. 2391. 2752. 2312. 2757. 2233. 1979. 2933. 2331. 2929. 2529. 2213. 2339. 2332. 2392. 3239. 3995. 2537. 3519. 9131. 3333. 2939. 9333. 9331. 3399. 2393. 9527. 5373. 3729. 5273. 3133. 3313. 3997. 7379. 7312. 7395. 7995. 7931. 5135. 5372. 9333. 9339. 3312. 9239. 3371. 3325. 3993. 3955. .9154 3939. 9399. 9193. 9252. 9359. 9239. 9917. 9932. 3951. 9122. 9529. 5312. 5111. 5321. 3939. 5323. 3335. 3333. 9713. 3395. 3997. 9935. 3395. 7293. 7599. 3333. 3233. 3593. 3371. 3939. 3395. 7712. 3522. 3391. 3331. 3997. 3333. 3375. 3933. 3231. 3132. 3379. 5353. 3119. 9939. 9331. 9321. 5577. 3333. 3355. 3315. 10234 5393. 3339. 7393. 5533. 9353. 3333. 3391. 3377. 3959. 9533. 13331. 7133. 9193. 9333. 7175. 9393. 13393. 13333. 7713. 9323. 11139. 11371. 3331. 3339. 5391. 3393. 13293. 7393. 5979. 5293. 3135. 3231. 3339. 9322. 3799. 3913. 9329. 9339. 9373. 9191. 9393. 9315. 9151. 9377. 13329. 13331. 13993. 13599. 13973. 3393. 13329. 11527. 3333. 3392. 13373. 11373. 12395. 12333. 13237. 13323. 13392. 19333. 19193. 13379. 19399. 19235. 19233. 19373. 13337. 12193. 13173. 13535. 13337. 13933. 13919. 13371. 12335. 9372. 11959. 12577. 12373. 13933. 19133. 19295. 19935. 15519. 15932. 15953. 15395. 15932. 13355. 17999. 17399. 13173. 13391. 13331. 19971. 19393. 20333. 23513. 23915. 23932. 23337. 15333. 13759. 19889. 19919. 186214 23331. 21739. 21399. 21731. 21537. 15993. 19133. 21371. 21133. 21933. 21539. 21333. 22559. 22331. 23397. 23237. 17233. 21139. 23332. 23933. 23335. 29399. 25259. 13397. 23331. 23339. 27259. 27975. 27759. 29335. 21253. 23933. 27397. 23291. 23371. 29939. 23129. 27533. 23251. 27393. 23932. 23317. 25323. 23395. 23339. 27313. 23213. 23313. 25131. 19939. 13539. 22959. 25233. 25732. 19233. 23393. 29339. 23221. 27139. 23327. 23737. 29919. 23235. 23323. 23352. 19533. 29993. 23379. 23323. 27555. 25937. 25233. 23927. 23913. 19323. 29353. 22735. 29533. 23995. Table 39. 182 Values for population size at age spans cannibalized. initial ages of cannibalism, and initial age of egg laying at growth rates of Graham (1976) (Figure 20b). 9730. 6‘09. ‘226. 3639. 3660. 3566. 3369. 3263. 3196. 3170. 3107. 2973. 2‘76. 2761. 2657. 2693. 260‘. 2561. 2107. 1666. 2357. 2092. 2769. 3115. 2361. 2001. 3365. 39‘6. ‘570. ‘6‘7. 3350. ‘676. 3562. 3631. 3007. 50“. 6063. ‘16‘. 32‘9. 5‘63. 630:. “72. 6292. 7170. 773‘. 6079. 61‘6. 6077. 6‘50. 66‘0. 666‘. 6013. 666‘. 3072. 9636. “76. 5337. ‘137. ‘976. 3233. 5‘05. 5607. 5366. 3713. 609‘. 6‘03. 6703. 66“. 702‘. 7126. 3211. 6690. 7573. 6576. 6709. 6956. 63‘1. 67". 99‘1. 10600. 7‘97. 93‘3. 10766. 7576. 10025. 10622. 11173. 11902. 120‘1. 12325. 12560. 12970. 9166. 11076. 12367. 13063. 12911. 12616. 1326‘. 13033. 13377. 13297. 13“6. 9795. 6017. 10306. 0135. 7036. 6396. 102‘0. 122‘0. 13012. 13336. 13970. 9967. 1263‘. 1‘609. 10‘77. 6‘77. 13371. 16212. 16696. 160‘0. 19163. 20067. 13665. 1769‘. 1923‘. 13796. 17716. 1930‘.' 201‘6. 1‘272. 17601. 20‘91. 216‘1. 13367. 12267. 10715. 16163. 19309. 13931. 11226. 9662. 16173. 12172. 173‘0. 19907. 1‘026. 16309. 20162. 21010. 210“. 21‘72. 21520. 2162‘. 22600. 2‘329. 23523. 25“‘. 26597. 26633. 23293. 17183. 22263. 2‘572. 17605. 1“72. 20932. 2‘060. 2‘309. 23022. 2‘776. 25769. 26‘03. 2679‘. 269‘5. 2310‘. 29066. 23925. 26“1. 2‘065. 17733. 19266. 22976. 23‘96. 23‘69. 20769. 20‘25. 13259. 19‘16. 1‘717. 16‘92. 16692. 16693. 16305. 21212. 1906‘. 21626. 23636. 2‘209. 196‘1. 17396. 16“0. 20927. 22730. 23‘11. 2“53. 2‘611. 25296. 25977. 23027. 2‘609. 25792. 26‘08. 2616‘. 2‘679. 17700. 23769. 25620. 16236. 23‘16. 26290. 27655. 27069. 26679. 26‘9‘. 19116. 22699. 25061. 2‘666. 25701. 2‘556. 2‘61‘. 25629. 25327. 26606. 26695. 19361. 2‘502. 2“66. 20552. 1756‘. 169‘s. 16312. 1“39. 17900. 203‘9. 20110. 16322. 1‘3‘6. 19166. 1‘162. 16“‘. 21301. 23670. 16717. 210‘6. 22526. 2‘6‘6. 25‘92. 2‘726. 2566‘. 26623. 22160. 19677. 23352. 2‘926. 2575‘. 17629. 22626. 16‘33. 13‘36. 20673. 23360. 2‘23‘. 169“. 22960. 25126. 265‘3. 26991. 167‘1. 22629. 2‘317. 25516. 25510. 2530‘. 16166. 21663. 23‘37. 23722. 2‘152. 236“. 23535. 23‘69. 250‘2. 16“6. 23537. 2‘635. 2‘662. 25623. Table 40. 183 Values for p0pu1ation size at age spans cannibalized, initial ages of cannibalism, and initial age of egg laying at growth rates of Graham (1968) (Figure 20b). 9730. 6363. ‘203. 3697. 3‘37. 33‘9. 3196. 3031. 2997. 29“. 2907. 2373. 2333. 26“. 27‘6. 2309. 2333. 2373. 2296. 2013. 233‘. 2113. 2329. 2713. 2323. 21‘3. 2733. 313‘. 3‘31. 3333. 2671. 366‘. ‘311. 3099. 2313. ‘117. ‘931. 3‘33. 2763. ‘393. 3323. 3330. 3339. 6196. 6706. 70‘0. 7196. 7091. 7‘23. 7376. 7363. 32‘1. 3932. ‘33‘. ‘332. 33‘7. ‘323. 3‘23. 3932. ‘113. ‘177. ‘2‘3. ‘277. ‘3‘3. “13. ‘319. ‘627. ‘673. ‘790. ‘391. 3739. ‘37‘. ‘763. 3230. 3372. 3330. ‘293. 3601. 6360. 6392. ‘91‘. 6316. 7200. 31‘3. 6770. 7319. 7630. 3213. 3‘60. 37‘3. 3373. 9091. 6‘63. 7371. 3663. 90‘0. 3793. 363‘. 3366. 3337. 3670. 3333. 3‘36. 6232. 320‘. 6‘33. 3200. ‘33‘. ‘1‘3. 3339. 67‘3. 7209. 7307. 7793. 3739. 7133. 3003. 3961. ‘933. 7233. 3‘31. 373‘. 9‘01. 99‘0. 10‘12. 7‘1‘. 9‘33. 10103. 7373. 9633.' 10733. 11063. 790‘. 9763. 11266. 12033. 3333. 6322. 3963. 3737. 10311. 7393. 6133. 3333. 3390. 6‘03. 3701. 9723. 7017. 3330. 962‘. 9613. 9330. 10039. 10112. 10132. 10037. 10313. 10333. 11033. 11‘39. 11733. 12111. 373‘. 11066. 12269. 3931. 7231. 10366. 12192. 12973. 13331. 13773. 1‘1‘3. 1‘331. 1‘3‘9. 1‘6‘6. 1‘301. 1‘620. 1‘696. 1‘763. 1‘693. 10329. 1271‘. 13727. 1‘1‘7. 1‘301. 1‘277. 1‘3‘7. 10633. 12732. 9907. 12373. 13633. 1‘292. 1‘333. 13‘23. 13773. 16377. 16397. 16663. 17163. 17333. 17963. 13603. 19102. 13762. 19399. 19320. 20176. 207“. 23333. 21333. 2171‘. 22036. 21‘23. 2193‘. 16179. 19630. 21093. 13736. 19332. 21332. 22633. 22937. 23137. 22670. 1631‘. 203‘3. 22236. 22333. 23309. 233‘3. 23332. 2“03. 2‘612. 23220. 23393. 13376. 2303‘. 2320‘. 26209. 26396. 27632. 23333. 20716. 23763. 233‘2. 30017. 23223. 27213. 23‘09. 20377. 23167. 27‘76. 23699. 2100‘. 2‘336. 26369. 23333. 29111. 29067. 29372. 29939. 23‘60. 27‘13. 23397. 292‘6. 29667. 217‘2. 26100. 20007. 16933. 23679. 23693. 27330. 2016‘. 2‘33‘. 26302. 2793‘. 23621. 20912. 2320‘. 26731. 23139. 23377. 23367. 20390. 23397. 27362. 23‘33. 29179. 2371‘. 23317. 27391. 2396‘. 2113‘. 23361. 23913. 27293. 23111. Table 41. 184 Values for population size at age spans hunted at original growth rates (Figure 213). 9730. 6989. 9268. 3930. 3808. 3738. 8599. 3513. 8996. 3393. 3820. 3229. 2516. 2692. 2860. 2991. 8130. 3096. 2199. 1790. 2993. 2257. 8152. 3921. 2938. 1691. 3676. 9625. 9910. 9885. 2709. 9166. 5398. 2937. 1678. 9396. 5657. 2999. 1659. 9998. 5790. 3009. 9593. 8952. 6099. 6099. 6022. 5683. 5852. 5918. 5718. 2826. 3590. 2210. 2789. 1727. 2170. 1909. 1895. 2252. 2203. 2187. 2193. 2197. 2169. 2181. 2201. 2220. 2268. 2296. 1220. 1660. 2192. 2616. 2661. 2691. 1857. 2076. 2715. 2769. 1870. 2068. 2719. 1388. 2027. 2613. 2998. 2597. 2598. 2896. 2561. 2587. 1880. 1889. 2939. 2709. 2916. 2295. 2339. 2188. 2199. 2189. 2111. 1259. 839. 1988. 1196. 976. 860. 1312. 1856. 2027. 1985. 1986. 1235. 1568. 1918. 1897. 718. 1581. 2001. 2068. 2959. 2088. 2075. 1299. 1638. 1863. 1378. 1686. 1985. 2061. 1139. 1973. 1923. 2099. 1397. 801. 719. 1936. 1893. 1372. 999. 950. 1699. 1299. 1796. 2015. 1818. 1609. 1888. 1990. 2079. 2001. 1933. 1891. 1830. 1869. 2002. 2082. 2002. 1918. 1895. 1099. 1508. 1872. 1172. 887. 1570. 1917. 2022. 2116. 2098. 2007. 1978. 1959. 1985. 1870. 1889. 1889. 1871. 1826. 1188. 1952. 1773. 1936. 2021. 1876. 1810. 1191. 1958. 988. 1987. 1783. 1859. 1802. 1?93. 1855. 1980. 1900. 1779. 1790. 1825. 1910. 1865. 1832. 1782. 1795. 1791. 1992. 1887. 1806. 1801. 1789. 1888. 1921. 1892. 1077. 1930. 1713. 1085. 1577. 1890. 1822. 1886. 1975. 1891. 1067. 1998. 1601. 1878. 2031. 1909. 1873. 1890. 1837. 1961. 2051. 1397. 1595. 1867. 1958. 1858. 1890. 1917. 1936. 1633. 1895. 2019. 1895. 1833. 1969. 1968. 1687. 1922. 2060. 1209. 1969. '1815. 1957. 2080. 1978. 1939. 1919. 1833. 1896. 2099. 1972. 1926. 1123. 1986. 1098. 770. 1969. 1739. 1991. 1950. 1655. 1897. 2089. 1985. 1320. 1589. 1882. 2039. 2128. 2029. 1181. 1582. 1889. 1985. 2110. 1991. 1929. 1878. 1889. 1208. 1719. 1907. 1892. 2010. Table 42. 185 rates of Graham (1976) (Figure 21a). Values for population size at age spans hunted at growth 9730. 6196. 3683. 3021. 2896. 2922.. 2818. 2777. 2730. 2692. 2631. 2621. 2108. 292:. 2988. 2899. 2721. 2788. 2067. 1718. 2888. 1966. 2878. 3861. 2372. 1908. 8280. 3806. 9223. 9:90. 2961. 9088. 9667. 3096. 2316. 3956. 9726. 3091. 2861. 912‘. 9898. 8191. 9899. 8822. 8707. 8928. 8999. 8832. 6021. 6087. 8932. 3798. 9918. 2968. 3883. 2968. 3120. 2173. 2867. 3180. 3808. 3889. 8388. 3987. 3998. 8818. 3828. 8989. 3989. 8888. 2898. 2791. 2979. 8211. 3208. 1268. 2232. 2903. 3191. 3363. 2818. 2876. 3219. 2180. 2898. 3118. 3138. 3803. 8879. 1998. 3928. 3989. 2983. 2898. 3197. 3823. 8216. 3162. 3262. 8189. 8187. 8190. 8108. 2299. 1821. 2299.. 1772. 1818. 1919. 2099. 2933. 2861. 2617. 2697. 2068. 2893. 2862. 1988. 1988. 2199. 2996. 2880. 2682. 2809. 2897. 2139. 2818. 2888. 1980. 2903. 2868. 2609. 1823. 2298. 2628. 2789. 1919. 1806. 1280. 1978. 2982. 1888. 1917. 1392. 22:9. 1716. 2917. 2779. 2018. 2618. 2898. 2906. 8018. 1071. 3069. 1087. 2990. 8101. 8162. 1118. 8182. 3100. 3112. 2088. 2691. 2972. 1981. 1980. 2887. 2719. 2897. 2969. 8079. 1113. 1139. 1197. 1150. 1067. 1099. 1103. 3105. 3099. 2206. 2872. 2808. 2886. 2917. 2927. 2909. 2138. 2819. 1798. 2281. 2987. 2899. 2691. 2798. 2699. 2808. 2818. 2711. 2677. 2688. 2696. 2792. 2799. 2712. 2802. 2729. 2821. 2869. 2823. 2875. 2902. 2909. 2779. 2780. 1878. 2326. 2993. 1667. 2196. 2987. 2591. 2617. 2697. 2892. 1778. 2219. 2959. 2961. 2600. 2889. 2895. 2697. 2613. 2677. 2688. 1988. 2889. 2986. 2976. 2809. 2877. 2881. 1920. 2290. 2961. 2808. 2838. 2873. 2683. 2086. 2889. 2880. 2678. 1887. 2272. 2889. 2689. 2818. 2889. 2932. 2968. 2888. 2880. 2980. 2963. 2976. 1998. 2980. 1726. 1887. 2089. 2388. 2607. 1982. 2990. 2668. 2788. 2898. 2116. 2809. 2662. 2779. 2877. 2900. 1988. 2990. 2728. 2807. 2927. 2912. 2919. 2888. 2990. 1971. 2969. 2898. 2709. 2771. 186 Table 43. Values for population size at age spans hunted at growth rates of Graham (1968) (Figure 21a). 9730. 6072. 2593. 2651. 2928. 2500. 2693. 3997. 3173. 2696. 3029. 2522. 2080. 2789. 2320. 2088. 0111. 2599. 2931. 2:92. 2937. 1799. 3190. 2573. 2561. 2599. 2191. 2128. 3159. 2699. 2672. 2911. 2680. 1766. 3121. 2618. 1889. 2336. 2018. 1582. 3260. 2723. 2261. 2295. 2761. 1980. 3281. 2699. 2592. 2270. 3010. 1996. 1289. 2791. 2628. 2231. 3108. 2299. 3359. 2821. 2720. 2125. 3236. 2927. 3358. 2827. 2770. 1528. 3299. 2923. 3330. 2909. 2769. 1888. 3253. 2518. 2361. 2889. 2815. 2012. 3330. 1939. 2892. 2927. 2789. 210'. 3319. 2332. 3181. 2696. 2789. 2190. 3909. 2571. 2183. 2818. 2791. 2183. 33,2. 1995. 1739. 2017. 2838. 1598. 3902. 1593. 2959. 2999. 2872. 1295. 3287. 2282. 2691. 2596. 2091. 1820. 2310. 2669. 2927. 1882. 2997. 1371. 2730. 2730. 2992. 2900. 1702. 1379. 2866. 2895. 3011. 2609. 1972. 2102. 2986. 3093. 3086. 2771. 2069. 1668. 2995. 3083. 3199. 2735. 2309. 1969. 2919. 2269. 3122. 2777. 2503. 1913. 2073. 2179. 31:0. 2169. 1869. 2129. 2509. 2919. 3122. 1888. 2261. 2306. 2660. 2221. 3179. 2910. 2313. 2339. 2769. 2797. 3220. 2712. 2519. 1690. 2057. 2992. 3181. 2787. 2610. 2162. 2356. 2990. 3150. 2918. 1997. 2969. 2567. 2113. 2939. 2913. 2000. 1797. 1627. 2608. 2109. 2902. 2562. 1561. 2207. 2939. 2920. 2990. 2710. 2269. 2371. 3193. 2916. 2981. 2165. 2616. 2391. 2191. 2939. 2987. 2897. 1978. 2999. 1653. 2819. 2999. 2011. 1528. 2969. 1929. 2600. 2307. 2959. 2352. 2521. 2290. 2090. 2693. 2022. 2792. 2950. 2752. 2906. 2795. 2861. 2032. 2903. 1970. 1692. 2813. 2936. 2672. 1930. 1519. 2126. 2819. 2969. 2935. 2235. 1928. 2338. 2780. 3090. 3139. 2991. 2301. 2900. 2792. 2989. 3273. 2559. 1716. 2080. 2100. 3019. 0392. 2975. 2911. 2959. 2959. 2119. 3310. 2991. 2763. 2381. 2573. 2691. 3999. 2:99. 2015. 2955. 2658.- 2833. 3623. 2991. 2609. 2519. 2666. 2992. 3112. 2616. 2879. 2981. 2678. 3106. Table 44. 187 Values for population size at original age spans cannibalized, initial ages of cannibalism, initial age of egg laying, and age spans hunted (Figure 21b). 9788. 8881. 8288. 3918. 8798. 8728. 3891. 3888. 3881. 3389. 3318. 3228. 2512. 2888. 2858. 2987. 8128. 3882. 2198. 1738. 2939. 2288. 3187. 3918. 2888. 1888. 8871. 8818. 8982. 8827. 2785. 8159. 8389. 2933. 1878. 8389. 5887. 2998. 1887. 8888. 8729. 2999. 8888. 5988. 8837. 8887. 8889. 3871. 8881. 8988. 8781. 2819. 8879. 2283. 2722. 1728. 2188. 1391. 1818. 2288. 2178. 2178. 2181. 2188. 2188. 8171. 8191. 2211. 2287. 2287. 1217. 1888. 2188. 2888. 2852. 2882. 1888. 2878. 2788. 2788. 1385. 2859. 2788. 1328. 2828. 2881. 2888. 2838. 2882. 2883. 2888. 2888. 1328. 1877. 2828. 2898. 8881. 2238. 2328. 2187. 2188. 2189. 2898. 1253. 838. 1878.. 1139. 978. 888. 1898. 1882. 2811. 1982. 1922. 1227. 1389. 1987. 1889. 778. 1872. 1989. 2887. 2882. 2878. 2882. 1289. 1829. 1882. 1871. 1878. 1971. 2887. 1181. 1883. 1918. 2888; 1338. 795. 789. 1829. 1888. 1388. 988. 988. 1832. 1291. 1783. 1999. 1889. 1897. 1878. 1979. 2888. 1988. 1919. 1879. 1828. 1978. 2111. 1979. 1987. 1888. 1888. 1198. 1731. 2882. 1158. 718. 1879. 1889. 1982. 2889. 2888. 1972. 1988. 1928. 1911. 1888. 1888. 1883. 1852. 1888. 1172. 1835. 1757. 1928. 2888. 1888. 1798. 1178. 1888. 978. 1872. 1733. 1838. 1783. 1778. 1837. 1989. 1878. 1788. 1728. 1888. 1890. 1881. 1888. 1718. 1728. 1778. 1918. 1853. 1778. 1788. 1755. 1838. 1885. 1882. 1887. 1395. 1879. 1885. 1555. 1828. 1888. 1872. 1983. 1832. 1888. 1889. 1792. 1888. 2821. 1988. 1888. 1881. 1829. 1982. 2882. 1388. 1587. 1887. 1988. 1888. 1829. 1988. 1828. 1823. 1882. 2882. 1883. 1822. 1951. 1888. 1888. 1989. 2888. 1198. 1858. 1888. 1988. 2888. 1985. 1927. 1981. 1821. 1885. 2832. 1988. 1918. 1118. 1877. 1887. 788. 1881. 1728. 1932. 1883. 1888. 1888. 2888. 1978. 1318. 1582. 1888. 2838. 2119.‘ 2818. 1178. 1588. 1881. 1978. 2181. 1982. 1928. 1889. 1888. 1197. 1788. 1898. 1888. 2881. 188 Table 45. Values for population size at age spans cannibalized, initial ages of cannibalism, initial age of egg laying, and age spans hunted, at growth rates of Graham (1976) (Figure 21b). 9738. 8311. 8889. 3112. 2829. 2888. 2789. 8828. 8588. 3895. 2883. 2388. 2888. 3835.. 3858. 2228. 2595. 2383. 2838. 3281. 3538. 1795. 2591. 2882. 2887. 3178. 2893. 2181. 2581. 2539. 2715. 8822. 2988. 1719. 2881. 2871. 1988. 2938. 2871. 1871. 2788. 2883. 2388. 2888. 2833. 1378. 2788. 2888. 2885. 2888. 2882. 2888. 2882. 2888. 2812. 2818. 2718. 2888. 2712. 2891. 2989. 2898. 2779. 2583. 2828. 2897. 3887. 2213. 2881. 2825. 2823. 2889. 3888. 2583. 2877. 2598. 1887. 2829. 3128. 2859. 2771. 1988. 2378. 2837. 2993. 2818. 2772. 2328. 2818. 2888. 2981. 2818. 2819. 2875. 1778. 2:13. 3889. 2887. 2882. 1878. 1398. 1728. 3188. 1938. 2888. 1888. 2188. 2128. 3288. 1789. 2882. 2188. 2881. 2189. 2187. 2388. 2888. 2828. 2811. 1872. 2888. 1898. 2881. 2883. 2882. 2838. 1878. 2333. 2583. 2588. 2778. 2322. 1888. 2831. 2738. 2878. 2888. 2885. 2258. 2128. 2898. 2738. 2888. 2889. 2858. 1792. 2897. 2882. 2988. 2879. 2883. 3812. 1988. 2329. 2987. 2528. 2881. 3898. 2599. 2392. 2788. 1799. 2:81. 8828. 2839. 1838. 2828. 2388. 2775. 8251. 3881. 2185. 2838. 2888. 2985. 2983. 2288. 2258. 2832. 2878. 3885. 8828. 2828. 2387. 2788. 2838. 2218. 8717. 2989. 1838. 2888. 2388. 2898. 3188. 2888. 2883. 2292. 2812. 2725. 2388. 2781. 2338. 2888. 2718. 2887. 8893. 2931. 2828. 2587. 2888. 2912. 8987. 2988. 1787. 2829. 2715. 2983. 3228. 3192. 1388. 2591. 2889. 1978. 2878. 3228. 1191. 2888. 2818. 2888. 8388. 3388. 1781. 1978. 2379. 2898. 5178. 3282. 2188. 2293. 2888. 2785. 3378. 3339. 1718. 1811. 2819. 2888. 8888. 2387. 1319. 2881. 2888. 2817. 8839. 2788. 1382. 2288. 2878. 2789. 8888. 3872. 1988. 2332. 2883. 2887. 8298. 3228. 1888. 2828. 1953. 2728. 8323. 3187. 2125. 2587. 2381. 1889. 8178. 3181. 2395. 2528. 2878. 2298. 8381. 3238. 1839. 2828. 2859. 2388. 8881. 3128. 2288. 2829. 2835. 2887. 8288. 3178. 2888. 2888. 2832. 2585. 189 Table 46. Values for population size at age spans cannibalized, initial ages of cannibalism, initial age of egg laying, and age spans hunted, at growth rates of Graham (1968) (Figure 21b). 9738. 6:65. 2155. 2788. 2882. 2835. 2688. 8205. 2682. 2760. 2:31. 2858. 2086. 36970 2121. 2156. 2691. 2870. 2330. 3857. 251,. 1859. 26:2. 2528. 2585. 3389. 2862. 2287. 2656. 2569. 2681. 3196. 28.6. 1796. 2629. 2:32. 1887. 3881. 11IS. 1518. 2787. 2688. 2223. 2997. 2383. 1582. 2319. 2576. 2869. 2988. 2861. 2816. 2838. 2651. 2685. 2987. 2:16. 2136. 2986. 2699. 2595. 2583. 2635. 2388. 2938. 2617. 2638. 1627. 2663. 2358. 2977. 2663. 2676. 1938. 2118. 2338. 2189. 2697. 2719. 1923. 2758. 1612. 2566. 2723. 2697. 1987. 276’. 2132. 2683. 2665. 2669. 1978. 2513. 2387. 282’. 2623. 2657. 1992. 216,. 1328. 1682. 1925. 2686. 1838. 2683. 1826. 2228. 2326. 2783. 1173. 2768. 1967. 2535. 2898. 1’68. 165.. 22.8. 2257. 2668. 1861. 2351. 1218. 2885. 2389. 2681. 2238. 1181. 1783. 2568. 2888. 2112. 2888. 1508. 1518. 2627. 2871. 2712. 2626. 2815. 1895. 2652. 2519. 2813. 2668. 2217. 1295. 267'. 1965. 28.2. 2683. 2386. 1773. 1668. 2272. 2777. 2617. 1837. 1991. 2:35. 2357. 278‘. 1596. 2189. 2117. 22:5. 1897. 2772. 2368. 2315. 2171. 2666. 2287. 2788. 2619. 2.32. 1568. 283‘. 2336. 2798. 2781. 2588. 1,21. 2351. 236’. 2771. 2798. 1956. 2119. 2:51. 1788. 2179. 2738. 2235. 1:63. 1851. 2876. 2366. 2316. 2883. 1831. 22". 2313. 251'. 2665. 2553. 1919. 2816. 2356. 2569. 2857. 2599. 2166. 3829. 1707. 2588. 2628. 2638. 1788. 2583. 1391. 2876. 2628. 1983. 1377. 2583. 1231. 2876. 2211. 2315. 1958. 2636. 1798. 1666. 2328. 2513. 2238. 2635. 2135. 2155. 2662. 2681. 1767. 2’82. 1723. 1616. 2668. 2655. 2289. 2126. 1362. 2:06. 2685. 2663. 2888. 2837. 1382. 2198. 2628. 2685. 2:91. 2635. 1915. 2278. 2637. 2615. 2692. 2186. 1618. 2255. 2886. 2663. 2758. 2715. 286‘. 2317. 2317. 1988. 2719. 2638. 2296. 2337. 2863. 2358. 2866. 2781. 1815. 2398. 2557. 2585. 297:. 2189. 2218. 2839. 2569. 2616. 3888. 2796. 2811. 2818. 2576. 2631. 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