1. science
2. biology
3. zoology
4. endangered species

BLACK-FOOTED FERRET (Mustela nigripes) POPULATION DYNAMICS: USE OF SIMULATION MODELING TO INVESTIGATE THE EFFECTS OF STOCHASTICITY, HABITAT GEOMETRY AND DISPERSAL by Robert W. Van Kirk A Thesis Presented to The Faculty of Humboldt State University In Partial Fulfillment of the Requirements for the Degree Master of Science March, 1990 BLACK-FOOTED FERRET (Mustela nigripes) POPULATION DYNAMICS: USE OF SIMULATION MODELING TO INVESTIGATE THE EFFECTS OF STOCHASTICITY, HABITAT GEOMETRY AND DISPERSAL by Robert W. Van Kirk Approved by the Master's Thesis Committee: Chair Approved by the Option Coordinator: Approved by the Graduate Dean: ABSTRACT
This study employed a computer simulation model to investigate the population dynamics of the black-footed ferret (Mustela nigripes). Three different black-footed ferret habitat sites were used in the study: the Meeteetse, Wyoming site, a site in Northern Montana, and a hypothetical complex. The model was fully stochastic and included de­
tails of BFF demography and life history, with particular attention given to the juvenile dispersal process. Actual prairie dog colony geography of each study site was approxi­
mated in the simulation by use of a hexagonal grid, and dispersal was modeled by moving individuals in discrete steps on the grid. We investigated the effects of demo­
graphic and environmental stochasticity, prairie dog colony distribution and dispersal success. Results supported seven conclusions: 1) demographic stochasticity has little effect on population persistence except when population size is extremely small; 2) increasing environmental stochasticity decreases population persistence substantially; 3) mean population size is much lower than the carrying capacity for the habitat; 4) extinction is more likely to occur when the number of occupied colonies becomes too low; 5) increase in dispersal mortality decreases population persistence; 6) the Meeteetse-tuned model may not accurately predict population trends on other sites without parameter changes; 7) introduction of small stepping stone colonies increases the frequency of successful colonizations from one large colony to another located some distance away. Secondary observations and management implications are also discussed. iii ACKNOWLEDGMENTS The work contained in this thesis is part of a year-long project in black-footed ferret population modeling. The research was partially funded by a California State Univer­
sity P.C.P. grant. I extend thanks to those who provided input to this thesis. Professor Roland Lamberson of the Humboldt State University Department of Mathematics, in his role as my advisor and principle investigator, initiated the black-footed ferret modeling project, obtained funding, provided direction, and offered many helpful suggestions. The other members of my committee, Professors Richard Vrem and Robert Cooper took time to review my progress at various stages, and their suggestions were helpful. Professor Howard Stauffer offered advice on computing techniques. Black-footed ferret captive propogation program director Dr. Thomas Thorne provided additional information on canine dis­
temper, the captive propogation program, and reintroduction of the ferrets into the wild. U.S. Fish and Wildlife Ser­
vice biologist Paul Springer presented first-hand observa­
tions from the South Dakota ferret study and also loaned color transparencies from his work. Randy Matchett and Steve Minta provided information on BFF habitat in Montana. Steve Forrest reviewed the original project technical re­
port, and his comments proved useful in final preparation of this thesis. Dr. Tim Clark offered constructive suggestions at several stages of model development. For his significant help with computer hardware, software and interfacing, I thank William Lennox, College of Science Instructional Computing Consultant at Humboldt State University. Finally, I would like to thank my fellow graduate students Curt Voss and Michael Butler, who also worked on the ferret project. Without the many long hours and late nights they spent computing, copying, reading, graphing, programming, and cursing, this project and my thesis would not have been com­
pleted. iv TABLE OF
CONTENTS Abstract �
iii
Acknowledgments �
iv
Table of Contents �
List of Figures �
vi
List of Tables �
vii
INTRODUCTION �
1 Purpose of This Study �
2 LITERATURE REVIEW �
3 Black-footed Ferret Case History � 3 Black-footed Ferret Life History and Ecology �
6 Components Critical to Population Viability �
9 Stochasticity �
10 Habitat Distribution �
10 Dispersal �
11 Canine Distemper �
12 Genetics �
13 Population Dynamics in a Patchy Environment �
14 Theory and Models of Animal Dispersal �
18 Current Black-footed Ferret Research and Modeling �
21 METHODS �
23 The Basic Model �
23 Stochasticity �
26 Habitat, Carrying Capacity and Dispersal Probability �
26 Meeteetse Site �
26 Montana Site �
31 Hypothetical Habitat Configuration �
37 Density Dependent Survivorship �
40 Dispersal Routine �
42 Parameter Values and Simulation Procedures �
44 RESULTS �
47 Effects of Stochasticity �
47 Population Dyanmics in a Patchy Environment �
47 Dispersal Results �
48 CONCLUSIONS AND DISCUSSION �
50 Demographic and Environmental Stochasticity �
50 Population Dynamics in a Patchy Environment �
56 Dispersal �
68 MANAGEMENT IMPLICATIONS �
85 Significance of Environmental Stochasticity �
85 Assessment of Black-footed Ferret Habitat �
87 Determination of Reintroduction Procedures �
88 Reduction of Dispersal Mortality � 88 Importance of Habitat �
89 Literature Cited �
92
LIST OF FIGURES Figure 1. Former range of the black-footed ferret �
4 Figure 2. Dynamic diagram of basic black-footed ferret population model used in this study �
25 Figure 3. Map of Meeteetse, Wyoming study site �
28 Figure 4. Hexagonal approximation of Meeteetse colonies �
29 Figure 5. Graph of juvenile dispersal probability versus colony size �
32 Figure 6. Map of Charles M. Russell National Wildlife 33 Refuge, Montana prairie dog colony complex �
34 Figure 7. Hexagonal approximation of CMRNWR complex �
Figure 8. Hypothetical colony arrangement �
38 Figure 9. Graph of winter survival probability versus colony population at start of winter �
41 Figure 10. Population versus time for Meeteetse control run showing mean + 1 standard deviation �
51 Figure 11. Population versus time for Meeteetse site with 52 no environmental stochasticity �
Figure 12. Population versus time for Meeteetse site with 53 extreme environmental stochasticity �
Figure 13. Population versus time for Meeteetse control run showing 90 percent confidence intervals �
57 Figure 14. Population versus time for Meeteetse site init-
58 ialized at a small population �
Figure 15. Population versus time for Meeteetse site init-
59 ialized at carrying capacity �
Figure 16. Population versus time for Meeteetse site with low dispersal step mortality �
69 Figure 17. Population versus time for Meeteetse site with high dispersal step mortality �
70 Figure 18. Distribution of straight-line distance of suc-
73 cessful dispersals �
Figure 19. Typical simulated dispersal pathsfor the 75 Meeteetse site �
Figure 20. Population versus time for CMRNWR site using 78 equation (2) to calculate dispersal rates �
Figure 21. Population versus time for CMRNWR site using 79 equation (3) to calculate dispersal rates �
Figure 22. Population versus time for hypothetical colony 81 arrangement including only the large colonies �
Figure 23. Population versus time for hypothetical colony 82 arrangement including one stepping stone �
Figure 24. Population versus time for hypothetical colony arrangement including three stepping stones....83 vi LIST OF TABLES Table 1. Meeteetse site colony parameters �
30 Table 2. Montana site colony parameters �
36 Table 3. Colony parameters for hypothetical prairie 39 dog colonies shown in Figure 8 �
Table 4. Parameter values used in simulations �
45 Table 5. Number of extinctions counted om 100 stochastic simulations for the Meeteetse site at various 55 levels of environmental stocasticity �
Table 6. Yearly populations by colony for the first 50 years of a simulation in which the Meeteetse site was initialized with 8 individuals in colony 11 and 9 in colony 12 �60 Table 7. Yearly populations by colony for the first 50 years of a Meeteetse control run simulation in which extinction occurred �
61 Table 8. Yearly populations by colony for the first 50 years of a CMRNWR site simulation in which equation (3) was used to calculate dispersal 62 rates �
Table 9. Number of extinctions counted in 100 stochastic simulations for the Meeteetse site with various population initializations � 63 Table 10. 90 percent confidence intervals for mean annual survival rates for different values of the dis-
71 persal step mortality probability �
Table 11. Number of extinctions counted in 100 stochastic simulations for the Meeteetse site with various values for the dispersal step mortality prob-
ability �
72 Table 12. Colonizations and extinctions counted in 100 stochastic, 100-year simulations using the hyp-
84 othetical colony arrangement shown in Figure 8 �
vii INTRODUCTION
For over 50 years, population biologists have realized that habitat configuration and dispersal have profound effects on population dynamics. Indeed, the dynamics of a population which inhabits a "patchy environment" are gov­
erned as much by the geometric distribution of the habitat patches as by the inherent demographics of the species. However, it has only been in the last 20 years that the theory of island biogeography has offered insights to the problem. Furthermore, the increasing rate of species ex­
tinction and habitat fragmentation throughout the world have added a new sense of urgency to the study of population dynamics in an environment consisting of discrete patches of suitable habitat. The study of this problem has recently been combined with minimum viable population analysis to assess habitat needs and management policy for many rare and endangered plant and animal species. One of the endangered species which lends itself par­
ticularly well to such an application is the black-footed ferret (Mustela nigripes).
Once inhabiting most of the North American plains and intermountain basins, the black-
footed ferret has been recently confined to existence in captivity. However, a remnant population was studied at Meeteetse, Wyoming from 1981 to 1985, providing many 1
2
insights into population dynamics of an animal which in­
habits discrete patches of suitable habitat and whose life history contains a well-developed dispersal mechanism. The prospect of reintroduction of the black-footed ferret into the wild in 1991 provides an excellent opportunity to model the dynamics of a small population of ferrets as part of a population viability assessment. Purpose of This Study The primary purpose of this study is to employ a simu­
lation model to investigate the population dynamics of a small population of black-footed ferrets. The effort will concentrate primarily on the Meeteeste site, not only be­
cause the Meeteetse field work provided a wealth of informa­
tion on the life history and demographics of the animal, but also because the Meeteetse prairie dog complex is the most likely site for the first reintroduction of black-footed ferrets into the wild. This paper will attempt to address the effects of environmental and demographic stochasticity, habitat configuration and dispersal behavior on the persis­
tence and dynamics of a black-footed ferret population at Meeteetse, drawing comparisons with the results of other studies and suggesting implications to future management of the black-footed ferret where appropriate. We will also apply the simulation model to a possible future reintroduc­
tion site on the Charles M. Russell National Wildlife Refuge 3
in Montana, in order to test the applicability of the model to sites other than Meeteetse. Furthermore, we will simu­
late a population occupying a hypothetical habitat in order to test the application of some of the island biogeography theories to black-footed ferret dispersal and colonization. LITERATURE REVIEW
Black-footed Ferret Case History Formerly ranging across the American plains from Canada to Mexico (Figure 1), the black-footed ferret (Mustela nigripes) was generally thought to be extinct following the collapse of a small population in South Dakota which was studied from 1964 to 1974 (Henderson et al., 1974; Anderson et al., 1986; Forrest et al., 1988). Massive habitat loss is generally blamed for the precipitous decline in ferret numbers since the turn of the century (Clark et al., 1987; Forrest et al., 1985b). The subsequent accidental discovery of a population near Meeteetse, Wyoming in September 1981 provided further opportunities to study this rare and secre­
tive mammal and renewed hopes that conservation efforts may someday result in the return of healthy populations of wild black-footed ferrets. Toward this end, six wild ferrets were trapped in the fall of 1985 to serve as founder animals 4
Figure 1. Former range of the black-footed ferret and lo­
cations of Meeteetse, Wyoming study area (square) and Char­
les M. Russell National Wildlife Refuge, Montana prairie dog habitat (triangle). (from Forrest et al. 1985b) 5
for a captive propogation program (Thorne, 1987). However, canine distemper was diagnosed in two of these ferrets, and eventually all six died in captivity from the disease. In an emergency effort to save the last known members of the species, the Wyoming Game and Fish Department and the U.S. Fish and Wildlife Service decided in early 1986 to capture all remaining wild ferrets. The last known wild black-
footed ferret was captured 28 February 1987, bringing the total to 18 individuals in captivity (Thorne, 1987; 1988). The captive breeding program is currently being con­
ducted cooperatively between the Fish and Wildlife Service and Wyoming Game and Fish Department at the Department's Sybille Wildlife Research and Conservation Education Unit near Laramie, Wyoming. Seven ferrets were weaned in 1987, and 34 were weaned in 1988. By the spring of 1989, 15 individuals had been transferred to the Henry Doorly Zoo in Omaha, Nebraska and the National Zoological Park's Conserva­
tion and Research Center in Front Royal, Virginia in an effort to reduce the risk of a catastrophe in one location eliminating the entire population. One immediate objective of the captive program is experimental reintroduction of black-footed ferrets into the wild in 1991 (Thorne, 1987; 1988). According to a personal interview with program director Dr. E. T. Thorne during July 1989, the reintroduc­
tion is almost certain to take place at the Meeteetse site. 6
Black-footed Ferret Life History and Ecology The black-footed ferret is one of several members of the family Mustelidae native to North America. However, its closest taxonomic relatives are the European polecat (Mu­
stela putorius), the Siberian polecat (M. eversmanni) and the fitch ferret (M. furo) (Forrest et al., 1985a; Anderson et al., 1986). The polecats are native to Eurasia, while the fitch ferret is a domesticated strain derived from the two polecats. Like other members of its genus, the black-
footed ferret is characterized by an elongated cylindrical body with short legs and well-developed claws. Distinguish­
ing features of the black-footed ferrert include a pale yellow-buff pelage accented by a black mask and black tips on the legs and tail (Henderson et al., 1974). Measured adult females range in total length from 479 to 565 mm; males are slightly larger. Body mass for individuals ob­
served at Meeteetse ranged from 645 g to 850 g for adult females and 915 g to 1125 g for adult males (Anderson et al., 1986). Black-footed ferrets inhabit burrows and are largely nocturnal (Henderson et al., 1974; Forrest et al., 1988). The black-footed ferret does not hibernate during the winter (Clark et al., 1986; Richardson et al., 1987). Mating is polygynous and occurs during March and April (Anderson et al., 1986). Females first breed as yearlings and produce an average litter of 3.3 kits (Forrest et al., 1988), which are 7
born in May and June. Juveniles appear above ground with the mother by the first week of July and become self-suffi­
cient by late August, having nearly attained adult weight (Henderson et al., 1974; Forrest et al., 1988). By early September the young ferrets disperse from the natal area to establish their own territories for the winter. Juvenile mortality is high, particularly during the dispersal period. Forrest et al. (1988) observed juvenile disappearance rates ranging from 56% to 81%. Because the young males tend to disperse longer distances than do females, the higher mor­
tality suffered by juvenile males skews the sex ratio from nearly 1:1 at birth to roughly 1 male to 2 females in the adult population (Forrest et al., 1985a; Anderson et al., 1986; Forrest et al., 1988). Adults, particularly females, exhibit considerable geographic fidelity. Adult mortality is somewhat lower than that of juveniles, with annual sur­
vival rates in the range of 0.5 to 0.6 (Forrest et al., 1988; Harris et al., in press). There appears to be no evidence of a post-reproductive period; however, Forrest et al. (1988) were unable to definitively age any wild individ­
ual at more than three years old. They do document a cap­
tive female known to be at least 11 years old (Forrest et al., 1985a). The most widely recognized feature of black-footed ferret ecology is the apparent obligate dependence of the ferret on the prairie dog (Cynomys spp.) (Henderson et al., 1974; Stromberg et al., 1983; Clark et al., 1985; Forrest et 8
al., 1985b; Powell et al., 1985; Clark et al., 1987). Though black-footed ferrets will prey upon other species, their diet consists primarily of prairie dogs. Furthermore, ferrets appear to exclusively inhabit abandoned prairie dog burrows (Fagerstone and Biggins, 1986; Forrest et al., 1988). Prairie dog eradication programs are a major cause of the decline in suitable black-footed ferret habitat. (Forrest et al., 1985b; Clark et al., 1987). Prairie dogs are social animals which live in large complexes of individ­
ual colonies or "towns." In a survey of prairie dog com­
plexes in Montana, Wyoming and South Dakota, Clark et al. (1987) reported that observed complexes consisted of between 5 and 103 colonies totaling 769 to 7800 ha of prairie dog activity. Mean colony size was 8 to 209 ha, and intercolony distance ranged from 0.2 to 3.2 km with means in the neigh­
borhood of 1.0 km. The geographic distribution of both the complexes and the colonies within the complexes is of ex­
treme importance to black-footed ferret population dynamics, as the survival of juveniles depends largely on their abil­
ity to successfully locate and establish themselves within a new colony (Forrest et al., 1985b). Historically, prairie dog complexes were spread nearly continuously across the American plains, providing the black-footed ferret with essentially unlimited habitat (Forrest et al., 1985b). An interesting feature of Cynomys population dynamics is a tendency towards sudden, aperiodic population fluctuations 9
(Clark et al., 1985). The prairie dog town was a center of activity for many animal species, particularly avian and mammalian predators which hunted both prairie dogs and ferrets (Henderson et al., 1974). Components Critical to Population Viability In order to model the dynamics of a small, isolated ferret population, Groves and Clark (1986) recommended that current theories of small population extinction and persis­
tence be considered. Shaffer (1981) identified four sources of uncertainty which affect a wild population: demographic stochasticity, environmental stochasticity, environmental catastrophe and genetic variation. Simberloff (1986) con­
sidered catastrophe to be an extreme case of environmental variance and adds social dysfunction to the list of factors affecting the dynamics of small populations. Lande (1988) considered Allee effects, which include such factors as difficulty in locating a mate at very low population den­
sities. Gilpin (1987) and Lande (1987) emphasized the importance of the geometry of habitat distribution to small populations. Based on these theories, we have identified three com­
ponents besides basic life history parameters which we in­
cluded in the modeling process reported in this study and two others which we excluded. The three considerations which we incorporated include demographic and environmental 10
variance (stochasticity), spatial distribution of black-
footed ferret habitat, and juvenile dispersal within this inhomogeneous habitat structure. We have chosen to exclude catastrophe in the form of a canine distemper epizootic and genetic considerations. However, for completeness, a brief summary of the relevance of each of these five factors to this study is presented here. More detailed considerations of habitat distribution and dispersal appear in subsequent sections. Stochasticity.
Shaffer (1981) recommended that simula­
tion models incorporate both demographic and environmental stochasticity. The former applies probabilities of sur­
vival, reproduction, dispersal, etc. to each individual of the population at each stage of the life history, while the latter applies to life history parameters a given probabil­
ity distribution which affects all similar members of the population equally and simultaneously (Shaffer, 1981; Lande 1988). Though environmental variation is usually considered to have greater effect on a population (Shaffer, 1987; Goodman, 1987), the importance of demographic stochasticity in very small populations cannot be ignored (Shaffer, 1981; Simberloff, 1986). Both types of stochasticity are easily incorporated into simulation models using standard computing techniques (ie. Ripley, 1987). Habitat distribution. The importance of the spatial arrangement of prairie dog colonies in a black-footed ferret population model comes immediately from the life history of 11
the ferret. Groves and Clark (1986) and Gilpin (1987) identified biogeography as a critical component in black-
footed ferret population dynamics. Levins (1970) defined the concept of a "metapopulation" consisting of many local populations. Historically, the "local" black-footed ferret population may have been the inhabitants of a given prairie dog complex like the one near Meeteetse, while the metapopulation would have been the entire black-footed ferret population over a much larger area, an extensive intermountain valley, for instance, which included many complexes arranged so that inter-complex communication of individuals occurred periodically but infrequently. The metapopulation concept can also be applied to black-footed ferrets on a smaller scale, that of individual prairie dog colonies within a given complex. Since the Meeteetse area falls into this category, this work refers to the metapopul­
ation as the "total population" or simply "the population" of the complex. The local population thus becomes the "colony sub-population". Dispersal.
Inclusion of biogeography in a black-footed ferret population model neccessitates detailed consideration of the juvenile dispersal process. Because dispersal is the primary source of both juvenile mortality and communication between isolated prairie dog colonies, Henderson et al. (1974), Forrest et al. (1985b) and Forrest et al. (1988) identified the importance of dispersal to black-footed 12
ferret demography. King and McMillan (1982) studied in detail the dispersal behavior of stoats (M. erminea) and conluded it to be an essential feature in the population dynamics of this black-footed ferret relative. Canine distemper.
Shaffer (1987) identified catastro­
phe as the single greatest threat to the persistence of a small population. Though Shaffer (1987) and Simberloff (1986) both questioned the consideration of catastrophe as distinct from an extreme case of environmental variance, the catastrophic effect of the canine distemper epizootic on the Meeteetse population suggests that canine distemper deserves separate attention in a study of an isolated black-footed ferret population. Dobson and May (1986) identified epi­
demic outbreaks as very important in the conservation of rare species, particularly those which have become confined to a small population in a single location. Thorne and Williams (1988), Williams et al. (1988) and Forrest et al. (1988) concluded that successful conservation of the black-
footed ferret will depend greatly on both the prevention of a canine distemper outbreak in captive' populations and on an increased understanding of canine distemper dynamics in a wild black-footed ferret population. However, a treatment of this topic has been omitted from this work, as another of the graduate students in our modeling program is undertaking a detailed analysis of the dynamics of a canine distemper epizootic in his Master's Thesis. 13
Genetics. Shaffer (1981), Simberloff (1986), Ewens et al. (1987) and Lande (1988) identified genetics as important in the study of small populations. Loss of genetic diver­
sity in a small population results in decreased fitness due to inbreeding depression and in reduction in the ability of the population to adapt to changes in its environment (Simberloff, 1986; Lande, 1988). Despite the traditional emphasis on genetics in conservation biology, Lande (1987) argued that demography is usually of more immediate impor­
tance in the viability of small populations. Gilpin (1987) recognized environmental stochasticity and habitat fragmen­
tation as possibly more important than genetics, at least in the short term, and Shaffer (1987) postulated that genetics will not always, and perhaps not even often, determine the minimum viable size of a wild population. Greenwood (1980) reported that inbreeding imposed by a diminished population is not always detrimental, and Simberloff (1986) noted that a species typically homozygous for many alleles is less likely to be affected by inbreeding. Pettus (1985) observed that many mammalian carnivores tend toward a relatively large degree of homozygosity, and both he and Gilpin (1987) theorized that the black-footed ferret may follow this pattern. Kilpatrick et al. (1986) provided laboratory evidence of homozygosity in the black-footed ferret. Thus, we have concluded that a viability study of a small 14
black-footed ferret population will not suffer greatly from exclusion of genetic factors. Population Dynamics in a Patchy Environment Though insights into population dynamics in a patchy environment were provided by Huffaker's (1958) classic and innovative study of mites (Eotetranychus sexmaculatus) on various arrangements of oranges (suitable habitat) within an array of rubber balls (unsuitable habitat), it was not until 1967 that MacArthur and Wilson's Theory of Island Biogeog­
raphy provided a unified theory of extinction and recoloni­
zation in insular populations and changed the nature of ecological thinking. Originally applied to oceanic islands, MacArthur and Wilson's theory was soon extended to "islands" of suitable habitat in a terrestrial environment. Levins (1970) defined the metapopulation concept, in which demogra­
phic equilibrium is achieved by a balance between extinc­
tions of local populations and migration among them. Gilpin (1987) defined the regular extinction and recolonization of a local population under conditions of metapopulation equi­
librium the "winking effect". Gadgil (1971) presented a simple yet elegant model of dispersal of individuals among discrete habitats. Gurney and Nisbet (1978) developed a more complex theoretical model, and Lande (1987) extended Levins' model to accomodate territorial species, most notab­
ly the northern spotted owl (Strix caurina occidentalis) 15
(Lande 1988). In his overview, Wiens (1976) admitted that computer simulation of population dynamics in a patchy environment is formidable, but Lefkovitch and Fahrig (1985) and Fahrig and Merriam (1985) provided not only a useful simulation but supporting field data as well. Smith (1974) and Fahrig and Paloheimo (1988) collected field data on the relationship between habitat configuration and dispersal. Several conclusions are nearly universal among research into population dynamics in a patchy environment, whether the patchiness is a natural feature of the habitat as with the black-footed ferret or a human-induced fragmentation of a once-continuous habitat as in the case of the spotted owl. The most important of these is that a population may become extinct if the rate of local extinction exceeds the rate of colonization, even though a sufficient area of suitable habitat exists (Levins, 1970). Lande (1987) reported that at any given time, even at demographic equilibrium, not all suitable patches are occupied. If occupancy falls below a certain critical level, the rate of recolonization becomes insufficent to counteract local patch extinctions. Gurney and Nisbet (1978) found that a metapopulation in an environ­
ment containing N suitable patches will persist for an appreciable time only if the average proportion of occupied patches is at least on the order of 3N-1/2. Lande (1987) concluded that the metapopulation will persist only when h is greater than 1-k, where h is the proportion of the total 16
territory that is suitable and k is the organism's "demographic potential", defined in terms of reproductive value and the ability of the juveniles to either inherit parental territory or search new territories. An immediate corollary is that the mean long term population size is less than the total carrying capacity of the habitat.
Gadgil (1971) analytically proved that the equilibrium size of the metapopulation is always less than or equal to the sum of the carrying capacities of the patch­
es. He also showed that each dispersal episode results in overcrowding on some sites and undercrowding on others, thus increasing density-dependent effects in disproportion to the total population size. Smith (1974) found that even though all local patches of pika (Ochotona princeps) habitat had been occupied at one time or another, metapopulation equi­
librium existed at less than complete occupancy. A third generally accepted axiom is that the geometry of a patchy habitat is significant in determining population persistence (Gilpin, 1987). Lefkovitch and Fahrig (1985) and Fahrig and Merriam (1985) found geometry of insular woodlot habitats critical to the dynamics of white-footed mouse (Peromyscus leucopus) populations. Woodlots that were connected to others by movement corridors, in this case fence rows, had a higher probability of supporting a popula­
tion than did isolated lots. In simulations of all possible unique connections of five distinct patches, lots belonging 17
to squares or pentagons supported larger populations than those belonging to lines or triangles. No isolated sub­
population persisted in simulation experiments. Smith (1974) observed that the size of individual patches and the distance between patches determined the equilibrium occupan­
cy. Larger patches in close proximity to each other result­
ed in a metapopulation equilibrium larger and nearer to the total habitat carrying capacity than did an arrangement of smaller patches further away from each other. Fahrig and Paloheimo (1988) found that spatial arrangement of habitat patches had less effect on species such as the cabbage butterfly (Pieris rapae) which disperse easily over long distances but have little ability to detect new patches than on organisms which disperse along corridors between suitable habitats. In addition to these general axioms, there are several other observations which are relevent to a study of popula­
tion dynamics in a patchy environment. One of these is that stochasticity in both demographics and the environment reduces equilibrium occupancy (Lande, 1987). Gadgil (1971) found that any variability in individual patch carrying capacities decreases the equilibrium metapopulation size. Allee effects such as the inability to find a mate tend to have greater importance in a patchy environment than in a continuous one and will also lower the equilibrium occupancy (Laude 1987). Another important concept in a patchy 18
environment is that of "edge effect", one example of which is decreased habitat quality near the edge of a patch (Lande 1988). This suggests that patches with geometric configura­
tions which maximize the ratio of area to perimeter will contain a greater amount of suitable habitat than patches of the same area with a larger perimeter. Gilpin (1987) con­
cluded that all of the effects of spatial habitat distribu­
tion must be considered to the greatest extent possible in studying the population dynamics of an endangered species. Theory and Models of Animal Dispersal Dispersal is generally considered to be nearly univer­
sal among animals (French 1971). Dobzhansky and Wright (1943) were among early researchers of dispersal, as they recognized its importance to the spread of genetic informa­
tion. Howard (1960) distinguished between "innate" or in­
stinctive and "environmental" or density-dependent disper­
sal, and he listed communication of genetic material, exten­
sion of range, recolonization of territories following local extinctions, and reduction of inbreeding and intraspecific competition as advantages of innate dispersal to a popula­
tion. Kitching (1971) emphasized that organisms which breed in discrete habitats must have a well-developed dispersal mechanism in their life histories. Greenwood (1980), Cock-
burn et al. (1985) and Rails et al. (1986) cited dispersal, particularly of juvenile males, as a primary mechanism for 19
the avoidance of inbreeding in many different animal spe­
cies. Hoogland (1982) observed that black-tailed prairie dogs (C. ludovicianus) appear to avoid inbreeding at least partially by dispersal of juvenile males away from the natal colony. Juvenile males are also the primary dispersers in both stoats and black-footed ferrets (King and McMillan, 1982; Forrest et al., 1988), presumably for the same reason. Most attempts at modeling animal dispersal have roots in Skellam's (1951) use of the continuous random walk model. Saila and Flowers (1969) used the diffusion equation to model fish migration, and Okubo (1980) provided a detailed treatment of many applications of diffusion models in eco­
logy. Bovet and Benhamou (1988) pointed out that the basic random walk is too simple to model animal's paths accurately because it fails to account for physio-kinetic factors which cause most animals to have a tendency to travel forward. Their extension of the basic diffusion model employed non­
uniform directional distribution. Others have developed discrete dispersal models. French (1971) simulated dispersal in desert rodents by use of a square grid of home ranges. Initial direction was determined randomly from a uniform distribution, and the individual dispersed in a straight line in the selected direction, despite Murray's (1967) comment that dispersal paths in nature are probably not straight lines. Kitching (1971) used a square grid which contained a number of 20
randomly arranged circular habitats. The radius of a habi­
tat site was proportional to the degree of attractiveness of that particular site. A mortality probability was applied at each dispersal step, and the initial direction of an individual's movement was selected from a uniform distribu­
tion, while subsequent directions were chosen from a normal distribution centered on the direction of the previous step. Cormack suggested use of a hexagonal grid in modeling animal dispersal (French, 1971). Howard (1960) reported that dispersal distances are not randomly distributed, but there seems to be little agreement on the actual frequency distribution. Though French (1971) and Wiens (1976) cited both bimodal and smooth log-normal distributions of path length, French's simulations resulted instead in angular exponential-type distributions with a "shoulder" at a distance of approximately four home ranges. Kitching's (1971) simulations indicated that the probability of a propagule successfully surviving dispersal to a new habitat patch decreased exponentially with distance, which is possibly an artifact of the mortality probability applied at each step in his model. Murray (1967) theorized that most dispersals are relatively short, and proposed that genetic factors determine the distance an individual will disperse. Though limited, field data from Meeteetse (For­
rest et al. 1985b, Forrest et al. 1988) suggest that the straight-line distance of successful inter-colony dispersals 21
may be bimodally distributed. At the Meeteetse site the juxtaposition of the two largest colonies is likely to confound the data to an extent that it is impossible to separate any genetic predisposition from the simple effects of local geometry. The relationship of dispersal to genetics and popula­
tion dynamics has already been discussed, but a few other ideas should be noted. Consistent with the theories of Howard (1960) and Murray (1967), Lidicker (1962) hypothe­
sized that dispersal in a population may result in a long-
term genetic equilibrium between predisposition to disperse and that to "stay home." Stochastic perturbations to this balance may result in density-dependent factors regulating the population at levels below the carrying capacity. Smith (1974) observed that high population densities force greater juvenile dispersal away from small habitat patches, increas­
ing extinction probabilities for these small patches. Rails et al. (1986) and Ewens et al. (1987) noted that in a patchy environment only a small amount of dispersal between patches is necessary to maintain heterozygosity in both the metapop­
ulation and the local populations. Current Black-footed Ferret Research and Modeling Two collections contain much of the current knowledge of black-footed ferrets, Great Basin Naturalist Memoirs No. 8, The Black-footed Ferret (Wood, 1986) and Black-footed 22
Ferret Workshop Proceedings (Anderson and Inkley, 1985). Thorne (1988) summarized current research into black-footed ferret reproduction, physiology and epidemiology. Houston et al. (1986) developed a habitat suitability index model which has been used to evaluate black-footed ferret habitat in Montana (Clark et al., 1987). Stromberg et al. (1983) used a metabolizable energy requirement model to estimate the annual prey requirements for a reproductive female ferret and her young. A predator-prey analysis then pro­
duced estimates of prairie dog population density neccesary to sustain black-footed ferrets. Powell et al. (1986) also modeled black-footed ferret energy expenditure; using the Siberian polecat as a biological model for estimating energy and nutrient acquisition from two black-footed ferret prey species. Our search yielded only three demographic black-footed ferret models, two as yet unpublished. Groves and Clark (1986) applied Meeteetse demographic data to MacArthur and Wilson's (1967) theoretical model and Lehmkuhl's (1984) genetic model to estimate black-footed ferret minimum viable population sizes of 40 adults and 214 breeding females, respectively. Harris et al. (in press) estimated extinction probabilities for an isolated black-footed ferret population using a stochastic age-class model with density-dependent survivorship and demographic parameters from Forrest et al. (1988). Simulations showed that an isolated population of 23
less than 100 individuals is prone to chance extinctions and that although environmental stochasticity introduced the greatest risk, extinction probability remained substantial with only demographic variability. Klebanoff et al. (un­
publ. mscpt.) developed an age-dependent deterministic predator-prey model to investigate the relationship between the dynamics of prairie dogs and those of the black-footed ferret. Their results indicate that higher prairie dog den­
sities than previously predicted from energetic models may be necessary to ensure a stable black-footed ferret-prairie dog system. They also suggested that consideration of habitat patch dynamics may add additional stability. METHODS
The Basic Model The simulation model employed in this study was deve­
loped by Prof. Roland Lamberson, Michael Butler, Curt Voss and Rob Van Kirk. We chose to include only females in the model. Because male black-footed ferrets are both highly mobile and polygynous breeders, we assume that an adequate number of males are always available. All survival rates, fecundities, and dispersal parameters used in this study refer to females only. With this in mind, the life history 24
of the black-footed ferret is adequately accounted for by the first-order linear difference equation, POP(K) = Sa·W·POP(K-1) + B-POP(K-1)-Sj -[(1 - D) + D•M]* W, (1) where:�
POP(K) = number of adult females at end of year K S.�
= adult summer survival rate W�
= winter survival rate B�
= per capita birth rate = juvenile summer survival rate D�
= dispersal rate M�
= dispersal (migration) success rate. The beginning of the "year" in this model coincides with birth of the kits, so that the "total population" is the number of females present immediately before parturi­
tion. The summer survival rate covers survivorship for the period May to October, and the winter survival rate, which has the same value for both adults and juveniles, models survivorship for the period November to April. Dispersing juveniles are subject to the additional mortality given by 1 - M during the dispersal period in September and October. The model assumes that adult females do not disperse (see dynamic diagram in Figure 2). The per capita birth rate is a breeding rate multiplied by the average number of females born to each breeding female.�
No Allee effects are in-
cluded. 25
Figure 2. Dynamic diagram and accompanying difference equa­
tion of the basic black-footed ferret population model used in this study. The total population in year k, given by POP(k) includes only adult females. All survival, birth and dispersal rates apply to females only. 26
Our model consists of equation (1) extended by stochas­
tically applying all rates, adding density-dependence to the winter survival and dispersal rates, and modeling migration by moving each dispersing juvenile on a hexagonal grid. Stochasticity Our program used the Box-Muller algorithm (Ripley, 1987) to generate values from a normal distribution and a pseudo-random number generator adapted from Park and Miller (1988). To model demographic stochasticity, we determined the survival, dispersal and breeding of each individual by comparing a uniformly distributed (0,1) random number with the appropriate rate. Litter size for each breeding female was computed by drawing from a normal distribution and rounding to the nearest non-zero integer. Environmental stochasticity was modeled by randomly choosing summer and winter survival rates for each year from a normal distribu­
tion with a given coefficient of variation (CV). We did not allow for variation in mean litter size between years, since there is no evidence for this in the field data (Henderson, et al., 1974; Forrest et al., 1988). Habitat, Carrying Capacity and Dispersal Probability We adapted a map of the Meeteetse Meeteetse site.W
prairie dog colonies from Forrest et al. (1985b) for use in this study, including only those colonies on which ferrets 27
had been regularly observed over the course of field obser­
vations from 1981 to 1986 (Figure 3). A hexagonal grid was then projected onto the map, and we approximated each colony as a collection of regular hexagons (Figure 4). The grid was scaled so that center-to-center distance between ad­
jacent hexagons was approximately 0.7 km, and the area of an individual hexagon was roughly 53 ha. The Meeteetse colo­
nies are inhabited by white-tailed prairie dogs (C. leucur­
us), for which Stromberg et al. (1983) reported a median density of 4/ha. Their model predicts that a sustained population of between 412 and 1236 white-tailed prairie dogs is required to satisfy the energy requirements of a female black-footed ferret and a litter of kits for one year. We thus defined "carrying capacity" as the number of females which could raise a litter on a given prairie dog colony and calculated that one female with litter required approximate­
ly 2.5 hexagons of white-tailed prairie dog habitat on our grid. We allowed fractional carrying capacities, interpret­
ing them as a portion of years the colony is occupied. Table 1 summarizes Meeteetse colony parameters used in the model. To introduce density-dependence into dispersal probabi­
lity, we assumed that, as in Smith's (1974) pikas, dispersal rates are greater for small colonies than for large ones. In addition, Forrest et al. (1988) observed several juvenile females which undertook only "short" dispersals to a dog colonies used in this study (shading). (from Forrest et al. 1985b) 28
Figure 3. Map of Meeteetse, Wyoming black-footed ferret study site showing prairie Figure 4. Hexagonal approximation of Meeteetse prairie dog colonies. 29 30
Table 1. Meeteetse site colony parameters. 1. from Forrest et al. (1985b) field observations 2. calculated with equation (2) 3. Carrying capacities are given as number of females with litter that can be sustained by white-tailed prairie dogs inhabiting the area covered by the given number hexagons, according to the results of Stromberg et al. (1983) and the explanation in the METHODS section of the text. 31
different area of the same large prairie dog colony. We considered these individuals as simply non-dispersers, thus further increasing the disparity in dispersal rates between small and large colonies. A dispersal rate function that satisfactorily accomodates these assumptions is given by: PDS(I) = exp[-0.03N(I)],�
(2) where: PDS(I) = rate of juvenile dispersal from colony I N(I)�
= number of hexagons comprising colony I. Though we employed equation (2), we tried other func­
tions and found Meeteetse simulation results to be insensi­
tive to the exact form as long as the given assumptions were met. Equation (2) gives average dispersal rates of 97 percent for the smallest Meeteetse colonies and 50 percent for the largest (see Table 1 and Figure 5). Montana Site.
We adapted a map of a prairie dog colony on the Charles M. Russell National Wildlife Refuge (CMRNWR) (Figure 6) from a map and accompanying survey information provided by the U.S. Fish and Wildlife Service, which over­
sees management of the refuge. As with the Meeteetse site, a hexagonal grid was then projected onto the map, and each colony was approximated as a collection of regular hexagons (Figure 7). For conistency, we scaled the grid on the CMRNWR map to the exact scale used on the Meeteetse map, so that each hexagon represents roughly 53 ha. The CMRNWR colonies are inhabited by black-tailed prairie dogs (C. ludovicianus), for which Stromberg et al. (1983) 32
colony size (number of hexagons) Figure 5. Graph of juvenile dispersal probability versus colony size for both equation (2) and equation (3). curve a: graph of equation (2), PDS(I) = exp[-0.03N(I)] curve b: graph of equation (3), PDS(I) = -0.03N(I) + 0.83 PDS(I) = probability of juvenile dispersal away from colony I N(I)�
= number of hexagons comprising colony I prairie dog colony complex used in this study. 33 Figure 6. Map of the Charles M. Russell National Wildlife Refuge, Montana 34
Figure 7. Hexagonal approximation of CMRNWR prairie dog colony complex. 35
reported a median density of 15/ha. Their model predicts that a median sustained population of 766 black-tailed prairie dogs is required to satisfy the energy requirements of a female black-footed ferret and a litter of kits for one year. In remaining consistent with our definition of "carr­
ying capacity" as the number of females which could raise a litter on a given prairie dog colony, we calculated that one female with litter requires approximately 1.0 hexagons of black-tailed prairie dog habitat on the grid. Table 2 sum­
marizes CMRNWR colony parameters used in the model. Although we did perform population simulations on the CMRNWR site using equation (2) as the dispersal rate func­
tion, it became evident that equation (2) results in disper­
sal rates which are much too high in a black-tailed prairie dog complex. Since black-tailed colonies not only tend to be smaller than white-tailed colonies, but also have a greater black-footed ferret carrying capacity than white-
tailed prairie dog colonies, it seems reasonable to assume that individuals are less likely to disperse away from a black-tailed colony than from a white-tailed colony of similar size. Furthermore, a personal communication from wildlife biologist Steve Forrest indicates that even on white-tailed colonies, equation (2) might overestimate the proportion of female black-footed ferrets which will dis­
perse away from a given colony. Thus, we performed 36
Table 2. Montana site colony parameters. 1. from data supplied by U.S. Fish and Wildlife Service 2. Carrying capacities are given as number of females with litter that can be sustained by black-tailed prairie dogs inhabiting the area covered by the given number of hexagons, as explained in the METHODS section of the text. 37
additional simulations on the CMRNWR site using a linear dispersal rate function given by: PDS(I) = -0.03N(I) + 0.83�
(3) where: PDS(I) = rate of juvenile dispersal from colony I N(I)�
= number of hexagons comprising colony I. Equation (3) gives average dispersal rates of 80 per­
cent for the smallest CMRNWR colonies and 35 percent for the largest (see Table 2 and Figure 5). Hypothetical Habitat Configuration.
The design of the hypothetical habitat arrangement was motivated by MacArthur and Wilson's (1967) discussion of the effects of small "stepping stone" islands on the colonization of large islands by species from other large islands. They showed analytically that a small island located midway between two large ones will greatly increase the frequency and amount of biotic exchange between the two large islands. To test the applicability of this theory to the case of a black-footed ferret population colonizing prairie dog colonies, we used the habitat shown in Figure 8.
In each simulation, colony 1 is the "source colony", and colony 2 is the "recipient colony". The smaller colonies 3,4 and 5 act as the "step­
ping stones". We performed simulations using colonies 1 and 2 only, colonies 1, 2 and 3 only, and all 5 colonies, res­
pectively, in order to appropriately test the effects of the stepping stone colonies upon colonization success of the We employed the same carrying capacity recipient colony.�
w
Figure. 8.
Hypothetical colony arrangement used to test stepping stone theories.
A l1 Vi:iHf!
Ai!S~'i:!A!Nn .il'--!.LS l.G10lir"-lnH
(X)
39
Table 3. Colony parameters for hypothetical prairie dog colonies shown in Figure 8. 1. calculated from the number of hexagons, where one hexagon equals 53 ha 2. calculated with equation (2) 3. Carrying capacities are given as the number of females with litter that can be sustained by white-tailed prairie dogs inhabitiing the area covered by the given number of hexagons, as explained in the METHODS section of the text. 40
and dispersal rate parameters for this habitat as we did for the Meeteetse habitat, namely, a carrying capacity of one female with litter per 2.5 hexagons, and dispersal probabil­
ities given by equation (2). Table 3 lists colony para­
meters for the hypothetical habitat site. Density Dependent Survivorship We incorporated density-dependent survivorship only into the winter survival rate. This allowed appropriate comparison of post-dispersal population size to our well-
defined carrying capacity and also accounted for the assump­
tion that not all successful dispersers are able to establish themselves in the new colony sufficiently to survive the winter. We assumed average survivorship to be constant at population densities below the carrying capacity of the colony. The model was again insensitive to exact form, and we found that a suitable continuous function is: Graphs of equation (3) for Wb = 0.8 and two different carrying capacities are given in Figure 9. 41 42
Dispersal Routine Individuals were moved in discrete steps on the hexago­
nal grid. Each propagule began dispersal from a hexagon randomly chosen from among those forming the boundary of the appropriate colony. Grid location resulting from the first dispersal step was selected from a uniform distribution of those hexagons adjacent to the initial position which were not contained in the colony. Subsequent directions were based on the direction of the previous step by considering that each hexagon is surrounded by six other identical hexagons in the grid. The probability of continuing in the same direction is 1/3, the probability of taking either of the two "forward" diagonal directions is 1/4, the probabil­
ity of taking either of the two "backward" diagonal direc­
tions is 1/12, and the probability of going back to the previous location is zero. This provided an approximately normal distribution of direction similar to that employed by Kitching (1971) and Bovet and Benhamou (1988). We assumed that survival probability decreases exponen­
tially with distance traveled in unsuitable habitat away from the source colony, and thus each dispersing individual was subject to a constant mortality probability, PD, at each step. An individual was considered to be within the "zone of recognition" of a new colony when it reached a grid sector adjacent to a colony other than its source colony. Upon entering the recognition zone, the individual was 43
automatically added to the population of the new colony and the dispersal was terminated. If a hexagon was adjacent to more than one new colony, a random uniform draw determined the colony into which the successful disperser would be added. The per step straight line distance of 0.7 km ap­
pears to be well within the distance an individual can travel in one night (Biggins et al., 1986), and at least in the winter, black-footed ferrets investigate nearly every burrow encountered on nightly forays (Richardson et al., 1987). These observations, along with the conclusion of Henderson et al. (1974) that the black-footed ferret has a well-developed sense of smell, suggest that the one-hexagon recognition zone may be a reasonable assumption. An individual's dispersal path was also terminated if the propagule had neither died nor found a new colony within 30 steps or if it was far enough away that the nearest colony could not be reached within the remaining steps. Though very little data exist on the specifics of black-
footed ferret dispersal, we chose 30 steps because all ob­
served inter-colony movements at Meeteetse had a straight-
line distance of less than 5.7 km (Forrest et al., 1985b) and because we found that even for very optimistic (low) values of the step-wise mortality probability, no individuals survived and were still migrating past 30 steps in the simulation. 44
Parameter Values and Simulation Procedures A list of parameter values used in our simulations is given in Table 4. The breeding rate of 0.9 is an average figure adapted from Harris et al. (in press), who used 0.85 for juveniles and 0.95 for adults. Forrest et al. (1988) reported an average litter size and standard deviation of 3.3 ± 0.89. Assuming a 1:1 sex ratio at birth (Anderson et al. 1986, Forrest et al. 1988), we divided these values by 2 to obtain parameters for the distribution of number of females per litter. We obtained approximate values for survival, dispersal and migration success rates by manipula­
ting parameters in a deterministic two-sex version of our model until average annual survival rates and sex ratios fell within ranges reported by Forrest et al. (1988). Parameters were further tuned in the stochastic simulation model to match field observations from the Meeteetse site. We had no field observations of values for the dispersal step mortality probability, PD, and for the CVs to be used in determining survival rate distributions. We thus chose to perform simulations at several different values of these parameters, seeking model results that matched field data as well as possible. A run consisted of 100 stochastic 100-year simulations, each with a different starting seed for the pseudo-random number generator. We estimated extinction probabilities by counting the number of extinctions per 100 distinct, 45
Table 4. Parameter values used in simulations. *
Values designated with an asterisk are used in all simu-
lations. All other values are those used in the Meeteetse site control run and may vary for other simulations. 1. Equation (2) is used in all simulations except one designated run using the CMRNWR prairie dog complex, in which equation (3) is employed. 46
stochastic simulations. Unless otherwise noted, the simula­
tions using the Meeteetse site were initialized such that at the beginning of year one, each colony contained the maximum number of breeding females observed in that colony by For­
rest et al. (1985b) (see Table 1). For consistency in comparing the effects of parameter changes, we designated one run as the "control", which was initialized as described above. The simulations in this run included what we con­
sidered to be moderate levels of environmental stochasticity and dispersal step mortality. Simulations using the CMRNWR site were initialized with each colony at calculated carry­
ing capacity. All simulations using the hypothetical habi­
tat were initialized with colony 1 at carrying capacity and no other colonies occupied. Other than the use of equation (3) in one of the CMRNWR runs, all runs using the CMRNWR and hypothetical habitat maps employed the same parameters as the Meeteetse control run. The program was written in FORTRAN, and simulations were run on Control Data Corp. Cyber 720 and Cyber 830 com­
puters. We should emphasize once again that this model includes only females. Population sizes reflect census at the end of winter, immediately prior to birth of the kits. Thus the term "total population" is defined in this study to be the number of females present immediately before parturition. 47
RESULTS
The simulations produced results pertaining to each of the three critical components identified in the introduc­
tion: stochasticity, population dynamics in a patchy en­
vironment and dispersal. Effects of Stochasticity Figures 10, 11 and 12 compare the effects of different levels of environmental stochasticity on population simula­
tions at the Meeteetse site. Figure 10 illustrates the control run, Figure 11 includes only demographic stochas­
ticity, and Figure 12 shows the effect of a large amount of environmental variance. Extinction probabilities for these and other runs pertaining to the effects of environmental stochasticity appear in Table 5. Population Dynamics in a Patchy Environment Tables 6 and 7 illustrate the dynamics of local extinc­
tion and recolonization at the Meeteetse site, and Table 8 illustrates the same phenomena at the CMRNWR site. The simulation producing Table 6 was initialized with individuals only in the two largest colonies to enhance illustration of the recolonization process. The simulation in Table 7 is typical of extinctions we observed. Table 8 48
illustrates a typical CMRNWR simulation in which equation (3) was used to calculate dispersal rates. Figures 13, 14 and 15 compare the effects of different initializations and show the mean equilibrium population size attained in the Meeteetse habitat. Figure 13 is the control run, which was initialized with each colony containing the maximum number of breeding females observed by Forrest et al. (1985b). Figure 14 shows initialization with only 13 individuals. Figure 15 shows initialization with each colony at carrying capacity, defined and computed from the nutritional require­
ment study of Stromberg et al. (1983) as described in METH­
ODS and summarized in Table 1.
Extinction probabilities for various initializations at the Meeteetse site are given in Table 9. Dispersal Results Figures 10, 16 and 17 show the effect of changes in the dispersal step mortality rate, PD, on population simulations at the Meeteetse site. The simulations in Figure 16 used a value of PD = 0.05 and those in Figure 17 used PD = 0.35. Figure 10 is the control run, which used PD = 0.20. Calcu­
lated mean annual survival, dispersal and migration success rates at the Meeteetse site for various values of PD appear in Table 10. Extinction probabilities at various levels of dispersal step mortality are given in Table 11. Frequency distributions of dispersal distance for two simulations and 49
Meeteetse field data appear in Figure 18, and some typical simulated dispersal paths in the Meeteetse complex are illustrated in Figure 19. Figures 20 and 21 illustrate differences in population trends and persistence at the CMRNWR site caused by use of the two different dispersal probability equations. Figure 20 shows population versus time and extinction probability when equation (2) was used to calculate dispersal rates, and Figure 21 gives the same information for simulations in which equation (3) was used. Table 12 and Figures 22, 23 and 24 illustrate the ef­
fects of the stepping stone colonies on colonization success and population trends and persistence for the hypothetical colony arrangement. Table 12 lists frequencies with which colony 2 was colonized by dispersers from a population originating in colony 1 under different conditions of dis­
persal step mortality and stepping stone arrangement. Figure 22 shows population versus time and extinction proba­
bility for simulations with the stepping stone colonies 3, 4 and 5 omitted. Figure 23 shows the effect of adding colony 3 as a single stepping stone midway between the two large colonies, and Figure 24 illustrates the effect of including the three stepping stone colonies 3, 4 and 5 between the large colonies 1 and 2 (see Figure 8). 50
CONCLUSIONS AND DISCUSSION The results support seven major conclusions: 1) demog­
raphic stochasticity has no noticable effect on population persistence except when the population size is already very small; 2) increase in environmental stochasticity decreases persistence and increases population size variance; 3) mean long-term population size is significantly lower than the total carrying capacity for the habitat; 4) extinction is more likely to occur in a stochastic environment with a patchy habitat distribution if the number of patches oc­
cupied becomes too low, even if total abundance is not extremely low; 5) increase in the dispersal step mortality rate decreases population persistence; 6) the Meeteetse­
tuned model may not adequately predict population trends and persistence probabilities at other sites without further modification; 7) introduction of small stepping stone colonies increases the frequency of successful colonizations from one large colony to another located some distance away. Demographic and Environmental Stochasticity The results indicate that demographic stochasticity alone does not cause a risk of extinction in Meeteetse simulations initialized with 29 individuals, though we did observe extinctions occurring as a direct result of 51 Figure 10. Population versus time for Meeteetse control run showing mean ± 1 standard deviation of 100 simulations. Extinctions: 3 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.20 variation on adult summer surv. rate�
0.10 variation on juvenile summer surv. rate�
0.25 variation on base winter survival rate�
0.10 Initialization: observed maximum number of breeding females 52
Figure 11. Population versus time showing mean ± 1 standard deviation of 100 simulations for the Meeteetse site with no environmental stochasticity (demographic stochasticity only). Extinctions: 0 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.20 variation on adult summer surv. rate�
0.00 variation on juvenile summer surv. rate�
0.00 variation on base winter survival rate�
0.00 Initialization: observed maximum number of breeding females 53
Figure 12. Population versus time showing mean ± 1 standard deviation of 100 simulations for the Meeteetse site with extreme environmental stochasticity. Extinctions: 30 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.20 variation on adult summer surv. rate�
0.00 0.00 variation on juvenile summer surv. rate�
variation on base winter survival rate�
0.25 Initialization: observed maximum number of breeding females 54
demographic stochasticity when simulations were initialized with 4 individuals. These results contradict those of Harris et al. (in press), who found that the probability of extinction due to demographic stochasticity remained sig­
nificant even at black-footed ferret population sizes of 40 individuals. However, direct comparison of their results to ours is difficult because the population sizes reported in their study include males and juveniles, while population figures reported in this study include only adult females. Figures 10, 11 and 12 illustrate that introduction of environmental stochasticity decreases persistence probab­
ility and increases population size variance. It also appears that the equilibrium population size achieved with a moderate amount of environmental stochasticity is smaller than the equilibrium size achieved by simulations including only demographic stochasticity. This observation agrees with those of Lande (1987) and Gadgil (1971). It is ap­
parent from Table 5 that persistence probability is slightly less sensitive to variation in the juvenile summer survival rate than to variation in the adult summer survival rate. This trend is not unexpected, since juvenile survivorship depends more heavily on dispersal success than on pre-dis­
persal (summer) survival. A more significant trend is that persistence is much less sensitive to variation in either adult or juvenile summer survival rates than to variation in the winter survival rate. This result is also not 55
Table 5. Number of extinctions counted in 100 stochastic simulations for the Meeteetse site at various levels of environmental stochasticity. 1. control run, population versus time shown in Figure 10 2. no environmental stochasticity, population versus time shown in Figure 11 3. extreme environmental stochasticity, population versus time shown in Figure 12 56
surprising and occurs in our model because the winter sur­
vival rate acts on all members of the population. We can also conclude that environmental stochasticity has a much greater effect on population persistence than demographic stochasticity. This conclusion is consistent with the results of Harris et al. (in press), Goodman (1987), Shaffer (1987) and Simberloff (1986). Population Dynamics in a Patchy Environment Perhaps the most significant result we observed is that the long-term mean population size is much smaller than the total carrying capacity for the habitat. Figure 13 shows that the Meeteetse control run achieves an equilibrium size of approximately 20 females, less than one half of the calculated carrying capacity of 46. Similarly, Figure 21 shows that the long-term mean for the CMRNWR site is about 22 females, roughly a third of the calculated carrying capacity of 60. Though the numerical results should not be taken as truth, the general result is clear. Long-term population size is established by a balancing of local extinction and recolonization, which, at any given time, leaves some colonies unoccupied, thus resulting in an equi­
librium population size substantially smaller than the total carrying capacity. This phenomenon is clearly illustrated in Tables 6, 7 and 8. With respect to this fundamental 57
Figure 13. Population versus time for the Meeteetse control run showing 90 percent confidence intervals for the mean of 100 simulations. Extinctions: 3 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.20 variation on adult summer surv. rate�
0.10 variation on juvenile summer surv. rate�
0.25 variation on base winter survival rate�
0.10 Initialization: observed maximum number of breeding females 58
Figure 14. Population versus time showing 90 percent con­
fidence intervals for the mean of 100 simulations with the Meeteetse site initialized at a small population. Extinctions: 6 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.20 variation on adult summer surv. rate�
0.10 variation on juvenile summer surv. rate�
0.25 variation on base winter survival rate�
0.10 Initialization: 6 in colony 11, 7 in colony 12 n
Figure 15. Population versus time showing 90 percent con­
fidence intervals for the mean of 100 simulations with the Meeteetse site initialized at carrying capacity. Extinctions: 3 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.20 variation on adult summer surv. rate�
0.10 variation on juvenile summer surv. rate�
0.25 variation on base winter survival rate�
0.10 Initialization: all colonies at carrying capacity 60
Table 6. Yearly populations by colony for the first 50 years of a simulation in which the Meeteetse site was init­
ialized with 8 individuals in colony 11 and 9 in colony 12. 61
Table 7. Yearly populations by colony for the first 50 years of a Meeteetse control run simulation in which extinc­
tion occurred. 62
Table 8. Yearly populations by colony for the first 50 years of a CMRNWR site simulations in which equation (3) was used to calculate dispersal rates. 63
Table 9. Number of extinctions counted in 100 stochastic simulations for the Meeteetse site with various population initializations. 1. as reported by Forrest et al. (1985b) and summarized in Table 1 2. control run, population versus time shown in Figure 13 3. population by colony for a typical simulation shown in Table 6 4. population versus time shown in Figure 14 64
concept of population dynamics in a patchy environment, our results agree with those of Smith (1974) and Gadgil (1971). Comparison of Figures 13, 14 and 15 shows that the long-term equilibrium population size for the Meeteetse habitat is insensitive to initialization, although it is ap­
parent from Table 9 that initialization at lower population sizes decreases persistence probability due to the increased effects of environmental and demographic stochasticity on the smaller populations. Our model also shows that extinction may occur if the number of patches occupied becomes too low. Comparison of year 18 in Table 6 with year 29 of Table 7 illustrates this concept. In the former case, the total population of 11 individuals is distributed among 5 colonies located in the central area of the Meeteetse complex. However, in year 29 of Table 7 the population of 11 individuals occupies only 4 colonies, one of which, colony 1, is sufficiently far away that communication via dispersal occurs only rarely. It is likely that the extinction in Table 7 occurred because too few colonies in the central area of the prairie dog complex were occupied. We have studied many simulations similar to the one illustrated in Table 6 and found that at equilibrium, the occupancy of the central Meeteetse colonies (numbers 3 through 16) averaged roughly 6 out of 14 colo­
nies. Extinction occurred in many cases when fewer than 4 of these colonies were occupied. We also observed this 65
phenomenon in CMRNWR simulations, such as the one illustrat­
ed in Table 8. Extinction was more likely to occur when the occupancy of the central colonies 4 through 12 became too low. These results are consistent with those of Gurney and Nisbet (1975) and Lande (1987), although it is difficult to compare their numerical results directly because of dif­
ferences in model structure. It is apparent from Tables 6, 7 and 8 that colonies lo­
cated near large colonies tend to remain occupied a greater percentage of the time than outlying colonies because of the large number of dispersers which originate from the large colonies and the ability of these dispersers to survive the shorter dispersals. This trend illustrates the important effect geographic distribution of the colonies has on the population dynamics of the complex. The absence of individuals in colony 1 of Table 6 is due to the inability of dispersing individuals to success­
fully locate this distant patch; our simulations produced very few successful dispersals to and from colony 1 of the Meeteetse site. However, ferrets were regularly observed in this colony during field observations (Forrest et al. 1985b), indicating that our dispersal routine may have underestimated the ability of propagules to successfully disperse to distant colonies. Details of the dispersal results are discussed below, but examination of Table 7 points out that if the simulation is initialized with 66
individuals in colony 1, a subpopulation will persist there for a time period much longer than that of field observation at Meeteetse. It is possible that during the Meeteetse field study, colony 1 supported a population without receiv­
ing any immigrants from other colonies. In fact, no suc­
cessful dispersals to or from colony 1 were observed in the field (Forrest et al. 1985b). Under historical habitat conditions, colony 1 may have received immigrants from prairie dog colonies which no longer exist. The subpopula­
tion observed there between 1981 and 1985 may have been a remnant eventually destined for extinction by the process illustrated in Table 7. Table 8 indicates that the hexagonal grid dispersal model was easily able to accomodate a prairie dog complex other than the one at Meeteetse, for which the model was originally constructed. The local and extinction and recol­
onization process shown in Table 8 is nearly identical to those illustrated for the Meeteetse site in Table 6 and 7, indicating that these results were not strictly artifacts of model construction. An interesting feature illustrated by Table 8 is the apparent periodic oscillation of the subpopulation in the large colony 9, which has a carrying capacity of 16 females. These oscillations are probably a result of the lower dis­
persal rates calculated by equation (3) and the effect of the density dependent winter survival rate in a colony with 67
such a large carrying capacity. A large number of offspring are produced, most of which do not attempt dispersal. The population at the beginning of winter is then very large compared to the carrying capacity, and density-dependent winter survival results in a severely lowered population, which eventually rebuilds and the cycle repeats. This periodic trend in the subpopulations of the large colonies was also evident to a great degree in the simulations em­
ploying the hypothetical site and to a lesser degree in the Meeteetse simulations. This trend may be a direct result of model design and may not reflect reality. These results show that population dynamics in an insular habitat structure is a very complex process which is not easily generalized. Persistence of the metapopulation in a stochastic, patchy environment depends not only on population size, but also on the the geometry of the patches and the distribution of the population among the patches. In many cases, occupancy of certain critical patches may be more important than total population size in determining persistence. The occupancy of these patches, in turn, appears to be a function of their location in the complex and the ability of dispersing individuals to successfully reach them. 68
Dispersal Figures 10, 16 and 17 and Table 11 show that an in­
crease in the dispersal step mortality rate decreases popu­
lation persistence at the Meeteetse site. We see from Table 10 that this decrease in persistence occurs because of the decrease in juvenile survivorship, which is caused by a significant decrease in dispersal success. Closer analysis reveals that the situation is not as simple as it may first appear. Table 10 also shows that for a given change in dispersal step mortality, adult survivorship increases by roughly the same amount that juvenile survivorship de­
creases, presumably because of a density-dependent response to fewer juveniles surviving dispersal. However, it is clear from Table 11 that the increase in adult survivorship does not compensate for decreased juvenile survivorship at low dispersal success rates. Simple analysis of a deter­
ministic Leslie matrix model of black-footed ferret popula­
tion dynamics shows that long-term viability is more sensi­
tive to changes in juvenile survivorship than to any other demographic parameter. The stochastic simulation results also seem to suggest this trend. Figure 18 helps to illustrate the effect of habitat configuration on dispersal success at the Meeteetse site. By decreasing dispersal step mortality from 0.20 to 0.05, we were able to increase the average number of steps taken by dispersing individuals, thus increasing the average total 69
Figure 16. Population versus time showing mean ± 1 standard deviation of 100 simulations for Meeteetse site with low dispersal step mortality. Extintions: 0 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.05 variation on adult summer surv. rate�
0.10 variation on juvenile summer surv. rate�
0.25 variation on base winter survival rate�
0.10 Initialization:�
observed maximum number of breeding females 70
Figure 17. Population versus time showing mean ± 1 standard deviation of 100 simulations for Meeteetse site with high dispersal step mortality. Extinctions: 39 ou of 100 simuations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.35 variation on adult summer surv. rate�
0.10 variation on juvenile summer surv. rate�
0.25 0.10 variation on base winter survival rate�
Initialization: observed maximum number of breeding females 71
Table 10. 90 percent confidence intervals for mean annual survival rates for different values of the dispersal step mortality probability. Values were calculated from a sample of 100 years selected randomly, 20 from each of 5 distinct, stochastic 100-year simulations. Values for the coefficients of variation on the adult summer, juvenile summer and winter survival rates were 0.10, 0.25 and 0.10, respectively on all simulations. 72
Table 11. Number of extinctions counted in 100 stochastic simulations for the Meeteetse site with various values for the dispersal step mortality probability. a. population versus time shown in Figure 16 b. control run, population versus time shown in Figure 10 c. population versus time shown in Figure 17 73
Figure 18. Distribution of straight-line distance of suc-
cessful dispersals from two simulations and Meeteetse field data (Forrest et al. 1985b). 74
dispersal path length. However, Figure 18 shows that this decrease in the dispersal step mortality rate does not significantly change the mean straight- line distance of successful dispersals, although it obviously changes the distribution of such distances. The surprising result that decrease in dispersal step mortality increases the occur­
rence of only the shortest dispersals suggests that the the configuration of the particular habitat under investigation has a greater effect on the mean distance of succesful dispersals than does total dispersal path distance. The simulated dispersal paths in Figure 19 further illustrate this phenomenon. The path originating in colony 3 is typi­
cal of unsuccessful dispersals we simulated; the path is long enough to reach colony 1, but it takes an inappropriate direction. Dispersals which originated in the closely-
spaced central colonies were much more likely to be success­
ful than those originating in the outlying colonies, regard­
less of total path length. These results agree with Smith's (1974) field observations that the dispersal success of pikas was greater when habitat patches were closely spaced. Forrest et al. (1985b) also reported that dispersing ferrets successfully encounter nearby colonies more frequently than they encounter distant colonies. We again conclude that the geometry of the habitat may be more important to metapopula­
tion viability than inherent demographic features of the species. Figure 19. Typical simulated dispersal paths for the Meeteetse site. 75 76
To continue the discussion of dispersal, we compared simulated dispersals with those observed in the field at Meeeteetse. Figure 15 initially suggests that our simula-
tions failed to produce enough long dispersals. However, straight-line distances in the field were measured from the individual's point of origin to its point of termination and included distance traveled within colonies. The straight-
line distances reported in this study are measured from the edge of the starting colony to the edge of the terminating colony and thus tend to be much shorter than those reported by Forrest et al. (1985b). Furthermore, all successful dispersals observed at Meeteetse were reproduced often in the control run of the simulation model, suggesting that our dispersal routine may well model black-footed ferret disper­
sal realistically. Thus far, we have investigated the effects of dispersal step mortality and habitat configuration on population trends and persistence. Though these factors are obviously of critical importance, Figures 20 and 21 illustrate the profound sensitivity of simulations at the CMRNWR site to changes in dispersal rates. Recalling from Figure 5 that equation (3) computes much higher dispersal rates than equation (2), we see that CMRNWR simulations using equation (2) are much more likely to result in extinction than those using equation (3). In this respect, the model tuned for use with the Meeteetse site (using equation (2)) seems to be 77
inappropriate for use with the CMRNWR site, possibly because of the difference in colony sizes and carrying capacities caused by white-tailed versus black-tailed prairie dogs. The dispersal rate equation (2) which appeared to be appropriate for Meeteetse seems to overestimate dispersal rates away from the smaller colonies of the CMRNWR site. At the suggestion of wildlife biologist Steve Forrest, who performed extensive field research at Meeteetse, we tried the alternative dispersal rate equation (3) in the simula­
tions illustrated in Figure 21. The comparison of Figure 21 with Figure 20 leads us to conclude that the model is very sensitive to changes in dispersal probability. Furthermore, it is possible that even though the model successfully illustrates the basic concepts of population dynamics in a patchy environment at the CMRNWR site, the Meeteetse-tuned model may not accurately predict population trends and persistence probabilities at other sites without further tuning to the features particular to the site. It is also entirely possible that the demographic parameters computed from Meeteetse field data do not reflect those that would be exhibited by a healthy black-footed ferret population in true equilibrium. To conclude the discussion of dispersal, we investigate the results of simulations using the hypothetical colony arrangement. Table 12 shows that with a dispersal step mortality given by PD = 0.20, the addition of the stepping 78
Figure 20. Population versus time showing mean ± 1 standard
deviation of 100 simulations for the CMRNWR site using equation (2) to calculate dispersal rates.
Extinctions: 60 out of 100 simulations
Parameters:
dispersal
coeff. of
coeff. of
coeff. of
0.20
step mortality probability�
variation on adult summer surv. rate�
0.10
0.25
variation on juvenile summer surv. rate�
variation on base winter survival rate�
0.10
Initialization: all colonies at carrying capacity
79
Figure 21. Population versus time showing mean ± 1 standard deviation of 100 simulations for the CMRNWR site using equa­
tion (3) to calculate dispersal rates. Extinctions: 4 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.20 variation on adult summer surv. rate�
0.10 variation on juvenile summer surv. rate�
0.25 variation on base winter survival rate�
0.10 Initialization: all colonies at carrying capacity 80
stone colony 3 decreases extinction probability from 39 per 100 to 27 per 100, presumably because of the increased frequency of communication via dispersal between the colonies. However, Figures 22 and 23 show that despite the significant decrease in extinction probability, the long-
term population trends are nearly identical in each case. In both of these situations, it does not appear that recolonization is occurring frequently enough to maintain a viable population over the long term. Addition of the two other stepping stone colonies 4 and 5 reduces extinction probability even further to only 17 per 100, as shown in Table 12, due to a large increase in the ability of dispersing individuals to successfully reach colony 2 and establish a population there. Figure 24 shows that with all three stepping stones included, the population exhibits an increasing trend, indicating that the population originating in colony 1 is successfully expanding its range to include the previously unoccupied colonies 2, 3, 4 and 5. This is exactly the trend predicted by MacArthur and Wilson (1967), and it illustrates that even though small colonies make up only a fraction of the total carrying capacity of a colony complex, they play an important role in both recolonization of new territory and maintenence of high colonization rates between the larger colonies in the complex. These higher colonization rates increase population persistence and provide another example of why 81
Figure 22. Population versus time showing 90 percent con­
fidence intervals for the mean of 100 simulations with the hypothetical colony arrangement including only the large colonies 1 and 2. Extinctions: 39 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.20 variation on adult summer surv. rate�
0.10 variation on juvenile summer surv. rate�
0.25 variation on base winter survival rate�
0.10 Initialization: colony 1 at carrying capacity, no other colonies occupied 82
Figure 23. Population versus time showing 90 percent con­
fidence intervals for the mean of 100 simulations with the hypothetical colony arrangement including the large colonies 1 and 2 and the stepping stone colony 3. Extinctions: 27 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.20 variation on adult summer surv. rate�
0.10 variation on juvenile summer surv. rate�
0.25 variation on base winter survival rate�
0.10 Initialization: colony 1 at carrying capacity, no other colonies occupied 83
Figure 24. Population versus time showing 90 percent con­
fidence intervals for the mean of 100 simulations using the hypothetical colony arrangement with all five colonies in­
cluded. Extinctions: 17 out of 100 simulations Parameters: dispersal
coeff. of
coeff. of
coeff. of
step mortality probability�
0.20 variation on adult summer surv. rate�
0.10 variation on juvenile summer surv. rate 0.25 variation on base winter survival rate 0.10 Initialization: colony 1 at carrying capacity, no other colonies occupied 84
Table 12. Colonizations and extinctions counted in 100 stochastic, 100-year simulations using the hypothetical colony arrangement shown in Figure 8. In each case, colony 1 is initialized at carrying capacity, and no other colonies initially contain any individuals. a. PD = dispersal step mortality probability b. population versus time shown in Figure 22 c. population versus time shown in Figure 23 d. population versus time shown in Figure 24 85
habitat configuration is such an important factor in population dynamics in a patchy environment. In summary, these results lead to the conclusion that dispersal is a complex process. Its effect on population dynamics is extremely important yet remains poorly under­
stood. At the very least, we can conclude that in species such as the black-footed ferret whose life history contains a well-developed dispersal mechanism, survivorship and population persistence is greatly dependent on habitat configuration. MANAGEMENT IMPLICATIONS
Our results have several implications to reintroduction and future management of wild black-footed ferret popula­
tions. These implications fall under five general headings: significance of environmental stochasticity, assessment of reintroduction sites, development of reintroduction proto­
col, reduction of dispersal mortality, and reduction of ex­
tinction risk. Significance of Environmental Stochasticity Increase in the amount of variance present in the environment clearly reduces the probability of population 86
persistence. We found that extreme environmental stochas­
ticity results in a very high extinction rate, and the extinction rate remains non-trivial even at moderate levels of environmental variance. The significance of these re-
sults is subject to debate, however. Although some theorists and managers would argue that a 97 percent probab­
ility of persistence for 100 years indicates that a reintro­
duction effort will almost certainly be successful, others may feel that even a three out of 100 chance of failure is too great a risk when considering the future of an endan­
gered species (see comments of Shaffer, 1987). Population size is obviously sensitive to variation in the environment, but there is no known method to accurately determine the actual amount of environmental variance at a given locale, nor how it should be reflected in the variance of demograph­
ic parameters. It may well be that the amount of stochas­
ticity we considered as "extreme" is very close to reality in the harsh high-plains habitat of northwestern Wyoming. In any case, our results suggest that consideration of environmental stochasticity is extremely important in the modeling process and that both theoretical and field re­
search into methods of estimating actual environmental variance would be of great use to wildlife managers in accurately assessing the extinction risk to a small popula­
tion. 87
Assessment of Black-footed Ferret Habitat One of the major results of this study is that equi­
librium population size in a patchy environment is less than the total carrying capacity of the patches. This result has immediate implications to accurate assessment of black-footed ferret reintroduction sites. It is clear that the spatial distribution of prairie dog colonies is extreme­
ly important to viability of a wild black-footed ferret population. Admittedly, it is very difficult to accurately determine the exact effect of various habitat configurations on the persistence probability of a black-footed ferret population. On the other hand, our results strongly suggest that assessment of habitat should not merely compute acre­
ages of prairie dog colonies and a corresponding estimate of ferret carrying capacity, because this approach will almost certainly overestimate the size of a black-footed ferret population that could be sustained in a given area. The habitat suitability index model of Houston et al. (1986) includes intercolony distance as a parameter, and Clark et al. (1987) used this model to analyze potential black-footed ferret reintroduction sites in Montana. They also empha­
sized the importance of habitat configuration to the viabil­
ity of a wild black-footed ferret population. These studies are hopefully just the beginning of research into methods of accurately assessing black-footed ferret habitat needs and appropriate choice of future reintroduction sites. 88
Determination of Reintroduction Procedures Another implication of our equilibrium population size results is that reintroduction may be successfully achieved with a relatively small number of founder animals. We have shown that long-term mean population size at the Meeteetse site is insensitive to the initialization, though it is obvious that smaller initial population sizes are more prone to chance extinction during the first few years. Careful management during these first years and additions to the total population in the form of subsequent reintroductions may reduce the risk of extinction of the small founder population. Our results do not dictate the optimal reintro­
duction strategy, but they at least suggest that release of a few individuals in each of many centrally-located colonies is preferable to reintroduction of a very large number of individuals into only a few colonies. Reduction of Dispersal Mortality The fourth implication of our results may spark debate among various factions of conservationists and managers. Our model shows that black-footed ferret population viabili­
ty is very sensitive to changes in juvenile survival rate. Furthermore, we have shown that juvenile survivorship is primarily a function of dispersal success. In a habitat consisting of only a relatively small prairie dog colony complex surrounded on all sides by inhospitable terrain, it 89
is apparent that most dispersing individuals die because of failure to encounter other suitable colonies away from the center of the complex. This result suggests that live cap­
ture of dispersing individuals may be a way to reduce loss of individuals to dispersal mortality. The procedure may be carried out in two ways, each with a different purpose. The most highly intrusive method is to capture individuals dispersing toward known suitable habitat and simply release them into the new colony, thus achieving the result of "natural" dispersal at a lower mortality cost. The second method is to capture only those individuals which are dis­
persing away from the central area of the complex. These individuals may either be added to the captive population or released into suitable habitat in other black-footed ferret reintroduction areas. This procedure reduces loss of in­
dividual ferrets while minimizing disturbance of the natural dispersal process in the center of the complex. These management procedures may not be easily achieved with a nocturnal animal such as the ferret, but their feasability must ultimately be determined by experienced managers and biologists. Importance of Habitat to Reduction of Extinction Risk The final and most significant implication of this study is that the best method of reducing the extinction risk to wild black-footed ferret populations is to insure 90
preservation and even extension of the prairie dog habitat on which the species depends. The dependence of black-
footed ferret persistence on habitat configuration has been repeatedly demonstrated in this study, but its importance cannot be overemphasized. The black-footed ferret requires large complexes in which colonies are numerous and closely-
spaced. As an example, it is possible that the best strate­
gy for reduction of risk due to a catastrophe such as canine distemper in a wild black-footed ferret population is to insure sufficient habitat that population sizes remain both high enough and appropriately distributed to withstand the effects of stochasticity following a canine distemper epizo­
otic. Our results also indicate that preservation of even the smallest prairie dog colonies may increase the ability of a small population to colonize new territory. If black-
footed ferret populations can be established in several prairie dog complexes throughout the American plains, manag­
ers will be more willing to accept a 3 or 4 percent extinc­
tion probability on any one of the sites. As Goodman (1987) pointed out, maintenence of dozens of populations in dif­
ferent areas would act as a buffer against the effects of chance extinction and catastrophe to a local population. It is possible that the species may once again survive in the wild in a balance between local complex extinction and recolonization, although it is clear that this recoloniza­
tion will neccessarily be performed by wildlife managers. 91
While it seems obvious that the first populations released into the wild will receive extremely close atten­
tion and management, some conservationists may argue that the procedures suggested here are "unnatural" and compromise the asthetics of a "wild" population. However, Soule (1987) noted that this argument lacks force in today's world. The human hand has dealt the black-footed ferret a nearly fatal blow during the first half this century. That same hand may be the species' only hope for a future in the wild. LITERATURE CITED
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