Introduction
Laboratory populations and colonies of animals are established and maintained for a variety of purposes with biomedical, reproductive, behavioral, and genetical research being among the most common uses. Animal populations are also established and maintained for conservation purposes, as is the case with endangered species captive breeding programs in zoological parks and similar institutions. The management of these populations differ in many substantial ways from those maintained primarily for research purposes. First and foremost, captive breeding programs usually focus on threatened and endangered species. For these programs, the conservation of the species is the ultimate objective and the primary concerns are the long-term maintenance of demographic viability and genetic diversity. Unlike most research laboratory colonies, it is these concerns that for the most part dictate which animals are to breed, with whom, and how often. The goal of long-term viability is made even more difficult by the 2nd major difference between laboratory and captive bred populations. Almost by definition, captive breeding populations of threatened and endangered species are small. The vast majority of mammal species held in zoos exist in total population sizes of 50 or fewer individuals. Loss of genetic diversity, problems related to inbreeding, and undesirable adaptation to the captive environment are major threats that emphasize the need for careful and intensive management of these populations.
A 3rd difference is that captive breeding programs invariably involve more than one colony. Populations are distributed among many zoos, often in different countries and continents. This is basically a result of the primary function of having animals in zoos: exhibitry. Nevertheless, because of the concerns mentioned above, these separate “colonies” are usually managed as a single demographic and genetic population with one common conservation objective. This only further complicates the management and administration of captive breeding programs.
Because of the need for intensive and meticulous management of captive breeding programs, computer modeling has long been an important component of their management, much more so than in laboratory research colonies. Modeling is used to define overall program goals (such as the size of populations and number of offspring to produce), is the basis for breeding recommendations, and is used to identify factors affecting the population's vital rates.
Although the differences between research laboratory colony management and exotic species captive population management are fundamental, there are, however, areas of mutual concern. Both share the need to regulate population growth, and computer modeling has been used for this purpose in captive breeding as well as research colonies. In addition, computer modeling has been used to develop strategies to maintain genetic diversity in both types of populations. Optimizing colony (population) performance relative to these goals is also a shared and important consideration that has been addressed using computer modeling. This paper provides a brief review of some of these applications of computer modeling for population management, both in laboratory research colonies and in captive breeding programs. The emphasis is on the latter since it is in this area that they have been used most extensively. However, it is hoped that a discussion of these applications might stimulate further use of computer modeling in both environments.
Background: Objectives of Captive Breeding Programs
The primary objective of captive breeding programs is to maintain demographically stable populations of sufficient size to preserve some high level of gene diversity (typically 90%) over a long time period (such as 100 years). The rationale for preserving high levels of gene diversity is twofold: to preserve the evolutionary potential of the population and to minimize the deleterious effects of inbreeding, which can be substantial ( Lacy and others 1995 ). Achieving these objectives also serves to meet many of the other functions required of zoo populations (exhibitry, conservation education, research, and public outreach) although at times there obviously can be conflicts among these various roles ( Hutchins and others 1995 ).
Regional or international cooperative captive breeding programs involving collections at multiple zoos, under the direction of a single “species coordinator”, have been established for most captive populations of endangered or threatened species. In North America, the American Association of Zoological Parks and Aquariums (AZA) established the Species Survival Program (SSP) to assist zoos in managing cooperative breeding programs. To date, the SSP includes over 70 species and similar programs exist in other regions of the globe.
Establishing and managing a captive population can be typically conceptualized as occurring in 3 phases: the founding, growth, and maintenance phases ( Figure 1 ). Population growth may be slow during the founding phase as husbandry techniques are developed and refined. Once these become established, the population will often grow rapidly with an accompanied increased dispersal of the population among many zoos. The population is encouraged to continue to grow until it reaches the desired (target) size. The target size will enable the population to maintain a high level of genetic diversity (e.g., 90%) over a 100-year period and is a function of the number of founders, potential growth rate of the population during the growth phase, how well the population is genetically managed, and the generation length ( Ballou and Foose 1995 ). Thus the target size is calculated specifically for each population using computer models. For example, in golden lion tamarins (Leontopithecus rosalia), a small endangered primate from the Atlantic Coastal rainforest in Brazil, the target size of the captive population is estimated to be about 480 individuals.
Schematic representation of the development of a captive breeding population. The population is grown to a specific target size which is sufficiently large to maintain a high level of gene diversity (usually 90%) over a 100-year time period.
Reproduction is slowed during the maintenance phase to keep the population at its target size. Genetic management (that is, the selection of breeding mates based on pedigree analysis) occurs during all 3 phases, although during the earlier phases there may be a higher priority placed on successful reproduction than on genetic issues (that is, who should breed with whom). The development of the captive population for the golden lion tamarin followed such a progression ( Figure 2 ).
Growth of the captive golden lion tamarin population showing increases in numbers of animals and institutions involved in the program since 1970. Data from the 1995 International Golden Lion Tamarin Studbook, J. Ballou, Studbook Keeper.
The need for demographic and genetic modeling is most pronounced during the latter 2 phases. It is during these phases that managers use computer models to determine population growth projections, how to manage for zero population growth, and how to optimally breed individuals to maximize retention of genetic diversity.
Golden Lion Tamarin (Leontopithecus rosalia) . Photo: Jessie Cohen, National Zoological Park.
Demographic Modeling and Population Management
As mentioned above, the object of demographic management is primarily to measure population growth rates; determine how reproduction and survival rates can be modified to meet colony objectives (such as whether to establish zero population growth, maximum population growth, or maximum reproductive efficiency); and evaluate vital rates and age structure for indications of potential problems. These applications can apply as readily to the management of laboratory research colonies as they do to captive populations.
All 3 objectives require estimates of age-specific survival and reproductive rates. In captive breeding programs, vital data are collected on each individual and maintained in standardized, computerized databases called studbooks. Vital data include a studbook number (a unique numeric identifier), date of birth, sex, parentage, location of birth, death date, cause of death, changes in location, and name or number of the animal given to the individual by the holding institution. These data are compiled and maintained by a “studbook keeper” who solicits periodic updates from all institutions holding individuals (either within a particular region or internationally). Similar records are usually maintained for laboratory colonies, with one difference being that in lab or research colonies records are usually maintained separately for different colonies. Perhaps the main advantage of the studbook approach is that data across institutions, and even species, are standardized, facilitating data collection, editing, and analysis using a common set of software.
This data set is the basis for estimating age-specific survival and reproductive rates and other summary demographic parameters, such as population growth rate, generation length, harvest rates, and age structures ( Keyfitz 1968 ). Over the last 10 years several studbook analysis software packages have become available to conduct these analyses directly from the standardized data. Among these are DEMOG (Demographic Modeling Software) ( Bingaman and Ballou 1996 ) and SPARKS (Single Species Animal Record Keeping) ( ISIS 1996 ).
The case of the black-footed ferret (Mustela nigripes) provides one example of how demographic modeling has been used to plan and schedule management objectives in a captive-breeding program. The black-footed ferret was thought extinct in the wild until 1981 when a small population (less than 120 individuals) was discovered in Wyoming. However, in 1985 and 1986 the population was decimated by canine distemper and in 1987 the remaining 18 ferrets were captured to start a captive breeding program with the intent of eventually reintroducing them back into the wild. Computer modeling was conducted to determine when the captive population would be of sufficient size to initiate a reintroduction program. Age-specific survival and reproductive rates were estimated based on what was known of ferret life-history, and the model indicated that the population could realistically achieve an annual growth rate (X) of 2.02 and reach sufficient size (approximately 200 adults) by 1990 ( Figure 3 ) ( Ballou and Oakleaf 1989 ). Plans for reintroduction were made accordingly. As it turned out, the population was slightly smaller than the predicted size in 1990 (179 instead of 200), and the reintroduction was postponed until the fall of 1991 ( Figure 3 ). However, the modeling provided a rough time-frame for reintroduction planning, and similar modeling exercises have been used for the California condor reintroduction program.
Comparison of the actual vs. modeled growth of the captive population of black-footed ferrets. The model projections were based on computer simulations conducted in 1986 and predicted that the population would reach sufficient size (200 adult ferrets) to initiate reintroduction efforts in 1990. The actual population growth was slightly slower and the population reached this threshold in 1991. Data from the 1993 Black-footed ferret studbook, courtesy of Bill Russell, University of Wyoming.
A 2nd example illustrates the use of modeling to regulate reproductive rates. As mentioned above, the target population size for golden lion tamarins is approximately 480 individuals. Reproduction must be modified to maintain zero population growth at this level. Age-specific survival and fecundity rates calculated using historical data show that without controlling reproduction, the population growth rate is about 25% per year. Computer modeling using the software DEMOG was used to determine how best to modify reproductive rates of specific age classes to reduce the growth rate to zero. The chosen solution, based on ease of implementation, was to delay age of 1st reproduction from age 2 to 3 and to limit breeding to only 40 pairs, females of age 3 to 14, per year. This strategy has been used to maintain the population at the desired size for the last 5 years ( Figure 2 ). This approach is easily extended to population regulation in laboratory research colonies. For example, Dyke and others (1986 , 1987 ) also used life-table modeling to determine optimal harvest rates for research colonies of baboons.
An important consideration in making these calculations is which subset of data should be used as the basis for the analysis. Often, it may not be appropriate to estimate demographic parameters using an entire historical data set. Management practices may differ significantly among regions or colonies for some species. For example, the species coordinator for the North American population of Przewalski's horse (Equus przewalskii) should estimate vital rates based on data from North American zoos rather than all zoos worldwide since husbandry standards vary significantly among global regions. This is less of a problem when data are derived from a single colony. However, for virtually all species, husbandry practices have improved significantly over time. Analyses may be more appropriately based on, say, the last 10 years of data rather than using the complete historical database. This requires the analysis software to be very flexible in defining the “window” for analysis. The software SPARKS has gone to great lengths to incorporate such flexibility. In SPARKS, the analysis window determines which individuals are “at risk” and can be defined on the basis of dates, geographic regions, specific institutions, regional management programs (for example, it can restrict analysis to only those animals in the SSP program) or any number of other identifying factors including sex, inbreeding level, and birth origin (wild-caught or captive born), to name only a few. For example, to examine the effect of changes in husbandry practices over time (such as changes in diet in a lab colony), one can calculate age and sex-specific vital rates for all individuals in the colony between 1980 and 1990 and compare their rates to those in the population between 1991 and 1996. This versatility makes the SPARKS software a powerful tool for quickly conducting detailed and specific demographic analyses.
The primary problem facing demographic analyses of laboratory research and captive populations is small sample size. Populations may not have been large enough or in existence long enough to provide data for statistically reliable estimates of vital rates. This problem plagues all but the largest and longest-running programs and is particularly acute for older age classes, since only a small proportion of the population survives to these ages. Survival and reproductive rates will be highly variable from one age class to the next. This high variability will be reflected in inaccurate estimates of population summary statistics such as growth rate and generation lengths.
Several efforts have been made to address this problem. One approach has been to smooth over variable age-specific rates using one of several smoothing functions. This is somewhat analogous to grouping and averaging rates across several age classes. Another approach has been to develop “standard” life-table models for different types of species based either on data from a species for which there is a large sample size or on a composite of data from several different species ( Dyke and others 1993 ). The standard can then be used to estimate life-tables for species or populations lacking data (that is, those populations having small sample size or missing data from certain, usually older, age classes). For example, Dyke and others (1995) developed a standard life-table for research colonies of chimpanzees (Pan troglodytes) based on data from 3 separate colonies. They used the standard to estimate the survival rates in a colony that lacked data beyond age class 27 ( Figure 4 ), as well as to project future costs of chimpanzee colonies ( Dyke and others 1996 ). While this technique is not without difficulties (see Dyke and others 1993 ), cautious use of standards to estimate partial life-tables holds much promise and would probably be more extensively used if it were incorporated into available software.
A “standard” survivorship curve for male chimpanzees, based on data from 3 colonies, is fitted to, and used to estimate, survivorship rates in a colony with only partial data through age 27. Dotted lines represent 95% confidence bands around the partial colony data. Reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc. ( Dyke and others 1995 ).
Both of these techniques (smoothing and the use of standards) beg the issue of measuring, and taking into consideration when modeling, the inherent variability in the data. A more appropriate solution, but also one that has not been readily available in analytical software, is to estimate statistical confidence limits both on the age-specific vital rates and on parameters and projections calculated from those estimates. This would provide us with more realistic tools for demographic management and is clearly an area requiring further development.
Genetic Modeling and Genetic Importance
In captive breeding programs, the objective of genetic management is to maintain high levels of genetic diversity and avoid inbreeding and selection. This often is not the primary objective in research colonies, which may intentionally be selecting for specific genetic traits. However, the importance of maintaining genetic variation has been recognized in research colonies maintained for other purposes (such as colonies of pathogen-free rhesus). In captive breeding programs, maintenance of genetic diversity is accomplished by explicitly specifying which animals are to breed, how often, and with whom they should be bred. To do this, one needs to calculate the genetic importance of all individuals in the population so the most important can be given breeding priority. Genetic importance is calculated by computer modeling of the population's pedigree. As in the case with demographic data, basic vital statistics maintained on every individual of the population provide the data for the pedigree. The pedigree should be traced back as far as possible, ideally to the population's founders. The objective of maintaining genetic diversity is therefore analogous to maintaining intact the gene pool of the founders to the best extent possible.
In these programs, genetic importance is calculated in 2 ways. The first is mean kinship (MK). A mean kinship value is calculated for each living individual in the population as the average relationship (measured as the kinship coefficient) between that individual and all living animals in the population. Individuals with many close relatives will have higher MK values than individuals with few close relatives. Individuals with low MK therefore are carrying less common genes than those with high MK and hence are more genetically valuable. A management program that minimizes average mean kinship also maximizes the retention of genetic diversity ( Ballou and Lacy 1995 ).
Computer programs have been written to facilitate making breeding recommendations based on this mean kinship strategy. The GENES software ( Lacy 1993 ) is the most commonly used by managers of captive populations. This program allows the manager to model the effects of proposed matings on the level of gene diversity. The program first calculates the MK values of all living individuals based on the pedigree. Then the user is provided with a list of males and females ranked according to their MK values (lowest MK ranked most important). The user can then select from the top of the list a male and female for mating. The program “mates” the individuals and adds to the pedigree a “hypothetical” offspring with that male and female as parents. The MK values for all individuals are then recalculated, a new sorted list of males and females provided, and the user can again select the next pair to breed. In this way, the user can iteratively develop a plan for that breeding cycle that optimally minimizes mean kinship values in the population. This modeling of the effect of hypothetical offspring on gene diversity is widely used to develop annual breeding recommendations for captive breeding programs worldwide.
A second measure of genetic importance is genome uniqueness (gu) . Again, a gu value is calculated for every living individual and is defined as the proportion of an individual's genes that are unique in the population (that is carried by no other living individual). Genome uniqueness is used to identify individuals carrying genes that are at high risk of being lost (not passed on to the next generation) ( Ballou and Lacy 1995 ). Although analytical methods for calculating gu exist, these are extremely computationally complex and gu values are usually calculated using the computer modeling technique known as “gene dropping”.
A gene-drop pedigree analysis simulates the transmission of genes in the pedigree from the founders to the living population ( MacCluer and others 1986 ). Initially, each founder is assigned 2 unique alleles ( Figure 5a ). The alleles are then passed on from parent to offspring, with each offspring receiving one allele chosen at random from each parent (modeling Mendelian segregation), until all individuals in the pedigree have an assigned genotype ( Figure 5b ). The frequency and distribution of founders' alleles in the living population are then recorded. This is repeated multiple times (perhaps several thousand times for complex pedigrees) and the frequency distributions of founder alleles are summarized across simulations. Genome uniqueness is calculated as the proportion of simulations in which an individual receives the only copy of a particular founder allele. Breeding priority is given to individuals with high gu .
Example of a gene drop analysis in a simple pedigree of 4 living animals (shown at the bottom) descended from 5 founders. (A) Each founder is assigned a unique pair of alleles--in this case alleles labeled “A” through “J”. (B) In each simulation, alleles are “dropped” randomly from parents to offspring until all individual have an assigned genotype. The figure shows the results of one such “gene drop”. The figure also shows the MK and gu values (based on 5000 simulations) for each of the living individuals.
Genome uniqueness and mean kinship provide 2 different, although related, estimates of genetic importance. In most pedigrees, they will be highly correlated; managing by MK alone is probably sufficient to maintain genetic diversity. However, in practice it is usually recommended that both gu and MK values be calculated to identify individuals that may rank highly in one measure but not the other. A detailed description of MK and gu is provided by Ballou and Lacy (1995).
The MK/gu strategy does not require knowledge of specific animal genotypes since its objective is to maximize retention of genome-wide diversity rather than diversity for specific genetic markers or at specific loci. However, when diversity at specific marker loci is desirable, as might be the case for laboratory research colonies established for research on genetically-based diseases, individual genetic importance can be defined in terms of the marker loci of interest. For example, to ensure preservation of rare genotypes in a baboon colony maintained for atherosclerosis research, Dyke and others (1987) calculated a genetic importance score for each individual based on their genotype at 8 biochemical genetic markers. Like MK, individuals with the lowest score had the rarest genotypes and were given breeding priority.
Ultimately the genetic recommendations (identifying priority breeders) and the demographic recommendations (numbers of offspring to produce) need to be combined to form the specific animal-by-animal recommendations for colony or population management. The method used by the international golden lion tamarin captive breeding program is one example of how this can be done. Because the population is being managed for zero population growth, 40 breeding pairs are needed each year (see above). However, genetically important animals are expected to produce more offspring than less important individuals. To accomplish this, the frequency distribution of mean kinship values is plotted and different offspring objectives are assigned to different levels of mean kinship ( Figure 6 ). The assignments are made in such a way that on the average each pair produces 2 viable offspring over their lifetime (that is, they replace themselves). For any given year's breeding recommendations, the 40 pairs are selected from among those pairs who have not yet met their lifetime offspring objectives according to their MK value. Similar approaches are used by most captive breeding programs.
Distribution of mean kinship values in the 1995 golden lion tamarin population. Above the line are the number of viable offspring recommended for individuals with those levels of mean kinship.
Dyke and others (1987) also considered both demographics and genetics in their management strategy for a baboon research colony at the Southwest Foundation for Biomedical Research. Life-table analyses were first used to define a harvest strategy that maximizes reproductive efficiency. Because maintenance of genetic diversity was also a priority, computer modeling of pedigrees was then used to ensure that this maximal harvest strategy did not result in a loss of genetic diversity ( Dyke and others 1986 ). Finally the selection of breeders was based on the number and ages of animals specified by the harvest strategy, as well as the genetic importance of each animal relative to those loci desired valuable.
The major limitation to genetic management and modeling of the type described here is that complete pedigrees are required. Both the mean kinship calculations and the gene-drop modeling assume that each individual's parents are known and lineages can be traced back to the founders. While husbandry and management practices for many species enable complete pedigrees to be known, this is more problematic for some species that are maintained in herds with multiple potential breeding males or as free-ranging colonies. In these situations, potential parentage can be assigned on the bases of behavioral observations or even molecular genetic analyses. However, when pedigree data is lacking for large groups of individuals or over a long time period, as might happen in the absence of detailed record keeping, these kinds of genetic models may not be appropriate and less detailed types of models may be required (see Lacy and others 1995 for a discussion of alternative methods).
Summary
In captive breeding populations as well as laboratory research colonies, computer modeling has proven to be an extremely valuable tool for management purposes: defining population size objectives, estimating required rates of harvest or reproduction, and identifying genetically important individuals. The techniques described in this paper are now routinely used in most captive breeding programs, partially because computer software has been developed and data bases standardized to facilitate their application but also partially because of the increasing need for prudent management of limited resources. The application of computer modeling has not been as extensive in laboratory research colonies. However, careful management based on modeling and analyses of population trends can help make maximum use of the animals and facilities available. For example, by basing breeding programs on mean kinship we are targeting the genetically most important individuals in the population. The end result is that colonies and populations are more efficient in meeting their objectives. For laboratory research colonies, this may mean more efficient and improved reproductive output at lower costs. For captive breeding programs this means we can afford to breed fewer individuals and maintain smaller overall population sizes to achieve the same objectives in terms of genetic diversity. The benefits are clear: smaller more carefully managed populations use fewer resources leaving more for other species also in need of captive breeding. The alternative, relaxing or ignoring genetic and demographic management, has clear economic and conservation costs: larger populations are required and thus fewer populations can be maintained under fixed resources. Additionally, unmanaged populations may either grow out of control or decline to extinction due to lack of monitoring. Failing to monitor inbreeding will lead to poorer health and higher mortality of inbred animals, which also incurs a cost in itself.
While endangered species captive breeding programs and research laboratory colonies differ significantly in their primary goals, both share the need for judicious management of animal resources. Computer modeling can help both the genetic and demographic management of these populations and thereby reduce resource expenditures.
References
