Effective Population Size and Maintenance of Genetic Diversity in Captive-Bred Populations of a Lake Victoria Cichlid

Abstract: We used microsatellite DNA markers to investigate the maintenance of genetic diversity within and between samples of subpopulations (spanning five captive-bred generations) of the haplochromine cichlid Prognathochromis perrieri . The subpopulations are maintained as part of the Lake Victoria Cichlid species survival plan. Changes in the frequencies of 24 alleles, over four polymorphic loci, were used to estimate effective population size (   N _e   ). Point estimates of N _e ranged from 2.5 to 7.7 individuals and were significantly smaller than the actual census size (   N _obs  ) for all subpopulations (32–243 individuals per generation), with the corresponding conservative N _e   /  N _obs ratios ranging from 0.01 to 0.12. Approximately 19% of the initial alleles were lost within the first four generations of captive breeding. Between-generation comparisons of expected heterozygosity showed significant losses ranging from 6% to 12% per generation. Seven private alleles were observed in the last sampled generation of four subpopulations, and analysis of population structure by F _ST indicated that approximately 33% of the total genetic diversity is maintained between the subpopulations from different institutions. To reduce the loss of genetic variation, we recommend that offspring production be equalized by periodically removing dominant males, which will encourage reproduction by additional males. Consideration should also be given to encouraging more institutions to maintain populations, because a significant fraction of the genetic variation exists as among-population differences resulting from random differentiation among subpopulations.     

Estimating the Effective Population Size of Conserved Populations

Accurate estimation of effective population size is important in attempts to conserve small populations of animals or plants. We review the genetic and ecological methods that have been used to estimate effective population size in the past and suggest that, while genetic methods may often be appropriate for the estimation of N _e, and its monitoring, ecological methods have the advantage of providing data that can help predict the effect of a changed environment on N _e. Estimation of N _e, is particularly complex in populations with overlapping generations, and we summarize previous empirical estimates of N _e that used ecological methods in such populations. Since it is often difficult to assess what parameters and assumptions have been used in previous calculations, we suggest a method that provides a good estimate of N _e, makes clear what assumptions are involved, and yet requires a minimum of information. The method is used to analyze data from 14 studies. In 36% (5) of these studies, our estimate is in excellent agreement with the original, and yet we use significantly less information, in 21% (3) the original estimate is markedly lower, in 43% (6) it is markedly higher. Reasons for the discrepancies are suggested. Two of the underestimates involve a failure in the original to account for a long maturation time, and four of life overestimates involve problems in the original with the correction for overlapping generations.     

Rapid Loss of Genetic Variation in Large Captive Populations of Drosophila Flies: Implications for the Genetic Management of Captive Populations

Levels of variation in eight large captive populations of D. melanogaster (census sizes ∼ 5000) that had been in captivity for periods from 6 months to 23 years (8 to 365 generations) were estimated from allozyme heterozygosities, lethal frequencies, and inversion heterozygosities and phenotypic variances, additive genetic variances ( V _A), and heritabilities ( h ²) for sternopleural bristle numbers. Correlations between all measures of variation except lethal frequencies were high and significant. All measures of genetic variation declined with time in captivity, with those for average heterozygosities, V _A, and h ² being significant. The effective population size ( N _e) was estimated to be 185–253 in these populations, only 0.037–0.051 of census size (N). Levels of allozyme heterozygosities declined rapidly in two large captive populations founded from another wild stock, being reduced by 86% and 62% within 2.5 years in spite of being maintained at sizes of approximately 1000 and 3500. Estimates of N _e/ N for these populations were only 0.016 and 0.004. Two estimates of N _e/ N for captive populations of D. pseudoobscura from data in the literature were also low at 0.036 and 0.012. Consequently, the rate of loss of genetic variation in captive populations and endangered species may be more rapid than hitherto recognized. Merely maintaining captive populations at large census sizes may not be sufficient to maintain essential genetic variation.     

Relationship of Effective to Census Size in Fluctuating Populations

Abstract: The effective size of a population (    N _e   ) rather than the census size (    N ) determines its rate of genetic drift. Knowing the ratio of effective to census size, N _e  /   N , is useful for estimating the effective size of a population from census data and for examining how different ecological factors influence effective size. Two different multigenerational ratios have been used in the literature based on either the arithmetic mean or the harmonic mean in the denominator. We clarify the interpretation and meaning of these ratios. The arithmetic mean N _e  /   N ratio compares the total number of real individuals to the long-term effective size of the population. The harmonic mean N _e  /   N ratio summarizes variation in the N _e  /   N ratio for each generation. In addition, we show that the ratio of the harmonic mean population size to the arithmetic mean population size provides a useful measure of how much fluctuation in size reduced the effective size of a population. We discuss applications of these ratios and emphasize how to use the harmonic mean N _e  /   N ratio to estimate the effective size of a population over a period of time for which census counts have been collected.     

Unprecedented Low Levels of Genetic Variation and Inbreeding Depression in an Island Population of the Black-Footed Rock-Wallaby

Abstract: It has been argued that demographic and environmental factors will cause small, isolated populations to become extinct before genetic factors have a significant negative impact. Islands provide an ideal opportunity to test this hypothesis because they often support small, isolated populations that are highly vulnerable to extinction. To assess the potential negative impact of isolation and small population size, we compared levels of genetic variation and fitness in island and mainland populations of the black-footed rock-wallaby ( Petrogale lateralis [Marsupialia: Macropodidae]). Our results indicate that the Barrow Island population of P. lateralis has unprecedented low levels of genetic variation (  H _e = 0.053, from 10 microsatellite loci) and suffers from inbreeding depression (reduced female fecundity, skewed sex ratio, increased levels of fluctuating asymmetry). Despite a long period of isolation ( ∼ 1600 generations) and small effective population size (  N _e ∼ 15), demographic and environmental factors have not yet driven this population to extinction. Nevertheless, it has been affected significantly by genetic factors. It has lost most of its genetic variation and become highly inbred (  F _e = 0.91), and it exhibits reduced fitness. Because several other island populations of P. lateralis also exhibit exceptionally low levels of genetic variation, this phenomenon may be widespread. Inbreeding in these populations is at a level associated with high rates of extinction in populations of domestic and laboratory species. Genetic factors cannot then be excluded as contributing to the extinction proneness of small, isolated populations.     

Effects of Habitat Fragmentation on Effective Population Size in the Endangered Rio Grande Silvery Minnow

Abstract:  We assessed spatial and temporal patterns of genetic diversity to evaluate effects of river fragmentation on remnant populations of the federally endangered Rio Grande silvery minnow ( Hybognathus amarus ). Analysis of microsatellite and mitochondrial DNA detected little spatial genetic structure over the current geographic range, consistent with high gene flow despite fragmentation by dams. Maximum-likelihood analysis of temporal genetic data indicated, however, that present-day effective population size ( N_eV ) of the largest extant population of this species was 78 and the ratio of effective size to adult numbers ( N_eV/N ) was ∼ 0.001 during the study period (1999 to 2001). Coalescent-based analytical methods provided an estimate of historical (river fragmentation was completed in 1975) effective size ( N_eI  ) that ranged between 10⁵ and 10⁶. We propose that disparity between contemporary and historical estimates of N_e and low contemporary N_e/N result from recent changes in demography related to river fragmentation. Rio Grande silvery minnows produce pelagic eggs and larvae subject to downstream transport through diversion dams. This life-history feature results in heavy losses of yearly reproductive effort to emigration and mortality, and extremely large variance in reproductive success among individuals and spawning localities. Interaction of pelagic early life history and river fragmentation has altered demographic and genetic dynamics of remnant populations and reduced N_e to critically low values over ecological time.     

Effective Population Size and Lifetime Reproductive Success

The mean and variance of lifetime reproductive success, E_LRS and V_LRS, influence the ratio of effective to census population size, N_e/N_c. Because the complete data needed to calculate E_LRS and V_LRS are seldom available, we provide alternatives for estimating N_e/N_c from incomplete data. These estimates should be useful to conservation biologists trying to compute the effective size of a censused population. An analytical approach makes assumptions regarding the process influencing offspring survival. We provide a method for examining the validity of those assumptions and show that particular violations can result in either over- or underestimates. When the assumptions are violated or when more data are available, we suggest estimating N_e/N_c using computer simulations of models based on individuals. We examine how such simulations can be used to estimate N_e/N_c using an individual-based model for Lesser Snow Geese ( Anser caerulescens ). We demonstrate that such estimates can be biased unless the simulations are based on complete cohorts and samples of known age. We show that because the estimate of N_e/N_c depends on the stage of the reproductive cycle used as a point of reference in the model, the census population size N_c must be based on the same stage to provide unbiased estimates of N_e.     

Modeling Problems in Conservation Genetics Using Captive Drosophila Populations: Consequences of Equalization of Family Sizes

Equalization of family sizes is recommended for use in captive breeding programs, as it is predicted to double effective population sizes, reduce inbreeding, and slow the loss of genetic variation. The effects of maintaining small captive populations with equalization of family sizes versus random choice of parents on levels of inbreeding genetic variation, reproductive fitness, and effective population sizes ( N _e) were evaluated in 10 lines of each treatment maintained with four pairs of parents per generation. The mean inbreeding coefficient ( F ) increased at a significantly slower rate with equalization than with random choice (means of 0.35 and 0.44 at generation 10). Average heterozygosities at generation 10, based on six polymorphic enzyme loci, were significantly higher with equalization (0.149) than with random choice (0.085), compared to the generation 0 level of 0.188. The competitive index measure of reproductive fitness at generation 11 was more than twice as high with equalization as with random choice, both being much lower than in the outbred base population. There was considerable variation among replicate lines within treatments in all the above measures and considerable overlap between lines from the two treatments. Estimates of N _e for equalization were greater than those for random choice, whether estimated from changes in average heterozygosities or from changes in F. Equalization of family sizes can be unequivocally recommended for use in the genetic management of captive populations.     

Calculating Ne and Ne/N in age-structured populations: a hybrid Felsenstein-Hill approach

The concept of effective population size (Ne) was developed under a discrete-generation model, but most species have overlapping generations. In the early 1970s, J. Felsenstein and W. G. Hill independently developed methods for calculating Ne in age-structured populations; the two approaches produce the same answer under certain conditions and have contrasting advantages and disadvantages. Here, we describe a hybrid approach that combines useful features of both. Like Felsenstein's model, the new method is based on age-specific survival and fertility rates and therefore can be directly applied to any species for which life table data are available. Like Hill, we relax the restrictive assumption in Felsenstein's model regarding random variance in reproductive success, which allows more general application. The basic principle underlying the new method is that age structure stratifies a population into winners and losers in the game of life: individuals that live longer have more opportunities to reproduce and therefore have a higher mean lifetime reproductive success. This creates different classes of individuals within the population, and grouping individuals by age at death provides a simple means of calculating lifetime variance in reproductive success of a newborn cohort. The new method has the following features: (1) it can accommodate unequal sex ratio and sex-specific vital rates and overdispersed variance in reproductive success; (2) it can calculate effective size in species that change sex during their lifetime; (3) it can calculate Ne and the ratio Ne/N based on various ways of defining N; (4) it allows one to explore the relationship between Ne and the effective number of breeders per year (Nb), which is a quantity that genetic estimators of contemporary Ne commonly provide information about; and (5) it is implemented in freely available software (AgeNe).     

Dimensionless Life Histories and Effective Population Size

The effective size ( N _e ) of a population can be estimated from demographic information. We evaluated a recent model, showing that N _e depends strongly on the relationship between age at reproductive maturity ( M ) and average adult lifespan ( A ). N _e converges on half the number of potentially reproducing adults ( N/2 ) as M decreases relative to A , but it increases linearly as M increases for a given value of A . Therefore, convergence of N _e on N/2 is more likely in organisms with a short sexual maturation period scaled to adult lifespan. To assess the generality of this convergence we asked whether most organisms are characterized by this requisite relationship between M and A . The dimensionless number M/A is approximately invariant within taxa, but it is markedly different across taxa. Previous work focused on birds and mammals, taxa with unusually small M/A (0.4 and 0.75). Other animal taxa take longer than most birds and mammals to reach maturity for a given reproductive lifespan, so they are characterized by larger M/A (e.g., fish, 2.0). In theory, these taxon-specific life histories strongly influence N _e . We conclude that N _e is expected to approach N/2 , provided that M/A is (unusually) small, and that N _e / N among poikilotherms may often exceed that of mammals and especially birds.     

Predicting the Deleterious Effects of Mutation Load in Fragmented Populations

Abstract:  Human-induced habitat fragmentation constitutes a major threat to biodiversity. Both genetic and demographic factors combine to drive small and isolated populations into extinction vortices. Nevertheless, the deleterious effects of inbreeding and drift load may depend on population structure, migration patterns, and mating systems and are difficult to predict in the absence of crossing experiments. We performed stochastic individual-based simulations aimed at predicting the effects of deleterious mutations on population fitness (offspring viability and median time to extinction) under a variety of settings (landscape configurations, migration models, and mating systems) on the basis of easy-to-collect demographic and genetic information. Pooling all simulations, a large part (70%) of variance in offspring viability was explained by a combination of genetic structure ( F_ST ) and within-deme heterozygosity ( H_S ). A similar part of variance in median time to extinction was explained by a combination of local population size ( N ) and heterozygosity ( H_S ). In both cases the predictive power increased above 80% when information on mating systems was available. These results provide robust predictive models to evaluate the viability prospects of fragmented populations.     

To flee or not to flee: predator avoidance by cheetahs at kills

Mammalian carnivores are unusual because their primary competitors for food are often their primary predators. This relationship is most evident at persistent kills where dominant competitors are attracted to both the carcass (as a free meal) and to the killers (as potential prey). Cheetahs (Acinonyx jubatus) are frequent victims of kleptoparasitism, and cubs, and sometimes adults, are killed by lions (Panthera leo) or spotted hyenas (Crocuta crocuta). Between 1980 and 2002, we observed 639 kills made by cheetahs in Serengeti National Park, Tanzania. These kills were often visited by scavengers, including relatively innocuous species such as vultures and jackals and potentially dangerous species, like spotted hyenas and lions. We used cheetah behavior at kills to test a number of predictions about how cheetahs should minimize risk at kill sites given they face an increased risk of predation of themselves or their cubs. In particular, we examined the propensity of cheetahs of different age/sex classes to hide carcasses after making a kill, vigilance at kills, and the delay in leaving after finishing feeding with respect to ecological factors and scavenger presence. The behavior of single females at kills did not suggest that they were trying to avoid being killed, but the behavior of males, often found in groups, was in line with this hypothesis. In contrast, the behavior of mother cheetahs at kills appeared to be influenced greatly by the risk of cubs being killed. Our results suggest that cheetahs use several behavioral counterstrategies to avoid interspecific predation of self or cubs.     

Relative Contributions of Sampling Error in Initial Population Size and Vital Rates to Outcomes of Population Viability Analysis

Abstract:  We evaluated the relative contributions of sampling error (randomly chosen standard errors applied as 0–30% of parameter estimates) in initial population size and vital rates (survival and reproduction) to the outcome of a simulated population viability analysis for grizzly bears (  Ursus arctos ). Error in initial population size accounted for the largest source of variation (model II analysis of variance, F _25,5= 10.8, p = 0.00001) in simulation outcomes, explaining 60.5% of the variance. In contrast, error in vital rates contributed little to simulation outcomes ( F _25,5= 0.61, p = 0.70), accounting for only 2.4% of model variation. Reduced global variation in vital rates, as a result of independent random sampling of annual deviates for each parameter, likely contributed to the results. Errors in estimates of initial population size, if ignored in PVA, have the potential to leave managers with estimates of population persistence that are of little value for making management decisions.     

Lifetime reproductive success and composition of the home range in a large herbivore

The relationship between individual performance and nonrandom use of habitat is fundamental to ecology; however, empirical tests of this relationship remain limited, especially for higher orders of selection like that of the home range. We quantified the association between lifetime reproductive success (LRS) and variables describing lifetime home ranges during the period of maternal care (spring to autumn) for 77 female roe deer (Capreolus capreolus) at Trois-Fontaines, Champagne-Ardenne, France (1976-2000). We maintained population growth rate (adjusted to account for removals of non-focal animals) near rmax, which enabled us to define the fitness-habitat relationship in the absence of density effects. Using a negative binomial model, we showed that a roe deer's incorporation into its home range of habitat components important to food, cover, and edge (meadows, thickets, and increased density of road allowances) was significantly related to LRS. Further, LRS decreased with increasing age of naturally reclaimed meadows at the time of a deer's birth, which may have reflected a cohort effect related to, but not entirely explained by, a decline in quality of meadows through time. Predictive capacity of the selected model, estimated as the median correlation (rs) between predicted and observed LRS among deer of cross-validation samples, was 0.55. The strength of this relationship suggests that processes like selection of the site of a home range during dispersal may play a more important role in determining fitness of individuals than previously thought. Individual fitness of highly sedentary income breeders with high reproductive output such as roe deer should be more dependent on home range quality during the period of maternal care compared to capital breeders with low reproductive output. Identification of the most important habitat attributes to survival and reproduction at low density (low levels of intraspecific competition) may prove useful for defining habitat value ("intrinsic habitat value").     

Individual heterogeneity in recapture probability and survival estimates in cheetah

Accurate estimates of demographic parameters are key for understanding and predicting population dynamics and for providing insights for effective wildlife management. Up until recently, no suitable methodology has been available to estimate survival probabilities of species with asynchronous reproduction and a high level of individual variation in capture probabilities. The present work develops a capture-mark-recapture model for cheetahs in the Serengeti National Park, Tanzania, which (a) deals with continuous reproduction, (b) takes into account the high level of individual heterogeneity in capture probabilities and (c) is spatially explicit. Results show that (1) our approach, which is an extensive modification of the Cormack-Jolly-Seber model, provides a lower female adult survival estimate and a higher male adolescent survival estimate than previous approaches to estimate cheetah survival in the area, (2) using sighting location alone is not sufficient to capture the individual variation in resighting probabilities for both sexes, and (3) precision in estimated survival probabilities is generally increased. Species which are individually recognizable, wide-ranging and/or where individuals differ substantially in sightability are particularly appropriate to our modelling approach, and our methodology would thus be appropriate for a wide number of species to provide more accurate estimates of survival.     

Application of the One-Migrant-per-Generation Rule to Conservation and Management

Abstract:  Endangered species are commonly found in several (partially) isolated populations dispersed on different fragments of a habitat, natural reserve, or zoo. A certain level of connectivity among such populations is essential for maintaining genetic variation within and between populations to allow local and global adaptation and for preventing inbreeding depression. A rule of thumb widely accepted by the conservation community is that one migrant per generation (OMPG) into a population is the appropriate level of gene flow. This rule is based on Wright's study of his island model under a long list of simplifying assumptions. I examined the robustness of the OMPG rule to the violation of each of the many assumptions, quantifying the effect with population genetics theory. I showed that, when interpreted as one effective migrant per generation, OMPG is generally valid for real populations departing from the ideal model in the discrepancies of actual (  N ) and effective (  N_e  ) population sizes and actual ( m ) and effective ( m_e  ) migration rates. I also addressed the issue of converting the effective number of migrants (  M_e= N_em_e  ) into the actual number of migrants ( M = Nm  ) of a certain age and sex. In particular, N_e < N , a case common for natural populations, did not necessarily require M > M_e to maintain a certain level of differentiation among populations. Rather, translating the elusive M_e into the manageable M depends on the specific causes (e.g., biased sex ratio, reproductive skew) that lead to N_e < N .     

Modelling cheetah relocation success in southern Africa using an Iterative Bayesian Network Development Cycle

Relocation is one of the strategies used by conservationists to deal with problem cheetahs in southern Africa. The success of a relocation event and the factors that influence it within the broader context of long-term viability of wild cheetah metapopulations was the focus of a Bayesian Network (BN) modelling workshop in South Africa. Using a new heuristics, Iterative Bayesian Network Development Cycle (IBNDC), described in this paper, several networks were formulated to distinguish between the unique relocation experiences and conditions in Botswana and South Africa. There were many common underlying factors, despite the disparate relocation strategies and sites in the two countries. The benefit of relocation BNs goes beyond the identification and quantification of the factors influencing the success of relocations and population viability. They equip conservationists with a powerful communication tool in their negotiations with land and livestock owners, which is key to the long-term survival of cheetahs in southern Africa. Importantly, the IBNDC provides the ecological modeller with a methodological process that combines several BN design frameworks to facilitate the development of a BN in a multi-expert and multi-field domain.     

Predicting Extinction Times from Environmental Stochasticity and Carrying Capacity

Managers of small populations often need to estimate the expected time to extinction T_e of their charges. Useful models for extinction times must be ecologically realistic and depend on measurable parameters. Many populations become extinct due to environmental stochasticity, even when the carrying capacity K is stable and the expected growth rate is positive. A model is proposed that gives T_e by diffusion analysis of the log population size n_t (= log_e N_t). The model population grows according to the equation N_t+1 = R_tN_t, with K as a ceiling. Application of the model requires estimation of the parameters k = logK, r_d = the expected change in n, v_r = Variance(log R), and ϱ the autocorrelation of the r_t. These are readily calculable from annual census data (r_d is trickiest to estimate). General formulas for T_e are derived. As a special case, when environmental fluctuations overwhelm expected growth (that is r_d 0), T_e = 2n_o(k - n_o/2)/v_r. If the r_t are autocorrelated, then the effective variance is v_re v_r (1 + ϱ)/(1 - ϱ). The theory is applied to populations of checkerspot butterfly, grizzly bear, wolf, and mountain lion.     

Components of variance in male lifetime copulatory and reproductive success in a seed bug

Summary Males and females of the seed bug, Neacoryphus bicrucis Say, were individually numbered in the field in southeastern Georgia (USA) and census taken daily for 6 weeks. Variation in male mating efficiency (ME = no. copulations/no. sightings) exceeded that in females and was significantly greater than that generated by a null model. Lifetime copulatory success, estimated as the product of ME and longevity, ranged from 0 to 41, with ME accounting for over 88% of the variation. Lifetime reproductive success (LRS), estimated as the product of ME, longevity, and clutch size, ranged from 0 to 898. Among males copulating at least once, ME accounted for over 40% of the variation in LRS, while longevity alone or in combination with clutch size accounted for 21% and 46%, respectively, of the variation in LRS. Failure of some males (26%) to copulate contributed 38% of the total variation in LRS. Thus, among males surviving to adulthood, sexual selection pressure arising from variation in ME is approximately as strong a force for phenotypic change as is natural selection pressure arising from variation in longevity.     

Determinants of reproductive success of the White-browed Sparrow Weaver,Plocepasser mahali

Summary Variation in reproductive success among 26 communal groups in a sampled population of Plocepasser mahali (White-browed Sparrow Weaver) was studied over a 3-year period in Zambia, Africa. Potential determinants of reproductive success, namely resource variables and group size, were examined and statistically analyzed for their significance in explaining annual variance in reproductive success among these groups. Resource variables included abundance of grass seeds (dry season food) and grasshoppers (wet season food), nest tree quality, and percentage availability of preferred feeding cover. Only the latter two proved appropriate for this analysis. Patterns of utilization did not correlate positively with food abundance, and grasshopper abundance fluctuated too much among the groups in a given year to be treated as a stable variable.From an analysis of multiple correlation coefficients in a stepwise multiple regression model, both group size and ground cover explained independently of each other 20%–30% of the variance in annual production of young surviving 6 months. Explained variance by these two variables also revealed that their relative importance varied considerably between years. Hypotheses are offered to explain the possible causal mechanisms these variables may have in influencing intergroup reproductive success and the possible reasons why vagaries in explained variance were observed. It is suggested that effects of group size and habitat quality may be more important than age-specific effects in modeling population growth and regulation for species like P. mahali.