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.     

Lineage Loss in Serengeti Cheetahs: Consequences of High Reproductive Variance and Heritability of Fitness on Effective Population Size

Abstract: In natural populations, many breeders do not leave surviving offspring, and as a result many potential genetic lineages are lost. I examined lineage extinction in Serengeti cheetahs ( Acinonyx jubatus ) and found that 76% of matrilines were lost over a 25-year period. Production of future breeders was nonrandom and generally confined to a few families. Five out of 63 matrilines accounted for 45% of the total cheetah population over the course of the study. Lineage persistence is perhaps best illustrated by the variance in lifetime reproductive success ( LRS) and heritability in this parameter. In female cheetahs, variance in LRS was high, and new data show that this LRS was heritable. Variance in LRS and heritability in LRS have dramatic consequences for effective population size, N _e. I calculated N _e for cheetahs, taking into account fluctuating population size, unequal sex ratio, non-Poisson distribution of reproductive success, and heritability of fitness. The N _e was most strongly affected by variance in reproductive success and especially heritability in reproductive success. The variance N _e was 44% of the actual population size, and the inclusion of heritability further reduced N _e to only 15% of the actual population, a ratio similar to that of a social carnivore with reproductive suppression. The current cheetah population in the Serengeti is below numbers suggested by N _e estimates as sufficient to maintain sufficient genetic diversity.     

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.     

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.     

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 .     

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.     

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.     

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.     

Comparisons of Genetic Diversity in the Endangered Adenophora lobophylla and Its Widespread Congener, A. potaninii

Abstract: Starch-gel electrophoresis was used to examine the levels and distribution of genetic diversity in two Adenophora species: the narrow endangered Adenophora lobophylla and its widespread congener, A. potaninii . Based on allozyme variation at 18 putative loci, we measured high levels of genetic variability both in the endangered and the widespread species, with 83.3% of the loci being polymorphic. The mean expected heterozygosity within populations (   H _ep  ) and within species (   H _es  ) were 0.234 and 0.244 for A. potaninii and were as high as 0.210 and 0.211 for A. lobophylla . There was higher differentiation among populations in A. potaninii (   F _ST = 0.155) than in A. lobophylla (   F _ST = 0.071). The high levels of genetic diversity in the present allozyme survey are consistent with the morphological variation observed in these species and may be attributed to high outcrossing rates in the Adenophora species. In addition, A. lobophylla was identified as a distinct species on the basis of Nei's genetic distances and thus should be given a high priority for protection. It is noteworthy that the endangered A. lobophylla maintains much higher genetic diversity than most endemic or narrowly distributed plant species in spite of its restricted distribution. We hypothesize that A. lobophylla has become endangered for ecological and stochastic reasons, including habitat destruction or environmental changes, mud slides, and human disturbance such as grazing and mowing. Consequently, habitat protection is of particular importance for conserving this endangered species.     

Relationship of Breeding System to Rarity in the Lakeside Daisy (Hymenoxys acaulis var. glabra)

The breeding system of a rare Great Lakes endemic, the lakeside daisy ( Hymenoxys acaulis var. glabra ), was investigated when plants from a remnant Illinois population produced no seeds for over 15 years. To determine if the Lakeside daisy was self-incompatible, 20 plants from two populations, Illinois and Ohio, were selfed and outcrossed. Seed/ovule ratios were compared among the different treatments and the location of the incompatibility reaction was identified. Lakeside daisy was found to be self-incompatible (sporophytic). The last Illinois population was effectively extinct because the remaining plants belonged to the same mating type ( N _e = 1) and only produced seeds when outcrossed to the Ohio plants. Cross-incompatibility was also observed among Ohio plants, suggesting that within large populations, compatible mating types may be rare locally. In addition, inbreeding depression (lower seed/ovule ratios in inbred than in outcrosses) was observed after one generation of inbreeding. Small populations of self-incompatible species are vulnerable to extinction if the number of self-incompatibility alleles, either as a result of a bottleneck or of genetic drift, falls below tbe number needed for the breeding system to function. Recovery protocols based on these genetic considerations were developed and implemented in 1988 when Lakeside daisy populations were established at three Illinois nature preserves.     

Genetic Diversity, Population Size, and Fitness in Central and Peripheral Populations of a Rare Plant Lychnis viscaria

Abstract: Genetic diversity is expected to decrease in small and isolated populations as a consequence of bottlenecks, founder effects, inbreeding, and genetic drift. The genetics and ecology of the rare perennial plant Lychnis viscaria (Caryophyllaceae) were studied in both peripheral and central populations within its distribution area. We aimed to investigate the overall level of genetic diversity, its spatial distribution, and possible differences between peripheral and central populations by examining several populations with electrophoresis. Our results showed that the level of genetic diversity varied substantially among populations (  H _exp = 0.000–0.116) and that the total level of genetic diversity (mean H _exp = 0.056) was low compared to that of other species with similar life-history attributes. The peripheral populations of L. viscaria had less genetic variation (mean H _exp = 0.034) than the central ones (0.114). Analysis of genetic structure suggested limited gene flow (mean F _ST = 0.430) and high differentiation among populations, emphasizing the role of genetic drift (  N _e m = 0.33). Isolation was even higher than expected based on the physical distance among populations. We also focused on the association between population size and genetic diversity and possible effects on fitness of these factors. Population size was positively correlated with genetic diversity. Population size and genetic diversity, however, were not associated with fitness components such as germination rate, seedling mass, or seed yield. There were no differences in the measured fitness components between peripheral and central populations. Even though small and peripheral populations had lower levels of genetic variation, they were as viable as larger populations, which emphasizes their potential value for conservation.     

Scale, Variable Density, and Conservation Planning for Mammalian Carnivores

Abstract: Many mammalian carnivores are in local or global decline. To slow this process, continued planning to protect these species is warranted, Still, the data bases that we have at our disposal do not adequately document population requirements for space at scales appropriate for conservation planning. To illustrate this problem, we have collected published data for 214 population censuses of carnivores. We tested for a relationship between the number of individuals censused and the size of study site for our entire data set. We conducted the same test for each family, for which we obtained sufficient and qualifying census data With areas ranging from less than 10 km² to over 40,000 km², we obtained a significant regression (p < .001; r²= 76%) for the sample as a whole. We examined the distribution of densities with increasing area and found that the relationship was not constant but decreased We noticed that numbers per census-area size increased with a slope (m < 1). We also noticed that the sizes of study areas were unevenly distributed Only 7% of the studies in our sample censused regions larger than 10,000 km². It remains unclear to what extent and how the density decreases with increasing scale We expect that extrapolations from small scales to larger ones are likely to underestimate space requirements for carnivores.     

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.     

Evaluating the Effectiveness of Corridors: a Genetic Approach

Abstract: The effectiveness of corridors in maintaining dispersal in fragmented landscapes is a question of considerable conservation and ecological importance. We tested the efficacy of corridors as residual landscape structures in maintaining population structure in the red-backed vole ( Clethrionomys gapperi ), a closed-canopy specialist, and the deer mouse (   Peromyscus maniculatus ), a habitat generalist. In coniferous forests managed for timber production in northeastern Washington, we sampled pairs of populations in three landscape classes: (1) contiguous landscapes, in which sites were located completely within a matrix of closed-canopy forest; (2) corridor landscapes, in which sites were connected by a corridor of closed-canopy forest; and (3) isolated landscapes, in which sites were separated from one another by clearcut or young regeneration stands. For each species, we used four microsatellite loci to quantify genetic distance between population pairs. Nei's genetic distance (   D _s  ) increased from smallest to largest in the order of contiguous, corridor, and isolated landscapes for C. gapperi. For P. maniculatus, genetic distances across landscape configurations were not significantly different. The differences between the two species indicate that they respond differently to the presence of forest corridors. In managed forests, corridors between unlogged habitats appear to maintain higher population connectivity for C. gapperi than landscapes without corridors.     

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.     

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).     

The effects of castration, sex ratio and population density on social segregation and habitat use in Soay sheep

We analysed 16 years of census data gathered on the island of Hirta (archipelago of St. Kilda) to investigate the effects of castration, population density, sex ratio, season and group type on habitat use and social segregation of Soay sheep. From 1978 to 1980, 72 male lambs were castrated. We used this experiment to study how a change in reproductive status could affect sociality and habitat choice of these males. Males, females and castrates were all segregated outside the rutting season in autumn. Castrates were the least segregated from females in spring and summer but were most segregated from them during the pre-rut. The more equal the sex ratios, the higher was the degree of social segregation. The three sex classes used similar habitat types, namely, Holcus agrostis, Agrostis festuca and Calluna habitats. Holcus agrostis and Agrostis festuca were top- and second-ranked in female and castrate habitat use, while Holcus agrostis and Calluna were the two top habitat types used by rams. It is unclear why males included Calluna heath habitats, but it cannot be excluded that they might have shifted their use depending on forage availability. A lack in differences in habitat use between castrates and females suggests that body size differences alone cannot be the driving factor for habitat segregation in male and female Soay sheep and that there are reasons other than body size that could motivate reproductive males to use additional habitat types, such as Calluna heath. Although habitat use shifted from one habitat type to the next between low- and high-population-density years and between seasons, there was no clear link between population density and how different groups (male, female or castrate) used these areas. We discuss effects of reproductive status, population density and sex ratio on social segregation and habitat use and suggest that these factors need to be taken into account when investigating causes of sexual segregation in ungulates.     

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.