Determinants of effective population size for loci with different modes of inheritance

Here we report an assessment of the determinants of effective population size (N(e)) in species with overlapping generations. Specifically, we used a stochastic demographic model to investigate the influence of different life-history variables on N(e)/N (where N = population census number) and the influence of sex differences in life-history variables on N(e) for loci with different modes of inheritance. We applied an individual-based modeling approach to two datasets: one from a natural population of savannah baboons (Papio cynocephalus) in the Amboseli basin of southern Kenya and one from a human tribal population (the Gainj of Papua New Guinea). Simulation-based estimates of N(e)/N averaged 0.329 for the Amboseli baboon population (SD = 0.116, 95% CI = 0.172 - 0.537) and 0.786 for the Gainj (SD = 0.184, 95% CI = 0.498 - 1.115). Although variance in male fitness had a substantial impact on N(e)/N in each of the two primate populations, ratios of N(e) values for autosomal and sex-linked loci exhibited no significant departures from Poisson-expected values. In each case, similarities in sex-specific N(e) values were attributable to the unexpectedly high variance in female fitness. Variance in male fitness resulted primarily from age-dependent variance in reproductive success, whereas variance in female fitness resulted primarily from stochastic variance in survival during the reproductive phase.     

Estimation of effective population size for the long-lived darkblotched rockfish Sebastes crameri

We report the variance effective population size (Ne) in darkblotched rockfish (Sebastes crameri) utilizing the temporal method for overlapping generations, which requires a combination of age-specific demography and genetic information from cohorts. Following calculations of age-specific survival and reproductive success from fishery data, we genotyped a sample (n = 1087) comprised by 6 cohorts (from 1995 to 2000) across 7 microsatellite loci. Our Ne estimate (Ne) plus 95% confidence interval was (Ne) = 9157 [6495-12 215], showing that the breeding population number could be 3-4 orders of magnitude smaller than the census population size (N) = 24 376 210). Our estimates resemble closely those found for fishes with similar life history, suggesting that the small (Ne)/(N) ratio for S. crameri is most likely explained by a combination of high variance in reproductive success among individuals, genetic structure, and demographic perturbations such as historical fishing. Because small (Ne)/(N) ratios have been commonly associated with potential loss of genetic variation, our estimates need careful consideration in rockfish management and conservation.     

Temporal genetic stability and high effective population size despite fisheries-induced life-history trait evolution in the North Sea sole

Heavy fishing and other anthropogenic influences can have profound impact on a species' resilience to harvesting. Besides the decrease in the census and effective population size, strong declines in mature adults and recruiting individuals may lead to almost irreversible genetic changes in life-history traits. Here, we investigated the evolution of genetic diversity and effective population size in the heavily exploited sole (Solea solea), through the analysis of historical DNA from a collection of 1379 sole otoliths dating back from 1957. Despite documented shifts in life-history traits, neutral genetic diversity inferred from 11 microsatellite markers showed a remarkable stability over a period of 50 years of heavy fishing. Using simulations and corrections for fisheries induced demographic variation, both single-sample estimates and temporal estimates of effective population size (N(e) ) were always higher than 1000, suggesting that despite the severe census size decrease over a 50-year period of harvesting, genetic drift is probably not strong enough to significantly decrease the neutral diversity of this species in the North Sea. However, the inferred ratio of effective population size to the census size (N(e) /N(c) ) appears very small (10(-5) ), suggesting that overall only a low proportion of adults contribute to the next generation. The high N(e) level together with the low N(e) /N(c) ratio is probably caused by a combination of an equalized reproductive output of younger cohorts, a decrease in generation time and a large variance in reproductive success typical for marine species. Because strong evolutionary changes in age and size at first maturation have been observed for sole, changes in adaptive genetic variation should be further monitored to detect the evolutionary consequences of human-induced selection.     

The effective size of mixed sexually and asexually reproducing populations

Using the transition matrix of inbreeding and coancestry coefficients, the inbreeding (N(eI)), variance (N(eV)), and asymptotic (N(e lambda)) effective sizes of mixed sexual and asexual populations are formulated in terms of asexuality rate (delta), variance of asexual (C) and sexual (K) reproductive contributions of individuals, correlation between asexual and sexual contributions (rho(ck)), selfing rate (beta), and census population size (N). The trajectory of N(eI) toward N(e lambda) changes crucially depending on delta, N, and beta, whereas that of N(eV) is rather consistent. With increasing asexuality, N(e lambda) either increases or decreases depending on C, K, and rho(ck). The parameter space in which a partially asexual population has a larger N(e lambda) than a fully sexual population is delineated. This structure is destroyed when N(1 - delta) < 1 or delta > 1 - 1/N. With such a high asexuality, tremendously many generations are required for the asymptotic size N(e lambda) to be established, and N(e lambda) is extremely large with any value of C, K, and rho(ck) because the population is dominated eventually by individuals of the same genotype and the allelic diversity within the individuals decays quite slowly. In reality, the asymptotic state would occur only occasionally, and instantaneous rather than asymptotic effective sizes should be practical when predicting evolutionary dynamics of highly asexual populations.     

Effective population size of steelhead trout: influence of variance in reproductive success, hatchery programs, and genetic compensation between life-history forms

The effective population size is influenced by many biological factors in natural populations. To evaluate their relative importance, we estimated the effective number of breeders per year (Nb) and effective population size per generation (Ne) in anadromous steelhead trout (Oncorhynchus mykiss) in the Hood River, Oregon (USA). Using demographic data and genetic parentage analysis on an almost complete sample of all adults that returned to the river over 15 years (>15,000 individuals), we estimated Nb for 13 run years and Ne for three entire generations. The results are as follows: (i) the ratio of Ne to the estimated census population size (N) was 0.17-0.40, with large variance in reproductive success among individuals being the primary cause of the reduction in Ne/N; (ii) fish from a traditional hatchery program (Htrad: nonlocal, multiple generations in a hatchery) had negative effects on Nb, not only by reducing mean reproductive success but also by increasing variance in reproductive success among breeding parents, whereas no sign of such effects was found in fish from supplementation hatchery programs (Hsupp: local, single generation in a hatchery); and (iii) Nb was relatively stable among run years, despite the widely fluctuating annual run sizes of anadromous adults. We found high levels of reproductive contribution of nonanadromous parents to anadromous offspring when anadromous run size is small, suggesting a genetic compensation between life-history forms (anadromous and nonanadromous). This is the first study showing that reproductive interaction between different life-history forms can buffer the genetic impact of fluctuating census size on Ne.     

Genetic effective size is three orders of magnitude smaller than adult census size in an abundant,Estuarine-dependent marine fish (Sciaenops ocellatus)

Using eight microsatellite loci and a variety of analytical methods, we estimated genetic effective size (N(e)) of an abundant and long-lived marine fish species, the red drum (Sciaenops ocellatus), in the northern Gulf of Mexico (Gulf). The ratio N(e)/N, where short-term variance N(e) was estimated via the temporal method from shifts in allele-frequency data over four cohorts and where N reflected a current estimate of adult census size in the northern Gulf, was approximately 0.001. In an idealized population, this ratio should approximate unity. The extraordinarily low value of N(e)/N appears to arise from high variance in individual reproductive success and perhaps more importantly from variance in productivity of critical spawning and nursery habitats located in spatially discrete bays and estuaries throughout the northern Gulf. An estimate of N(e) based on a coalescent approach, which measures long-term, inbreeding effective size, was four orders of magnitude lower than the estimate of current census size, suggesting that factors presently driving N(e)/N to low values among red drum in the northern Gulf may have operated similarly in the past. Models that predict N(e)/N exclusively from demographic and life-history features will seriously overestimate N(e) if variance in reproductive success and variance in productivity among spatially discrete demes is underestimated. Our results indicate that these variances, especially variance in productivity among demes, must be large for red drum. Moreover, our study indicates that vertebrate populations with enormous adult census numbers may still be at risk relative to decline and extinction from genetic factors.     

Reproductive success and effective population size in woodrats (Neotoma macrotis)

Discrepancies between the census size and the genetically effective size of populations (N(e)) can be caused by a number of behavioural and demographic factors operating within populations. Specifically, strong skew in male reproductive success, as would be expected in a polygynous mating system, could cause a substantial decrease in N(e) relative to census size. Because the mating system of Neotoma macrotis had previously been described as one nearing harem polygyny, I examined the distribution of reproductive success and genetic variation within a population of this species. Combining genetic data and three years of field observations, I show that variance in reproductive success does not deviate from poisson expectations within either sex and variance in success is similar between the sexes. Furthermore, both males and females had multiple partners across litters in addition to some evidence of multiple paternity within litters. Despite a lack of strong skew in reproductive success, an estimate of N(e) based on a number of demographic parameters suggests that the ratio of N(e)/N in this population is 0.48. Although the ratio of N(e)/N suggests that the population is experiencing higher rates of genetic drift than would be expected based on census size alone, the population maintains high levels of genetic diversity. Estimates of neighbourhood size and patterns of recruitment to the study site suggest that immigration plays an important role in this population and may contribute to the maintenance of high levels of genetic diversity.     

The effective number of a population that varies cyclically in size. I. Discrete generations

We consider a dioecious population having numbers of males and females that vary over time in cycles of length k. It is shown that if k is small in comparison with the numbers of males and females in any generation of the cycle, the effective population number (or size), N(e), is approximately equal to the harmonic mean of the effective population sizes during any given cycle. This result holds whether the locus under consideration is autosomal or sex-linked and whether inbreeding effective population numbers or variance effective population numbers are involved in the calculation of N(e). If, however, only two successive generations in the cycle are considered and the population changes in size between these generations, the inbreeding effective population number, N(eI), differs from the variance effective population number, N(eV). The mutation effective population number turns out to be the same as the number derived using calculations involving probabilities of identity by descent. It is also shown that, at least in one special case, the eigenvalue effective population number is the same as N(eV).     

Comparative demography of a specialist and generalist fruit fly: Implications for host use and pest management

Host plants used by phytophagous insects can have significant consequences on demography parameters, overall lifetime fitness and their subsequent population dynamics. Here, we conduct a comparative demographic study between the specialist Zeugodacus cucumis (French) and generalist Bactrocera tryoni (Froggatt) (Diptera: Tephritidae) to determine whether the host plants used by these fly species play any role in their overall lifetime fitness and explains current host use patterns. These two fly species are pests within the north-eastern region of Australia and we further aimed to use complete life-history data to determine the population parameters and models that would help identify the sensitive life-history stage that could be targeted for effective field management. Eggs collected from laboratory-reared flies were inoculated into organically grown fruits of both the primary and alternate host plant cultivars of both fly species. The proportion surviving each life stage from egg through to adult and fecundity were monitored for all cohorts from the different plant cultivars. Complete stage-base life-tables for cohorts of each fly species developing from each fruit cultivar were constructed, and the key demographic parameters and population models were analysed using PopTools matrix model programme. Our results showed that the host used by each fly species had significant consequences on fly demographic parameters and hence their overall lifetime fitness. The generalist B. tryoni was able to compensate for the fitness loss experienced at the pre-adult stage by having adults with higher fecundity, but this was not the case for the specialist Z. cucumis. Stage-base population models revealed that the population growth rate of both species was highly sensitive at the adult reproductive stage, indicating that manipulating probability of survival at this life stage would effectively manage populations of these pest species. This study provides the empirical evidence of undertaking complete life history demography studies of phytophagous insects to accurately understand their lifetime fitness consequences of using a certain host, their observed host use patterns, and overall population dynamics. We suggest that any efforts to manage dacine fruit fly pest population should consider life-history consequences of host use.     

The effects of cyclic dynamics and mating system on the effective size of an island mouflon population

The Haute Island mouflon (Ovis aries) population is isolated on one small (6.5 km2) island of the remote Kerguelen archipelago. Given a promiscuous mating system, a cyclic demography and a strong female-biased sex ratio after population crashes, we expected a low effective population size (Ne). We estimated Ne using demographic and temporal genetic approaches based on genetic information at 25 microsatellite loci from 62 and 58 mouflons sampled in 1988 and 2003, respectively. Genetic Ne estimates were higher than expected, varying between 104 and 250 depending on the methods used. Both demographic and genetic approaches show the Haute Island Ne is buffered against population crashes. The unexpectedly high Ne likely results from the cyclic winter crashes that allow young males to reproduce, limiting the variance of male reproductive success. Based on individual-based simulations, we suggest that despite a strongly female-biased sex ratio, the effects of the mating system on the effective population size more closely resemble random mating or weak polygyny.     

Disentangling reasons for low Y chromosome variation in the greater white-toothed shrew (Crocidura russula)

Y chromosome variation is determined by several confounding factors including mutation rate, effective population size, demography, and selection. Disentangling these factors is essential to better understand the evolutionary properties of the Y chromosome. We analyzed genetic variation on the Y chromosome, X chromosome, and mtDNA of the greater white-toothed shrew, a species with low variance in male reproductive success and limited sex-biased dispersal, which enables us to control to some extent for life-history effects. We also compared ancestral (Moroccan) to derived (European) populations to investigate the role of demographic history in determining Y variation. Recent colonization of Europe by a small number of founders (combined with low mutation rates) is largely responsible for low diversity observed on the European Y and X chromosomes compared to mtDNA. After accounting for mutation rate, copy number, and demography, the Y chromosome still displays a deficit in variation relative to the X in both populations. This is possibly influenced by directional selection, but the slightly higher variance in male reproductive success is also likely to play a role, even though the difference is small compared to that in highly polygynous species. This study illustrates that demography and life-history effects should be scrutinized before inferring strong selective pressure as a reason for low diversity on the Y chromosome.     

Demographic and genetic estimates of effective population size (Ne) reveals genetic compensation in steelhead trout

Estimates of effective population size (Ne) are required to predict the impacts of genetic drift and inbreeding on the evolutionary dynamics of populations. How the ratio of Ne to the number of sexually mature adults (N) varies in natural vertebrate populations has not been addressed. We examined the sensitivity of Ne/N to fluctuations of N and determined the major variables responsible for changing the ratio over a period of 17 years in a population of steelhead trout (Oncorhynchus mykiss) from Washington State. Demographic and genetic methods were used to estimate Ne. Genetic estimates of Ne were gained via temporal and linkage disequilibrium methods using data from eight microsatellite loci. DNA for genetic analysis was amplified from archived smolt scales. The Ne/N from 1977 to 1994, estimated using the temporal method, was 0.73 and the comprehensive demographic estimate of Ne/N over the same time period was 0.53. Demographic estimates of Ne indicated that variance in reproductive success had the most substantial impact on reducing Ne in this population, followed by fluctuations in population size. We found increased Ne/N ratios at low N, which we identified as genetic compensation. Combining the information from the demographic and genetic methods of estimating Ne allowed us to determine that a reduction in variance in reproductive success must be responsible for this compensation effect. Understanding genetic compensation in natural populations will be valuable for predicting the effects of changes in N (i.e. periods of high population density and bottlenecks) on the fitness and genetic variation of natural populations.     

Genetic consequences of polygyny and social structure in an Indian fruit bat, Cynopterus sphinx. II. Variance in male mating success and effective population size

Variance in reproductive success is a primary determinant of genetically effective population size (Ne), and thus has important implications for the role of genetic drift in the evolutionary dynamics of animal taxa characterized by polygynous mating systems. Here we report the results of a study designed to test the hypothesis that polygynous mating results in significantly reduced Ne in an age-structured population. This hypothesis was tested in a natural population of a harem-forming fruit bat, Cynopterus sphinx (Chiroptera: Pteropodidae), in western India. The influence of the mating system on the ratio of variance Ne to adult census number (N) was assessed using a mathematical model designed for age-structured populations that incorporated demographic and genetic data. Male mating success was assessed by means of direct and indirect paternity analysis using 10-locus microsatellite genotypes of adults and progeny from two consecutive breeding periods (n = 431 individually marked bats). Combined results from both analyses were used to infer the effective number of male parents in each breeding period. The relative proportion of successfully reproducing males and the size distribution of paternal sibships comprising each offspring cohort revealed an extremely high within-season variance in male mating success (up to 9.2 times higher than Poisson expectation). The resultant estimate of Ne/N for the C. sphinx study population was 0.42. As a result of polygynous mating, the predicted rate of drift (1/2Ne per generation) was 17.6% higher than expected from a Poisson distribution of male mating success. However, the estimated Ne/N was well within the 0.25-0.75 range expected for age-structured populations under normal demographic conditions. The life-history schedule of C. sphinx is characterized by a disproportionately short sexual maturation period scaled to adult life span. Consequently, the influence of polygynous mating on Ne/N is mitigated by the extensive overlap of generations. In C. sphinx, turnover of breeding males between seasons ensures a broader sampling of the adult male gamete pool than expected from the variance in mating success within a single breeding period.     

Effective number of breeding adults in Bufo bufo estimated from age-specific variation at minisatellite loci

Estimates of the effective number of breeding adults were derived for three semi-isolated populations of the common toad Bufo bufo based on temporal (i.e. adult-progeny) variance in allele frequency for three highly polymorphic minisatellite loci. Estimates of spatial variance in allele frequency among populations and of age-specific measures of genetic variability are also described. Each population was characterized by a low effective adult breeding number ( N _b) based on a large age-specific variance in mini-satellite allele frequency. Estimates of N _b (range 21–46 for population means across three loci) were ≊ 55–230-fold lower than estimates of total adult census size. The implications of low effective breeding numbers for long-term maintenance of genetic variability and population viability are discussed relative to the species' reproductive ecology, current land-use practices, and present and historical habitat modification and loss. The utility of indirect measures of population parameters such as N _b and N _e based on time-series data of minisatellite allele frequencies is discussed relative to similar measures estimated from commonly used genetic markers such as protein allozymes.     

Genetic diversity, population structure, effective population size and demographic history of the Finnish wolf population

The Finnish wolf population (Canis lupus) was sampled during three different periods (1996-1998, 1999-2001 and 2002-2004), and 118 individuals were genotyped with 10 microsatellite markers. Large genetic variation was found in the population despite a recent demographic bottleneck. No spatial population subdivision was found even though a significant negative relationship between genetic relatedness and geographic distance suggested isolation by distance. Very few individuals did not belong to the local wolf population as determined by assignment analyses, suggesting a low level of immigration in the population. We used the temporal approach and several statistical methods to estimate the variance effective size of the population. All methods gave similar estimates of effective population size, approximately 40 wolves. These estimates were slightly larger than the estimated census size of breeding individuals. A Bayesian model based on Markov chain Monte Carlo simulations indicated strong evidence for a long-term population decline. These results suggest that the contemporary wolf population size is roughly 8% of its historical size, and that the population decline dates back to late 19th century or early 20th century. Despite an increase of over 50% in the census size of the population during the whole study period, there was only weak evidence that the effective population size during the last period was higher than during the first. This may be caused by increased inbreeding, diminished dispersal within the population, and decreased immigration to the population during the last study period.     

Effective size of a fluctuating age-structured population

Previous theories on the effective size of age-structured populations assumed a constant environment and, usually, a constant population size and age structure. We derive formulas for the variance effective size of populations subject to fluctuations in age structure and total population size produced by a combination of demographic and environmental stochasticity. Haploid and monoecious or dioecious diploid populations are analyzed. Recent results from stochastic demography are employed to derive a two-dimensional diffusion approximation for the joint dynamics of the total population size, N, and the frequency of a selectively neutral allele, p. The infinitesimal variance for p, multiplied by the generation time, yields an expression for the effective population size per generation. This depends on the current value of N, the generation time, demographic stochasticity, and genetic stochasticity due to Mendelian segregation, but is independent of environmental stochasticity. A formula for the effective population size over longer time intervals incorporates deterministic growth and environmental stochasticity to account for changes in N.     

Sexual and lifetime selection on body size in a marine fish: the importance of life-history trade-offs

Many field measurements of viability and sexual selection on body size indicate that large size is favoured. However, life-history theory predicts that body size may be optimized and that patterns of selection may often be stabilizing rather than directional. One reason for this discrepancy may be that field estimates of selection tend to focus on limited components of fitness and may not fully measure life-history trade-offs. We use an 8-year, demographic field study to examine both sexual selection and lifetime selection on body size of a coral reef fish (the bicolour damselfish, Stegastes partitus). Selection via reproductive success of adults was very strong (standardized selection differential=1.04). However, this effect was balanced by trade-offs between large adult size and reduced cumulative survival during the juvenile phase. When we measured lifetime fitness (net reproductive rate), selection was strongly stabilizing and only weakly directional, consistent with predictions from life-history theory.     

Evaluating the effect of stage-specific survivorship on the N(e)/N ratio

Evaluating effective population size (Ne) and the effective size to census size ratio (Ne/N) in species with Type III survivorship curves is complicated when key demographic parameters [mean (k macro) and variance (V(k)) of family size] are measured during early life stages. The method of Crow & Morton (1955) for scaling demographic data collected at a juvenile stage to expected values at adulthood is extended to consider sequential episodes of random and family correlated survival. Results show the following: (i) The order in which the episodes of random and family-correlated survival occur does not affect N(e) or N(e)/N; (ii) If a population experiences an episode of family-correlated survival, N(e)/N scaled to its expected value in a population of constant size (k macro= 2) is simply the survival rate during the family-correlated stage. If multiple such stages occur, scaled N(e)/N is the product of the survivals during all family-correlated life stages; (iii) Under the assumption of random post-enumeration survival, adjusting the variance effective size to its expected value at k macro= 2 is equivalent to computing the inbreeding effective size at the earlier life stage. Application to experimental data for hatchery populations of Pacific salmon (Oncorhynchus spp.) indicates that nonrandom survival during the marine phase led to estimated reductions in effective size of 0-62 (mean 19) in 12 different cohorts. This approach can provide insights into N(e)/N in highly fecund species, including some marine species in which N(e) has been estimated to be several orders of magnitude less than N.     

The consequences of the variance-mean rescaling effect on effective population size

The effective population size (N_e), and the ratio between N_e and census population size (N) are often used as measures of population viability. We show that using the harmonic mean of population sizes over time – a common proxy for N_e– has some important evolutionary consequences and implications for conservation management. This stems from the fact that there is no unambiguous relationship between the arithmetic and harmonic means for populations fluctuating in size. As long as the variance of population size increases moderately with increasing arithmetic mean population size, the harmonic mean also increases. However, if the variance of population size increases more rapidly, which existing data often suggest, then the harmonic mean may actually decrease with increasing arithmetic mean. Thus maximizing N may not maximize N_e, but could instead lower the adaptive potential and hence limit the evolutionary response to environmental change. Large census size has the clear advantage of lowering demographic stochasticity, and hence extinction risk, and under certain conditions large census size also minimizes the loss of genetic variation. Consequently, maximising census size has served as a useful dogma in ecology, genetics and conservation. Nonetheless, due to the intricate relationships among N_e, population viability and the properties of population fluctuations, we suggest that this dogma should be taken only as a rule of thumb.     

Concurrent habitat and life history influences on effective/census population size ratios in stream-dwelling trout

Lower effective sizes (N(e)) than census sizes (N) are routinely documented in natural populations, but knowledge of how multiple factors interact to lower N(e)/N ratios is often limited. We show how combined habitat and life-history influences drive a 2.4- to 6.1-fold difference in N(e)/N ratios between two pristine brook trout (Salvelinus fontinalis) populations occupying streams separated by only 750 m. Local habitat features, particularly drainage area and stream depth, govern trout biomass produced in each stream. They also generate higher trout densities in the shallower stream by favoring smaller body size and earlier age-at-maturity. The combination of higher densities and reduced breeding site availability in the shallower stream likely leads to more competition among breeding trout, which results in greater variance in individual reproductive success and a greater reduction in N(e) relative to N. A similar disparity between juvenile or adult densities and breeding habitat availability is reported for other species and hence may also result in divergent N(e)/N ratios elsewhere. These divergent N(e)/N ratios between adjacent populations are also an instructive reminder for species conservation programs that genetic and demographic parameters may differ dramatically within species.