Do estimates of contemporary effective population size tell us what we want to know?

Estimation of effective population size (N_e) from genetic marker data is a major focus for biodiversity conservation because it is essential to know at what rates inbreeding is increasing and additive genetic variation is lost. But are these the rates assessed when applying commonly used N_e estimation techniques? Here we use recently developed analytical tools and demonstrate that in the case of substructured populations the answer is no. This is because the following: Genetic change can be quantified in several ways reflecting different types of N_e such as inbreeding (N_eI), variance (N_eV), additive genetic variance (N_eAV), linkage disequilibrium equilibrium (N_eLD), eigenvalue (N_eE) and coalescence (N_eCo) effective size. They are all the same for an isolated population of constant size, but the realized values of these effective sizes can differ dramatically in populations under migration. Commonly applied N_e‐estimators target N_eV or N_eLD of individual subpopulations. While such estimates are safe proxies for the rates of inbreeding and loss of additive genetic variation under isolation, we show that they are poor indicators of these rates in populations affected by migration. In fact, both the local and global inbreeding (N_eI) and additive genetic variance (N_eAV) effective sizes are consistently underestimated in a subdivided population. This is serious because these are the effective sizes that are relevant to the widely accepted 50/500 rule for short and long term genetic conservation.  The bias can be infinitely large and is due to inappropriate parameters being estimated when applying theory for isolated populations to subdivided ones.     

Multiple estimates of effective population size for monitoring a long‐lived vertebrate: an application to Yellowstone grizzly bears

Effective population size (N_e) is a key parameter for monitoring the genetic health of threatened populations because it reflects a population's evolutionary potential and risk of extinction due to genetic stochasticity. However, its application to wildlife monitoring has been limited because it is difficult to measure in natural populations. The isolated and well‐studied population of grizzly bears (Ursus arctos) in the Greater Yellowstone Ecosystem provides a rare opportunity to examine the usefulness of different N_e estimators for monitoring. We genotyped 729 Yellowstone grizzly bears using 20 microsatellites and applied three single‐sample estimators to examine contemporary trends in generation interval (GI), effective number of breeders (N_b) and N_e during 1982–2007. We also used multisample methods to estimate variance (N_eV) and inbreeding N_e (N_eI). Single‐sample estimates revealed positive trajectories, with over a fourfold increase in N_e (≈100 to 450) and near doubling of the GI (≈8 to 14) from the 1980s to 2000s. N_eV (240–319) and N_eI (256) were comparable with the harmonic mean single‐sample N_e (213) over the time period. Reanalysing historical data, we found N_eV increased from ≈80 in the 1910s–1960s to ≈280 in the contemporary population. The estimated ratio of effective to total census size (N_e/N_c) was stable and high (0.42–0.66) compared to previous brown bear studies. These results support independent demographic evidence for Yellowstone grizzly bear population growth since the 1980s. They further demonstrate how genetic monitoring of N_e can complement demographic‐based monitoring of N_c and vital rates, providing a valuable tool for wildlife managers.     

Effects of population characteristics and structure on estimates of effective population size in a house sparrow metapopulation

Effective population size (N_e) is a key parameter to understand evolutionary processes and the viability of endangered populations as it determines the rate of genetic drift and inbreeding. Low N_e can lead to inbreeding depression and reduced population adaptability. In this study, we estimated contemporary N_e using genetic estimators (LDNE, ONeSAMP, MLNE and CoNe) as well as a demographic estimator in a natural insular house sparrow metapopulation. We investigated whether population characteristics (population size, sex ratio, immigration rate, variance in population size and population growth rate) explained variation within and among populations in the ratio of effective to census population size (N_e/N_c). In general, N_e/N_c ratios increased with immigration rates. Genetic N_e was much larger than demographic N_e, probably due to a greater effect of immigration on genetic than demographic processes in local populations. Moreover, although estimates of genetic N_e seemed to track N_c quite well, the genetic N_e‐estimates were often larger than N_c within populations. Estimates of genetic N_e for the metapopulation were however within the expected range (<N_c). Our results suggest that in fragmented populations, even low levels of gene flow may have important consequences for the interpretation of genetic estimates of N_e. Consequently, further studies are needed to understand how N_e estimated in local populations or the total metapopulation relates to actual rates of genetic drift and inbreeding.     

gesp: A computer program for modelling genetic effective population size,inbreeding and divergence in substructured populations

The genetically effective population size (N_e) is of key importance for quantifying rates of inbreeding and genetic drift and is often used in conservation management to set targets for genetic viability. The concept was developed for single, isolated populations and the mathematical means for analysing the expected N_e in complex, subdivided populations have previously not been available. We recently developed such analytical theory and central parts of that work have now been incorporated into a freely available software tool presented here. gesp (Genetic Effective population size, inbreeding and divergence in Substructured Populations) is R‐based and designed to model short‐ and long‐term patterns of genetic differentiation and effective population size of subdivided populations. The algorithms performed by gesp allow exact computation of global and local inbreeding and eigenvalue effective population size, predictions of genetic divergence among populations (G_ST) as well as departures from random mating (F_IS, F_IT) while varying (i) subpopulation census and effective size, separately or including trend of the global population size, (ii) rate and direction of migration between all pairs of subpopulations, (iii) degree of relatedness and divergence among subpopulations, (iv) ploidy (haploid or diploid) and (v) degree of selfing. Here, we describe gesp and exemplify its use in conservation genetics modelling.     

INBREEDING AND VARIANCE EFFECTIVE SIZES FOR NONRANDOM MATING POPULATIONS

Following an inbreeding approach and assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, I have derived expressions for the inbreeding effective size, N_eI, for a finite diploid population with variable census sizes for three cases: monoecious populations with partial selfing; dioecious populations of equal numbers of males and females with partial sib mating; and unequal numbers of males and females with random mating. For the first two cases, recurrence equations for the inbreeding coefficient are also obtained, which allow inbreeding coefficients to be predicted exactly in both early and late generations. Following the variance of change in gene frequency approach, a general expression for variance effective size, N_eV, is obtained for a population with unequal numbers of male and female individuals, arbitrary family size distribution, and nonrandom mating. All the parameters involved are allowed to change over generations. For some special cases, the equation reduces to the simple expressions approximately as derived by previous authors. Comparisons are made between equations derived by the present study and those obtained by previous authors. Some of the published equations for N_eI and N_eV are shown to be incomplete or incorrect. Stochastic simulations are run to check the results where disagreements with others are involved.     

Genetic effective size,Ne, tracks density in a small freshwater cyprinid,Pecos bluntnose shiner (Notropis simus pecosensis)

Genetic monitoring tracks changes in measures of diversity including allelic richness, heterozygosity and genetic effective size over time, and has emerged as an important tool for understanding evolutionary consequences of population management. One proposed application of genetic monitoring has been to estimate abundance and its trajectory through time. Here, genetic monitoring was conducted across five consecutive year for the Pecos bluntnose shiner, a federally threatened minnow. Temporal changes in allele frequencies at seven microsatellite DNA loci were used to estimate variance effective size (N_eV) across adjacent years in the time series. Likewise, effective size was computed using the linkage disequilibrium method (N_eD) for each sample. Estimates of N_e were then compared to estimates of adult fish density obtained from traditional demographic monitoring. For Pecos bluntnose shiner, density (catch‐per‐unit‐effort), N_eV and N_eD were positively associated across this time series. Results for Pecos bluntnose shiner were compared to a related and ecologically similar species, the Rio Grande silvery minnow. In this species, density and N_eV were negatively associated, which suggested decoupling of abundance and effective size trajectories. Conversely, density and N_eD were positively associated. For Rio Grande silvery minnow, discrepancies among estimates of N_e and their relationships with adult fish density could be related to effects of high variance in reproductive success in the wild and/or effects of supplementation of the wild population with captive‐bred and reared fish. The efficacy of N_e as a predictor of density and abundance may depend on intrinsic population dynamics of the species and how these dynamics are influenced by the landscape features, management protocols and other factors.     

Migration and inbreeding: the importance of recipient population size for genetic management

Sewall Wright demonstrated 70 years ago thatthe number of migrants required to maintainspecified levels of gene flow (i.e. avoidexcessive inbreeding) is virtually independentof the size of the recipient population. According to conventional wisdom, this idea isvalid provided population size exceeds 20. Itis well known that this independence implicitlyassumes that a population's effective size(N _e) is equal to its census size(N). However, it is not obvious whetherindependence between the required number ofmigrants (to avoid excessive inbreeding) andpopulation size constitutes a reasonableassumption for real populations of conservationconcern. Relying on empirical data, wedemonstrate that for real populations, theassumption (i.e. N _e = N) isroutinely violated to a degree such that therequired number of migrants is stronglydependent on the size of the recipientpopulation. Because a population's effectivesize (N _e) is typically much smallerthan its census size (N), the number ofmigrants required to avoid inbreeding isactually dependent on N even when it isconsiderably greater than 20. For example,when N _e/N = 0.1, the number ofmigrants required to maintain the inbreedingcoefficient (F) at 0.2 doubles (from 4 to8) as N increases from 9 to 60. Similarly, when N _e/N = 0.05, thenumber of migrants required increases by 50%as N increases from 18 to 45, andincreases again by 50% as N increasesfrom 45 to 260. Thus, for populations muchlarger than 20, the required number of migrantsincreases asymptotically with N, anddramatically so when N _e/N1. Simple conventions regarding the requisitenumber of migrants may not apply to manypopulations of conservation concern. Geneticmanagement should routinely rely on models thatexplicitly account for this and other recentconsiderations. Failure to do so mayjeopardize the viability of populations thatare sensitive to altered levels of inbreeding.     

Evaluating methods for estimating local effective population size with and without migration

Effective population size is a fundamental parameter in population genetics, evolutionary biology, and conservation biology, yet its estimation can be fraught with difficulties. Several methods to estimate N_e from genetic data have been developed that take advantage of various approaches for inferring N_e. The ability of these methods to accurately estimate N_e, however, has not been comprehensively examined. In this study, we employ seven of the most cited methods for estimating N_e from genetic data (Colony2, CoNe, Estim, MLNe, ONeSAMP, TMVP, and NeEstimator including LDNe) across simulated datasets with populations experiencing migration or no migration. The simulated population demographies are an isolated population with no immigration, an island model metapopulation with a sink population receiving immigrants, and an isolation by distance stepping stone model of populations. We find considerable variance in performance of these methods, both within and across demographic scenarios, with some methods performing very poorly. The most accurate estimates of N_e can be obtained by using LDNe, MLNe, or TMVP; however each of these approaches is outperformed by another in a differing demographic scenario. Knowledge of the approximate demography of population as well as the availability of temporal data largely improves N_e estimates.     

Estimating effective population size using RADseq: Effects of SNP selection and sample size

Effective population size (N_e) is a key parameter of population genetics. However, N_e remains challenging to estimate for natural populations as several factors are likely to bias estimates. These factors include sampling design, sequencing method, and data filtering. One issue inherent to the restriction site‐associated DNA sequencing (RADseq) protocol is missing data and SNP selection criteria (e.g., minimum minor allele frequency, number of SNPs). To evaluate the potential impact of SNP selection criteria on N_e estimates (Linkage Disequilibrium method) we used RADseq data for a nonmodel species, the thornback ray. In this data set, the inbreeding coefficient F_IS was positively correlated with the amount of missing data, implying data were missing nonrandomly. The precision of N_eestimates decreased with the number of SNPs. Mean N_e estimates (averaged across 50 random data sets with2000 SNPs) ranged between 237 and 1784. Increasing the percentage of missing data from 25% to 50% increased N_e estimates between 82% and 120%, while increasing the minor allele frequency (MAF) threshold from 0.01 to 0.1 decreased estimates between 71% and 75%. Considering these effects is important when interpreting RADseq data‐derived estimates of effective population size in empirical studies.     

INCREASED PROBABILITY OF EXTINCTION DUE TO DECREASED GENETIC EFFECTIVE POPULATION SIZE: EXPERIMENTAL POPULATIONS OF CLARKIA PULCHELLA

We established replicated experimental populations of the annual plant Clarkia pulchella to evaluate the existence of a causal relationship between loss of genetic variation and population survival probability. Two treatments differing in the relatedness of the founders, and thus in the genetic effective population size (N_e), were maintained as isolated populations in a natural environment. After three generations, the low N_e treatment had significantly lower germination and survival rates than did the high N_e treatment. These lower germination and survival rates led to decreased mean fitness in the low N_e populations: estimated mean fitness in the low N_e populations was only 21% of the estimated mean fitness in the high N_e populations. This inbreeding depression led to a reduction in population survival: at the conclusion of the experiment, 75% of the high N_e populations were still extant, whereas only 31% of the low N_e populations had survived. Decreased genetic effective population size, which leads to both inbreeding and the loss of alleles by genetic drift, increased the probability of population extinction over that expected from demographic and environmental stochasticity alone. This demonstrates that the genetic effective population size can strongly affect the probability of population persistence.     

Estimating effective population size from linkage disequilibrium: severe bias in small samples

Effective population size (N _e) is a central concept in evolutionary biology and conservation genetics. It predicts rates of loss of neutral genetic variation, fixation of deleterious and favourable alleles, and the increase of inbreeding experienced by a population. A method exists for the estimation of N _e from the observed linkage disequilibrium between unlinked loci in a population sample. While an increasing number of studies have applied this method in natural and managed populations, its reliability has not yet been evaluated. We developed a computer program to calculate this estimator of N _e using the most widely used linkage disequilibrium algorithm and used simulations to show that this estimator is strongly biased when the sample size is small (<‰100) and below the true N _e. This is probably due to the linkage disequilibrium generated by the sampling process itself and the inadequate correction for this phenomenon in the method. Results suggest that N _e estimates derived using this method should be regarded with caution in many cases. To improve the method’s reliability and usefulness we propose a way to determine whether a given sample size exceeds the population N _e and can therefore be used for the computation of an unbiased estimate.     

THE EFFECTIVE SIZE OF A HIERARCHICALLY STRUCTURED POPULATION

A knowledge of the effective size of a population (N_e) is important in understanding its current and future evolutionary potential. Unfortunately, the effective size of a hierarchically structured population is not, in general, equal to the sum of its parts. In particular, the inbreeding structure has a major influence on N_e. Here I link N_e to Wright's hierarchical measures of inbreeding, F_IS and F_ST, for an island-structured population (or metapopulation) of size N_T. The influence of F_ST depends strongly on the degree to which island productivity is regulated. In the absence of local regulation (the interdemic model), interdemic genetic drift reduces N_e. When such drift is combined with local inbreeding under otherwise ideal conditions, the effects of F_IS and F_ST are identical: increasing inbreeding either within or between islands reduces N_e, with N_e = N_T/[(1 + F_IS)(1 + F_ST) ? 2F_ISF_ST]. However, if islands are all equally productive because of local density regulation (the traditional island model), then N_e = N_T/[(1 + F_IS)(1 –F_ST)] and the effect of F_ST is reversed. Under the interdemic model, random variation in the habitat quality (and hence productivity) of islands act to markedly decrease N_e. This variation has no effect under the island model because, by definition, all islands are equally productive. Even when no permanent island structure exists, spatial differences in habitat quality can significantly increase the overall variance in reproductive success of both males and females and hence lower N_e. Each of these basic results holds when other nonideal factors are added to the model. These factors, deviations from a 1:1 sex ratio, greater than Poisson variance in female reproductive success, and variation in male mating success due to polygynous mating systems, all act to lower N_e. The effects of male and female variance on N_e have important differences because only females affect island productivity. Finally, it is noted that to use these relationships, F_IS and F_ST must be estimated according to Wright's definition (and corrected to have a zero expectation under the null model). A commonly used partitioning (θ, θ_g) can be biased if either island size or the number of islands is small.     

Inbreeding depression and drift load in small populations at demographic disequilibrium

Inbreeding depression is a major driver of mating system evolution and has critical implications for population viability. Theoretical and empirical attention has been paid to predicting how inbreeding depression varies with population size. Lower inbreeding depression is predicted in small populations at equilibrium, primarily due to higher inbreeding rates facilitating purging and/or fixation of deleterious alleles (drift load), but predictions at demographic and genetic disequilibrium are less clear. In this study, we experimentally evaluate how lifetime inbreeding depression and drift load, estimated by heterosis, vary with census (N_c) and effective (estimated as genetic diversity, H_e) population size across six populations of the biennial Sabatia angularis as well as present novel models of inbreeding depression and heterosis under varying demographic scenarios at disequilibrium (fragmentation, bottlenecks, disturbances). Our experimental study reveals high average inbreeding depression and heterosis across populations. Across our small sample, heterosis declined with H_e, as predicted, whereas inbreeding depression did not vary with H_e and actually decreased with N_c. Our theoretical results demonstrate that inbreeding depression and heterosis levels can vary widely across populations at disequilibrium despite similar H_e and highlight that joint demographic and genetic dynamics are key to predicting patterns of genetic load in nonequilibrium systems.     

Low effective population size and survivorship in a grassland grouse

Assessments of census size (N _c) and effective population size (N _e) are necessary for the conservation of species exhibiting population declines. We examined two populations (Oklahoma and New Mexico) of the lesser prairie-chicken (Tympanuchus pallidicinctus), a declining lek-breeding bird, in which one population (Oklahoma) has larger clutch size and more nesting attempts per year but lower survival caused by human changes to the landscape. We estimated demographic and genetic estimates of N _e for each population and found that both populations have low N _e estimates with a risk of inbreeding depression. Although Oklahoma females produce a larger number of offspring, the proportion of females successfully reproducing is not higher than in New Mexico. Higher reproductive effort has likely reached a physiological limit in Oklahoma prairie-chickens but has not led to a higher N _e or even a larger N _c than New Mexico. We propose that future conservation efforts focus on maximizing survivorship and decreasing the variance in reproductive success because these factors are more likely than increasing reproductive output alone to yield population persistence in lek-breeding species.     

Asymmetric gene flow and the evolutionary maintenance of genetic diversity in small,peripheral Atlantic salmon populations

Small populations may be expected to harbour less genetic variation than large populations, but the relation between census size (N), effective population size (N _e), and genetic diversity is not well understood. We compared microsatellite variation in four small peripheral Atlantic salmon populations from the Iberian peninsula and three larger populations from Scotland to test whether genetic diversity was related to population size. We also examined the historical decline of one Iberian population over a 50-year period using archival scales in order to test whether a marked reduction in abundance was accompanied by a decrease in genetic diversity. Estimates of effective population size (N _e) calculated by three temporal methods were consistently low in Iberian populations, ranging from 12 to 31 individuals per generation considering migration, and from 38 to 175 individuals per generation if they were regarded as closed populations. Corresponding N _e/N ratios varied from 0.02 to 0.04 assuming migration (mean=0.03) and from 0.04 to 0.18 (mean=0.10) assuming closed populations. Population bottlenecks, inferred from the excess of heterozygosity in relation to allelic diversity, were detected in all four Iberian populations, particularly in those year classes derived from a smaller number of returning adults. However, despite their small size and declining status, Iberian populations continue to display relatively high levels of heterozygosity and allelic richness, similar to those found in larger Scottish populations. Furthermore, in the R. Asón no evidence was found for a historical loss of genetic diversity despite a marked decline in abundance during the last five decades. Thus, our results point to two familiar paradigms in salmonid conservation: (1)␣endangered populations can maintain relatively high levels of genetic variation despite their small size, and (2) marked population declines may not necessarily result in a significant loss of genetic diversity. Although there are several explanations for such results, microsatellite data and physical tagging suggest that high levels of dispersal and asymmetric gene flow have probably helped to maintain genetic diversity in these peripheral populations, and thus to avoid the negative consequences of inbreeding.     

Effective population size does not predict codon usage bias in mammals

Synonymous codons are not used at equal frequency throughout the genome, a phenomenon termed codon usage bias (CUB). It is often assumed that interspecific variation in the intensity of CUB is related to species differences in effective population sizes (N_e), with selection on CUB operating less efficiently in species with small N_e. Here, we specifically ask whether variation in N_e predicts differences in CUB in mammals and report two main findings. First, across 41 mammalian genomes, CUB was not correlated with two indirect proxies of N_e (body mass and generation time), even though there was statistically significant evidence of selection shaping CUB across all species. Interestingly, autosomal genes showed higher codon usage bias compared to X‐linked genes, and high‐recombination genes showed higher codon usage bias compared to low recombination genes, suggesting intraspecific variation in N_e predicts variation in CUB. Second, across six mammalian species with genetic estimates of N_e (human, chimpanzee, rabbit, and three mouse species: Mus musculus, M. domesticus, and M. castaneus), N_e and CUB were weakly and inconsistently correlated. At least in mammals, interspecific divergence in N_e does not strongly predict variation in CUB. One hypothesis is that each species responds to a unique distribution of selection coefficients, confounding any straightforward link between N_e and CUB.     

Simple method for calculating confidence limits around inbreeding rate and effective population size estimates from pedigrees

An important concept in population genetics is effective population size (N_e), which describes the expected rate of loss of genetic variability from a population. One way to estimate N_e is using a pedigree. However, there are no methods for comparing the N_e estimated from a pedigree with that expected from life-history models. In the paper we show how N_e can be estimated from the change in inbreeding rate (f) estimated from a pedigree. The mean individual inbreeding rate in a population at a given time must be calculated from averaged values for males and females, where each age class is weighted by its reproductive value. We show an exact method for placing confidence intervals around f and N_e using a binomial distribution, and present a method for approximating this interval for large N_es using a Poisson distribution. These confidence intervals can be used to compare f and N_e from a pedigree to expected values from demographic models, and to compare N_es of two populations.     

Temporal genetic variation of mitochondrial DNA and the female effective population size of red drum (Sciaenops ocellatus) in the northern Gulf of Mexico

We studied genetic drift of mitochondrial DNA (mtDNA) haplotype frequencies in a natural population of red drum (Sciaenops ocellatus) from the northern Gulf of Mexico (Gulf). The amount of genetic drift observed across temporally adjacent year classes (1986–89) was used to estimate variance effective (female) population size (N_ef). N_ef was estimated to be 14 308 and the ratio of female effective size to adult female census size was approximately 0.004, which is among the lowest value reported for vertebrate animals. Low effective size relative to census size among red drum in the northern Gulf may result from yearly fluctuations in the number of breeding females, high variance in female reproductive success, or both. Despite low genetic effective size relative to census size, the genetic effective population size of red drum in the northern Gulf appears sufficiently large to preclude potentially deleterious effects of inbreeding.     

An empirical test of the estimation of historical effective population size using Drosophila melanogaster

The availability of a large number of high-density markers (SNPs) allows the estimation of historical effective population size (N_e) from linkage disequilibrium between loci. A recent refinement of methods to estimate historical N_e from the recent past has been shown to be rather accurate with simulation data. The method has also been applied to real data for numerous species. However, the simulation data cannot encompass all the complexities of real genomes, and the performance of any estimation method with real data is always uncertain, as the true demography of the populations is not known. Here, we carried out an experimental design with Drosophila melanogaster to test the method with real data following a known demographic history. We used a population maintained in the laboratory with a constant census size of about 2800 individuals and subjected the population to a drastic decline to a size of 100 individuals. After a few generations, the population was expanded back to the previous size and after a few further generations again expanded to twice the initial size. Estimates of historical N_e were obtained with the software GONE both for autosomal and X chromosomes from samples of 17 individuals sequenced for the whole genome. Estimates of the historical effective size were able to infer the patterns of changes that occurred in the populations showing generally good performance of the method. We discuss the limitations of the method and the application of the software carried out so far.     

Impact of precocious male parr on the effective size of a wild population of Atlantic salmon

1. There is growing evidence that sexually mature but morphologically juvenile males of Atlantic salmon (precocious or mature male parr) actively participate in reproduction and, therefore, in the genetic composition of the populations of this species. The impact of mature male parr on the effective population size (N_e) of such populations has been previously studied under experimental settings, but no studies have been performed directly on natural populations. 2. Continuous monitoring and sampling of all sea returns is possible in the Lérez River (northwest of Spain). From demographic data on variances of reproductive success and genetic data from six microsatellite marker loci we carried out parentage assignment and assessed the impact of male parr on demographic and genetic estimates of N_e in two consecutive years. 3. Our results reveal that: (i) approximately 60% of the total sire paternity is attributable to mature parr; (ii) mature parr decrease the variance of reproductive success of males by a threefold factor and increase the effective population size of males by a 10‐fold factor; (iii) however, they do not substantially affect the variance of reproductive success and the effective size of females; (iv) mature parr increase two‐to threefold the overall effective size of the population but the ratio N_e/N, where N is the population size including or not mature parr in each case, is not affected.