Genetic estimates of contemporary effective population size: what can they tell us about the importance of genetic stochasticity for wild population persistence?

Genetic stochasticity due to small population size contributes to population extinction, especially when population fragmentation disrupts gene flow. Estimates of effective population size ( N _e) can therefore be informative about population persistence, but there is a need for an assessment of their consistency and informative relevance. Here we review the body of empirical estimates of N _e for wild populations obtained with the temporal genetic method and published since Frankham's (1995 ) review. Theoretical considerations have identified important sources of bias for this analytical approach, and we use empirical data to investigate the extent of these biases. We find that particularly model selection and sampling require more attention in future studies.
We report a median unbiased N _e estimate of 260 (among 83 studies) and find that this median estimate tends to be smaller for populations of conservation concern, which may therefore be more sensitive to genetic stochasticity. Furthermore, we report a median N _e/ N ratio of 0.14, and find that this ratio may actually be higher for small populations, suggesting changes in biological interactions at low population abundances. We confirm the role of gene flow in countering genetic stochasticity by finding that N _e correlates strongest with neutral genetic metrics when populations can be considered isolated. This underlines the importance of gene flow for the estimation of N _e, and of population connectivity for conservation in general. Reductions in contemporary gene flow due to ongoing habitat fragmentation will likely increase the prevalence of genetic stochasticity, which should therefore remain a focal point in the conservation of biodiversity.     

Short-term genetic changes: evaluating effective population size estimates in a comprehensively described brown trout (Salmo trutta) population

The effective population size (N(e)) is notoriously difficult to accurately estimate in wild populations as it is influenced by a number of parameters that are difficult to delineate in natural systems. The different methods that are used to estimate N(e) are affected variously by different processes at the population level, such as the life-history characteristics of the organism, gene flow, and population substructure, as well as by the frequency patterns of genetic markers used and the sampling design. Here, we compare N(e) estimates obtained by different genetic methods and from demographic data and elucidate how the estimates are affected by various factors in an exhaustively sampled and comprehensively described natural brown trout (Salmo trutta) system. In general, the methods yielded rather congruent estimates, and we ascribe that to the adequate genotyping and exhaustive sampling. Effects of violating the assumptions of the different methods were nevertheless apparent. In accordance with theoretical studies, skewed allele frequencies would underestimate temporal allele frequency changes and thereby upwardly bias N(e) if not accounted for. Overlapping generations and iteroparity would also upwardly bias N(e) when applied to temporal samples taken over short time spans. Gene flow from a genetically not very dissimilar source population decreases temporal allele frequency changes and thereby acts to increase estimates of N(e). Our study reiterates the importance of adequate sampling, quantification of life-history parameters and gene flow, and incorporating these data into the N(e) estimation.     

Temporal estimates of effective population size in species with overlapping generations

The standard temporal method for estimating effective population size (N(e)) assumes that generations are discrete, but it is routinely applied to species with overlapping generations. We evaluated bias in the estimates N(e) caused by violation of this assumption, using simulated data for three model species: humans (type I survival), sparrow (type II), and barnacle (type III). We verify a previous proposal by Felsenstein that weighting individuals by reproductive value is the correct way to calculate parametric population allele frequencies, in which case the rate of change in age-structured populations conforms to that predicted by discrete-generation models. When the standard temporal method is applied to age-structured species, typical sampling regimes (sampling only newborns or adults; randomly sampling the entire population) do not yield properly weighted allele frequencies and result in biased N(e). The direction and magnitude of the bias are shown to depend on the sampling method and the species' life history. Results for populations that grow (or decline) at a constant rate paralleled those for populations of constant size. If sufficient demographic data are available and certain sampling restrictions are met, the Jorde-Ryman modification of the temporal method can be applied to any species with overlapping generations. Alternatively, spacing the temporal samples many generations apart maximizes the drift signal compared to sampling biases associated with age structure.     

Estimating genetic drift and effective population size from temporal shifts in dominant gene marker frequencies

Measurement of temporal change in allele frequencies represents an indirect method for estimating the genetically effective size of populations. When allele frequencies are estimated for gene markers that display dominant gene expression, such as, e.g. random amplified polymorphic DNA (RAPD) and amplified fragment length polymorphism (AFLP) markers, the estimates can be seriously biased. We quantify bias for previous allele frequency estimators and present a new expression that is generally less biased and provides a more precise assessment of temporal allele frequency change. We further develop an estimator for effective population size that is appropriate when dealing with dominant gene markers. Comparison with estimates based on codominantly expressed genes, such as allozymes or microsatellites, indicates that about twice as many loci or sampled individuals are required when using dominant markers to achieve the same precision.     

Empirical Bayes procedure for estimating genetic distance between populations and effective population size

We developed an empirical Bayes procedure to estimate genetic distances between populations using allele frequencies. This procedure makes it possible to describe the skewness of the genetic distance while taking full account of the uncertainty of the sample allele frequencies. Dirichlet priors of the allele frequencies are specified, and the posterior distributions of the various composite parameters are obtained by Monte Carlo simulation. To avoid overdependence on subjective priors, we adopt a hierarchical model and estimate hyperparameters by maximizing the joint marginal-likelihood function. Taking advantage of the empirical Bayesian procedure, we extend the method to estimate the effective population size using temporal changes in allele frequencies. The method is applied to data sets on red sea bream, herring, northern pike, and ayu broodstock. It is shown that overdispersion overestimates the genetic distance and underestimates the effective population size, if it is not taken into account during the analysis. The joint marginal-likelihood function also estimates the rate of gene flow into island populations.     

Unbiased estimator for genetic drift and effective population size

Amounts of genetic drift and the effective size of populations can be estimated from observed temporal shifts in sample allele frequencies. Bias in this so-called temporal method has been noted in cases of small sample sizes and when allele frequencies are highly skewed. We characterize bias in commonly applied estimators under different sampling plans and propose an alternative estimator for genetic drift and effective size that weights alleles differently. Numerical evaluations of exact probability distributions and computer simulations verify that this new estimator yields unbiased estimates also when based on a modest number of alleles and loci. At the cost of a larger standard deviation, it thus eliminates the bias associated with earlier estimators. The new estimator should be particularly useful for microsatellite loci and panels of SNPs, representing a large number of alleles, many of which will occur at low frequencies.     

Scaling Occupancy Estimates up to Abundance for Wolves

Management of wildlife populations often requires reliable estimates of population size or distribution. Estimating abundance can be logistically difficult, and occupancy models have been used as a less expensive proxy for abundance estimation. Another alternative is to use independent estimates of home-range size and mean group size to directly scale occupancy estimates up to abundance. We used simulations to explore when scaling occupancy up to abundance is reliable, and as an example we applied an occupancy approach to estimate abundance of wolves (Canis lupus) from roadside snow-tracking surveys in northern Wisconsin, USA, in 2016 and 2018. Estimates of wolf abundance were plausible and compared favorably with independent estimates produced by territory mapping, and snow-tracking data requirements were lower than for territory mapping. Simulation results suggested that reasonable abundance estimates could be obtained under some conditions but also that severe positive bias could result under other conditions, especially when populations were small and dispersed, home range size was small, and areal sampling units were large. Positive bias in abundance estimates occurs because of closure assumption violations when tracks from a single wolf or pack are detected in >1 sample unit, and the sum of the sample unit areas where tracks were detected exceed the sum of the home range areas. Bias was minimized when sampling units were small relative to home range size or when sampling units were route segments that approximate point sample units, and when home ranges were highly aggregated. We conclude that, although caution is warranted when scaling occupancy estimates up to abundance, scaled occupancy models can provide feasible and reliable estimates of abundance, assuming home range size and mean group size are accurately known or estimated, sampling units are appropriately chosen, and covariates that aggregate home ranges can be used to accurately predict occupancy probability. © 2021 The Authors. The Journal of Wildlife Management published by Wiley Periodicals LLC on behalf of The Wildlife Society.     

Monitoring temporal trends in spatially structured populations: how should sampling effort be allocated between space and time?

Estimating temporal trends in spatially structured populations has a critical role to play in understanding regional changes in biological populations and developing management strategies. Designing effective monitoring programmes to estimate these trends requires important decisions to be made about how to allocate sampling effort among spatial replicates (i.e. number of sites) and temporal replicates (i.e. how often to survey) to minimise uncertainty in trend estimates. In particular, the optimal mix of spatial and temporal replicates is likely to depend upon the spatial and temporal correlations in population dynamics. Although there has been considerable interest in the ecological literature on understanding spatial and temporal correlations in species’ population dynamics, little attention has been paid to its consequences for monitoring design. We address this issue using model‐based survey design to identify the optimal allocation of sampling effort among spatial and temporal replicates for estimating population trends under different levels of spatial and temporal correlation. Based on linear trends, we show that how we should allocate sampling effort among spatial and temporal replicates depends crucially on the spatial and temporal correlations in population dynamics, environmental variation, observation error and the spatial variation in temporal trends. When spatial correlation is low and temporal correlation is high, the best option is likely to be to sample many sites infrequently, particularly when observation error and/or spatial variation in temporal trends are high. When spatial correlation is high and temporal correlation is low, the best option is likely to be to sample few sites frequently, particularly when observation error and/or spatial variation in temporal trends are low. When abundances are spatially independent, it is always preferable to maximise spatial replication. This provides important insights into how spatio‐temporal monitoring programmes should be designed to estimate temporal trends in spatially structured populations.     

Reconstructing recent divergence: evaluating nonequilibrium population structure in New Zealand chinook salmon

Newly established or perturbed populations are often the focus of conservation concerns but they pose special challenges for population genetics because drift?migration equilibrium is unlikely. To advance our understanding of the evolution of such populations, we investigated structure and gene flow among populations of chinook salmon that formed via natural straying following introduction to New Zealand in the early 1900s. We examined 11 microsatellite loci from samples collected in several sites and years to address two questions: (i) what population differentiation has arisen in the ≈ 30 generations since salmon were introduced to New Zealand, relative to temporal variation within populations; and (ii) what are the approximate effective population sizes and amounts of gene flow in these populations? These questions are routinely addressed in studies of indigenous populations, but less often in the case of new populations and rarely with consideration of equilibrium assumptions. We show that despite the recent introduction, continued gene flow and high temporal variability among samples, detectable population structure has arisen among the New Zealand populations, consistent with their colonization pattern and isolation by geographical distance. Furthermore, we use simple individual‐based simulations and estimates of effective population sizes to estimate the effective gene flow among drainages under likely nonequilibrium conditions. Similar methodology may be broadly applicable to other studies of population structure and phenotypic evolution under similar nonequilibrium, high gene flow conditions.     

Using maximum likelihood to estimate population size from temporal changes in allele frequencies.

We develop a maximum-likelihood framework for using temporal changes in allele frequencies to estimate the number of breeding individuals in a population. We use simulations to compare the performance of this estimator to an F-statistic estimator of variance effective population size. The maximum-likelihood estimator had a lower variance and smaller bias. Taking advantage of the likelihood framework, we extend the model to include exponential growth and show that temporal allele frequency data from three or more sampling events can be used to test for population growth.     

Maximum likelihood estimation of population growth rates based on the coalescent.

We describe a method for co-estimating 4Nemu (four times the product of effective population size and neutral mutation rate) and population growth rate from sequence samples using Metropolis-Hastings sampling. Population growth (or decline) is assumed to be exponential. The estimates of growth rate are biased upwards, especially when 4Nemu is low; there is also a slight upwards bias in the estimate of 4Nemu itself due to correlation between the parameters. This bias cannot be attributed solely to Metropolis-Hastings sampling but appears to be an inherent property of the estimator and is expected to appear in any approach which estimates growth rate from genealogy structure. Sampling additional unlinked loci is much more effective in reducing the bias than increasing the number or length of sequences from the same locus.     

A potential bias in the temporal method for estimating Ne in admixed populations under natural selection

Indirect genetic methods are frequently used to estimate the effective population size (N(e)) or effective number of breeders (N(b)) in natural populations. Although assumptions behind these methods are often violated, there have been few attempts to evaluate how accurate these estimates really are in practice. Here we investigate the influence of natural selection following a population admixture on the temporal method for estimating N(e). Our analytical and simulation results suggest that N(e) is often underestimated in this method when subpopulations differ substantially in allele frequencies and in reproductive success. The underestimation is exacerbated when true N(e) and the fraction of the low-fitness group are large. As an empirical example, we compared N(b) estimated in natural populations of steelhead trout (Oncorhynchus mykiss) using the temporal method (N(b[temp])) with estimates based on direct demographic methods (N(b[demo])) and the linkage disequilibrium method (N(b[LD])). While N(b[LD]) was generally in close agreement with N(b[demo]), N(b[temp]) was much lower in sample sets that were dominated by nonlocal hatchery fish with low reproductive success, as predicted by the analytical results. This bias in the temporal method, which arises when genes associated with a particular group of parents are selected against in the offspring sample, has not been widely appreciated before. Such situations may be particularly common when artificial propagation or translocations are used for conservation. The linkage disequilibrium method, which requires data from only one sample, is robust to this type of bias, although it can be affected by other factors.     

Consequences of unequal population size, asymmetric gene flow and sex-biased dispersal on population structure in brook charr (Salvelinus fontinalis)

Unravelling relationships between dispersal and population structure requires considering the impacts of assumption violations of indirect gene flow models in a given system. We combined temporal, individual and coalescent-based analyses of microsatellite DNA variation to explore the general hypothesis that unequal effective population size (Ne), asymmetric gene flow (m) and nonrandom (sex-biased) individual dispersal had an important effect on spatiotemporal population structuring in lake-dwelling brook charr (Salvelinus fontinalis). This integrative examination shed light on the dichotomous structuring observed between an outlet and three tributary-spawning populations and their potential for adaptive divergence. It revealed further that finer tributary population structuring incongruent with drainage structure has been shaped by asymmetric m from one population with a large Ne towards two populations of smaller Ne. Gene flow among the tributaries was also mediated mainly by male-biased dispersal. However, longer distance dispersal from tributaries to the outflow was female-biased. Spatially dependent sex-biased dispersal may have contributed therefore to gene flow at different levels of population structuring. Our results demonstrate how dispersal and population structure may interrelate to produce spatial variation in intraspecific diversity, and are therefore relevant for conservation programmes seeking to define conservation units or predict recolonization rates of extirpated populations.     

Effective population size of natural populations of Drosophila buzzatii, with a comparative evaluation of nine methods of estimation

Allozyme and microsatellite data from numerous populations of Drosophila buzzatii have been used (i) to determine to what degree N(e) varies among generations within populations, and among populations, and (ii) to evaluate the congruence of four temporal and five single-sample estimators of N(e) . Effective size of different populations varied over two orders of magnitude, most populations are not temporally stable in genetic composition, and N(e) showed large variation over generations in some populations. Short-term N(e) estimates from the temporal methods were highly correlated, but the smallest estimates were the most precise for all four methods, and the most consistent across methods. Except for one population, N(e) estimates were lower when assuming gene flow than when assuming populations that were closed. However, attempts to jointly estimate N(e) and immigration rate were of little value because the source of migrants was unknown. Correlations among the estimates from the single-sample methods generally were not significant although, as for the temporal methods, estimates were most consistent when they were small. These single-sample estimates of current N(e) are generally smaller than the short-term temporal estimates. Nevertheless, population genetic variation is not being depleted, presumably because of past or ongoing migration. A clearer picture of current and short-term effective population sizes will only follow with better knowledge of migration rates between populations. Different methods are not necessarily estimating the same N(e) , they are subject to different bias, and the biology, demography and history of the population(s) may affect different estimators differently.     

Effective population size estimation on Sardina pilchardus in the Bay of Biscay using a temporal genetic approach

Over three consecutive years, we surveyed the temporal variability in genetic structure of sardine populations in the Bay of Biscay and effective population size. Based on individual age, the genetic structure of year classes of the fishes was also surveyed, showing that populations of sardines have weak but significant genetic differences between sampling years and between year classes. We used two different methods to assess effective population size. The methods resulted in different values but a similar range, indicating a low effective population for Sardina pilchardus . Effective population size decreased over the 3 years, probably resulting from an abundance of fish in the Bay. Based on these results, we conclude that temporal variability in the genetic structure of the sardine population and effective size are likely related to environmental conditions in the Bay. Finally, we propose to use effective population size to estimate biomass of sardines in the Bay.  © 2007 The Linnean Society of London, Biological Journal of the Linnean Society , 2007, 90 , 591–602.     

Genetic monitoring reveals temporal stability over 30 years in a small, lake-resident brown trout population

Knowledge of the degree of temporal stability of population genetic structure and composition is important for understanding microevolutionary processes and addressing issues of human impact of natural populations. We know little about how representative single samples in time are to reflect population genetic constitution, and we explore the temporal genetic variability patterns over a 30-year period of annual sampling of a lake-resident brown trout (Salmo trutta) population, covering 37 consecutive cohorts and five generations. Levels of variation remain largely stable over this period, with no indication of substructuring within the lake. We detect genetic drift, however, and the genetically effective population size (N(e)) was assessed from allele-frequency shifts between consecutive cohorts using an unbiased estimator that accounts for the effect of overlapping generation. The overall mean N(e) is estimated as 74. We find indications that N(e) varies over time, but there is no obvious temporal trend. We also estimated N(e) using a one-sample approach based on linkage disequilibrium (LD) that does not account for the effect of overlapping generations. Combining one-sample estimates for all years gives an N(e) estimate of 76. This similarity between estimates may be coincidental or reflecting a general robustness of the LD approach to violations of the discrete generations assumption. In contrast to the observed genetic stability, body size and catch per effort have increased over the study period. Estimates of annual effective number of breeders (N(b)) correlated with catch per effort, suggesting that genetic monitoring can be used for detecting fluctuations in abundance.     

Temporal change in genetic structure and effective population size in steelhead trout (Oncorhynchus mykiss)

There is a wealth of published molecular population genetic studies, however, most do not include historic samples and thus implicitly assume temporal genetic stability. We tested for changes in genetic diversity and structure in three populations of steelhead trout (Oncorhynchus mykiss) from a northern British Columbia watershed using seven microsatellite loci over 40 years. We found little change in genetic diversity (mean allele numbers and observed and expected heterozygosity), despite large variation in the estimated numbers of steelhead returning to the watershed over the same time period. However, the temporal stability in genetic diversity is not reflected in population structure, which appears to be high among populations, yet significantly variable over time. The neighbour-joining tree showed that, overall, two of the populations (Zymoetz and Kispiox) clustered separately from the third (Babine); a finding which was not consistent with their geographical separation. The clustering pattern was also not temporally consistent. We used the temporal method to estimate the effective number of breeders (Nb ) for the three populations; our values (Nb = 17-102) were low for the large and presumed vigorous populations of steelhead trout sampled. The low Nb values were also not consistent with the generally high genetic diversity estimates, suggesting the possibility of intermittent gene flow among the three populations. The use of temporal analyses in population genetic samples should be a priority; first, to verify observed patterns in contemporary data, and second, to build a dataset of temporal analyses to allow generalizations to be made concerning temporal genetic stability and effective population size in natural populations.     

Measuring Gene Flow among Populations Having High Levels of Genetic Fragmentation

We present an analysis of the genetic structures of 22 species of salamanders, with regard to levels of gene flow among populations. We estimate the gene flow parameter, Nm (the product of the effective population number and rate of migration among populations) using two alternative methods described by Wright and Slatkin. For most species, these two methods give approximately congruent estimates of Nm; when estimates differ, the method of Wright produces values slightly larger than those derived by the method of Slatkin. We analyze these results in light of independently derived historical inferences of the fragmentation of populations. This analysis suggests that the Nm values calculated from protein polymorphisms may contain information more relevant to historical patterns of gene exchange than to the current population dynamics; moderately large values of Nm may be calculated for species containing populations known to be no longer exchanging genes. Application of a method for estimating the maximum possible rate of gene exchange among populations indicates that, for most species studied here, gene flow among populations probably is no greater than the mutation rate. We suggest that most plethodontid species cannot be viewed as units whose cohesion is maintained by continuing gene exchange. Furthermore, we suggest that phenotypic uniformity among populations is not easily explained by hypotheses of continual stabilizing selection and propose that future work concentrate upon clarification of the genetic and epigenetic factors conferring self-maintenance or autopoietic properties on living systems.     

Variance of Stratified Survey Estimators With Probability of Detection Adjustments

Abstract: Estimates of wildlife population sizes are frequently constructed by combining counts of observed animals from a stratified survey of aerial sampling units with an estimated probability of detecting animals. Unlike traditional stratified survey designs, stratum-specific estimates of population size will be correlated if a common detection model is used to adjust counts for undetected animals in all strata. We illustrate this concept in the context of aerial surveys, considering 2 cases: 1) a single-detection parameter is estimated under the assumption of constant detection probabilities, and 2) a logistic-regression model is used to estimate heterogeneous detection probabilities. Naïve estimates of variance formed by summing stratum-specific estimates of variance may result in significant bias, particularly if there are a large number of strata, if detection probabilities are small, or if estimates of detection probabilities are imprecise. (JOURNAL OF WILDLIFE MANAGEMENT 72(3):837–844; 2008)     

Additional Circular Systematic Sampling Methods

Several systematic sampling methods have been used to estimate the population mean when size of the population is a multiple of sample size. Among these, only few methods have been extended and used to estimate mean of the population when its size is not a multiple of sample size. In this paper, new methods called balanced circular systematic sampling and centered circular systematic sampling are introduced by extending balanced systematic sampling method and centered systematic sampling method respectively. These methods are compared with circular systematic sampling using average variance of corrected sample means for populations exhibiting approximate linear and parabolic trends. The suggested methods are found suitable to estimate the population mean.