When are genetic methods useful for estimating contemporary abundance and detecting population trends?

The utility of microsatellite markers for inferring population size and trend has not been rigorously examined, even though these markers are commonly used to monitor the demography of natural populations. We assessed the ability of a linkage disequilibrium estimator of effective population size (N_e) and a simple capture-recapture estimator of abundance (N) to quantify the size and trend of stable or declining populations (true N = 100–10,000), using simulated Wright–Fisher populations. Neither method accurately or precisely estimated abundance at sample sizes of S = 30 individuals, regardless of true N. However, if larger samples of S = 60 or 120 individuals were collected, these methods provided useful insights into abundance and trends for populations of N = 100–500. At small population sizes (N = 100 or 250), precision of the N_e estimates was improved slightly more by a doubling of loci sampled than by a doubling of individuals sampled. In general, monitoring N_e proved a more robust means of identifying stable and declining populations than monitoring N over most of the parameter space we explored, and performance of the N_e estimator is further enhanced if the N_e/N ratio is low. However, at the largest population size (N = 10,000), N estimation outperformed N_e. Both methods generally required ≥ 5 generations to pass between sampling events to correctly identify population trend.     

Early detection of population fragmentation using linkage disequilibrium estimation of effective population size

Population subdivision due to habitat loss and modification, exploitation of wild populations and altered spatial population dynamics is of increasing concern in nature. Detecting population fragmentation is therefore crucial for conservation management. Using computer simulations, we show that a single sample estimator of N _e based on linkage disequilibrium is a highly sensitive and promising indicator of recent population fragmentation and bottlenecks, even with some continued gene flow. For example, fragmentation of a panmictic population of N _e = 1,000 into demes of N _e = 100 can be detected with high probability after a single generation when estimates from this method are compared to prefragmentation estimates, given data for ~20 microsatellite loci in samples of 50 individuals. We consider a range of loci (10–40) and individuals (25–100) typical of current studies of natural populations and show that increasing the number of loci gives nearly the same increase in precision as increasing the number of individuals sampled. We also evaluated effects of incomplete fragmentation and found this N _e-reduction signal is still apparent in the presence of considerable migration (m ~ 0.10–0.25). Single-sample genetic estimates of N _e thus show considerable promise for early detection of population fragmentation and decline.     

A comparison of single‐sample estimators of effective population sizes from genetic marker data

In molecular ecology and conservation genetics studies, the important parameter of effective population size (N_e) is increasingly estimated from a single sample of individuals taken at random from a population and genotyped at a number of marker loci. Several estimators are developed, based on the information of linkage disequilibrium (LD), heterozygote excess (HE), molecular coancestry (MC) and sibship frequency (SF) in marker data. The most popular is the LD estimator, because it is more accurate than HE and MC estimators and is simpler to calculate than SF estimator. However, little is known about the accuracy of LD estimator relative to that of SF and about the robustness of all single‐sample estimators when some simplifying assumptions (e.g. random mating, no linkage, no genotyping errors) are violated. This study fills the gaps and uses extensive simulations to compare the biases and accuracies of the four estimators for different population properties (e.g. bottlenecks, nonrandom mating, haplodiploid), marker properties (e.g. linkage, polymorphisms) and sample properties (e.g. numbers of individuals and markers) and to compare the robustness of the four estimators when marker data are imperfect (with allelic dropouts). Extensive simulations show that SF estimator is more accurate, has a much wider application scope (e.g. suitable to nonrandom mating such as selfing, haplodiploid species, dominant markers) and is more robust (e.g. to the presence of linkage and genotyping errors of markers) than the other estimators. An empirical data set from a Yellowstone grizzly bear population was analysed to demonstrate the use of the SF estimator in practice.     

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.     

A comparison of single‐sample effective size estimators using empirical toad (Bufo calamita) population data: genetic compensation and population size‐genetic diversity correlations

The accuracy and precision of four single‐sample estimators of effective population size, N_e (heterozygote excess, linkage disequilibrium, Bayesian partial likelihood and sibship analysis) were compared using empirical data (microsatellite genotypes) from multiple natterjack toad (Bufo calamita) populations in Britain (n = 16) and elsewhere in Europe (n = 10). Census size data were available for the British populations. Because toads have overlapping generations, all of these methods estimated the number of effective breeders N_b rather than N_e. The heterozygote excess method only provided results, without confidence limits, for nine of the British populations. Linkage disequilibrium gave estimates for 10 British populations, but only six had finite confidence limits. The Bayesian and sibship methods both produced estimates with finite confidence limits for all the populations. Although the Bayesian method was the most precise, on most criteria (insensitivity to locus number, correlation with other effective and census size estimates and correlation with genetic diversity) the sibship method performed best. The results also provided evidence of genetic compensation in natterjack toads, and highlighted how the relationship between effective size and genetic diversity can vary as a function of geographical scale.     

Effect of Mating Structure on Variation in Linkage Disequilibrium

Measurement of linkage disequilibrium involves two sampling processes. First, there is the sampling of gametes in the population to form successive generations, and this generates disequilibrium dependent on the effective population size (N_e) and the mating structure. Second, there is sampling of a finite number (n) of individuals to estimate the population disequilibrium.——Two-locus descent measures are used to describe the mating system and are transformed to disequilibrium moments at the final sampling. Approximate eigenvectors for the transition matrix of descent measures are used to obtain formulae for the variance of the observed disequilibria as a function of N_e, mating structure, n, and linkage or recombination parameter.——The variance of disequilibrium is the same for monoecious populations with or without random selfing and for dioecious populations with random pairing for each progeny. With monogamy, the variance is slightly higher, the proportional difference being greater for unlinked loci.     

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.     

Making sense of genetic estimates of effective population size

The last decade has seen an explosion of interest in use of genetic markers to estimate effective population size, N_e. Effective population size is important both theoretically (N_e is a key parameter in almost every aspect of evolutionary biology) and for practical application (N_e determines rates of genetic drift and loss of genetic variability and modulates the effectiveness of selection, so it is crucial to consider in conservation). As documented by Palstra & Fraser ( 2012 ), most of the recent growth in N_e estimation can be attributed to development or refinement of methods that can use a single sample of individuals (the older temporal method requires at least two samples separated in time). As with other population genetic methods, performance of new N_e estimators is typically evaluated with simulated data for a few scenarios selected by the author(s). Inevitably, these initial evaluations fail to fully consider the consequences of violating simplifying assumptions, such as discrete generations, closed populations of constant size and selective neutrality. Subsequently, many researchers studying natural or captive populations have reported estimates of N_e for multiple methods; often these estimates are congruent, but that is not always the case. Because true N_e is rarely known in these empirical studies, it is difficult to make sense of the results when estimates differ substantially among methods. What is needed is a rigorous, comparative analysis under realistic scenarios for which true N_e is known. Recently, Gilbert & Whitlock ( 2015 ) did just that for both single‐sample and temporal methods under a wide range of migration schemes. In the current issue of Molecular Ecology, Wang ( 2016 ) uses simulations to evaluate performance of four single‐sample N_e estimators. In addition to assessing effects of true N_e, sample size, and number of loci, Wang also evaluated performance under changing abundance, physical linkage and genotyping errors, as well as for some alternative life histories (high rates of selfing; haplodiploids). Wang showed that the sibship frequency (SF) and linkage disequilibrium (LD) methods perform dramatically better than the heterozygote excess and molecular coancestry methods under most scenarios (see Fig. 1, modified from figure 2 in Wang 2016 ), and he also concluded that SF is generally more versatile than LD. This article represents a truly Herculean effort, and results should be of considerable value to researchers interested in applying these methods to real‐world situations.     

Genomic selection in forest tree breeding

Genomic selection (GS) involves selection decisions based on genomic breeding values estimated as the sum of the effects of genome-wide markers capturing most quantitative trait loci (QTL) for the target trait(s). GS is revolutionizing breeding practice in domestic animals. The same approach and concepts can be readily applied to forest tree breeding where long generation times and late expressing complex traits are also a challenge. GS in forest trees would have additional advantages: large training populations can be easily assembled and accurately phenotyped for several traits, and the extent of linkage disequilibrium (LD) can be high in elite populations with small effective population size (N _e) frequently used in advanced forest tree breeding programs. Deterministic equations were used to assess the impact of LD (modeled by N _e and intermarker distance), the size of the training set, trait heritability, and the number of QTL on the predicted accuracy of GS. Results indicate that GS has the potential to radically improve the efficiency of tree breeding. The benchmark accuracy of conventional BLUP selection is reached by GS even at a marker density ~2 markers/cM when N _e ≤ 30, while up to 20 markers/cM are necessary for larger N _e. Shortening the breeding cycle by 50% with GS provides an increase ≥100% in selection efficiency. With the rapid technological advances and declining costs of genotyping, our cautiously optimistic outlook is that GS has great potential to accelerate tree breeding. However, further simulation studies and proof-of-concept experiments of GS are needed before recommending it for operational implementation.     

Estimation of effective population size in continuously distributed populations: there goes the neighborhood

Use of genetic methods to estimate effective population size (N_e) is rapidly increasing, but all approaches make simplifying assumptions unlikely to be met in real populations. In particular, all assume a single, unstructured population, and none has been evaluated for use with continuously distributed species. We simulated continuous populations with local mating structure, as envisioned by Wright''s concept of neighborhood size (NS), and evaluated performance of a single-sample estimator based on linkage disequilibrium (LD), which provides an estimate of the effective number of parents that produced the sample (N_b). Results illustrate the interacting effects of two phenomena, drift and mixture, that contribute to LD. Samples from areas equal to or smaller than a breeding window produced estimates close to the NS. As the sampling window increased in size to encompass multiple genetic neighborhoods, mixture LD from a two-locus Wahlund effect overwhelmed the reduction in drift LD from incorporating offspring from more parents. As a consequence, never approached the global N_e, even when the geographic scale of sampling was large. Results indicate that caution is needed in applying standard methods for estimating effective size to continuously distributed populations.     

Expansion history and environmental suitability shape effective population size in a plant invasion

The margins of an expanding range are predicted to be challenging environments for adaptation. Marginal populations should often experience low effective population sizes (N_e) where genetic drift is high due to demographic expansion and/or census population size is low due to unfavourable environmental conditions. Nevertheless, invasive species demonstrate increasing evidence of rapid evolution and potential adaptation to novel environments encountered during colonization, calling into question whether significant reductions in N_e are realized during range expansions in nature. Here we report one of the first empirical tests of the joint effects of expansion dynamics and environment on effective population size variation during invasive range expansion. We estimate contemporary values of N_e using rates of linkage disequilibrium among genome‐wide markers within introduced populations of the highly invasive plant Centaurea solstitialis (yellow starthistle) in North America (California, USA), and within native Eurasian populations. As predicted, we find that N_e within the invaded range is positively correlated with both expansion history (time since founding) and habitat quality (abiotic climate). History and climate had independent additive effects with similar effect sizes, indicating an important role for both factors in this invasion. These results support theoretical expectations for the population genetics of range expansion, though whether these processes can ultimately arrest the spread of an invasive species remains an unanswered question.     

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.     

A bias correction for estimates of effective population size based on linkage disequilibrium at unlinked gene loci*

Analysis of linkage disequilibrium (=mean squared correlation of allele frequencies at different gene loci) provides a means of estimating effective population size (N _e) from a single sample, but this method has seen much less use than the temporal method (which requires at least two samples). It is shown that for realistic numbers of loci and alleles, the linkage disequilibrium method can provide precision comparable to that of the temporal method. However, computer simulations show that estimates of N _e based on for unlinked, diallelic gene loci are sharply biased downwards ( in some cases) if sample size (S) is less than true N _e. The bias is shown to arise from inaccuracies in published formula for when S and/or N _e are small. Empirically derived modifications to for two mating systems (random mating and lifetime monogamy) effectively eliminate the bias (residual bias in % in most cases). The modified method also performs well in estimating N _e in non-ideal populations with skewed sex ratio or non-random variance in reproductive success. Recent population declines are not likely to seriously affect , but if N has recently increased from a bottleneck can be biased downwards for a few generations. These results should facilitate application of the disequilibrium method for estimating contemporary N _e in natural populations. However, a comprehensive assessment of performance of with highly polymorphic markers such as microsatellites is needed.The US Governmentȁ9s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Breeding without breeding: minimum fingerprinting effort with respect to the effective population size

We present a probabilistic model to minimize the fingerprinting effort associated with the implementation of the “breeding without breeding” scheme under partial pedigree reconstruction. Our approach is directed at achieving a declared target population’s minimum effective population size (N _e ), following the pedigree reconstruction and genotypic selection and is based on the graph theory algorithm. The primary advantage of the proposed method is to reduce the cost associated with fingerprinting before the implementation of the pedigree reconstruction for seed parent–offspring derived from breeding arboreta and production or natural populations. Stochastic simulation was conducted to test the method’s efficiency assuming a simple polygenic model and a single trait. Hypothetical population consisted of 30 parental trees that were paired at random (selfing excluded), resulting in 600 individuals (potential candidates for forwards selection). The male parentage was assumed initially unknown. The model was used to estimate the minimum genotyping sample size needed to reaching the prescribed N _e . Results were compared with the known pedigree data. The model was successful in revealing the true relationship pattern over the whole range of N _e . Two to three offspring entered genotyping to meet the N _e  = 2 while 41 to 43 were required to satisfy the N _e  = 14. Importantly, genetic gain was affected at the lower limits of the genotyping effort. Doubling the number of parents resulted in considerable reduction of the genotyping effort at higher N _e values.     

Temporal genetic samples indicate small effective population size of the endangered yellow-eyed penguin

There is an increasing awareness that the long-term viability of endemic island populations is negatively affected by genetic factors associated with population bottlenecks and/or persistence at small population size. Here we use contemporary samples and historic museum specimens (collected 1888–1938) to estimate the effective population size (N _e) for the endangered yellow-eyed penguin (Megadyptes antipodes) in South Island, New Zealand, and evaluate the genetic concern for this iconic species. The South Island population of M. antipodes—constituting almost half of the species’ census size—is thought to be descended from a small number of founders that reached New Zealand just a few hundred years ago. Despite intensive conservation measures, this population has shown dramatic fluctuations in size over recent decades. We compare estimates of the harmonic mean N _e for this population, obtained using one moment and three likelihood based-temporal methods, including one method that simultaneously estimates migration rate. Evaluation of the N _e estimates reveals a harmonic mean N _e in the low hundreds. Additionally, the inferred low immigration rates (m = 0.003) agree well with contemporary migration rate estimates between the South Island and subantarctic populations of M. antipodes. The low N _e of South Island M. antipodes is likely affected by strong fluctuations in population size, and high variance in reproductive success. These results show that genetic concerns for this population are valid and that the long-term viability of this species may be compromised by reduced adaptive potential.     

Accounting for missing data in the estimation of contemporary genetic effective population size (Ne)

Theoretical models are often applied to population genetic data sets without fully considering the effect of missing data. Researchers can deal with missing data by removing individuals that have failed to yield genotypes and/or by removing loci that have failed to yield allelic determinations, but despite their best efforts, most data sets still contain some missing data. As a consequence, realized sample size differs among loci, and this poses a problem for unbiased methods that must explicitly account for random sampling error. One commonly used solution for the calculation of contemporary effective population size (N_e) is to calculate the effective sample size as an unweighted mean or harmonic mean across loci. This is not ideal because it fails to account for the fact that loci with different numbers of alleles have different information content. Here we consider this problem for genetic estimators of contemporary effective population size (N_e). To evaluate bias and precision of several statistical approaches for dealing with missing data, we simulated populations with known N_e and various degrees of missing data. Across all scenarios, one method of correcting for missing data (fixed‐inverse variance‐weighted harmonic mean) consistently performed the best for both single‐sample and two‐sample (temporal) methods of estimating N_e and outperformed some methods currently in widespread use. The approach adopted here may be a starting point to adjust other population genetics methods that include per‐locus sample size components.     

Linkage disequilibrium in a finite population that is partially selfing

The linkage disequilibrium expected in a finite, partially selfing population is analyzed, assuming the infinite allele model. Formulas for the expected sum of squares of the linkage disequilibria and the squared standard linkage disequilibrium are derived from the equilibrium values of sixteen inbreeding coefficients required to describe the behavior of the system. These formulas are identical to those obtained with random mating if the effective population size N_e = (1-½S)N and the effective recombination value r_e = (1-S)r/(1-½S), where S is the proportion of selfing, are substituted for the population size and the recombination value. Therefore, the effect of partial selfing at equilibrium is to reduce the population size by a factor 1-½S and the recombination value by a factor (1-S)/(1-½S).     

Interval Estimation of the Effective Population Size from Heterozygote‐Excess in SNP Markers

The effective population size N_e is an important parameter in population genetics and conservation biology. In recent years, there has been great interest in the use of molecular markers to estimate N_e. Although the point estimates from molecular markers in general suffer from a low reliability, the use of single nucleotide polymorphism (SNP) markers over a wide range of genome is expected to remarkably improve the reliability. In this study, expressions were derived for interval estimates of N_e from one published method, the heterozygote‐excess method, when it is applied to SNP markers. The conditional variance theory is applied to the derivation of a confidence interval for N_e under random union of gametes, monogamy and polygyny. Stochastic simulation shows that the obtained confidence interval is slightly conservative, but fairly useful for practical applications. The result is illustrated with real data on SNP markers in a pig strain.     

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.     

Linkage Disequilibrium Decay and Past Population History in the Human Genome

The fluctuation of population size has not been well studied in the previous studies of theoretical linkage disequilibrium (LD) expectation. In this study, an improved theoretical prediction of LD decay was derived to account for the effects of changes in effective population sizes. The equation was used to estimate effective population size (N_e) assuming a constant N_e and LD at equilibrium, and these N_e estimates implied the past changes of N_e for a certain number of generations until equilibrium, which differed based on recombination rate. As the influence of recent population history on the N_e estimates is larger than old population history, recent changes in population size can be inferred more accurately than old changes. The theoretical predictions based on this improved expression showed accurate agreement with the simulated values. When applied to human genome data, the detailed recent history of human populations was obtained. The inferred past population history of each population showed good correspondence with historical studies. Specifically, four populations (three African ancestries and one Mexican ancestry) showed population growth that was significantly less than that of other populations, and two populations originated from China showed prominent exponential growth. During the examination of overall LD decay in the human genome, a selection pressure on chromosome 14, the gephyrin gene, was observed in all populations.