Low-coverage sequencing and Wahlund effect severely bias estimates of inbreeding, heterozygosity and effective population size in North American wolves.

vonHoldt et al. ((2024), Molecular Ecology, 33, e17231) (vH24) used low-coverage (average ~ 7X read depth) restriction site-associated DNA sequence data to estimate individual inbreeding and heterozygosity, and recent effective population size (Ne), in Great Lakes (GL) and Northern Rocky Mountain (RM) wolves. They concluded that RM heterozygosity rapidly declined between 1991 and 2020, and that Ne declined substantially in GL and RM over the last 50 generations. Here, we evaluate the effects of low sequence coverage and sampling strategy on vH24's findings and provide general recommendations for using sequence data to evaluate inbreeding, heterozygosity and Ne. Low-coverage sequencing resulted in downwardly biased estimates of individual inbreeding and heterozygosity, and an erroneous large temporal decline in RM heterozygosity due to declining read depth through time. Additionally, vH24's sampling strategy-which combined individuals from several genetically differentiated populations and across at least eight wolf generations-is expected to have resulted in severe downward bias in estimates of recent Ne for RM. We recommend using high-coverage sequence data ( ≥ $$ \ge $$ 15-20X) to estimate inbreeding and heterozygosity. Carefully filtering individuals, loci and genotypes, and using genotype imputation or likelihoods can help to minimise bias when low-coverage sequence data must be used. For estimation of contemporary Ne, the marginal benefits of using more than 103-104 loci are small, so aggressive filtering of loci with low average read depth potentially can retain most individuals without sacrificing much precision. Individuals are relatively more valuable than loci because analyses of contemporary Ne should focus on roughly single-generation samples from local breeding populations.

Null Models for the Opportunity for Selection.

AbstractCrow's "opportunity for selection" (I=variance in relative fitness) is an important albeit controversial eco-evolutionary concept, particularly regarding the most appropriate null model(s). Here, we treat this topic in a comprehensive way by considering opportunities for both fertility selection (If) and viability selection (Im) for discrete generations, both seasonal and lifetime reproductive success in age-structured species, and experimental designs that include either a full or partial life cycle, with complete enumeration or random subsampling. For each scenario, a null model that includes random demographic stochasticity can be constructed that follows Crow's initial formulation that I=If+Im. The two components of I are qualitatively different. Whereas an adjusted If (ΔIf) can be computed that accounts for random demographic stochasticity in offspring number, Im cannot be similarly adjusted in the absence of data on phenotypic traits under viability selection. Including as potential parents some individuals that die before reproductive age produces an overall zero-inflated Poisson null model. It is always important to remember that (1) Crow's I represents only the opportunity for selection and not selection itself and (2) the species' biology can lead to random stochasticity in offspring number that is either overdispersed or underdispersed compared with the Poisson (Wright-Fisher) expectation.

Robustness of Hill's overlapping-generation method for calculating Ne to extreme patterns of reproductive success.

For species with overlapping generations, the most widely used method to calculate effective population size (Ne) is Hill's, the key parameter for which is lifetime variance in offspring number ([Formula: see text]). Hill's model assumes a stable age structure and constant abundance, and sensitivity to those assumptions has been evaluated previously. Here I evaluate the robustness of Hill's model to extreme patterns of reproductive success, whose effects have not been previously examined: (1) very strong reproductive skew; (2) strong temporal autocorrelations in individual reproductive success; and (3) strong covariance of individual reproduction and survival. Genetic drift (loss of heterozygosity and increase in allele frequency variance) was simulated in age-structured populations using methods that generated no autocorrelations or covariances (Model NoCor); or created strong positive (Model Positive) or strong negative (Model Negative) temporal autocorrelations in reproduction and covariances between reproduction and survival. Compared to Model NoCor, the other models led to greatly elevated or reduced [Formula: see text], and hence greatly reduced or elevated Ne, respectively. A new index is introduced (ρα,α+), which is the correlation between (1) the number of offspring produced by each individual at the age at maturity (α), and (2) the total number of offspring produced during the rest of their lifetimes. Mean ρα,α+ was ≈0 under Model NoCor, strongly positive under Model Positive, and strongly negative under Model Negative. Even under the most extreme reproductive scenarios in Models Positive and Negative, when [Formula: see text] was calculated from the realized population pedigree and used to calculate Ne in Hill's model, the result accurately predicted the rate of genetic drift in simulated populations. These results held for scenarios where age-specific reproductive skew was random (variance ≈ mean) and highly overdispersed (variance up to 20 times the mean). Collectively, these results are good news for researchers as they demonstrate the robustness of Hill's model even in extreme reproductive scenarios.

The opportunity for selection: A slippery concept in ecology and evolution.

Natural selection can only occur if individuals differ in fitness. For this reason, the variance in relative fitness has been equated with the 'opportunity for selection' ( I ), which has a long, albeit somewhat controversial, history. In this paper we discuss the use/misuse of I and related metrics in evolutionary ecology. The opportunity is only realised if some fraction of I is caused by trait variation. Thus, I > 0 does not imply that selection is occurring, as sometimes erroneously assumed, because all fitness variation could be independent of phenotype. The selection intensity on any given trait cannot exceed I , but this upper limit will never be reached because (a) stochastic factors always affect fitness, and (b) there might be multiple traits under selection. The expected magnitude of the stochastic component of I is negatively correlated with mean fitness. Uncertainty in realised I is also larger when mean fitness or population/sample size are low. Variation in I across time or space thus can be dominated (or solely driven) by variation in the strength of demographic stochasticity. We illustrate these points using simulations and empirical data from a population study on great tits Parus major. Our analysis shows that the scope for fecundity selection in the great tits is substantially higher when using annual number of recruits as the fitness measure, rather than fledglings or eggs, even after adjusting for the dependence of I on mean fitness. This suggests nonrandom survival of juveniles across families between life stages. Indeed, previous work on this population has shown that offspring recruitment is often nonrandom with respect to clutch size and laying date of parents, for example. We conclude that one cannot make direct inferences about selection based on fitness data alone. However, examining variation in ∆ I F (the opportunity for fecundity selection adjusted for mean fitness) across life stages, years or environments can offer clues as to when/where fecundity selection might be strongest, which can be useful for research planning and experimental design.

What Is Ne, Anyway?

Few doubt that effective population size (Ne) is one of the most important parameters in evolutionary biology, but how many can say they really understand the concept? Ne is the evolutionary analog of the number of individuals (or adults) in the population, N. Whereas ecological consequences of population size depend on N, evolutionary consequences (rates of loss of genetic diversity and increase in inbreeding; relative effectiveness of selection) depend on Ne. Formal definitions typically relate effective size to a key population genetic parameter, such as loss of heterozygosity or variance in allele frequency. However, for practical application to real populations, it is more useful to define Ne in terms of 3 demographic parameters: number of potential parents (adult N), and mean and variance in offspring number. Defined this way, Ne determines the rate of random genetic drift across the entire genome in the offspring generation. Other evolutionary forces (mutation, migration, selection)-together with factors such as variation in recombination rate-can also affect genetic variation, and this leads to heterogeneity across the genome in observed rates of genetic change. For some, it has been convenient to interpret this heterogeneity in terms of heterogeneity in Ne, but unfortunately, this has muddled the concepts of genetic drift and effective population size. A commonly repeated misconception is that Ne is the number of parents that actually contribute genes to the next generation (NP). In reality, NP can be smaller or larger than Ne, and the NP/Ne ratio depends on the sex ratio, the mean and variance in offspring number, and whether inbreeding or variance Ne is of interest.

Implications of Large-Effect Loci for Conservation: A Review and Case Study with Pacific Salmon.

The increasing feasibility of assembling large genomic datasets for non-model species presents both opportunities and challenges for applied conservation and management. A popular theme in recent studies is the search for large-effect loci that explain substantial portions of phenotypic variance for a key trait(s). If such loci can be linked to adaptations, 2 important questions arise: 1) Should information from these loci be used to reconfigure conservation units (CUs), even if this conflicts with overall patterns of genetic differentiation? 2) How should this information be used in viability assessments of populations and larger CUs? In this review, we address these questions in the context of recent studies of Chinook salmon and steelhead (anadromous form of rainbow trout) that show strong associations between adult migration timing and specific alleles in one small genomic region. Based on the polygenic paradigm (most traits are controlled by many genes of small effect) and genetic data available at the time showing that early-migrating populations are most closely related to nearby late-migrating populations, adult migration differences in Pacific salmon and steelhead were considered to reflect diversity within CUs rather than separate CUs. Recent data, however, suggest that specific alleles are required for early migration, and that these alleles are lost in populations where conditions do not support early-migrating phenotypes. Contrasting determinations under the US Endangered Species Act and the State of California's equivalent legislation illustrate the complexities of incorporating genomics data into CU configuration decisions. Regardless how CUs are defined, viability assessments should consider that 1) early-migrating phenotypes experience disproportionate risks across large geographic areas, so it becomes important to identify early-migrating populations that can serve as reliable sources for these valuable genetic resources; and 2) genetic architecture, especially the existence of large-effect loci, can affect evolutionary potential and adaptability.

Relative Precision of the Sibship and LD Methods for Estimating Effective Population Size With Genomics-Scale Datasets.

Computer simulations were used to compare relative precision of 2 widely used single-sample methods for estimating effective population size (Ne)-the sibship method and the linkage disequilibrium (LD) method. Emphasis is on performance when thousands of gene loci are used, which now can easily be achieved even for nonmodel species. Results show that unless Ne is very small, if at least 500-2000 diallelic loci are used, precision of the LD method is higher than the maximum possible precision for the sibship method, which occurs when all sibling relationships have been correctly identified. Results also show that when precision is high for both methods, their estimates of Ne are highly and positively correlated, which limits additional gains in precision that might be obtained by combining information from the 2 estimators.

Big Data in Conservation Genomics: Boosting Skills, Hedging Bets, and Staying Current in the Field.

A current challenge in the fields of evolutionary, ecological, and conservation genomics is balancing production of large-scale datasets with additional training often required to handle such datasets. Thus, there is an increasing need for conservation geneticists to continually learn and train to stay up-to-date through avenues such as symposia, meetings, and workshops. The ConGen meeting is a near-annual workshop that strives to guide participants in understanding population genetics principles, study design, data processing, analysis, interpretation, and applications to real-world conservation issues. Each year of ConGen gathers a diverse set of instructors, students, and resulting lectures, hands-on sessions, and discussions. Here, we summarize key lessons learned from the 2019 meeting and more recent updates to the field with a focus on big data in conservation genomics. First, we highlight classical and contemporary issues in study design that are especially relevant to working with big datasets, including the intricacies of data filtering. We next emphasize the importance of building analytical skills and simulating data, and how these skills have applications within and outside of conservation genetics careers. We also highlight recent technological advances and novel applications to conservation of wild populations. Finally, we provide data and recommendations to support ongoing efforts by ConGen organizers and instructors-and beyond-to increase participation of underrepresented minorities in conservation and eco-evolutionary sciences. The future success of conservation genetics requires both continual training in handling big data and a diverse group of people and approaches to tackle key issues, including the global biodiversity-loss crisis.

The evolution of microendemism in a reef fish (Hypoplectrus maya).

Marine species tend to have extensive distributions, which are commonly attributed to the dispersal potential provided by planktonic larvae and the rarity of absolute barriers to dispersal in the ocean. Under this paradigm, the occurrence of marine microendemism without geographic isolation in species with planktonic larvae poses a dilemma. The recently described Maya hamlet (Hypoplectrus maya, Serranidae) is exactly such a case, being endemic to a 50-km segment of the Mesoamerican Barrier Reef System (MBRS). We use whole-genome analysis to infer the demographic history of the Maya hamlet and contrast it with the sympatric and pan-Caribbean black (H. nigricans), barred (H. puella) and butter (H. unicolor) hamlets, as well as the allopatric but phenotypically similar blue hamlet (H. gemma). We show that H. maya is indeed a distinct evolutionary lineage, with genomic signatures of inbreeding and a unique demographic history of continuous decrease in effective population size since it diverged from congeners just ~3,000 generations ago. We suggest that this case of microendemism may be driven by the combination of a narrow ecological niche and restrictive oceanographic conditions in the southern MBRS, which is consistent with the occurrence of an unusually high number of marine microendemics in this region. The restricted distribution of the Maya hamlet, its decline in both census and effective population sizes, and the degradation of its habitat place it at risk of extinction. We conclude that the evolution of marine microendemism can be a fast and dynamic process, with extinction possibly occurring before speciation is complete.

Life history and temporal variability of escape events interactively determine the fitness consequences of aquaculture escapees on wild populations.

Domesticated individuals are likely to be maladaptive in the wild due to adaptation to captivity. Escaped aquaculture fish can cause unintended fitness and demographic consequences for their wild conspecifics through interbreeding and competition. Escape events from different sources exhibit great heterogeneity in their frequencies and magnitudes, ranging from rare but large spillover during a storm, to continuous low-level leakage caused by operational errors. The timescale of escape events determines the distribution of gene flow from aquaculture to the wild. The evolutionary consequences of this variation in timescale will depend on the degree of generation overlap and the focal species' life history attributes, especially those under selection in aquaculture (e.g., growth rate, which can influence additional demographically important traits such as age at maturity). To evaluate the effects of variable escape both within and across generations, we construct an age-structured model of coupled genetic and demographic dynamics and parameterize it for species with contrasting life history characteristics (Salmo salar and Gadus morhua). Our results are consistent with earlier discrete-generation models that constant, low-level spillover can have a greater impact than rare, large pulses of leakage, even after accounting for the averaging effects of overlapping generations. The age-structured model also allows detailed evaluation of the role of different life history traits, which reveals that species with longer generation times might experience greater fitness consequences of aquaculture spillover but are less sensitive to variability in spillover. Additionally, environment-induced earlier maturity of escapees can increase the fitness effects on wild fish, especially those with shorter generation times. Our results suggest that effective management to minimize the unintended fitness consequences of aquaculture releases might require extensive monitoring efforts on constant, low-level spillover and assessment of the focal species' life history characteristics.

Consequences of sex change for effective population size.

Sequential hermaphroditism, where males change to females (protandry) or the reverse (protogyny), is widespread in animals and plants, and can be an evolutionarily stable strategy (ESS) if fecundity rises faster with age in the second sex. Sequential hermaphrodites also generally have sex ratios skewed towards the initial sex, and standard theory based on fixed sexes indicates that this should reduce effective population size ( Ne) and increase the deleterious effects of genetic drift. We show that despite having skewed sex ratios, populations that change sex at the ESS age do not have reduced Ne compared with fixed-sex populations with an even sex ratio. This implies that the ability of individuals to operate as both male and female allows the population to avoid some evolutionary constraints imposed by fixed sexes. Furthermore, Ne would be maximized if sex change occurred at a different (generally earlier) age than is selected for at the individual level, which suggests a potential conflict between individual and group selection. We also develop a novel method to quantify the strength of selection for sex reversal.

Null Alleles and FIS × FST Correlations.

Three published papers in this journal have considered the proposition that, under a Wahlund effect caused by population mixture, a positive correlation is expected between single-locus values of FIS for a sample from the mixture and FST between the populations contributing to the mixture. Two of the papers assumed unbiased samples to estimate FST but did not consider possible effects of null alleles; the other paper focused on effects of nulls but used biased samples that also included Wahlund effects to estimate FST. The result is an information gap regarding scenarios that include null alleles but have unbiased estimates of FST. Simulations were used to fill this information gap, with the following results: 1) converting ~10% of alleles to nulls substantially reduced apparent heterozygosity and substantially increased FIS, with few exceptions; 2) adding null alleles also increased FST at most loci, although the effect was much more modest; 3) null alleles generally degraded correlations between FIS and FST, but the relationship remained relatively strong for FST ≥ 0.06; and 4) null alleles had only a small effect on correlations between r2, a measure of linkage disequilibrium between pairs of loci, and the product of FST values for those loci. These results argue for some caution in interpreting FIS × FST correlations under conditions where null alleles might be common and suggest that two-locus analyses might provide more robust assessments of Wahlund effects.

Is the Red Wolf a Listable Unit Under the US Endangered Species Act?

Defining units that can be afforded legal protection is a crucial, albeit challenging, step in conservation planning. As we illustrate with a case study of the red wolf (Canis rufus) from the southeastern United States, this step is especially complex when the evolutionary history of the focal taxon is uncertain. The US Endangered Species Act (ESA) allows listing of species, subspecies, or Distinct Population Segments (DPSs) of vertebrates. Red wolves were listed as an endangered species in 1973, and their status remains precarious. However, some recent genetic studies suggest that red wolves are part of a small wolf species (C. lycaon) specialized for heavily forested habitats of eastern North America, whereas other authors suggest that red wolves arose, perhaps within the last ~400 years, through hybridization between gray wolves (C. lupus) and coyotes (C. latrans). Using published genetic, morphological, behavioral, and ecological data, we evaluated whether each evolutionary hypothesis would lead to a listable unit for red wolves. Although the potential hybrid origin of red wolves, combined with abundant evidence for recent hybridization with coyotes, raises questions about status as a separate species or subspecies, we conclude that under any proposed evolutionary scenario red wolves meet both criteria to be considered a DPS: they are Discrete compared with other conspecific populations, and they are Significant to the taxon to which they belong. As population-level units can qualify for legal protection under endangered-species legislation in many countries throughout the world, this general approach could potentially be applied more broadly.

Accounting for Age Structure and Spatial Structure in Eco-Evolutionary Analyses of a Large, Mobile Vertebrate.

The idealized concept of a population is integral to ecology, evolutionary biology, and natural resource management. To make analyses tractable, most models adopt simplifying assumptions, which almost inevitably are violated by real species in nature. Here, we focus on both demographic and genetic estimates of effective population size per generation (Ne), the effective number of breeders per year (Nb), and Wright's neighborhood size (NS) for black bears (Ursus americanus) that are continuously distributed in the northern lower peninsula of Michigan, United States. We illustrate practical application of recently developed methods to account for violations of 2 common, simplifying assumptions about populations: 1) reproduction occurs in discrete generations and 2) mating occurs randomly among all individuals. We use a 9-year harvest dataset of >3300 individuals, together with genetic determination of 221 parent-offspring pairs, to estimate male and female vital rates, including age-specific survival, age-specific fecundity, and age-specific variance in fecundity (for which empirical data are rare). We find strong evidence for overdispersed variance in reproductive success of same-age individuals in both sexes, and we show that constraints on litter size have a strong influence on results. We also estimate that another life-history trait that is often ignored (skip breeding by females) has a relatively modest influence, reducing Nb by 9% and increasing Ne by 3%. We conclude that isolation by distance depresses genetic estimates of Nb, which implicitly assume a randomly mating population. Estimated demographic NS (100, based on parent-offspring dispersal) was similar to genetic NS (85, based on regression of genetic distance and geographic distance), indicating that the >36000 km2 study area includes about 4-5 black-bear neighborhoods. Results from this expansive data set provide important insight into effects of violating assumptions when estimating evolutionary parameters for long-lived, free-ranging species. In conjunction with recently developed analytical methodology, the ready availability of nonlethal DNA sampling methods and the ability to rapidly and cheaply survey many thousands of molecular markers should facilitate eco-evolutionary studies like this for many more species in nature.

Purging putative siblings from population genetic data sets: a cautionary view.

Interest has surged recently in removing siblings from population genetic data sets before conducting downstream analyses. However, even if the pedigree is inferred correctly, this has the potential to do more harm than good. We used computer simulations and empirical samples of coho salmon to evaluate strategies for adjusting samples to account for family structure. We compared performance in full samples and sibling-reduced samples of estimators of allele frequency (P^), population differentiation (F^ST) and effective population size (N^e). RESULTS: (i) unless simulated samples included large family groups together with a component of unrelated individuals, removing siblings generally reduced precision of P^ and F^ST; (ii) N^e based on the linkage disequilibrium method was largely unbiased using full random samples but became increasingly upwardly biased under aggressive purging of siblings. Under nonrandom sampling (some families over-represented), N^e using full samples was downwardly biased; removing just the right 'Goldilocks' fraction of siblings could produce an unbiased estimate, but this sweet spot varied widely among scenarios; (iii) weighting individuals based on the inferred pedigree (to produce a best linear unbiased estimator, BLUE) maximized precision of P^ when the inferred pedigree was correct but performed poorly when the pedigree was wrong; (iv) a variant of sibling removal that leaves intact small sibling groups appears to be more robust to errors in inferences about family structure. Our results illustrate the complex challenges posed by presence of family structure, suggest that no single optimal solution exists and argue for caution in adjusting population genetic data sets for the presence of putative siblings without fully understanding the consequences.

Performance of IUCN proxies for generation length.

One of the criteria used by the International Union for Conservation of Nature (IUCN) to assess threat status is the rate of decline in abundance over 3 generations or 10 years, whichever is longer. The traditional method for calculating generation length (T) uses age-specific survival and fecundity, but these data are rarely available. Consequently, proxies that require less information are often used, which introduces potential biases. The IUCN recommends 2 proxies based on adult mortality rate, T̂d = α + 1/d, and reproductive life span, T̂z = α + z* RL, where α is age at first reproduction, d is adult mortality rate, RL is reproductive life span, and z is a coefficient derived from data for comparable species. We used published life tables for 78 animal and plant populations to evaluate precision and bias of these proxies by comparing T̂d and T̂z with true generation length. Mean error rates in estimating T were 31% for T̂d and 20% for T̂z, but error rates for T̂d were 16% when we subtracted 1 year ( T̂d( adj )=T̂d-1 ), as suggested by theory; T̂d( adj ) also provided largely unbiased estimates regardless of the true generation length. Performance of T̂z depends on compilation of detailed data for comparable species, but our results suggest taxonomy is not a reliable indicator of comparability. All 3 proxies depend heavily on a reliable estimate of age at first reproduction, as we illustrated with 2 test species. The relatively large mean errors for all proxies emphasized the importance of collecting the detailed life-history information necessary to calculate true generation length. Unfortunately, publication of such data is less common than it was decades ago. We identified generic patterns of age-specific change in vital rates that can be used to predict expected patterns of bias from applying T̂d( adj ).

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, Ne . Effective population size is important both theoretically (Ne is a key parameter in almost every aspect of evolutionary biology) and for practical application (Ne 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 (), most of the recent growth in Ne 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 Ne 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 Ne for multiple methods; often these estimates are congruent, but that is not always the case. Because true Ne 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 Ne is known. Recently, Gilbert & Whitlock () 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 () uses simulations to evaluate performance of four single-sample Ne estimators. In addition to assessing effects of true Ne , 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 ), 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.

Testing for Hardy-Weinberg proportions: have we lost the plot?

Testing for Hardy-Weinberg proportions (HWP) is routine in almost all genetic studies of natural populations, but many researchers do not demonstrate a full understanding of the purposes of these tests or how to interpret the results. Common problems include a lack of understanding of statistical power and the difference between statistical significance and biological significance, how to interpret results of multiple tests, and how to distinguish between various factors that can cause statistically significant departures. In this perspective, which focuses on analysis of genetic data for nonmodel species, I 1) review factors that can cause departures from HWP at individual loci and linkage disequilibrium (LD) at pairs of loci; 2) discuss commonly used tests for HWP and LD, with an emphasis on multiple-testing issues; 3) show how to distinguish among possible causes of departures from HWP; and 4) outline some simple steps to follow when significant test results are found. Finally, I 5) identify some issues that merit particular attention as we move into an era in which analysis of genomics-scale datasets for nonmodel species is commonplace.

Practical application of the linkage disequilibrium method for estimating contemporary effective population size: A review.

The method to estimate contemporary effective population size (Ne ) based on patterns of linkage disequilibrium (LD) at unlinked loci has been widely applied to natural and managed populations. The underlying model makes many simplifying assumptions, most of which have been evaluated in numerous studies published over the last two decades. Here, these performance evaluations are reviewed and summarized, with a focus on information that facilitates practical application to real populations in nature. Potential sources of bias that are discussed include calculation of r2 (a measure of LD), adjustments for sampling error, physical linkage, age structure, migration and spatial structure, mutation and selection, mating systems, changes in abundance, rare alleles, missing data, genotyping errors, data filtering choices and methods for combining multiple Ne estimates. Factors that affect precision are reviewed, including pseudoreplication that limits the information gained from large genomics datasets, constraints imposed by small samples of individuals, and the challenges in obtaining robust estimates for large populations. Topics that merit further research include the potential to weight r2 values by allele frequency, lump samples of individuals, use genotypic likelihoods rather than called genotypes, prune large LD values and apply the method to species practising partial monogamy.