The empirical Bayes estimators of fine‐scale population structure in high gene flow species

An empirical Bayes (EB) pairwise F_ST estimator was previously introduced and evaluated for its performance by numerical simulation. In this study, we conducted coalescent simulations and generated genetic population structure mechanistically, and compared the performance of the EBF_ST with Nei's G_ST, Nei and Chesser's bias‐corrected G_ST (G_{ST_NC}), Weir and Cockerham's θ (θ_WC) and θ with finite sample correction (θ_{WC_F}). We also introduced EB estimators for Hedrick’ G’_ST and Jost’ D. We applied these estimators to publicly available SNP genotypes of Atlantic herring. We also examined the power to detect the environmental factors causing the population structure. Our coalescent simulations revealed that the finite sample correction of θ_WC is necessary to assess population structure using pairwise F_ST values. For microsatellite markers, EBF_ST performed the best among the present estimators regarding both bias and precision under high gene flow scenarios (). For 300 SNPs, EBF_ST had the highest precision in all cases, but the bias was negative and greater than those for G_{ST_NC} and θ_{WC_F} in all cases. G_{ST_NC} and θ_{WC_F} performed very similarly at all levels of F_ST. As the number of loci increased up to 10 000, the precision of G_{ST_NC} and θ_{WC_F} became slightly better than for EBF_ST for cases with , even though the size of the bias remained constant. The EB estimators described the fine‐scale population structure of the herring and revealed that ~56% of the genetic differentiation was caused by sea surface temperature and salinity. The R package finepop for implementing all estimators used here is available on CRAN.     

Calculations of population differentiation based on GST and D: forget GST but not all of statistics!

G _ST‐values and its relatives (F_ST) belong to the most used parameters to define genetic differences between populations. Originally, they were developed for allozymes with very low number of alleles. Using highly polymorphic microsatellite markers it was often puzzling that G_ST‐values were very low but statistically significant. In their papers, Jost (2008) and Hedrick (2005) explained that G_ST‐values do not show genetic differentiation, and Jost suggested calculating D‐values instead. Theoretical mathematical considerations are often difficult to follow; therefore, we chose an applied approach comparing two artificial populations with different number of alleles at equal frequencies and known genetic divergence. Our results show that even for more than one allele per population G_ST‐values do not calculate population differentiation correctly; in contrast, D‐values do reflect the genetic differentiation indicating that data based on G_ST‐values need to be re‐evaluated. In our approach, statistical evaluations remained similar. We provide information about the impact of different sample sizes on D‐values in relation to number of alleles and genetic divergence.     

Estimation,variance and optimal sampling of gene diversity

An extension of Nei's analysis of diversity in a subdivided population is proposed for a haploid locus. The differentiation G _STbecomes a natural extension of Wright's F _STand generalizes Weir and Cockerham's parameter of co-ancestry by relaxing the assumption of identical correlation for all the alleles. Inter- and intrapopulation variances of the estimated diversities and differentiation are derived. Finally, the optimal sampling strategy for measuring G _STwhen a fixed number of individuals can be analysed is considered. It is shown that, at a given locus, there is a unique sample size per population which yields the smallest variance of G _ST,regardless of the number of populations studied. These theoretical developments are illustrated with an analysis of chloroplast DNA diversity in a forest tree. The results emphasize the necessity of sampling many populations, rather than many individuals per population, for an accurate measurement of the subdivision of gene diversity at a single locus.     

MAXIMUM-LIKELIHOOD ESTIMATION OF POPULATION DIVERGENCE TIMES AND POPULATION PHYLOGENY IN MODELS WITHOUT MUTATION

In this paper we present a method for estimating population divergence times by maximum likelihood in models without mutation. The maximum-likelihood estimator is compared to a commonly applied estimator based on Wright's F_ST statistic. Simulations suggest that the maximum-likelihood estimator is less biased and has a lower variance than the F_ST-based estimator. The maximum-likelihood estimator provides a statistical framework for the analysis of population history given genetic data. We demonstrate how maximum-likelihood estimates of the branching pattern of divergence of multiple populations may be obtained. We also describe how the method may be applied to test hypotheses such as whether populations have maintained equal population sizes. We illustrate the method by applying it to two previously published sets of human restriction fragment length polymorphism (RFLP) data.     

Does GST underestimate genetic differentiation from marker data?

The widely applied genetic differentiation statistics F_ST and G_ST have recently been criticized for underestimating differentiation when applied to highly polymorphic markers such as microsatellites. New statistics claimed to be unaffected by marker polymorphisms have been proposed and advocated to replace the traditional F_ST and G_ST. This study shows that G_ST gives accurate estimates and underestimates of differentiation when demographic factors are more and less important than mutations, respectively. In the former case, all markers, regardless of diversity (H_S), have the same G_ST value in expectation and thus give replicated estimates of differentiation. In the latter case, markers of higher H_S have lower G_ST values, resulting in a negative, roughly linear correlation between G_ST and H_S across loci. I propose that the correlation coefficient between G_ST and H_S across loci, r_GH, can be used to distinguish the two cases and to detect mutational effects on G_ST. A highly negative and significant r_GH, when coupled with highly variable G_ST values among loci, would reveal that marker G_ST values are affected substantially by mutations and marker diversity, underestimate population differentiation, and are not comparable among studies, species and markers. Simulated and empirical data sets are used to check the power and statistical behaviour, and to demonstrate the usefulness of the correlation analysis.     

Heterozygote deficiency,population substructure and their implications in DNA fingerprinting

Summary Substructured populations exhibit an overall deficiency of heterozygosity whose proportional magnitude depends on the nature of substructuring, i.e., the number of subpopulations (s), their time of divergence (t) from the ancestral population, and the rate of gene flow amongst them (m). Since apparent heterozygote deficiency could be caused by many factors other than population substructuring, one must examine the nature of substructuring that could produce the observed extent of heterozygote deficiency, in order to infer the substructuring from an observed heterozygote deficiency. Using the equivalence of proportional heterozygote deficiency and the coefficient of gene differentiation (G _ST), we can generate isolines of G _ST as functions of s, t (in units of 2N _e generations, N _e being the effective population size) and m. Analytical results suggest that large G _ST values cannot be reached by substructuring alone, unless the number of subpopulations are large and they remain isolated over a long period of time. Application of the theory to population data on six variable number of tandem repeats (VNTR) loci in US Caucasians and US Blacks demonstrates that the observed heterozygote deficiencies at these loci cannot be explained by substructuring within these populations alone. This is so because such large values of G _ST (3%–10%) would require an absence of gene exchange between the subpopulations and a divergence time from each other of at least 25000 years ago, neither of which is compatible with the demography and ethnohistory of US Caucasians and Blacks. In contrast, the inability to detect extreme-sized alleles and/or incomplete resolution of nearly similar-sized alleles following Southern gel electrophoresis could easily explain the observed heterozygote deficiencies. The implications of these results are discussed in the context of the forensic use of DNA-typing data, and justify the employment of population genetic principles in forensic genetics.     

Estimating FST and kinship for arbitrary population structures

F_ST and kinship are key parameters often estimated in modern population genetics studies in order to quantitatively characterize structure and relatedness. Kinship matrices have also become a fundamental quantity used in genome-wide association studies and heritability estimation. The most frequently-used estimators of F_ST and kinship are method-of-moments estimators whose accuracies depend strongly on the existence of simple underlying forms of structure, such as the independent subpopulations model of non-overlapping, independently evolving subpopulations. However, modern data sets have revealed that these simple models of structure likely do not hold in many populations, including humans. In this work, we analyze the behavior of these estimators in the presence of arbitrarily-complex population structures, which results in an improved estimation framework specifically designed for arbitrary population structures. After generalizing the definition of F_ST to arbitrary population structures and establishing a framework for assessing bias and consistency of genome-wide estimators, we calculate the accuracy of existing F_ST and kinship estimators under arbitrary population structures, characterizing biases and estimation challenges unobserved under their originally-assumed models of structure. We then present our new approach, which consistently estimates kinship and F_ST when the minimum kinship value in the dataset is estimated consistently. We illustrate our results using simulated genotypes from an admixture model, constructing a one-dimensional geographic scenario that departs nontrivially from the independent subpopulations model. Our simulations reveal the potential for severe biases in estimates of existing approaches that are overcome by our new framework. This work may significantly improve future analyses that rely on accurate kinship and F_ST estimates.     

General <Emphasis Type="Italic">G</Emphasis><Subscript>ST</Subscript> and <Emphasis Type="Italic">θ</Emphasis> inflation due to biased intra-population sampling,and its consequences for the conservation of the Canarian Flora

While knowledge of the degree of inter-population genetic differentiation underlies the understanding of microevolutionary processes in any organism, its calculation through G _ST, F _ST, or θ (which, unlike the previous two, was designed to correct for unequal and small sample sizes) is often based in severely restricted intra-population samples, which are nonetheless tacitly assumed adequate to their accurate estimation. Empirical assessment of the influence of the number and intra-population distribution of samples on the values of G _ST and θ for several Canarian endemic plants compellingly suggests that (1) contrary to expectations based on simulated datasets, θ does not account for empirical sampling bias better than G _ST; (2) sample sizes being equal, collections scattered across each population’s occupancy area entail significantly lower over-estimates of G _ST and θ than if they only consider one of the population extremes, especially in narrow allogamous taxa with small populations; (3) in small samples, a scattered sampling strategy is significantly less sensitive to G _ST inflation than sampling in one of the population extremes; and (4) a software-related component of bias should be considered when pooling values of G _ST from different studies to calculate averages. Thus, unlike the sampling methods used for many plant endemics from the Canaries and other regions, collections for a reliable estimation of inter-population differentiation using molecular markers should encompass the whole occupancy area of each population, and include a higher proportion of individuals respect to the total size in narrow endemics than in widespread congeners. Critically, the high average allozyme inter-population differentiation reported for the Canarian endemic Flora is possibly an over-estimate, and could be explained predominantly by the generally biased intra-population sampling associated with G _ST estimates, rather than by specific factors of insularity that restrict gene flow radically, as it has been hitherto assumed.     

What is genetic differentiation,and how should we measure it—GST,D, neither or both?

Estimates of the fixation index, F_ST, have been used as measures of population differentiation for many decades. However, there have been persistent voices in the literature suggesting that these statistics do not measure true differentiation. In particular, the statistics Nei's G_ST and Wier and Cockerham's θ have been criticized for being ‘constrained’ to not equal one in some situations that seem to represent maximal differentiation. Here, we address the issue of how to evaluate exactly how much information a particular statistic contains about the process of differentiation. This criterion can be used to counter most concerns about the performance of G_ST (and related statistics), while also being reconciled with the insights of those who have proposed alternative measures of differentiation. In particular, the likelihood‐based framework that we put forward can justify the use of G_ST as an effective measure of differentiation, but also shows that in some situations G_ST is insufficient on its own and needs supplementing by another measure such as Jost's D or Hedrick's G′_ST. This approach will become increasingly important in the future, as greater emphasis is placed on analysing large data sets.     

Genetic analysis of four wild chum salmon<Emphasis Type="Italic">Oncorhynchus keta</Emphasis> populations in China based on microsatellite markers

Synopsis To assess the genetic variation and population structure of wild chum salmon in China, we analyzed microsatellite loci for populations in the Amur, Wusuli, Suifen Current and the Tumen rivers. We evaluated expected heterozygosity with two estimators of genetic differentiation (F_ST and G_ST) and Nei’s standard genetic distance. The average expected heterozygosity across the 10 loci was 0.65 in the Wusuli River and the Suifen Current River, 0.64 in the Amur River and 0.66 in the Tumen River, The results of this study show that the recent declines in chum salmon have not led to low levels of genetic variability in China. The proportion of inter-population subdivision among chum salmon was between 5.7 and 6.8%. According to the estimator used, the NJ tree based on Nei’s standard genetic distance indicated that there were two different branches (the Sea of Okhotsk branch and the Sea of Japan branch), the Amur River and the Wusuli River populations were closer, while the Suifen Current River and the Tumen River clustered together. The genetic test for population bottlenecks provided no evidence for a significant genetic signature of population decline, which is consistent with the record of the four populations we have in the last few years.     

Spatio‐temporal Genetic Structure of a Tropical Bee Species Suggests High Dispersal Over a Fragmented Landscape

Habitat destruction threatens biodiversity by reducing the amount of available resources and connectivity among geographic areas. For organisms living in fragmented habitats, population persistence may depend on dispersal, which maintains gene flow among fragments and can prevent inbreeding within them. It is centrally important to understand patterns of dispersal for bees living in fragmented areas given the importance of pollination systems and recently documented declines in bee populations. We used population and landscape genetic techniques to characterize patterns of dispersal over a large fragmented area in southern Costa Rica for the orchid bee species Euglossa championi. First, we estimated levels of genetic differentiation among forest fragments as ?_PT, an analog to the traditional summary statistic F_ST, as well as two statistics that may more adequately represent levels of differentiation, G’_ST and D_est. Second, we used a Bayesian approach to determine the number and composition of genetic groups in our sample. Third we investigated how genetic differentiation changes with distance. Fourth, we determined the extent to which deforested areas restrict dispersal. Finally, we estimated the extent to which there were temporal differences in allele frequencies within the same forest fragments. Within years we found low levels of differentiation even over 80 km, and no effect of land use type on level of genetic differentiation. However, we found significant genetic differentiation between years. Taken together our results suggest that there are high levels of gene flow over this geographic area, and that individuals show low site fidelity over time.     

A COMPARISON OF THREE INDIRECT METHODS FOR ESTIMATING AVERAGE LEVELS OF GENE FLOW

Three methods for estimating the average level of gene flow in natural population are discussed and compared. The three methods are F_ST, rare alleles, and maximum likelihood. All three methods yield estimates of the combination of parameters (the number of migrants [Nm] in a demic model or the neighborhood size [4πDσ²] in a continuum model) that determines the relative importance of gene flow and genetic drift. We review the theory underlying these methods and derive new analytic results for the expectation of F_ST in stepping-stone and continuum models when small sets of samples are taken. We also compare the effectiveness of the different methods using a variety of simulated data. We found that the F_ST and rare-alleles methods yield comparable estimates under a wide variety of conditions when the population being sampled is demographically stable. They are roughly equally sensitive to selection and to variation in population structure, and they approach their equilibrium values at approximately the same rate. We found that two different maximum-likelihood methods tend to yield biased estimates when relatively small numbers of locations are sampled but more accurate estimates when larger numbers are sampled. Our conclusion is that, although F_ST and rare-alleles methods are expected to be equally effective in analyzing ideal data, practical problems in estimating the frequencies of rare alleles in electrophoretic studies suggest that F_ST is likely to be more useful under realistic conditions.     

LANDSCAPE GENOMICS OF POPULUS TRICHOCARPA: THE ROLE OF HYBRIDIZATION,LIMITED GENE FLOW,AND NATURAL SELECTION IN SHAPING PATTERNS OF POPULATION STRUCTURE

Populus trichocarpa is an ecologically important tree across western North America. We used a large population sample of 498 accessions over a wide geographical area genotyped with a 34K Populus SNP array to quantify geographical patterns of genetic variation in this species (landscape genomics). We present evidence that three processes contribute to the observed patterns: (1) introgression from the sister species P. balsamifera, (2) isolation by distance (IBD), and (3) natural selection. Introgression was detected only at the margins of the species’ distribution. IBD was significant across the sampled area as a whole, but no evidence of restricted gene flow was detected in a core of drainages from southern British Columbia (BC). We identified a large number of F_ST outliers. Gene Ontology analyses revealed that F_ST outliers are overrepresented in genes involved in circadian rhythm and response to red/far‐red light when the entire dataset is considered, whereas in southern BC heat response genes are overrepresented. We also identified strong correlations between geoclimate variables and allele frequencies at F_ST outlier loci that provide clues regarding the selective pressures acting at these loci.     

Background selection and FST: Consequences for detecting local adaptation

Background selection is a process whereby recurrent deleterious mutations cause a decrease in the effective population size and genetic diversity at linked loci. Several authors have suggested that variation in the intensity of background selection could cause variation in F_ST across the genome, which could confound signals of local adaptation in genome scans. We performed realistic simulations of DNA sequences, using recombination maps from humans and sticklebacks, to investigate how variation in the intensity of background selection affects F_ST and other statistics of population differentiation in sexual, outcrossing species. We show that, in populations connected by gene flow, Weir and Cockerham's (1984; Evolution, 38 , 1358) estimator of F_ST is largely insensitive to locus‐to‐locus variation in the intensity of background selection. Unlike F_ST, however, d_XY is negatively correlated with background selection. Moreover, background selection does not greatly affect the false‐positive rate in F_ST outlier studies in populations connected by gene flow. Overall, our study indicates that background selection will not greatly interfere with finding the variants responsible for local adaptation.     

Measuring genetic relatedness in natural populations: Methodology

The estimation of relatedness within social groups, such as the colonies of a population of social insects, is an important field for evaluating hypotheses concerning the evolution and maintenance of social behaviour. The methodology of this estimation from genetic data in the absence of pedigree information has been poorly understood; we develop this methodology for b, the regression coefficient of relatedness, and discuss its applications. Both b and G (the pedigree coefficient of relatedness) are potentially asymmetric coefficients, whereas φ, r, and F_ST are necessarily symmetric. We develop an estimator for b suitable for small samples, and also one for standard deviation, and examine the properties of both using sampling simulations. The b estimator returns values slightly below E(b), and the standard deviation estimator yields conservative confidence intervals. A comparative study of b and F_ST shows that, given the same set of data, b is estimated with greater reliability than is F_ST. As is the case for F_ST, b can be used to examine population structure at various levels, and b possesses the advantage of an estimator for its standard error, which can also be used to test for heterogeneity among the loci surveyed. The actual numbers of identical genes held in common by interacting individuals, and not simply their proportions, need to be considered in using coefficients of relatedness in inclusive fitness calculations. This necessity is handled by the weighted coefficients of relatedness, G′ and b′, which have been referred to in the literature as r (as have most relatedness measures).     

Comparison of genetic differentiation at marker loci and quantitative traits

The comparison of the degree of differentiation in neutral marker loci and genes coding quantitative traits with standardized and equivalent measures of genetic differentiation (F_ST and Q_ST, respectively) can provide insights into two important but seldom explored questions in evolutionary genetics: (i) what is the relative importance of random genetic drift and directional natural selection as causes of population differentiation in quantitative traits, and (ii) does the degree of divergence in neutral marker loci predict the degree of divergence in genes coding quantitative traits? Examination of data from 18 independent studies of plants and animals using both standard statistical and meta‐analytical methods revealed a number of interesting points. First, the degree of differentiation in quantitative traits (Q_ST) typically exceeds that observed in neutral marker genes (F_ST), suggesting a prominent role for natural selection in accounting for patterns of quantitative trait differentiation among contemporary populations. Second, the F_ST – Q_ST difference is more pronounced for allozyme markers and morphological traits, than for other kinds of molecular markers and life‐history traits. Third, very few studies reveal situations were Q_ST < F_ST, suggesting that selection pressures, and hence optimal phenotypes, in different populations of the same species are unlikely to be often similar. Fourth, there is a strong correlation between Q_ST and F_ST indices across the different studies for allozyme (r=0.81), microsatellite (r=0.87) and combined (r=0.75) marker data, suggesting that the degree of genetic differentiation in neutral marker loci is closely predictive of the degree of differentiation in loci coding quantitative traits. However, these interpretations are subject to a number of assumptions about the data and methods used to derive the estimates of population differentiation in the two sets of traits.     

Genetic variation of polymorphic <Emphasis Type="Italic">NOS</Emphasis> STR locus in ten Indian population groups

Genotyping of 313 random individuals belonging to ten different population groups from three different states of India was performed for polymorphic pentanucleotide repeat present in the 5′ flanking region of nitric oxide synthase gene (NOS2A) to study the effect of geographical and linguistic affiliations on the genetic affinities among these groups. Likelihood ratio tests showed that all the ten populations for this locus were in Hardy-Weinberg equilibrium. Eleven different alleles ranging from 7 repeat to 17 repeats and 46 different genotypes were observed. The observed and the expected heterozygosity ranged from 0.72–0.94 and 0.84–0.89, respectively. The discriminating power of this locus is ≥ 0.86 and the polymorphism information content of this locus in ten population groups ranged from 0.80 to 0.85. High PIC, PD and PE value of this STR showed this marker to be informative and can be used for DNA typing and population studies. The eight populations from Kerala showed a lower G _ST value of 0.016 compared to the G _ST of ten populations (G _ST = 0.019), thereby showing that the populations from the same state showed higher genetic proximity probably due to linguistic and geographical proximity between them. The article was received from the author in the original.     

A trait‐based approach to predict population genetic structure in bees

Understanding population genetic structure is key to developing predictions about species susceptibility to environmental change, such as habitat fragmentation and climate change. It has been theorized that life‐history traits may constrain some species in their dispersal and lead to greater signatures of population genetic structure. In this study, we use a quantitative comparative approach to assess if patterns of population genetic structure in bees are driven by three key species‐level life‐history traits: body size, sociality, and diet breadth. Specifically, we reviewed the current literature on bee population genetic structure, as measured by the differentiation indices Nei's G_ST, Hedrick's G′_ST, and Jost's D. We then used phylogenetic generalised linear models to estimate the correlation between the evolution of these traits and patterns of genetic differentiation. Our analyses revealed a negative and significant effect of body size on genetic structure, regardless of differentiation index utilized. For Hedrick's G′_ST and Jost's D, we also found a significant impact of sociality, where social species exhibited lower levels of differentiation than solitary species. We did not find an effect of diet specialization on population genetic structure. Overall, our results suggest that physical dispersal or other functions related to body size are among the most critical for mediating population structure for bees. We further highlight the importance of standardizing population genetic measures to more easily compare studies and to identify the most susceptible species to landscape and climatic changes.     

genodive version 3.0: Easy‐to‐use software for the analysis of genetic data of diploids and polyploids

genodive version 3.0 is a user‐friendly program for the analysis of population genetic data. This version presents a major update from the previous version and now offers a wide spectrum of different types of analyses. genodive has an intuitive graphical user interface that allows direct manipulation of the data through transformation, imputation of missing data, and exclusion and inclusion of individuals, population and/or loci. Furthermore, genodive seamlessly supports 15 different file formats for importing or exporting data from or to other programs. One major feature of genodive is that it supports both diploid and polyploid data, up to octaploidy (2n = 8x) for some analyses, but up to hexadecaploidy (2n = 16x) for other analyses. The different types of analyses offered by genodive include multiple statistics for estimating population differentiation (φ_ST, F_ST, F?_ST, G_ST, G?_ST, G??_ST, D_est, R_ST, ρ), analysis of molecular variance‐based K‐means clustering, Hardy–Weinberg equilibrium, hybrid index, population assignment, clone assignment, Mantel test, Spatial Autocorrelation, 23 ways of calculating genetic distances, and both principal components and principal coordinates analyses. A unique feature of genodive is that it can also open data sets with nongenetic variables, for example environmental data or geographical coordinates that can be included in the analysis. In addition, genodive makes it possible to run several external programs (lfmm , structure , instruct and vegan ) directly from its own user interface, avoiding the need for data reformatting and use of the command line. genodive is available for computers running Mac OS X 10.7 or higher and can be downloaded freely from: http://www.patrickmeirmans.com/software .     

Quantifying population structure on short timescales

Quantifying the contribution of the various processes that influence population genetic structure is important, but difficult. One of the reasons is that no single measure appropriately quantifies all aspects of genetic structure. An increasing number of studies is analysing population structure using the statistic D, which measures genetic differentiation, next to G_ST, which quantifies the standardized variance in allele frequencies among populations. Few studies have evaluated which statistic is most appropriate in particular situations. In this study, we evaluated which index is more suitable in quantifying postglacial divergence between three‐spined stickleback (Gasterosteus aculeatus) populations from Western Europe. Population structure on this short timescale (10 000 generations) is probably shaped by colonization history, followed by migration and drift. Using microsatellite markers and anticipating that D and G_ST might have different capacities to reveal these processes, we evaluated population structure at two levels: (i) between lowland and upland populations, aiming to infer historical processes; and (ii) among upland populations, aiming to quantify contemporary processes. In the first case, only D revealed clear clusters of populations, putatively indicative of population ancestry. In the second case, only G_ST was indicative for the balance between migration and drift. Simulations of colonization and subsequent divergence in a hierarchical stepping stone model confirmed this discrepancy, which becomes particularly strong for markers with moderate to high mutation rates. We conclude that on short timescales, and across strong clines in population size and connectivity, D is useful to infer colonization history, whereas G_ST is sensitive to more recent demographic events.