Empirical Distributions of F ST from Large-Scale Human Polymorphism Data

Studies of the apportionment of human genetic variation have long established that most human variation is within population groups and that the additional variation between population groups is small but greatest when comparing different continental populations. These studies often used Wright’s F _ST that apportions the standardized variance in allele frequencies within and between population groups. Because local adaptations increase population differentiation, high-F _ST may be found at closely linked loci under selection and used to identify genes undergoing directional or heterotic selection. We re-examined these processes using HapMap data. We analyzed 3 million SNPs on 602 samples from eight worldwide populations and a consensus subset of 1 million SNPs found in all populations. We identified four major features of the data: First, a hierarchically F _ST analysis showed that only a paucity (12%) of the total genetic variation is distributed between continental populations and even a lesser genetic variation (1%) is found between intra-continental populations. Second, the global F _ST distribution closely follows an exponential distribution. Third, although the overall F _ST distribution is similarly shaped (inverse J), F _ST distributions varies markedly by allele frequency when divided into non-overlapping groups by allele frequency range. Because the mean allele frequency is a crude indicator of allele age, these distributions mark the time-dependent change in genetic differentiation. Finally, the change in mean-F _ST of these groups is linear in allele frequency. These results suggest that investigating the extremes of the F _ST distribution for each allele frequency group is more efficient for detecting selection. Consequently, we demonstrate that such extreme SNPs are more clustered along the chromosomes than expected from linkage disequilibrium for each allele frequency group. These genomic regions are therefore likely candidates for natural selection.     

The joint effects of selection and dominance on the QST - FST contrast

Q_ST measures the differentiation of quantitative traits between populations. It is often compared to F_ST, which measures population differentiation at neutral marker loci due to drift, migration, and mutation. When Q_ST is different from F_ST, it is usually taken as evidence that selection has either restrained or accelerated the differentiation of the quantitative trait relative to neutral markers. However, a number of other factors such as inbreeding, dominance, and epistasis may also affect the Q_ST − F_ST contrast. In this study, we examine the effects of dominance, selection, and inbreeding on Q_ST − F_ST. We compare Q_ST with F_ST at selected and neutral loci for populations at equilibrium between selection, drift, mutation, and migration using both analytic and simulation approaches. Interestingly, when divergent selection is acting on a locus, inbreeding and dominance generally inflate Q_ST relative to F_ST when they are both measured at the quantitative locus at equilibrium. As a consequence, dominance is unlikely to hide the signature of divergent selection on the Q_ST − F_ST contrast. However, although in theory dominance and inbreeding affect the expectation for Q_ST − F_ST, of most concern is the very large variance in both Q_ST and F_ST, suggesting that we should be cautious in attributing small differences between Q_ST and F_ST to selection.     

Coalescence Times and FST Under a Skewed Offspring Distribution Among Individuals in a Population

Estimates of gene flow between subpopulations based on F_ST (or N_ST) are shown to be confounded by the reproduction parameters of a model of skewed offspring distribution. Genetic evidence of population subdivision can be observed even when gene flow is very high, if the offspring distribution is skewed. A skewed offspring distribution arises when individuals can have very many offspring with some probability. This leads to high probability of identity by descent within subpopulations and results in genetic heterogeneity between subpopulations even when Nm is very large. Thus, we consider a limiting model in which the rates of coalescence and migration can be much higher than for a Wright–Fisher population. We derive the densities of pairwise coalescence times and expressions for F_ST and other statistics under both the finite island model and a many-demes limit model. The results can explain the observed genetic heterogeneity among subpopulations of certain marine organisms despite substantial gene flow.     

Inference of population genetic parameters from an irregular time series of seasonal influenza virus sequences

Basic summary statistics that quantify the population genetic structure of influenza virus are important for understanding and inferring the evolutionary and epidemiological processes. However, the sampling dates of global virus sequences in the last several decades are scattered nonuniformly throughout the calendar. Such temporal structure of samples and the small effective size of viral population hampers the use of conventional methods to calculate summary statistics. Here, we define statistics that overcome this problem by correcting for the sampling-time difference in quantifying a pairwise sequence difference. A simple linear regression method jointly estimates the mutation rate and the level of sequence polymorphism, thus providing an estimate of the effective population size. It also leads to the definition of Wright’s F_ST for arbitrary time-series data. Furthermore, as an alternative to Tajima’s D statistic or the site-frequency spectrum, a mismatch distribution corrected for sampling-time differences can be obtained and compared between actual and simulated data. Application of these methods to seasonal influenza A/H3N2 viruses sampled between 1980 and 2017 and sequences simulated under the model of recurrent positive selection with metapopulation dynamics allowed us to estimate the synonymous mutation rate and find parameter values for selection and demographic structure that fit the observation. We found that the mutation rates of HA and PB1 segments before 2007 were particularly high and that including recurrent positive selection in our model was essential for the genealogical structure of the HA segment. Methods developed here can be generally applied to population genetic inferences using serially sampled genetic data.     

Conservation genetics of the annual hemiparasitic plant <Emphasis Type="Italic">Melampyrum sylvaticum</Emphasis> (Orobanchaceae) in the UK and Scandinavia

Melampyrum sylvaticum is an endangered annual hemiparasitic plant that is found in only 19 small and isolated populations in the United Kingdom (UK). To evaluate the genetic consequences of this patchy distribution we compared levels of diversity, inbreeding and differentiation from ten populations from the UK with eight relatively large populations from Sweden and Norway where the species is more continuously distributed. We demonstrate that in both the UK and Scandinavia, the species is highly inbreeding (global F _IS = 0.899). Levels of population differentiation were high (F’_ST = 0.892) and significantly higher amongst UK populations (F’_ST = 0.949) than Scandinavian populations (F’_ST = 0.762; P < 0.01). The isolated populations in the UK have, on average, lower genetic diversity (allelic richness, proportion of loci that are polymorphic, gene diversity) than Scandinavian populations, and this diversity difference is associated with the smaller census size and population area of UK populations. From a conservation perspective, the naturally inbreeding nature of the species may buffer the species against immediate effects of inbreeding depression, but the markedly lower levels of genetic diversity in UK populations may represent a genetic constraint to evolutionary change. In addition, the high levels of population differentiation suggest that gene flow among populations will not be effective at replenishing lost variation. We thus recommend supporting in situ conservation management with ex situ populations and human-mediated seed dispersal among selected populations in the UK.     

Combining multiple analytical approaches for the identification of population structure and genetic delineation of two subspecies of the endemic Arabian burnet moth Reissita simonyi (Zygaenidae; Lepidoptera)

Habitat fragmentation and landscape topology may influence the genetic structure and connectivity between natural populations. Six microsatellite loci were used to infer the population structure of 35 populations (N = 788) of the alpine Arabian burnet moth Reissita simonyi (Lepidoptera, Zygaenidae) in Yemen and Oman. Due to the patchy distribution of larval food plants, R. simonyi is not continuously distributed throughout the studied area and the two recognized subspecies of this endemic species (Reissita s. simonyi/R. s. yemenicola) are apparently discretely distributed. All microsatellites showed prevalence of null alleles and therefore a thorough investigation of the impact of null alleles on different population genetic parameters (F _ST, inbreeding coefficients, and Population Graph topologies) is given. In general, null alleles reduced genetic covariance and independence of allele frequencies resulting in a more connected genetic topology in Population Graphs and an overestimation of pairwise F _ST values and inbreeding coefficients. Despite the presence of null alleles, Population Graphs also showed a much higher genetic connectivity within subspecies (and lower genetic differentiation (via F _ST)) than between; supporting existing taxonomic distinction. Partial Mantel tests showed that both geographical distance and altitude were highly correlated with the observed distribution of genetic structure within R. simonyi. In conclusion, we identified geographical and altitudinal distances in R. simonyi as well as an intervening desert area to be the main factors for spatial genetic structure in this species and show that the taxonomic division into two subspecies is confirmed by genetic analysis.     

Signatures of adaptation and genetic structure among the mainland populations of Pinus radiata (D. Don) inferred from SNP loci

Insights into the relative contributions of locus specific and genome-wide effects on population genetic diversity can be gained through separation of their resulting genetic signals. Here we explore patterns of adaptive and neutral genetic diversity in the disjunct natural populations of Pinus radiata (D. Don) from mainland California. A first-generation common garden of 447 individuals revealed significant differentiation of wood phenotypes among populations (P _ST), possibly reflecting local adaptation in response to environment. We subsequently screened all trees for genetic diversity at 149 candidate gene single nucleotide polymorphism (SNP) loci for signatures of adaptation. Ten loci were identified as being possible targets of diversifying selection following F _ST outlier tests. Multivariate canonical correlation performed on a data set of 444 individuals identified significant covariance between environment, adaptive phenotypes and outlier SNP diversity, lending support to the case for local adaptation suggested from F _ST and P _ST tests. Covariation among discrete sets of outlier SNPs and adaptive phenotypes (inferred from multivariate loadings) with environment are supported by existing studies of candidate gene function and genotype–phenotype association. Canonical analyses failed to detect significant correlations between environment and 139 non-outlier SNP loci, which were applied to estimate neutral patterns of genetic differentiation among populations (F _ST 4.3 %). Using this data set, significant hierarchical structure was detected, indicating three populations on the mainland. The hierarchical relationships based on neutral SNP markers (and SSR) were in contrast with those inferred from putatively adaptive loci, potentially highlighting the independent action of selection and demography in shaping genetic structure in this species.     

The genetic mating structure of subdivided populations I. Open-mating model

The genetic mating structure of a subdivided population can describe how parental genotypes gave rise to zygotes. When parents of the same genotype are considered together as one class (“open-mating”), three independent parameters of inbreeding and mating structure are needed to describe this structure at a diallelic locus. One is Wright's fixation index F. The other two are mating structure parameters, derived herein and termed the “effective selfing” rate E and the “inbreeding assortative selfing” rate D. E is the genetically equivalent proportion of self-fertilization at a single locus, and is given by standardized second and third central moments of gene frequencies of mates. E is a summary measure of inbreeding that includes effects due to self-fertilization and mating to relatives, as well as correlations between mates induced by Wahlund effects and/or selective diversification among neighborhoods. The second parameter D measures the tendency of inbred or more homozygous individuals to effectively self more (or less) than outbred or more heterozygous individuals. D is related to the maintenance of variation of inbreeding among individuals and/or to the prevalence of spatial variation of selection. D is independent of E, but together with E controls the generational change of inbreeding, ΔF. Extensions of the model to unequal allele frequencies in male vs female mates, and to multi-allelic loci, are also examined.     

F(ST) and Q(ST) under neutrality

A commonly used test for natural selection has been to compare population differentiation for neutral molecular loci estimated by F_ST and for the additive genetic component of quantitative traits estimated by Q_ST. Past analytical and empirical studies have led to the conclusion that when averaged over replicate evolutionary histories, Q_ST = F_ST under neutrality. We used analytical and simulation techniques to study the impact of stochastic fluctuation among replicate outcomes of an evolutionary process, or the evolutionary variance, of Q_ST and F_ST for a neutral quantitative trait determined by n unlinked diallelic loci with additive gene action. We studied analytical models of two scenarios. In one, a pair of demes has recently been formed through subdivision of a panmictic population; in the other, a pair of demes has been evolving in allopatry for a long time. A rigorous analysis of these two models showed that in general, it is not necessarily true that mean Q_ST = F_ST (across evolutionary replicates) for a neutral, additive quantitative trait. In addition, we used finite-island model simulations to show there is a strong positive correlation between Q_ST and the difference Q_ST − F_ST because the evolutionary variance of Q_ST is much larger than that of F_ST. If traits with relatively large Q_ST values are preferentially sampled for study, the difference between Q_ST and F_ST will also be large and positive because of this correlation. Many recent studies have used tests of the null hypothesis Q_ST = F_ST to identify diversifying or uniform selection among subpopulations for quantitative traits. Our findings suggest that the distributions of Q_ST and F_ST under the null hypothesis of neutrality will depend on species-specific biology such as the number of subpopulations and the history of subpopulation divergence. In addition, the manner in which researchers select quantitative traits for study may introduce bias into the tests. As a result, researchers must be cautious before concluding that selection is occurring when Q_ST ≠ F_ST.     

Discriminating between the Effects of Founding Events and Reproductive Mode on the Genetic Structure of Triops Populations (Branchiopoda: Notostraca)

Crustaceans that initially colonize a freshwater temporary pond can strongly bias the subsequent genetic composition of the population, causing nearby populations to be genetically distinct. In addition, these crustaceans have various reproductive modes that can influence genetic differentiation and diversity within and between populations. We report on two species of tadpole shrimp, Triops newberryi and Triops longicaudatus “short”, with different reproductive modes. Reproduction in the tadpole shrimp can occur clonally (parthenogenesis), with self fertilization (hermaphroditism), or through outcrossing of hermaphrodites with males (androdioecy). For all these reproductive modes, population genetic theory predicts decreased genetic diversity and increased population differentiation. Here we use mitochondrial control region (mtCR) sequences and nuclear microsatellite loci to determine if the difference in reproductive mode affects the high genetic structure typical of persistent founder effects. Previous authors indicated that T. newberryi is androdioecious because populations are composed of hermaphrodites and males, and T. longicaudatus “short” is hermaphroditic or parthenogenetic because males are absent. In our data, T. newberryi and T. longicaudatus “short” populations were highly structured genetically over short geographic distances for mtCR sequences and microsatellite loci (T. newberryi: Φ_ST = 0.644, F _ST = 0.252, respectively; T. l. “short”: invariant mtCR sequences, F _ST = 0.600). Differences between the two Triops species in a number of diversity measures were generally consistent with expectations from population genetic theory regarding reproductive mode; however, three of four comparisons were not statistically significant. We conclude the high genetic differentiation between populations is likely due to founder effects and results suggest both species are composed of selfing hermaphrodites with some level of outcrossing; the presence of males in T. newberryi does not appreciably reduce inbreeding. We cannot exclude the possibility that males in T. newberryi are non-reproductive individuals and the two species have the same mating system.     

Genetic diversity and structure of an endemic and critically endangered stream river salamander (Caudata: Ambystoma leorae) in Mexico

Small or isolated populations are highly susceptible to stochastic events. They are prone and vulnerable to random demographic or environmental fluctuations that could lead to extinction due to the loss of alleles through genetic drift and increased inbreeding. We studied Ambystoma leorae an endemic and critically threatened species. We analyzed the genetic diversity and structure, effective population size, presence of bottlenecks and inbreeding coefficient of 96 individuals based on nine microsatellite loci. We found high levels of genetic diversity expressed as heterozygosity (H_o = 0.804, H_e = 0.613, H_e* = 0.626 and H_Nei = 0.622). The population presents few alleles (4–9 per locus) and genotypes (3–14 per locus) compared with other mole salamanders species. We identified three genetically differentiated subpopulations with a significant level of genetic structure (F_ST = 0.021, R_ST = 0.044 y D_est = 0.010, 95 % CI). We also detected a reduction signal in population size and evidence of a genetic bottleneck (M = 0.367). The effective population size is small (Ne = 45.2), but similar to another mole salamanders with restricted distributions or with recently fragmented habitat. The inbreeding coefficient levels detected are low (F_IS = ?0.619–0.102) as is gene flow. Despite, high levels of genetic diversity A. leorae is critically endangered because it is a small isolated population.     

Estimation and adjustment of microsatellite null alleles in nonequilibrium populations

Nonamplified (null) alleles are a common feature of microsatellite genotyping and can bias estimates of allele and genotype frequencies, thereby hindering population genetic analyses. The frequency of microsatellite null alleles in diploid populations can be estimated for populations that are in Hardy–Weinberg equilibrium. However, many microsatellite data sets are from nonequilibrium populations, often with known inbreeding coefficients (F) or fixation indices (F_IS or F_ST). Here, we propose a novel null allele estimator that can be used to estimate the null allele frequency and adjust visible allele frequencies in populations for which independent estimates of F, F_IS or F_ST are available. The algorithm is currently available as an Excel macro that can be downloaded at no cost from http://www.microchecker.hull.ac.uk/ and will be incorporated into the software micro ‐checker .     

Generalization of the QST framework in hierarchically structured populations: Impacts of inbreeding and dominance

Q_ST is a differentiation parameter based on the decomposition of the genetic variance of a trait. In the case of additive inheritance and absence of selection, it is analogous to the genic differentiation measured on individual loci, F_ST. Thus, Q_ST?F_ST comparison is used to infer selection: selective divergence when Q_ST > F_ST, or convergence when Q_ST < F_ST. The definition of Q‐statistics was extended to two‐level hierarchical population structures with Hardy–Weinberg equilibrium. Here, we generalize the Q‐statistics framework to any hierarchical population structure. First, we developed the analytical definition of hierarchical Q‐statistics for populations not at Hardy–Weinberg equilibrium. We show that the Q‐statistics values obtained with the Hardy–Weinberg definition are lower than their corresponding F‐statistics when F_IS > 0 (higher when F_IS < 0). Then, we used an island model simulation approach to investigate the impact of inbreeding and dominance on the Q_ST?F_ST framework in a hierarchical population structure. We show that, while differentiation at the lower hierarchical level (Q_SR) is a monotonic function of migration, differentiation at the upper level (Q_RT) is not. In the case of additive inheritance, we show that inbreeding inflates the variance of Q_RT, which can increase the frequency of Q_RT > F_RT cases. We also show that dominance drastically reduces Q‐statistics below F‐statistics for any level of the hierarchy. Therefore, high values of Q‐statistics are good indicators of selection, but low values are not in the case of dominance.     

Genetic diversity of nine faba bean (Vicia faba L.) populations revealed by isozyme markers

Seven isozyme systems (Sod, 6-Pgd, Me, Est, Skdh, Fdh and Gdh) representing nine loci were used to study the genetic diversity of nine faba bean populations. Seven loci revealed polymorphic bands and showed the same quaternary structure as that found in several species. They revealed a high number of phenotypes. Indeed, from 3 to 9 phenotypes per locus were investigated in this study. The percentage of polymorphic loci (P = 59.3 %) was higher than that mentioned in the autogamous species (P = 20.3 %) and less than the optimum (P=96 %) indicated for allogamous plants. Total genetic diversity (H _T) and within population genetic diversity (H _S) were estimated with the isozyme markers. The contribution of among population genetic diversity (D _ST) to total genetic diversity was 22%. Enzyme markers pointed out an average inbreeding level for whole population (F _IT) and within population (F _IS). Within population genetic diversity represents 78% of total diversity. Intra-population genetic diversity (H _S = 0.206) was ranged with the respect of allogamous species and was clearly higher than that of among population genetic diversity (D _ST = 0.057) indicating an out-crossing predominance in the studied populations. The expected heterozygosity was higher than that observed heterozygosity at the allogamous species was confirmed in this study. Although, the mean estimated gene flow was less than 1(Nm=0.814), the dendrogram based on Nei’s genetic distance of the 9 populations using UPGMA method showed some genetic drift between populations.     

The Distribution and Host Shifts of Cotton-Melon Aphids in Northern China

Aphis gossypii Glover (Hemiptera: Aphididae) is a serious pest of cotton in northern China. A microsatellite analysis was used to characterize the genetic structure of A. gossypii populations from different geographic, host plant, and seasonal populations in 2014. Among 906 individuals, 507 multilocus genotypes were identified, with genotypic richness values of 0.07–1.00 for the populations. We observed moderate levels of genetic differentiation among geographic populations (F_ST = 0.103; 95% confidence interval: 0.065–0.145) and host plant populations (F_ST = 0.237; 95% confidence interval: 0.187–0.296). A Mantel test of isolation by distance revealed no significant correlations between Slatkin’s linearized F_ST and the natural logarithm of geographic distance. A Bayesian analysis of population genetic structures identified three clusters. An analysis of molecular variance revealed significant differences among the three clusters (F = 0.26596, P < 0.0001), among seasons (F = 0.04244, P = 0.00381), and among host populations (F = 0.12975, P = 0.0029). Thus, the A. gossypii populations in northern China exhibit considerable genotypic diversity. Additionally, our findings indicated that the 31 analyzed populations could be classified as one of three host biotypes (i.e., cotton, cucumber, and pomegranate biotypes). There were also clear seasonal effects on population genetic structure diversity among aphids collected from Anyang.     

Identifying outlier loci in admixed and in continuous populations using ancestral population differentiation statistics

Finding genetic signatures of local adaptation is of great interest for many population genetic studies. Common approaches to sorting selective loci from their genomic background focus on the extreme values of the fixation index, F_ST, across loci. However, the computation of the fixation index becomes challenging when the population is genetically continuous, when predefining subpopulations is a difficult task, and in the presence of admixed individuals in the sample. In this study, we present a new method to identify loci under selection based on an extension of the F_ST statistic to samples with admixed individuals. In our approach, F_ST values are computed from the ancestry coefficients obtained with ancestry estimation programs. More specifically, we used factor models to estimate F_ST, and we compared our neutrality tests with those derived from a principal component analysis approach. The performances of the tests were illustrated using simulated data and by re‐analysing genomic data from European lines of the plant species Arabidopsis thaliana and human genomic data from the population reference sample, POPRES.     

Assessing population genetic structure of sorghum landraces from North-western Morocco using allozyme and microsatellite markers

 The level of genetic diversity and the population genetic structure of sorghum landraces from North-western Morocco have been investigated based on direct field-sampling using both allozyme and microsatellite markers. As expected, microsatellite markers showed a much higher degree of polymorphism than allozymes, but relative measures of genetic structure such as Wright’s inbreeding coefficient F _IS and Nei’s coefficient of genetic differentiation G _ST were similar for the two sets of markers. Substantial inbreeding was found to occur within fields, which confirms that sorghum is predominantly selfing under cultivation. Most of the genetic diversity in Moroccan landraces occurs within fields (more than 85%), as opposed to among fields or among regions, a result which contrasts to those of studies based on accessions from germplasm collections. It is suggested that individual fields of sorghum constitute valuable units of conservation in the context of in situ conservation practices. Received: 8 December 1998 / Accepted: 28 December 1998     

Strong isolation by distance among local populations of an endangered butterfly species (Euphydryas aurinia)

The marsh fritillary (Euphydryas aurinia) is a critically endangered butterfly species in Denmark known to be particularly vulnerable to habitat fragmentation due to its poor dispersal capacity. We identified and genotyped 318 novel SNP loci across 273 individuals obtained from 10 small and fragmented populations in Denmark using a genotyping‐by‐sequencing (GBS) approach to investigate its population genetic structure. Our results showed clear genetic substructuring and highly significant population differentiation based on genetic divergence (F _ST) among the 10 populations. The populations clustered in three overall clusters, and due to further substructuring among these, it was possible to clearly distinguish six clusters in total. We found highly significant deviations from Hardy–Weinberg equilibrium due to heterozygote deficiency within every population investigated, which indicates substructuring and/or inbreeding (due to mating among closely related individuals). The stringent filtering procedure that we have applied to our genotype quality could have overestimated the heterozygote deficiency and the degree of substructuring of our clusters but is allowing relative comparisons of the genetic parameters among clusters. Genetic divergence increased significantly with geographic distance, suggesting limited gene flow at spatial scales comparable to the dispersal distance of individual butterflies and strong isolation by distance. Altogether, our results clearly indicate that the marsh fritillary populations are genetically isolated. Further, our results highlight that the relevant spatial scale for conservation of rare, low mobile species may be smaller than previously anticipated.     

Population genetics and fine-scale genetic structure of Rhizopogon roseolus in the Tottori sand dune

We investigated the population genetics and fine-scale genetic structure of Rhizopogon roseolus. A total of 173 R. roseolus sporocarps were collected from two stands in the Tottori sand dune. We developed and applied five novel polymorphic microsatellite (SSR; simple sequence repeat) markers for sporocarp genotyping. In total, we identified 110 genets, most of which were small in size. Spatial autocorrelation analyses revealed a significantly positive genetic structure in short-distance classes. The inbreeding coefficient value was significant in both stands (F_IS = 0.18), while the F_ST value (F_ST = 0.020) indicated little genetic differentiation between the two populations. The majority of alleles were distributed in both stands with similar frequencies. These results suggest that short-distance spore dispersal plays a dominant role in generating new genets, and eventually increases the frequency of inbreeding in the Tottori sand dune, whereas rare gene flow between the two stands, possibly associated with spore dispersal by mycophagous animals, could reduce genetic differentiation.