ESTIMATING HIERARCHICAL F-STATISTICS

This paper presents an analysis of variance (ANOVA) approach by which estimation of F-statistics can be made from data with an arbitrary s-level hierarchical population structure. Assuming a complete random-effect model, a general ANOVA procedure is developed to estimate F-statistics as ratios of different variance components for all levels of population subdivision in the hierarchy. A generalized relationship among F-statistics is also derived to extend the well-known relationship originally found by Sewall Wright. Although not entirely free from the bias particular to small number of subdivisions at each hierarchy and extreme gene frequencies, the ANOVA estimators of F-statistics consider sampling effects at each level of hierarchy, thus removing the bias incurred in the other estimators that are commonly based on direct substitution of unknown gene frequencies by their sample estimates. Therefore, the ANOVA estimation procedure presented here may become increasingly useful in analyzing complex population structure because of increasing use of the estimated hierarchical F-statistics to infer genetic and demographic structures of natural populations within and among species.     

Gene variation and genetic differentiation among populations of the solitary mud dauber wasp Trypoxylon (Trypargilum) albitarse Fabricius 1804 (Hymenoptera, Crabronidae)

Trypoxylon is a genus of solitary crabronid wasps whose population genetics is poorly known. The purpose of the present study was to investigate the genetic variation and differentiation among five populations of Trypoxylon albitarse, a species widely distributed throughout the Neotropics, with records from Panama to northern Argentina. Eight species-specific microsatellite loci were used for genotyping 96 adult wasps (one female per nest) sampled at five sites in Brazil. The analysis of allelic richness and private alleles indicated high genetic diversity in the populations sampled. Pairwise comparisons using the F _st and D _est indices revealed significant differentiation for all, but one pair of populations. F _st, D _est, AMOVA and assignment test values pointed to inter-population differentiation. Additionally, the analysis of population structure using Bayesian and PCA methods characterized two alternative genetic groups. The Mantel test indicated no correlation between genetic and geographic distances. Despite evidence of considerable dispersal capacity for T. albitarse, the data indicate low to moderate population structuring in this species.     

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.     

Assessment of Population Differentiation Using DNA Fingerprinting and Modified Wright's FST-Statistics

Using our results and literature data on multilocus DNA fingerprinting, we propose a method of obtaining unbiased estimates of the between-population genetic similarity index and a measure of population subdivision based on modified Wright's F _ST-statistics. On the basis of multiple comparison T ² Hotelling's test and Holmes' procedure, the F _ST-statistics was applied to assess differentiation of four (Pacific and Atlantic) subpopulations of humpback whale Megaptera novaeangliae, six populations of Californian island gray fox Urocyon littoralis, and geographically isolated Ob' and Yakutia populations of Siberian white crane Crus leucogeranus. It was shown that the regional humpback whale subpopulations do not constitute a single panmictic unit (P < 10^–4). The subdivision index of the Pacific and Atlantic populations expressed in terms of F-statistics varied from 0.101 to 0.157. The differentiation estimates for the island fox populations, which ranged from 0.2109 to 0.4027, indicate that subdivision of these populations is a function of the distance between the islands, island size, and population size. In particular, the smallest and the greatest differences were found respectively between the populations of the geographically closest northern islands (F _ST = 0.2157, F _ST = 0.2109) and between those of the most distant northern and southern islands (F _ST = 0.4027, F _ST = 0.3869). Subdivision of the island populations with minimum areas and low population number was intermediate (F _ST = 0.3789). Mean values of heterozygosity, within-population genetic similarity index, and the number of coinciding fragments for two random individuals of Siberian white crane from the Ob' and Yakutia population were not statistically significantly different (P 0.852, P 0.491, P 0.325). However, pairwise comparisons of mean F _ST values indicated that the differentiation estimates for samples from these populations fall within the limits of population subdivision (P = 0.01). The subdivision estimate (0.108–0.133) of various groups of Siberian white cranes is comparable to interregional subdivision of humpback whale. Based on the results of this study, we recommend the approach based on modified Wright's F _ST-statistics for studying genetic population structure aimed at detecting population subdivision.     

The Exact Distributions of F IS under Partial Asexuality in Small Finite Populations with Mutation

Reproductive systems like partial asexuality participate to shape the evolution of genetic diversity within populations, which is often quantified by the inbreeding coefficient F _IS. Understanding how those mating systems impact the possible distributions of F _IS values in theoretical populations helps to unravel forces shaping the evolution of real populations. We proposed a population genetics model based on genotypic states in a finite population with mutation. For populations with less than 400 individuals, we assessed the impact of the rates of asexuality on the full exact distributions of F _IS, the probabilities of positive and negative F _IS, the probabilities of fixation and the probabilities to observe changes in the sign of F _IS over one generation. After an infinite number of generations, we distinguished three main patterns of effects of the rates of asexuality on genetic diversity that also varied according to the interactions of mutation and genetic drift. Even rare asexual events in mainly sexual populations impacted the balance between negative and positive F _IS and the occurrence of extreme values. It also drastically modified the probability to change the sign of F _IS value at one locus over one generation. When mutation prevailed over genetic drift, increasing rates of asexuality continuously increased the variance of F _IS that reached its highest value in fully asexual populations. In consequence, even ancient asexual populations showed the entire F _IS spectrum, including strong positive F _IS. The prevalence of heterozygous loci only occurred in full asexual populations when genetic drift dominated.     

Marker‐based estimates of relatedness and inbreeding coefficients: an assessment of current methods

Inbreeding (F) of and relatedness (r) between individuals are now routinely calculated from marker data in studies in the fields of quantitative genetics, conservation genetics, forensics, evolution and ecology. Although definable in terms of either correlation coefficient or probability of identity by descent (IBD) relative to a reference, they are better interpreted as correlations in marker‐based analyses because the reference in practice is frequently the current sample or population whose F and r are being estimated. In such situations, negative estimates have a biological meaning, a substantial proportion of the estimates are expected to be negative, and the average estimates are close to zero for r and equivalent to F_IS for F. I show that although current r estimators were developed from the IBD‐based concept of relatedness, some of them conform to the correlation‐based concept of relatedness and some do not. The latter estimators can be modified, however, so that they estimate r as a correlation coefficient. I also show that F and r estimates can be misleading and become biased and marker dependent when a sample containing a high proportion of highly inbred and/or closely related individuals is used as reference. In analyses depending on the comparison between r (or F) estimates and a priori values expected under ideal conditions (e.g. for identifying genealogical relationship), the estimators should be used with caution.     

Estimates of population differentiation in pink salmon Oncorhynchus gorbuscha with using of the microsatellite markers may be underestimated due to high population sizes

Data on the variation at eight microsatellite loci in the Far East salmon Oncorhynchus gorbuscha samples caught in 1984–1985 and 2001–2006 are analyzed. F-statistics indices at all levels of the hierarchical spatial structures are very small. At the same time, the differentiation between populations (according to F _ST estimates) in the odd-year broodline of pink salmon does not exceed the temporal variation within populations. In the even-year broodline, the F-statistics indices at the interregional and intraregional levels are significantly greater than those in the odd-year broodline. F _ST estimates (averaged over the same set of loci) vary widely within the range: the highest values are observed in populations of the coast of North America (except Alaska) and in the new range in the European North of Russia, whereas in the populations of the Asian part of the range and Alaska they are one order of magnitude smaller. The causes of the heterogeneity of the estimates of genetic differentiation within the range and between the broodlines of odd and even years are discussed. Since the mean population size estimates were correlated with the F _ST values, it was assumed that the effect of random genetic drift, the main factor of population divergence in selectively neutral loci, weakens with an increase in the population size. Because of the greater population sizes in pink salmon compared to other salmon species, as well due to the uneven distribution of populations of different size, the usage of microsatellite markers may lead to an underestimation of the true divergence of populations and their regional groups and, consequently, to an overestimation of genetic migration.     

Genetic structure of natural populations ofDryas iulia (Lepidoptera: Nymphalidae) revealed by enzyme polymorphism and mitochondrial DNA (mtDNA) restriction fragment length polymorphism (RFLP)

Dryas iulia appears to have undergone a mode of evolution different from that of other members of its subfamily (Heliconiinae). While other species constitute highly subdivided and inbred populations, those ofD. iulia are thought to be large and uniform. Analyzing six samples from Southern Brazil (state of Rio Grande do Sul) in relation to three enzyme systems (EST, LAP, and PGM) and their mtDNA RFLP patterns, we found that they are very similar at the molecular level. TheF statistics for enzyme polymorphism data revealed that inbreeding makes a great contribution to the population homozygosity, sinceF _IS equals 0.1322 andF _ST equals 0.0023. Since the chi-square test showed thatF _ST is not significant, we conclude that all localities belong to the same population. The mtDNA differentiation was about 12 times greater than for nuclear genes;F _ST was equivalent to 0.0265. We suggest that this difference is due to a higher dispersal of males, in relation to females.     

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.     

Population connectivity,dispersal, and swimming behavior in Daphnia

The water flea Daphnia has the capacity to respond rapidly to environmental stressors, to disperse over large geographical scales, and to preserve its genetic material by forming egg banks in the sediment. Spatial and temporal distributions of D. magna have been extensively studied over the last decades using behavioral or genetic tools, although the correlation between the two has rarely been the focus. In the present study, we therefore investigated the population genetic structure and behavioral response to a lethal threat, ultraviolet radiation (UVR), among individuals from two different water bodies. Our results show two genetic populations with moderate gene flow, highly correlated with geographical location and with inheritable traits through generations. However, despite the strong genetic differences between populations, we show homogeneous refuge demand between populations when exposed to the lethal threat solar UVR.     

Genetic Variation and Differentiation among Populations of Chum Salmon Oncorhynchus ketaWalbaum from Southern Russian Far East

Allozyme variation of populations of chum salmon Oncorhynchus ketafrom southern Russian Far East was examined. Of 55 loci screened, 31 were polymorphic. Within-population variation accounted for most of the allele diversity; F _STaveraged over loci was 0.052. Linkage disequilibrium was found in less than 5% of locus pairs in the chum population examined. Analysis of within- and among-population variance components of linkage disequilibrium using D-statistics (Ohta, 1982) showed that most genetic variation was distributed among populations.     

Evaluating sample allocation and effort in detecting population differentiation for discrete and continuously distributed individuals

One of the most pressing issues in spatial genetics concerns sampling. Traditionally, substructure and gene flow are estimated for individuals sampled within discrete populations. Because many species may be continuously distributed across a landscape without discrete boundaries, understanding sampling issues becomes paramount. Given large-scale, geographically broad conservation efforts, researchers are looking for guidance as to the trade-offs between sampling more individuals within a population versus few individuals scattered across more populations. Here, we conducted simulations that address these issues. We first established two archetypical patterns of dispersion: (1) individuals within discrete populations, and (2) continuously distributed individuals with limited dispersal. We used genotypes generated from a spatially-explicit, individual-based program and simulated genetic structure in individuals from nine different population sizes across a landscape that either had barriers to movement (defining discrete populations) or isolation-by-distance patterns (defining continuously distributed individuals). Then, given each pattern of dispersion, we allocated samples across four different sampling strategies for each of the nine population sizes in various configurations for sampling more individuals within a population versus fewer individuals scattered across more populations. We assessed the population genetic substructure with both the population-based metric, F _ST, and an individual-based metric, D _PS regardless of the true pattern of dispersion to allow us to better understand the effect of incorrectly matching the metric and the distribution (e.g., F _ST with continuously distributed individuals, and vice versa). We show that sampling many subpopulations (or sampling areas), thus sampling fewer individuals per subpopulation, overestimates measures of population subdivision with the population-based metric for both patterns of dispersion. In contrast, using the individual-based metric gives the opposite results: sampling too few subpopulations, and many individuals per subpopulation, produces an underestimate of the strength of isolation-by-distance. By comparing all results, we were able to suggest a strong predictive model of a chosen genetic structure metric for elucidating the sampling design trade-offs given each pattern of dispersion and configuration on the landscape.     

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.     

Genetic variability of dromedary camel populations based on microsatellite markers

Understanding existing levels of genetic variability of camel populations is capital for conservation activities. This study aims to provide information on the genetic diversity of four dromedary populations, including Guerzni, Harcha, Khouari and Marmouri. Blood samples from 227 individuals belonging to the aforementioned populations were obtained and genotyped by 16 microsatellite markers. A total of 215 alleles were observed, with the mean number of alleles per locus being 13.4 ± 6.26. All loci were polymorphic in the studied populations. The average expected heterozygosity varied from a maximum of 0.748 ± 0.122 in Guerzni population to a minimum of 0.702 ± 0.128 in Harcha population; Guerzni population showed the highest value of observed heterozygosity (0.699 ± 0.088), whereas Harcha population the lowest (0.646 ± 0.130). Mean estimates of F-statistics obtained over loci were F_IS = 0.0726, F_IT = 0.0876 and F_ST = 0.0162. The lowest genetic distance was obtained between Guerzni and Khouari (0.023), and the highest genetic distance between Harcha and Marmouri (0.251). The neighbour-joining phylogenetic tree showed two groups of populations indicating a cluster of Guerzni, Khouari and Marmouri, and a clear isolation of Harcha. The genetic distances, the factorial correspondence analysis, the analysis of genetic structure and the phylogenetic tree between populations revealed significant differences between Harcha and other populations, and a high similarity between Guerzni, Khouari and Marmouri. It is concluded from this study that the camel genetic resources studied are well diversified. However, the herd management, especially the random selection of breeding animals, can increase the level of genetic mixing between different populations, mainly among Guerzni, Khouari and Marmouri, that live in the same habitat and grazing area.     

Determinants of Genetic Structure in a Nonequilibrium Metapopulation of the Plant Silene latifolia

Population genetic differentiation will be influenced by the demographic history of populations, opportunities for migration among neighboring demes and founder effects associated with repeated extinction and recolonization. In natural populations, these factors are expected to interact with each other and their magnitudes will vary depending on the spatial distribution and age structure of local demes. Although each of these effects has been individually identified as important in structuring genetic variance, their relative magnitude is seldom estimated in nature. We conducted a population genetic analysis in a metapopulation of the angiosperm, Silene latifolia, from which we had more than 20 years of data on the spatial distribution, demographic history, and extinction and colonization of demes. We used hierarchical Bayesian methods to disentangle which features of the populations contributed to among population variation in allele frequencies, including the magnitude and direction of their effects. We show that population age, long-term size and degree of connectivity all combine to affect the distribution of genetic variance; small, recently-founded, isolated populations contributed most to increase F _ST in the metapopulation. However, the effects of population size and population age are best understood as being modulated through the effects of connectivity to other extant populations, i.e. F _ST diminishes as populations age, but at a rate that depends how isolated the population is. These spatial and temporal correlates of population structure give insight into how migration, founder effect and within-deme genetic drift have combined to enhance and restrict genetic divergence in a natural metapopulation.     

The similarity index and DNA fingerprinting

DNA-fingerprint similarity is being used increasingly to make inferences about levels of genetic variation within and between natural populations. It is shown that the similarity index--the average fraction of shared restriction fragments--provides upwardly biased estimates of population homozygosity but nearly unbiased estimates of the average identity-in-state for random pairs of individuals. A method is suggested for partitioning the DNA-fingerprint dissimilarity into within- and between-population components. Some simple expressions are given for the sampling variances of these estimators.     

Some notes on the distribution and certain modifications of Mahalanobis' generalized distance (D2)

Different modifications of Mahalanobis' generalized distance (D²) utilized in anthropological research are given, and it is shown that they all derive from the distribution of D² when the distances between the populations investigated are real. To investigate whether observed distances are real, testing of D² for significance is stressed. It is demonstrated that D² ought to be tested for significance according to its relation to the F-distribution, but that it may be related to the chi-squared distribution as an approximation when the numbers of individuals in the samples are very large. The great disadvantages of utilizing this approximation for smaller numbers of individuals in the samples are demonstrated, as well as the dependence of D² on sample size and the number of measurements used when testing for significance.     

Population Genomics of the Euryhaline Teleost Poecilia latipinna

Global climate change and increases in sea levels will affect coastal marine communities. The conservation of these ecologically important areas will be a challenge because of their wide geographic distribution, ecological diversity and species richness. To address this problem, we need to better understand how the genetic variation of the species in these communities is distributed within local populations, among populations and between distant regions. In this study we apply genotyping by sequencing (GBS) and examine 955 SNPs to determine Sailfin molly (Poecilia latipinna) genetic diversity among three geographically close mangrove salt marsh flats in the Florida Keys compared to populations in southern and northern Florida. The questions we are asking are whether there is sufficient genetic variation among isolated estuarine fish within populations and whether there are significant divergences among populations. Additionally, we want to know if GBS approaches agree with previous studies using more traditional molecular approaches. We are able to identify large genetic diversity within each saltmarsh community (π ≈ 36%). Additionally, among the Florida Key populations and the mainland or between southern and northern Florida regions, there are significant differences in allele frequencies seen in population structure and evolutionary relationships among individuals. Surprisingly, even though the cumulative F_ST value using all 955 SNPs within the three Florida Key populations is small, there are 29 loci with significant F_ST values, and 11 of these were outliers suggestive of adaptive divergence. These data suggest that among the salt marsh flats surveyed here, there is significant genetic diversity within each population and small but significant differences among populations. Much of the genetic variation within and among populations found here with GBS is very similar to previous studies using allozymes and microsatellites. However, the meaningful difference between GBS and these previous measures of genetic diversity is the number of loci examined, which allows more precise delineations of population structure as well as facilitates identifying loci with excessive F_ST values that could indicate adaptive divergence.     

GENETIC CONSEQUENCES OF SEED DISPERSAL IN THREE SYMPATRIC FOREST HERBS. I. HIERARCHICAL POPULATION-GENETIC STRUCTURE

To examine the effects of seed dispersal on spatial genetic structure, we compare three sympatric species of forest herbs in the family Apiaceae whose fruits differ widely in morphological adaptations for animal-attached dispersal. Cryptotaenia canadensis has smooth fruits that are gravity dispersed, whereas Osmorhiza claytonii and Sanicula odorata fruits have appendages that facilitate their attachment to animals. The relative seed-dispersal ability among species, measured as their ability to remain attached to mammal fur, is ranked Sanicula > Osmorhiza > Cryptotaenia. We use a nested hierarchical sampling design to analyze genetic structure at spatial scales ranging from a few meters to hundreds of kilometers. Genetic differentiation among population subdivisions, estimated by average genetic distance and hierarchical F-statistics, has an inverse relationship with dispersal ability such that Cryptotaenia > Osmorhiza > Sanicula. In each species, genetic differentiation increases with distance among population subdivisions. Stochastic variation in gene flow, arising from seed dispersal by attachment to animals, may partly explain the weak relationship between pairwise spatial and genetic distance among populations and heterogeneity in estimates of single locus F-statistics. A hierarchical island model of gene flow is invoked to describe the effects of seed dispersal on population genetic structure. Seed dispersal is the predominant factor affecting variation in gene flow among these ecologically similar, taxonomically related species.     

Thrips tabaci Population Genetic Structure and Polyploidy in Relation to Competency as a Vector of Tomato Spotted Wilt Virus

Knowledge of population-level genetic differences can help explain variation among populations of insect vectors in their role in the epidemiology of specific viruses. Variation in competency to transmit Tomato spotted wilt virus (TSWV) that exists among populations of Thrips tabaci has been associated with the presence of cryptic species that exhibit different modes of reproduction and host ranges. However, recent findings suggest that vector competency of T. tabaci at any given location depends on the thrips and virus populations that are present. This study characterizes the population genetic structure of T. tabaci collected from four locations in North Carolina and examines the relationship between population genetic structure and variation in TSWV transmission by T. tabaci. Mitochondrial COI sequence analysis revealed the presence of two genetically distinct groups with one characterized by thelytokous, parthenogenetic reproduction and the other by arrhenotokous, sexual reproduction. Using a set of 11 microsatellite markers that we developed to investigate T. tabaci population genetic structure, we identified 17 clonal groups and found significant genetic structuring among the four NC populations that corresponded to the geographic locations where the populations were collected. Application of microsatellite markers also led to the discovery of polyploidy in this species. All four populations contained tetraploid individuals, and three contained both diploid and tetraploid individuals. Analysis of variation in transmission ofTSWV among isofemale lines initiated with individuals used in this study revealed that ‘clone assignment,’ ‘virus isolate’ and their interaction significantly influenced vector competency. These results highlight the importance of interactions between specific T. tabaci clonal types and specific TSWV isolates underlying transmission of TSWV by T. tabaci.