Measuring population differentiation using GST or D? A simulation study with microsatellite DNA markers under a finite island model and nonequilibrium conditions

The genetic differentiation of populations is a key parameter in population genetic investigations. Wright's F(ST) (and its relatives such as G(ST) ) has been a standard measure of differentiation. However, the deficiencies of these indexes have been increasingly realized in recent years, leading to some new measures being proposed, such as Jost's D (Molecular Ecology, 2008; 17, 4015). The existence of these new metrics has stimulated considerable debate and induced some confusion on which statistics should be used for estimating population differentiation. Here, we report a simulation study with neutral microsatellite DNA loci under a finite island model to compare the performance of G(ST) and D, particularly under nonequilibrium conditions. Our results suggest that there exist fundamental differences between the two statistics, and neither G(ST) nor D operates satisfactorily in all situations for quantifying differentiation. D is very sensitive to mutation models but G(ST) noticeably less so, which limits D's utility in population parameter estimation and comparisons across genetic markers. Also, the initial heterozygosity of the starting populations has some important effects on both the individual behaviours of G(ST) and D and their relative behaviours in early differentiation, and this effect is much greater for D than G(ST) . In the early stages of differentiation, when initial heterozygosity is relatively low (<0.5, if the number of subpopulations is large), G(ST) increases faster than D; the opposite is true when initial heterozygosity is high. Therefore, the state of the ancestral population appears to have some lasting impacts on population differentiation. In general, G(ST) can measure differentiation fairly well when heterozygosity is low whatever the causes; however, when heterozygosity is high (e.g. as a result of either high mutation rate or high initial heterozygosity) and gene flow is moderate to strong, G(ST) fails to measure differentiation. Interestingly, when population size is not very small (e.g. N ≥ 1000), G(ST) measures differentiation quite linearly with time over a long duration when gene flow is absent or very weak even if mutation rate is not low (e.g. μ = 0.001). In contrast, D, as a differentiation measure, performs rather robustly in all these situations. In practice, both indexes should be calculated and the relative levels of heterozygosities (especially H(S) ) and gene flow taken into account. We suggest that a comparison of the two indexes can generate useful insights into the evolutionary processes that influence population differentiation.     

Rate and directionality of mutations and effects of allele size constraints at anonymous, gene-associated, and disease-causing trinucleotide loci.

We studied the patterns of within- and between-population variation at 29 trinucleotide loci in a random sample of 200 healthy individuals from four diverse populations: Germans, Nigerians, Chinese, and New Guinea highlanders. The loci were grouped as disease-causing (seven loci with CAG repeats), gene-associated (seven loci with CAG/CCG repeats and eight loci with AAT repeats), or anonymous (seven loci with AAT repeats). We used heterozygosity and variance of allele size (expressed in units of repeat counts) as measures of within-population variability and GST (based on heterozygosity as well as on allele size variance) as the measure of genetic differentiation between populations. Our observations are: (1) locus type is the major significant factor for differences in within-population genetic variability; (2) the disease-causing CAG repeats (in the nondisease range of repeat counts) have the highest within-population variation, followed by the AAT-repeat anonymous loci, the AAT-repeat gene-associated loci, and the CAG/CTG-repeat gene-associated loci; (3) an imbalance index beta, the ratio of the estimates of the product of effective population size and mutation rate based on allele size variance and heterozygosity, is the largest for disease-causing loci, followed by AAT- and CAG/CCG-repeat gene-associated loci and AAT-repeat anonymous loci; (4) mean allele size correlates positively with allele size variance for AAT- and CAG/CCG-repeat gene-associated loci and negatively for anonymous loci; and (5) GST is highest for the disease-causing loci. These observations are explained by specific differences of rates and patterns of mutations in these four groups of trinucleotide loci, taking into consideration the effects of the past demographic history of the modern human population.     

THE EFFICACY OF DIVERGENCE HITCHHIKING IN GENERATING GENOMIC ISLANDS DURING ECOLOGICAL SPECIATION

Genes under divergent selection flow less readily between populations than other loci. This observation has led to verbal “divergence hitchhiking” models of speciation in which decreased interpopulation gene flow surrounding loci under divergent selection can generate large regions of differentiation within the genome (genomic islands). The efficacy of this model in promoting speciation depends on the size of the region affected by divergence hitchhiking. Empirical evidence is mixed, with examples of both large and small genomic islands. To address these empirical discrepancies and to formalize the theory, we present mathematical models of divergence hitchhiking, which examine neutral differentiation around selected sites. For a single locus under selection, regions of differentiation do not extend far along a chromosome away from a selected site unless both effective population sizes and migration rates are low. When multiple loci are considered, regions of differentiation can be larger. However, with many loci under selection, genome‐wide divergence occurs and genomic islands are erased. The results show that divergence hitchhiking can generate large regions of differentiation, but that the conditions under which this occurs are limited. Thus, speciation may often require multifarious selection acting on many, isolated and physically unlinked genes. How hitchhiking promotes further adaptive divergence warrants consideration.     

A power analysis of microsatellite-based statistics for inferring past population growth

We present results concerning the power to detect past population growth using three microsatellite-based statistics available in the current literature: (1) that based on between-locus variability, (2) that based on the shape of allele size distribution, and (3) that based on the imbalance between variance and heterozygosity at a locus. The analysis is based on the single-step stepwise mutation model. The power of the statistics is evaluated for constant, as well as variable, mutation rates across loci. The latter case is important, since it is a standard procedure to pool data collected at a number of loci, and mutation rates at microsatellite loci are known to be different. Our analysis indicates that the statistic based on the imbalance between allele size variance and heterozygosity at a locus has the highest power for detection of population growth, particularly when mutation rates vary across loci.     

Allozyme diversity and genetic divergence of the dolly varden Salvelinus malma Walbaum from the Kuril islands

Genetic variation was studied in the southern subspecies of the Asian Dolly Varden Salvelinus malma krascheninnikovi from the Kuril Islands. Thirty-six genetic loci controlling 19 enzyme systems were analyzed in 13 Dolly Varden populations from the Shumshu, Paramushir, Onekotan, Rasshua, Simushir, Urup, Iturup, and Kunashir islands. In the studied populations, the proportion of polymorphic loci was 35 to 85% and the mean heterozygosity was 0.104 to 0.173; populations from the Kunashir Island were characterized by maximum heterozygosity. In the island populations examined, significant inter-population heterogeneity of allele frequencies was found for all studied population pairs. For the total population of all islands, the inter-population diversity (GST = 0.188) was comparable to this parameter for the total population from the Kunashir Island (GST = 0.170). Genetic distances between populations did not correlate with the corresponding geographical distances, which indicates the lack of a pronounced gene exchange between the island populations. Cluster analysis and multidimensional scaling based on genetic distances did not reveal clear groups among the studied populations but indicated greater similarity within the Iturup-Simushir-Urup-Paramushir group and a greater genetic divergence of the Kunashir, Onekotan, Rasshua, and especially Shumshu populations. In the Shumshu population, allele frequencies indicate the admixture of genes of the northern Dolly Varden. The observed pattern of genetic differentiation was probably caused largely by genetic drift under the conditions of a limited gene flow because of homing (which is typical of the Dolly Varden) and the presence of isolated nonanadromous populations. The population-genetic analysis of the Dolly Varden from the Kuril Islands does not give grounds to distinguish any other isolated Dolly Varden species in this region than S. malma, which is represented by the southern form S. m. krascheninnikovi with an admixture of the northern form S. m. malma in the Shumshu Island.     

G'ST and D do not replace FST

The genetic differentiation among populations is affected by mutation as well as by migration, drift and selection. For loci with high mutation rates, such as microsatellites, the amount of mutation can influence the values of indices of differentiation such as G(ST) and F(ST). For many purposes, this effect is undesirable, and as a result, new indices such as G'(ST) and D have been proposed to measure population differentiation. This paper shows that these new indices are not effective measures of the causes or consequences of population structure. Both G'(ST) and D depend heavily on mutation rate, but both are insensitive to any population genetic process when the mutation rate is high relative to the migration rate. Furthermore, D is specific to the locus being measured, and so little can be inferred about the population demography from D. However, at equilibrium, D may provide an index of whether a particular marker is more strongly affected by mutation than by migration. I argue that F(ST) is a more important summary of the effects of population structure than D and that R(ST) or other measures that explicitly account for the mutation process are much better than G(ST), G'(ST), or D for highly mutable markers. Markers with lower mutation rates will often be easier to interpret.     

Hitchhiking effect of a beneficial mutation spreading in a subdivided population

A central problem in population genetics is to detect and analyze positive natural selection by which beneficial mutations are driven to fixation. The hitchhiking effect of a rapidly spreading beneficial mutation, which results in local removal of standing genetic variation, allows such an analysis using DNA sequence polymorphism. However, the current mathematical theory that predicts the pattern of genetic hitchhiking relies on the assumption that a beneficial mutation increases to a high frequency in a single random-mating population, which is certainly violated in reality. Individuals in natural populations are distributed over a geographic space. The spread of a beneficial allele can be delayed by limited migration of individuals over the space and its hitchhiking effect can also be affected. To study this effect of geographic structure on genetic hitchhiking, we analyze a simple model of directional selection in a subdivided population. In contrast to previous studies on hitchhiking in subdivided populations, we mainly investigate the range of sufficiently high migration rates that would homogenize genetic variation at neutral loci. We provide a heuristic mathematical analysis that describes how the genealogical structure at a neutral locus linked to the locus under selection is expected to change in a population divided into two demes. Our results indicate that the overall strength of genetic hitchhiking--the degree to which expected heterozygosity decreases--is diminished by population subdivision, mainly because opportunity for the breakdown of hitchhiking by recombination increases as the spread of the beneficial mutation across demes is delayed when migration rate is much smaller than the strength of selection. Furthermore, the amount of genetic variation after a selective sweep is expected to be unequal over demes: a greater reduction in expected heterozygosity occurs in the subpopulation from which the beneficial mutation originates than in its neighboring subpopulations. This raises a possibility of detecting a "hidden" geographic structure of population by carefully analyzing the pattern of a selective sweep.     

Reduced microsatellite heterozygosity in island endemics supports the role of long-term effective population size in avian microsatellite diversity

Because of the high mutation rate of microsatellites, polymorphism at microsatellite loci might be predicted to reflect the effective population size over a time span of about 10,000?years and thus to be associated with biogeographic factors impacting species on that time frame. This prediction was tested by comparing heterozygosity at microsatellite loci from 294 bird species, including 58 species endemic to oceanic islands. Controlling statistically for phylogenetic effects, mean heterozygosity was significantly reduced in oceanic island endemics compared to other species. There was also an effect of current endangerment, statistically independent of the effect of island endemicity. These results support the hypothesis that long-term effective population size can be an important causative factor behind differences among species with respect to microsatellite heterozygosity.     

A standardized genetic differentiation measure

Interpretation of genetic differentiation values is often problematic because of their dependence on the level of genetic variation. For example, the maximum level of GST is less than the average within population homozygosity so that for highly variable loci, even when no alleles are shared between subpopulations, GST may be low. To remedy this difficulty, a standardized measure of genetic differentiation is introduced here, one which has the same range, 0-1, for all levels of genetic variation. With this measure, the magnitude is the proportion of the maximum differentiation possible for the level of subpopulation homozygosity observed. This is particularly important for situations in which the mutation rate is of the same magnitude or higher than the rate of gene flow. The standardized measure allows comparison between loci with different levels of genetic variation, such as allozymes and microsatellite loci, or mtDNA and Y-chromosome genes, and for genetic differentiation for organisms with different effective population sizes.     

GENETIC HITCHHIKING AND THE DYNAMIC BUILDUP OF GENOMIC DIVERGENCE DURING SPECIATION WITH GENE FLOW

A major issue in evolutionary biology is explaining patterns of differentiation observed in population genomic data, as divergence can be due to both direct selection on a locus and genetic hitchhiking. “Divergence hitchhiking” (DH) theory postulates that divergent selection on a locus reduces gene flow at physically linked sites, facilitating the formation of localized clusters of tightly linked, diverged loci. “Genome hitchhiking” (GH) theory emphasizes genome‐wide effects of divergent selection. Past theoretical investigations of DH and GH focused on static snapshots of divergence. Here, we used simulations assessing a variety of strengths of selection, migration rates, population sizes, and mutation rates to investigate the relative importance of direct selection, GH, and DH in facilitating the dynamic buildup of genomic divergence as speciation proceeds through time. When divergently selected mutations were limiting, GH promoted divergence, but DH had little measurable effect. When populations were small and divergently selected mutations were common, DH enhanced the accumulation of weakly selected mutations, but this contributed little to reproductive isolation. In general, GH promoted reproductive isolation by reducing effective migration rates below that due to direct selection alone, and was important for genome‐wide “congealing” or “coupling” of differentiation (F_ST) across loci as speciation progressed.     

Divergent selection and heterogeneous genomic divergence

Levels of genetic differentiation between populations can be highly variable across the genome, with divergent selection contributing to such heterogeneous genomic divergence. For example, loci under divergent selection and those tightly physically linked to them may exhibit stronger differentiation than neutral regions with weak or no linkage to such loci. Divergent selection can also increase genome‐wide neutral differentiation by reducing gene flow (e.g. by causing ecological speciation), thus promoting divergence via the stochastic effects of genetic drift. These consequences of divergent selection are being reported in recently accumulating studies that identify: (i) ‘outlier loci’ with higher levels of divergence than expected under neutrality, and (ii) a positive association between the degree of adaptive phenotypic divergence and levels of molecular genetic differentiation across population pairs [‘isolation by adaptation’ (IBA)]. The latter pattern arises because as adaptive divergence increases, gene flow is reduced (thereby promoting drift) and genetic hitchhiking increased. Here, we review and integrate these previously disconnected concepts and literatures. We find that studies generally report 5–10% of loci to be outliers. These selected regions were often dispersed across the genome, commonly exhibited replicated divergence across different population pairs, and could sometimes be associated with specific ecological variables. IBA was not infrequently observed, even at neutral loci putatively unlinked to those under divergent selection. Overall, we conclude that divergent selection makes diverse contributions to heterogeneous genomic divergence. Nonetheless, the number, size, and distribution of genomic regions affected by selection varied substantially among studies, leading us to discuss the potential role of divergent selection in the growth of regions of differentiation (i.e. genomic islands of divergence), a topic in need of future investigation.     

华东地区青冈种群的遗传多样性及遗传分化

采用垂直板型聚丙烯酰胺凝胶电泳测定了华东地区6个青冈(Cyclobalanopsis glauca(Thunb.)Oerst.)种群的遗传多样性和遗传分化程度以及基因流。青冈种和种群水平都维持有较高的遗传多样性,期望杂合度分别为0.2252和0.2126,观察杂合度分别为0.1661和0.1771。种群间的遗传分化程度较低,分化度仅为5.6％,种群间的遗传一致度和遗传距离的均值分别为0.9729和0.0276。种群间的分化时间为1.4～27万年。基因流分别为4.21和20.49。     

Establishment of new mutations under divergence and genome hitchhiking

Theoretical models addressing genome-wide patterns of divergence during speciation are needed to help us understand the evolutionary processes generating empirical patterns. Here, we examine a critical issue concerning speciation-with-gene flow: to what degree does physical linkage (r < 0.5) of new mutations to already diverged genes aid the build-up of genomic islands of differentiation? We used simulation and analytical approaches to partition the probability of establishment for a new divergently selected mutation when the mutation (i) is the first to arise in an undifferentiated genome (the direct effect of selection), (ii) arises unlinked to any selected loci (r = 0.5), but within a genome that has some already diverged genes (the effect of genome-wide reductions in gene flow for facilitating divergence, which we term 'genome hitchhiking'), and (iii) arises in physical linkage to a diverged locus (divergence hitchhiking). We find that the strength of selection acting directly on a new mutation is generally the most important predictor for establishment, with divergence and genomic hitchhiking having smaller effects. We outline the specific conditions under which divergence and genome hitchhiking can aid mutation establishment. The results generate predictions about genome divergence at different points in the speciation process and avenues for further work.     

Estimates of DNA and protein sequence divergence: an examination of some assumptions

Some of the assumptions underlying estimates of DNA and protein sequence divergence are examined. A solution for the variance of these estimates that allows for different mutation rates and different population sizes in each species and for an arbitrary structure in the initial population is obtained. It is shown that these conditions do not strongly affect estimates of divergence. In general, they cause the variance of divergence to be smaller than a binomial variance. Thus, the binomial variance that is usually assumed for these estimates is safely conservative. It is shown that variability in the mutation rate among sites can have an effect as large as or larger than variability in the mutation rate among bases. Variability in the mutation rate among bases and among sites causes the number of substitutions between two sequences to be underestimated. Protein and DNA sequences from several species are collected to estimate the variability in mutation rates among sites. When many homologous sequences are known, standard methods to estimate this variability can be used. The estimates of this variability show that this factor is important when considering the spectrum of spontaneous mutations and is strongly reflected in the divergence of sequences. Smaller variability is found for the third position of codons than for the first and second codon positions. This may be because of less selective constraints on this position or because the third position has been saturated with mutations for the sequences examined.      

The effect of epistasis on sexually antagonistic genetic variation

There is increasing evidence of segregating sexually antagonistic (SA) genetic variation for fitness in laboratory and wild populations, yet the conditions for the maintenance of such variation can be restrictive. Epistatic interactions between genes can contribute to the maintenance of genetic variance in fitness and we suggest that epistasis between SA genes should be pervasive. Here, we explore its effect on SA genetic variation in fitness using a two locus model with negative epistasis. Our results demonstrate that epistasis often increases the parameter space showing polymorphism for SA loci. This is because selection in one locus is affected by allele frequencies at the other, which can act to balance net selection in males and females. Increased linkage between SA loci had more marginal effects. We also show that under some conditions, large portions of the parameter space evolve to a state where male benefit alleles are fixed at one locus and female benefit alleles at the other. This novel effect of epistasis on SA loci, which we term the ‘equity effect’, may have important effects on population differentiation and may contribute to speciation. More generally, these results support the suggestion that epistasis contributes to population divergence.     

Statistical properties of population differentiation estimators under stepwise mutation in a finite island model

Microsatellite loci mutate at an extremely high rate and are generally thought to evolve through a stepwise mutation model. Several differentiation statistics taking into account the particular mutation scheme of the microsatellite have been proposed. The most commonly used is R(ST) which is independent of the mutation rate under a generalized stepwise mutation model. F(ST) and R(ST) are commonly reported in the literature, but often differ widely. Here we compare their statistical performances using individual-based simulations of a finite island model. The simulations were run under different levels of gene flow, mutation rates, population number and sizes. In addition to the per locus statistical properties, we compare two ways of combining R(ST) over loci. Our simulations show that even under a strict stepwise mutation model, no statistic is best overall. All estimators suffer to different extents from large bias and variance. While R(ST) better reflects population differentiation in populations characterized by very low gene-exchange, F(ST) gives better estimates in cases of high levels of gene flow. The number of loci sampled (12, 24, or 96) has only a minor effect on the relative performance of the estimators under study. For all estimators there is a striking effect of the number of samples, with the differentiation estimates showing very odd distributions for two samples.     

Ascertainment bias in estimates of average heterozygosity.

Population geneticists work with a nonrandom sample of the human genome. Conventional practice ensures that unusually variable loci are most likely to be discovered and thus included in the sample of loci. Consequently, estimates of average heterozygosity are biased upward. In what follows we describe a model of this bias. When the mutation rate varies among loci, bias is increased. This effect is only moderate, however, so that a model of invariant mutation rates provides a reasonable approximation. Bias is pronounced when estimated heterozygosity is < approximately 35% Consequently, it probably affects estimates from classical polymorphisms as well as from restriction-site polymorphisms. Estimates from short-tandem-repeat polymorphisms have negligible bias, because of their high heterozygosity. Bias should vary not only among categories of polymorphism but also among populations. It should be largest in European populations, since these are the populations in which most polymorphisms were discovered. As this argument predicts, European estimates exceed those of Africa and Asia at systems with large bias. The magnitude of this European excess is consistent with the version of our model in which mutation rates vary across loci.     

Rates of DNA sequence evolution are not sex-biased in Drosophila melanogaster and D. simulans

To determine whether male- or female-biased mutation rates have affected the molecular evolution of Drosophila melanogaster and D. simulans, we calculated the male-to-female ratio of germline cell divisions ([symbol: see text]) from germline generation data and the male-to-female ratio of mutation rate ([symbol: see text]) by comparing chromosomal levels of nucleotide divergence. We found that the ratio of germline cell divisions changes from indicating a weak female bias to indicating a weak male bias as the age of reproduction increases. The range of [symbol: see text] values that we observed, however, does not lead us to expect much, if any, difference in mutation rate between the sexes. Silent and intron nucleotide divergence were compared between nine loci on the X chromosome and nine loci on the second and third chromosomes. The average levels of nucleotide divergence were not significantly different across the chromosomes, although both silent and intron sites show a trend toward slightly more divergence on the X. These results indicate a lack of sex- or chromosome-biased molecular evolution in D. melanogaster and D. simulans.      

Patterns of differentiation and hybridization in North American wolflike canids, revealed by analysis of microsatellite loci

Genetic divergence and gene flow among closely related populations are difficult to measure because mutation rates of most nuclear loci are so low that new mutations have not had sufficient time to appear and become fixed. Microsatellite loci are repeat arrays of simple sequences that have high mutation rates and are abundant in the eukaryotic genome. Large population samples can be screened for variation by using the polymerase chain reaction and polyacrylamide gel electrophoresis to separate alleles. We analyzed 10 microsatellite loci to quantify genetic differentiation and hybridization in three species of North American wolflike canids. We expected to find a pattern of genetic differentiation by distance to exist among wolflike canid populations, because of the finite dispersal distances of individuals. Moreover, we predicted that, because wolflike canids are highly mobile, hybrid zones may be more extensive and show substantial changes in allele frequency, relative to nonhybridizing populations. We demonstrate that wolves and coyotes do not show a pattern of genetic differentiation by distance. Genetic subdivision in coyotes, as measured by theta and Gst, is not significantly different from zero, reflecting persistent gene flow among newly established populations. However, gray wolves show significant subdivision that may be either due to drift in past Ice Age refugia populations or a result of other causes. Finally, in areas where gray wolves and coyotes hybridize, allele frequencies of gray wolves are affected, but those of coyotes are not. Past hybridization between the two species in the south-central United States may account for the origin of the red wolf.      

On the effects of background selection in small populations on comparisons of molecular variation

Deleterious mutations affect genetic variation at linked neutral loci. Neutral variation can be reduced due to background selection, but in small population and with tight linkage such variation may increase due to associative overdominance. Here I report the results of computer simulations of diploid genotypes in small populations, where I look at the effect of deleterious mutations and linkage on comparisons of intra- and interspecific variation. Each chromosome consisted of 2000 loci where deleterious and neutral mutations occurred. The ratio of nonsynonymous to synonymous substitution rates (Ka/Ks) either increases with tight linkage or is unaffected, depending on the strength of selection. The ratio of the numbers of segregating mutations to the number of fixed mutations decreases under the conditions leading to background selection but can increase at tight linkage. Numbers of segregating sites (Sn) are less affected than nucleotide site diversity (pi), pi reduces more than Sn at intermediate linkage, but pi increases more than Sn when linkage is tight. Similar effects as found for Sn and pi are observed for heterozygosity and variance in allele size of tandem repeat loci.