Low genetic diversity and lack of population structure in the endangered Galápagos penguin (<Emphasis Type="Italic">Spheniscus mendiculus</Emphasis>)

Long-term monitoring of the endangered Galápagos penguin (Spheniscus mendiculus) has indicated poor reproductive periods and severe population fluctuations in association with El Niño – Southern Oscillation events. An earlier mark and recapture study indicated that adults exhibit some degree of breeding-site and mate fidelity, and that juveniles potentially move more frequently than adults; however, the extent to which migrants and gene flow occur between islands within the Galápagos archipelago is largely unknown. This study tested the hypothesis that geographic isolation and adult breeding philopatry has led to a degree of genetic differentiation between island subpopulations within the archipelago. We examined the genetic diversity within and among different subpopulations and the extent to which gene flow occurs between island subpopulations. Estimates of allelic richness and gene diversity were not significantly different between subpopulations. Tests to detect genetic heterogeneity failed to reject the H ₀ of no difference in allele frequencies for chi-square (P = 0.28) and Fisher’s exact test (P = 0.19). All pairwise values of the F _ST variant θ were not significant, while a power analysis revealed a >99% probability of detecting a biologically true F _ST of 0.05. Migration estimates in BAYESASS+ suggest symmetrical gene flow throughout the species’ distribution. Our results indicate a low level of genetic diversity throughout the population and a seemingly high level of gene flow between subpopulations. We argue that the Galápagos penguin should be managed as one panmictic population and we discuss the risk of disease threats in the archipelago.     

Drift variances of FSTand GST statistics obtained from a finite number of isolated populations

Approximate formulas for the mean and variance of the F_STor G_ST statistic in a finite number of isolated populations are developed under the effect of random genetic drift. Computer simulation has shown that the approximate formulas give a fairly accurate result unless the initial frequency of one of the alleles involved is close to 1 and t/2N is large, where N is the effective size of a subpopulation and t is the number of generations. It is shown that when the number of subpopulations (s) is small, the mean of F_STor G_ST depends on the initial gene frequencies as well as on s. When the initial frequencies of all alleles are nearly equal to each other and the number of subpopulations is large, the distribution of F_ST in the early generations is bell-shaped. In this case Lewontin and Krakauer's k parameter is approximately 2 or less. However, if one of the initial allele frequencies is close to 1, the distribution is skewed and leptokurtic, and the k parameter often becomes larger than 2 in later generations. Thus, even under pure random genetic drift, Lewontin and Krakauer's test of selective neutrality of polymorphic genes in terms of F_ST is not always valid. It is also shown that Jacquard's approximate formula for k generally gives an overestimate.     

Genealogy and subpopulation differentiation under various models of population structure

 The structured coalescent is used to calculate some quantities relating to the genealogy of a pair of homologous genes and to the degree of subpopulation differentiation, under a range of models of subdivided populations and assuming the infinite alleles model of neutral mutation. The classical island and stepping-stone models of population structure are considered, as well as two less symmetric models. For each model, we calculate the Laplace transform of the distribution of the coalescence time of a pair of genes from specified locations and the corresponding mean and variance. These results are then used to calculate the values of Wright’s coefficient F _ST , its limit as the mutation rate tends to zero and the limit of its derivative with respect to the mutation rate as the mutation rate tends to zero. From this derivative it is seen that F _ST can depend strongly on the mutation rate, for example in the case of an essentially one-dimensional habitat with many subpopulations where gene flow is restricted to neighbouring subpopulations. Received: 1 October 1997 / Revised version: 15 March 1998     

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.     

Relative performance of Bayesian clustering software for inferring population substructure and individual assignment at low levels of population differentiation

Traditional methods for characterizing genetic differentiation among populations rely on a priori grouping of individuals. Bayesian clustering methods avoid this limitation by using linkage and Hardy–Weinberg disequilibrium to decompose a sample of individuals into genetically distinct groups. There are several software programs available for Bayesian clustering analyses, all of which describe a decrease in the ability to detect distinct clusters as levels of genetic differentiation among populations decrease. However, no study has yet compared the performance of such methods at low levels of population differentiation, which may be common in species where populations have experienced recent separation or high levels of gene flow. We used simulated data to evaluate the performance of three Bayesian clustering software programs, PARTITION, STRUCTURE, and BAPS, at levels of population differentiation below F _ST=0.1. PARTITION was unable to correctly identify the number of subpopulations until levels of F _ST reached around 0.09. Both STRUCTURE and BAPS performed very well at low levels of population differentiation, and were able to correctly identify the number of subpopulations at F _ST around 0.03. The average proportion of an individual’s genome assigned to its true population of origin increased with increasing F _ST for both programs, reaching over 92% at an F _ST of 0.05. The average number of misassignments (assignments to the incorrect subpopulation) continued to decrease as F _ST increased, and when F _ST was 0.05, fewer than 3% of individuals were misassigned using either program. Both STRUCTURE and BAPS worked extremely well for inferring the number of clusters when clusters were not well-differentiated (F _ST=0.02–0.03), but our results suggest that F _ST must be at least 0.05 to reach an assignment accuracy of greater than 97%.     

Is F ST obsolete?

Since the introduction of allozyme methods inthe mid 1960s it has been a standard practiceto report Wright's measure of populationsubdivision, F _ST, for surveys ofgenetic variation. Its widespread use hasprovided us with a sense of what values can beexpected in particular situations and how theycan be interpreted. With some theoreticaljustification, F _ST has also beenused to estimate rates of gene flow. Howeverthere are conditions under which F _STis inappropriate for gene flow estimation andcan lead to incorrect or even absurdconclusions. These pitfalls have promptedcritics to suggest that F _ST hasfailed to deliver what its proponents havepromised and should be abandoned. A furtherchallenge has been the development of newmethods that offer even greater promise. Thusit is reasonable to ask if perhaps it is timeto retire F _ST and turn to new andmore powerful methods for the inference of geneflow from genetic markers. Here I will arguethat although gene flow should be estimated bymore powerful approaches whenever practical,F _ST remains a useful measure of theaverage effects of gene flow and will continueto be used for comparative purposes.     

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.     

Estimates of Genetic Differentiation Measured by F(ST) Do Not Necessarily Require Large Sample Sizes When Using Many SNP Markers

Population genetic studies provide insights into the evolutionary processes that influence the distribution of sequence variants within and among wild populations. F_ST is among the most widely used measures for genetic differentiation and plays a central role in ecological and evolutionary genetic studies. It is commonly thought that large sample sizes are required in order to precisely infer F_ST and that small sample sizes lead to overestimation of genetic differentiation. Until recently, studies in ecological model organisms incorporated a limited number of genetic markers, but since the emergence of next generation sequencing, the panel size of genetic markers available even in non-reference organisms has rapidly increased. In this study we examine whether a large number of genetic markers can substitute for small sample sizes when estimating F_ST. We tested the behavior of three different estimators that infer F_ST and that are commonly used in population genetic studies. By simulating populations, we assessed the effects of sample size and the number of markers on the various estimates of genetic differentiation. Furthermore, we tested the effect of ascertainment bias on these estimates. We show that the population sample size can be significantly reduced (as small as n = 4–6) when using an appropriate estimator and a large number of bi-allelic genetic markers (k>1,000). Therefore, conservation genetic studies can now obtain almost the same statistical power as studies performed on model organisms using markers developed with next-generation sequencing.     

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.     

Genetic structure of the wild boar population in Portugal: Evidence of a recent bottleneck

The present study assesses the degree of genetic structure and the presence of recent genetic bottlenecks in the wild boar population in Portugal. One hundred and ten individuals were sampled after capture during organised legal drive hunts, conducted in 58 municipalities across the continental territory, during the game seasons of 2002/2003 and 2003/2004. Individuals were genetically typed at six microsatellite loci using multiplex PCR amplification. Significant deviations from Hardy–Weinberg equilibrium were found for the total population of wild boar in Portugal. Wild boar population genetic structure was assessed using Bayesian methods, suggesting the existence of three subpopulations (North, Centre and South). Tests were conducted to detect the presence of potential migrants and hybrids between subpopulations. After exclusion of these individuals, three sets of wild boars representative of respective subpopulations were distinguished and tested for the effects of recent bottlenecks. Genetic distances between pairs of subpopulations were quantified using F_ST and R_ST estimators, revealing a variation of 0.138–0.178 and 0.107–0.198, respectively. On the basis of genetic and distribution data for Portuguese wild boar from the beginning of the 20th century, a model of strong demographic decline and contraction to isolated refuge areas at the national level, followed by a recovery and expansion towards former distribution limits is suggested. Some evidence points to present admixture among subpopulations in contact areas.     

Large effective population sizes and high levels of gene flow between subpopulations of Lilium cernuum (Liliaceae)

The Baekdudaegan, a mountain range that runs north to south along the Korean Peninsula, has been suggested to harbor important glacial refugia for boreal and temperate plant species. A series of allozyme-based genetic studies supports this trend. A large effective population size (N_e) is suggested as one of major factors contributing to maintaining moderate or high levels of within-population genetic variation in these plant species. To test this hypothesis, we examined the levels and patterns of allozyme diversity, tested recent bottlenecks, and estimated recent migration rates in 10 subpopulations (collected within a distance of ca. 640 m) of the boreal Lilium cernuum at Mt. Deokhang, in the central part of the Baekdudaegan. We found high levels of within-population genetic variation as well as a low between-population genetic differentiation (H_e = 0.206 and F_ST = 0.019). Based on the F_ST estimate and mean recent migration rate, we approximately calculated a total effective population size of 508 across 10 subpopulations. Consistent with this, we found no evidence of recent bottlenecks in the subpopulations. This study reveals that subpopulations of L. cernuum at Mt. Deokhang are effectively large (on the order of hundreds), and that high levels of gene flow occur among them, probably due to the species' high potential for seed dispersal. These demographic and life-history traits, coupled with its high levels of genetic diversity, suggests that this cold-adapted species would have found large refugial areas in these mountains (i.e., macrorefugia) during the Last Glacial Maximum.     

Distribution of mating‐type alleles and genetic variability in field populations of Leptosphaeria maculans in western Canada

Leptosphaeria maculans is the most important fungal pathogen of canola (Brassica napus, oilseed rape) that causes the devastating stem canker in canola fields of western Canada. The population genetic structure of L. maculans, represented by nine subpopulations from a 6‐year period and three different provinces in western Canada, was determined using ten minisatellite markers. Isolates collected at different locations in six consecutive years had an even distribution of MAT1‐1 and MAT1‐2 across the nine subpopulations. All subpopulations of L. maculans exhibited a moderate gene diversity (H = 0.356–0.585). The majority of the genetic variation occurred within subpopulations. Approximately 8% and 4% of the variations were distributed between sampling year and location, respectively. Genetic distance (F_ST) results, using analysis of molecular variation (AMOVA), indicated that subpopulation pairing within isolates by year ranged from F_ST = 0.010 to 0.109, and the location subpopulation ranged from F_ST = 0.038 to 0.085. Bayesian clustering analyses of multiloci inferred two distinct clusters in all the subpopulations examined. This study indicates a relatively high degree of gene exchange between the different L. maculans isolates. Our results suggest that this can occur in the wide growing areas of canola fields in western Canada. This gene exchange produced different gene allele frequencies and divergence between populations.     

GENE FLOW IN GROUND BEETLES (COLEOPTERA: CARABIDAE) OF DIFFERING HABITAT PREFERENCE AND FLIGHT-WING DEVELOPMENT

Estimates of gene flow vary 100-fold among five carabid species, ranging from the winged lowland subtropical Agonum elongatulum to the flightless montane temperate Platynus angustatus. Results based on Wright's (1943) F_ST method, and Slatkin's (1981) graphical and (1985a) private-allele methods are concordant. Genetic heterogeneity, measured by Wright's F_ST, is not correlated with degree of flight-wing development; one fully winged species exhibits heterogeneity of the same order as a vestigially winged species. Genetic heterogeneity is positively correlated with the average elevation of collection sites for these species. Lower levels of gene flow associated with greater genetic subdivision may occur in upland areas because of habitat fragmentation (due to topographic diversity) and habitat persistence (leading to a lower extinction rate for populations). In at least one species, the distribution of stable infraspecific polymorphisms indicates that the high estimate of present-day gene flow is likely to be due to historical gene flow and not to present-day conditions.     

THE EFFECT OF COLLECTIVE DISPERSAL ON THE GENETIC STRUCTURE OF A SUBDIVIDED POPULATION

Correlated dispersal paths between two or more individuals are widespread across many taxa. The population genetic implications of this collective dispersal have received relatively little attention. Here we develop two‐sample coalescent theory that incorporates collective dispersal in a finite island model to predict expected coalescence times, genetic diversities, and F‐statistics. We show that collective dispersal reduces mixing in the system, which decreases expected coalescence times and increases F_ST. The effects are strongest in systems with high migration rates. Collective dispersal breaks the invariance of within‐deme coalescence times to migration rate, whatever the deme size. It can also cause F_ST to increase with migration rate because the ratio of within‐ to between‐deme coalescence times can decrease as migration rate approaches unity. This effect is most biologically relevant when deme size is small. We find qualitatively similar results for diploid and gametic dispersal. We also demonstrate with simulations and analytical theory the strong similarity between the effects of collective dispersal and anisotropic dispersal. These findings have implications for our understanding of the balance between drift–migration–mutation in models of neutral evolution. This has applied consequences for the interpretation of genetic structure (e.g., chaotic genetic patchiness) and estimation of migration rates from genetic data.     

Genetic variance in the F2 generation of divergently selected parents

 Either by selective breeding for population divergence or by using natural population differences, F₂ and advanced generation hybrids can be developed with high variances. We relate the size of the genetic variance to the population divergence based on a forward and backward mutation model at a locus with two alleles with additive gene action. The effects of population size and initial gene frequency are also explored. Larger parental population sizes increase the F₂ genetic variance if the initial probability distribution is uniform or U-shaped. However, population size has the opposite effect if the initial distribution of gene frequencies is skewed such as it would be with newly arriving alleles. These alleles contribute to the genetic variance sooner when the selection pressure is higher or when the effective population size is smaller. Received: 5 April 1998 / Accepted: 22 April 1998     

Isolated in an ocean of grass: low levels of gene flow between termite subpopulations

Habitat fragmentation is one of the most important causes of biodiversity loss, but many species are distributed in naturally patchy habitats. Such species are often organized in highly dynamic metapopulations or in patchy populations with high gene flow between subpopulations. Yet, there are also species that exist in stable patchy habitats with small subpopulations and presumably low dispersal rates. Here, we present population genetic data for the ‘magnetic’ termite Amitermes meridionalis, which show that short distances between subpopulations do not hinder exceptionally strong genetic differentiation (F_ST: 0.339; R_ST: 0.636). Despite the strong genetic differentiation between subpopulations, we did not find evidence for genetic impoverishment. We propose that loss of genetic diversity might be counteracted by a long colony life with low colony turnover. Indeed, we found evidence for the inheritance of colonies by so‐called ‘replacement reproductives’. Inhabiting a mound for several generations might result in loss of gene diversity within a colony but maintenance of gene diversity at the subpopulation level.     

Testing for Spatially Divergent Selection: Comparing QST to FST

Q_ST is a standardized measure of the genetic differentiation of a quantitative trait among populations. The distribution of Q_ST''s for neutral traits can be predicted from the F_ST for neutral marker loci. To test for the neutral differentiation of a quantitative trait among populations, it is necessary to ask whether the Q_ST of that trait is in the tail of the probability distribution of neutral traits. This neutral distribution can be estimated using the Lewontin–Krakauer distribution and the F_ST from a relatively small number of marker loci. We develop a simulation method to test whether the Q_ST of a given trait is consistent with the null hypothesis of selective neutrality over space. The method is most powerful with small mean F_ST, strong selection, and a large number (>10) of measured populations. The power and type I error rate of the new method are far superior to the traditional method of comparing Q_ST and F_ST.IN 1993, Spitze (1993) and Prout and Barker (1993) introduced Q_ST, a quantitative genetic analog of Wright''s F_ST. Just as F_ST gives a standardized measure of the genetic differentiation among populations for a genetic locus, Q_ST measures the amount of genetic variance among populations relative to the total genetic variance. In the years since, Q_ST has been frequently used to test for the effects of spatially divergent (or less commonly, spatially uniform) selection (see reviews in Lynch et al. 1999; Merilä and Crnokrak 2001; McKay and Latta 2002; Howe et al. 2003; Leinonen et al. 2008; Whitlock 2008). In principle, the average Q_ST of a neutral additive quantitative trait is expected to be equal to the mean value of F_ST for neutral genetic loci. F_ST can be readily measured on commonly available genetic markers, and Q_ST can be measured as well with an appropriate breeding design in a common-garden setting. As a result, Q_ST promises to be an index of the effect of selection on the quantitative trait. If Q_ST is higher than F_ST, then this is taken as evidence of spatially divergent selection on the trait. If Q_ST is much smaller than F_ST, then this has been taken as evidence of spatially uniform stabilizing selection, which makes the trait diverge less than expected by chance.The comparison with F_ST is essential to rule out genetic drift as an alternative mechanism for phenotypic divergence among populations. Because finite populations may diverge genetically in the absence of selection, divergence must be greater than expected by drift alone if we are to conclusively demonstrate that divergent selection has played a role in genetic differentiation among populations. Therefore it has become common practice to use F_ST of putatively neutral markers as a control for the effects of genetic drift and to compare observed Q_ST values for traits to these neutral F_ST values.These comparisons follow two separate methods, to address related but distinct questions. First, many studies of quantitative genetic differentiation measure the Q_ST of many traits and the F_ST of many loci, followed by a comparison of the mean Q_ST to the mean F_ST. Such a comparison may judge whether the conditions are suitable in that species for local adaptation, that is, whether selective differences between populations are large enough relative to gene flow to allow adaptive differentiation (Whitlock 2008). We do not consider this sort of comparison in this article.The other type of comparison asks whether the Q_ST of a single trait is greater than expected by drift, as measured by F_ST. This type of comparison is most common, but it is statistically difficult. Unfortunately, as emphasized in a recent review by Whitlock (2008), there is great variation in the expected F_ST among neutral loci and among the Q_ST of different neutral traits (see Figure 1). The majority of this variation results from evolutionary differences between loci and not sampling error in the observations. Rogers and Harpending (1983) imply that the distribution of Q_ST of a single neutral trait should be approximately equivalent to that for F_ST of a single neutral locus, and this has been confirmed by simulation for traits determined by additive loci compared to biallelic marker loci (Whitlock 2008). The two distributions are similar, but there is great heterogeneity among traits or loci. As a result, to show that selection is acting on a trait, it is necessary to show that the value of Q_ST has a low probability of being observed given the distribution of neutral Q_ST.Open in a separate windowFigure 1.—The distribution of F_ST for neutral loci and Q_ST for neutral quantitative traits. The histograms show the results of simulations of a set of 10 local populations each of 100 individuals, connected by 5% migration following island model assumptions. The solid line shows the distribution predicted by the Lewontin–Krakauer distribution. The distribution of Q_ST for neutral traits is very similar to the distribution of F_ST for single neutral loci, as can be seen by their mutual good fit to the Lewontin–Krakauer distribution (Figure modified from Whitlock 2008).Comparing Q_ST to the distribution inferred from F_ST is difficult for two reasons. First, typical data sets rarely include enough loci to directly infer the distribution of F_ST without extra inferential steps. In our approach, we use the distribution of Q_ST predicted from the mean F_ST and the χ² distribution by Lewontin and Krakauer (1973) to bridge this gap. Whitlock (2008) has shown that this distribution is appropriate for nearly all realistic situations for traits determined by additive genetic effects. Second, Q_ST for a trait is rarely measured with high precision, so the position of a given estimated Q_ST value in the distribution cannot be known without error.To test the null hypothesis that the spatial distribution of a particular trait is not affected by selection, we wish to compare the observed of that trait (marked with a hat to indicate it is an estimate) to the distribution of Q_ST expected for neutral traits. Unfortunately, calculating the distribution of Q_ST for neutral traits is not straightforward, because the estimate of Q_ST for a particular trait is variable for several reasons. The estimate of Q_ST is subject to measurement error, caused by the finite samples of families and individuals in the quantitative genetic experiment. These cause error in the estimate of the additive genetic variance within populations (V_A,within) and the genetic variance among populations (V_G,among), which translate into error of the estimate of Q_ST. In addition, there is another source of variation in Q_ST among neutral traits, caused by the idiosyncrasies of the evolutionary process in each local population in the study. The true value of Q_ST for the set of populations being studied can vary tremendously around its expectation, even for neutral traits, because by chance a finite set of populations may drift in a similar direction (Whitlock 2008). As a result, measurements of Q_ST can vary because of both statistical and evolutionary variation.Fortunately, these two sources of variation are fairly well understood individually. The sampling error for the estimates of the variance components can be estimated from standard approaches, and this variation can be well approximated using information from the mean squares of the analysis of the breeding experiment (O''Hara and Merilä 2005). The variation in neutral Q_ST that results from heterogeneity of evolutionary history can be approximated by the Lewontin–Krakauer distribution (Lewontin and Krakauer 1973), if information is available on the mean Q_ST of neutral traits (Whitlock 2008). This approximation does not depend on the demographic details of the populations in question (Whitlock 2008), but the effects of deviations from assumptions of additive gene effect have not yet been tested. The mean of the distribution of values of Q_ST for neutral traits is usually not known, but fortunately the mean of the distribution of F_ST of neutral loci is expected to be approximately equal to the mean Q_ST of neutral traits (Spitze 1993), and this does not depend on demographic details (Whitlock 1999). Therefore the mean F_ST measured from a series of genetic markers thought to be selectively neutral can be combined with the Lewontin–Krakauer distribution to predict the distribution of true neutral Q_ST across the range of possible evolutionary trajectories.Given that the mean value of of neutral traits is expected to equal the mean F_ST of neutral markers under certain assumptions (discussed later), we will use as a test statistic and compare the observed quantity to the zero value proposed by the null hypothesis. We will use a traditional hypothesis testing approach, which means that we need to specify the sampling distribution of under the assumption of neutrality. Traditionally, the sampling distribution of is inferred from the data on the trait itself, for example, using bootstrapping to infer the sampling distribution. This is appropriate when calculating a confidence interval for Q_ST but is a biased measure of the sampling variance of neutral Q_ST. The variance of the sampling distribution of varies with its expected value; larger values of true Q_ST have more variable sampling distributions than traits with smaller true Q_ST. This association between Q_ST and its sampling error is quite strong, as shown in Figure 2. As a result, if the sampling properties of neutral are inferred from a trait with high Q_ST, the estimate of the variance of the null distribution will be too high, and the hypothesis test comparing to F_ST will be conservative. On the other hand, if a low Q_ST is used to estimate the variance of the null distribution, the estimated error will be too small, and the test will reject true null hypotheses too often.Open in a separate windowFigure 2.—The width of the estimated sampling distribution of varies with mean Q_ST. The solid line shows the sampling distribution of Q_ST when the true mean Q_ST value is 0.05. The dotted line shows the sampling distribution that would be estimated for Q_ST from a trait that by chance was at the first percentile of this distribution, and the dashed line shows the sampling distribution that would be inferred from a value taken at the 99th percentile. If the Q_ST of a trait differs from the expectation by chance, then the width of the sampling distribution will also be estimated with substantial error. In particular, the error variance of is overestimated with Q_ST estimates that are too high and underestimated for small Q_ST values.We address this problem by using F_ST from putatively neutral maker loci in combination with estimates of the additive genetic variance within populations to predict the sampling variance that would be expected for the Q_ST of a neutral trait. We show that the power and type I error rate of this test are greatly superior to traditional methods.     

Genomic diversity and differentiation of a managed island wild boar population

The evolution of island populations in natural systems is driven by local adaptation and genetic drift. However, evolutionary pathways may be altered by humans in several ways. The wild boar (WB) (Sus scrofa) is an iconic game species occurring in several islands, where it has been strongly managed since prehistoric times. We examined genomic diversity at 49 803 single-nucleotide polymorphisms in 99 Sardinian WBs and compared them with 196 wild specimens from mainland Europe and 105 domestic pigs (DP; 11 breeds). High levels of genetic variation were observed in Sardinia (80.9% of the total number of polymorphisms), which can be only in part associated to recent genetic introgression. Both Principal Component Analysis and Bayesian clustering approach revealed that the Sardinian WB population is highly differentiated from the other European populations (F_ST=0.126–0.138), and from DP (F_ST=0.169). Such evidences were mostly unaffected by an uneven sample size, although clustering results in reference populations changed when the number of individuals was standardized. Runs of homozygosity (ROHs) pattern and distribution in Sardinian WB are consistent with a past expansion following a bottleneck (small ROHs) and recent population substructuring (highly homozygous individuals). The observed effect of a non-random selection of Sardinian individuals on diversity, F_ST and ROH estimates, stressed the importance of sampling design in the study of structured or introgressed populations. Our results support the heterogeneity and distinctiveness of the Sardinian population and prompt further investigations on its origins and conservation status.     

A clever solution to a vexing problem

F_ST (as well as related measures such as G_ST) has long been used both as a measure of the relative amount of genetic variation between populations and as an indicator of the amount of gene flow among populations. Unfortunately, F_ST and its clones are also sensitive to mutation, particularly when the mutation rate per locus is greater than the migration rate among populations. Relatively high mutation rates cause estimates of F_ST and G_ST to be much lower than researchers sometimes expect, when migration rates are low in the studied species. Several recent suggestions for dealing with this problem have been unsatisfactory for one reason or another, and no general solution exists (if we are not to abandon these otherwise useful measures of differentiation). In an important article in this issue, Jinliang Wang (2015) shows that it is possible to identify whether the genetic markers in a given study are likely to give estimates of F_ST that are strongly affected by mutation. The proposed test is simple and elegant, and with it, molecular ecologists can determine whether the F_ST from their makers can be depended on for further inference about their species’ genome and the demographic forces which shaped its patterns.     

QST–FST comparisons with unbalanced half‐sib designs

Q_ST, a measure of quantitative genetic differentiation among populations, is an index that can suggest local adaptation if Q_ST for a trait is sufficiently larger than the mean F_ST of neutral genetic markers. A previous method by Whitlock and Guillaume derived a simulation resampling approach to statistically test for a difference between Q_ST and F_ST, but that method is limited to balanced data sets with offspring related as half‐sibs through shared fathers. We extend this approach (i) to allow for a model more suitable for some plant populations or breeding designs in which offspring are related through mothers (assuming independent fathers for each offspring; half‐sibs by dam); and (ii) by explicitly allowing for unbalanced data sets. The resulting approach is made available through the R package QstFstComp.