Evolutionary inference from QST

Q(ST) is a commonly used metric of the degree of genetic differentiation among populations displayed by quantitative traits. Typically, Q(ST) is compared to F(ST) measured on putatively neutral loci; if Q(ST)=F(ST), this is taken as evidence of spatially heterogeneous and diversifying selection. This paper reviews the uses, assumptions and statistics of Q(ST) and F(ST) comparisons. Unfortunately, Q(ST)/F(ST) comparisons are statistically challenging. For a single trait, Q(ST) must be compared not to the mean F(ST) but to the distribution of F(ST) values. The sources of biases and sampling error for Q(ST) are reviewed, and a new method for comparing Q(ST) and F(ST) is suggested. Simulation results suggest that the distribution of neutral F(ST) and Q(ST) values are little affected by various deviations from the island model. Consequently, the distributions of Q(ST) and F(ST) are well approximated by the Lewontin-Krakauer prediction, even with realistic deviations from the island-model assumptions.     

Molecular and quantitative genetic divergence among populations of house mice with known evolutionary histories

Evolutionary biologists have long been interested in the processes influencing population differentiation, but separating the effects of neutral and adaptive evolution has been an obstacle for studies of population subdivision. A recently developed method allows tests of whether disruptive (ie, spatially variable) or stabilizing (ie, spatially uniform) selection is influencing phenotypic differentiation among subpopulations. This method, referred to as the F(ST) vs Q(ST) comparison, separates the total additive genetic variance into within- and among-population components and evaluates this level of differentiation against a neutral hypothesis. Thus, levels of neutral molecular (F(ST)) and quantitative genetic (Q(ST)) divergence are compared to evaluate the effects of selection and genetic drift on phenotypic differentiation. Although the utility of such comparisons appears great, its accuracy has not yet been evaluated in populations with known evolutionary histories. In this study, F(ST) vs Q(ST) comparisons were evaluated using laboratory populations of house mice with known evolutionary histories. In this model system, the F(ST) vs Q(ST) comparisons between the selection groups should reveal quantitative trait differentiation consistent with disruptive selection, while the F(ST) vs Q(ST) comparisons among lines within the selection groups should suggest quantitative trait differentiation in agreement with drift. We find that F(ST) vs Q(ST) comparisons generally produce the correct evolutionary inference at each level in the population hierarchy. Additionally, we demonstrate that when strong selection is applied between populations Q(ST) increases relative to Q(ST) among populations diverging by drift. Finally, we show that the statistical properties of Q(ST), a variance component ratio, need further investigation.     

Comparisons between QST and FST—how wrong have we been?

The comparison between quantitative genetic divergence (Q(ST) ) and neutral genetic divergence (F(ST) ) among populations has become the standard test for historical signatures of selection on quantitative traits. However, when the mutation rate of neutral markers is relatively high in comparison with gene flow, estimates of F(ST) will decrease, resulting in upwardly biased comparisons of Q(ST) vs. F(ST) . Reviewing empirical studies, the difference between Q(ST) and F(ST) is positively related to marker heterozygosity. After refuting alternative explanations for this pattern, we conclude that marker mutation rate indeed has had a biasing effect on published Q(ST) -F(ST) comparisons. Hence, it is no longer clear that populations have commonly diverged in response to divergent selection. We present and discuss potential solutions to this bias. Comparing Q(ST) with recent indices of neutral divergence that statistically correct for marker heterozygosity (Hedrick's G'st and Jost's D) is not advised, because these indices are not theoretically equivalent to Q(ST) . One valid solution is to estimate F(ST) from neutral markers with mutation rates comparable to those of the loci underlying quantitative traits (e.g. SNPs). Q(ST) can also be compared to Φ(ST) (Phi(ST) ) of amova, as long as the genetic distance among allelic variants used to estimate Φ(ST) reflects evolutionary history: in that case, neutral divergence is independent of mutation rate. In contrast to their common usage in comparisons of Q(ST) and F(ST) , microsatellites typically have high mutation rates and do not evolve according to a simple evolutionary model, so are best avoided in Q(ST) -F(ST) comparisons.     

If FST does not measure neutral genetic differentiation,then comparing it with QST is misleading. Or is it?

The comparison between neutral genetic differentiation (F(ST) ) and quantitative genetic differentiation (Q(ST) ) is commonly used to test for signatures of selection in population divergence. However, there is an ongoing discussion about what F(ST) actually measures, even resulting in some alternative metrics to express neutral genetic differentiation. If there is a problem with F(ST) , this could have repercussions for its comparison with Q(ST) as well. We show that as the mutation rate of the neutral marker increases, F(ST) decreases: a higher within-population heterozygosity (He) yields a lower F(ST) value. However, the same is true for Q(ST) : a higher mutation rate for the underlying QTL also results in a lower Q(ST) estimate. The effect of mutation rate is equivalent in Q(ST) and F(ST) . Hence, the comparison between Q(ST) and F(ST) remains valid, if one uses neutral markers whose mutation rates are not too high compared to those of quantitative traits. Usage of highly variable neutral markers such as hypervariable microsatellites can lead to serious biases and the incorrect inference that divergent selection has acted on populations. Much of the discussion on F(ST) seems to stem from the misunderstanding that it measures the differentiation of populations, whereas it actually measures the fixation of alleles. In their capacity as measures of population differentiation, Hedrick's G'(ST) and Jost's D reach their maximum value of 1 when populations do not share alleles even when there remains variation within populations, which invalidates them for comparisons with Q(ST) .     

The effect of neutral nonadditive gene action on the quantitative index of population divergence

For neutral additive genes, the quantitative index of population divergence (Q(ST)) is equivalent to Wright's fixation index (F(ST)). Thus, divergent or convergent selection is usually invoked, respectively, as a cause of the observed increase (Q(ST) > F(ST)) or decrease (Q(ST) < F(ST)) of Q(ST) from its neutral expectation (Q(ST) = F(ST)). However, neutral nonadditive gene action can mimic the additive expectations under selection. We have studied theoretically the effect of consecutive population bottlenecks on the difference F(ST) - Q(ST) for two neutral biallelic epistatic loci, covering all types of marginal gene action. With simple dominance, Q(ST) < F(ST) for only low to moderate frequencies of the recessive alleles; otherwise, Q(ST) > F(ST). Additional epistasis extends the condition Q(ST) < F(ST) to a broader range of frequencies. Irrespective of the type of nonadditive action, Q(ST) < F(ST) generally implies an increase of both the within-line additive variance after bottlenecks over its ancestral value (V(A)) and the between-line variance over its additive expectation (2F(ST)V(A)). Thus, both the redistribution of the genetic variance after bottlenecks and the F(ST) - Q(ST) value are governed largely by the marginal properties of single loci. The results indicate that the use of the F(ST) - Q(ST) criterion to investigate the relative importance of drift and selection in population differentiation should be restricted to pure additive traits.     

Comparative studies of quantitative trait and neutral marker divergence: a meta-analysis

Comparative studies of quantitative genetic and neutral marker differentiation have provided means for assessing the relative roles of natural selection and random genetic drift in explaining among-population divergence. This information can be useful for our fundamental understanding of population differentiation, as well as for identifying management units in conservation biology. Here, we provide comprehensive review and meta-analysis of the empirical studies that have compared quantitative genetic (Q(ST)) and neutral marker (F(ST)) differentiation among natural populations. Our analyses confirm the conclusion from previous reviews - based on ca. 100% more data - that the Q(ST) values are on average higher than F(ST) values [mean difference 0.12 (SD 0.27)] suggesting a predominant role for natural selection as a cause of differentiation in quantitative traits. However, although the influence of trait (life history, morphological and behavioural) and marker type (e.g. microsatellites and allozymes) on the variance of the difference between Q(ST) and F(ST) is small, there is much heterogeneity in the data attributable to variation between specific studies and traits. The latter is understandable as there is no reason to expect that natural selection would be acting in similar fashion on all populations and traits (except for fitness itself). We also found evidence to suggest that Q(ST) and F(ST) values across studies are positively correlated, but the significance of this finding remains unclear. We discuss these results in the context of utility of the Q(ST)-F(ST) comparisons as a tool for inferring natural selection, as well as associated methodological and interpretational problems involved with individual and meta-analytic studies.     

Experimental demonstration of a causal relationship between heterogeneity of selection and genetic differentiation in quantitative traits

Comparisons of estimates of genetic differentiation at molecular markers (F(ST)) and at quantitative traits (Q(ST)) are a means of inferring the level and heterogeneity of selection in natural populations. However, such comparisons are questionable because they require that the influence of drift and selection on Q(ST) be detectable over possible background influences of environmental or nonadditive genetic effects on Q(ST)-values. Here we test this using an experimental evolution approach in metapopulations of Arabidopsis thaliana experiencing different levels of drift and selection heterogeneity. We estimated the intensity and heterogeneity of selection on morphological and phenological traits via selection differentials. We demonstrate that Q(ST)-values increased with increasing selection heterogeneity when genetic drift was limited. The effect of selection on Q(ST) was thus detectable despite significant genotype-by-environment interactions that most probably biased the estimates of genetic differentiation. Although they cannot be used as a direct validation of the conclusions of prior studies, our results strongly support both the relevance of Q(ST) as an estimator of genetic differentiation and the role of local selection in shaping the genetic differentiation of natural populations.     

The effects of dominance, regular inbreeding and sampling design on Q(ST), an estimator of population differentiation for quantitative traits

To test whether quantitative traits are under directional or homogenizing selection, it is common practice to compare population differentiation estimates at molecular markers (F(ST)) and quantitative traits (Q(ST)). If the trait is neutral and its determinism is additive, then theory predicts that Q(ST) = F(ST), while Q(ST) > F(ST) is predicted under directional selection for different local optima, and Q(ST) < F(ST) is predicted under homogenizing selection. However, nonadditive effects can alter these predictions. Here, we investigate the influence of dominance on the relation between Q(ST) and F(ST) for neutral traits. Using analytical results and computer simulations, we show that dominance generally deflates Q(ST) relative to F(ST). Under inbreeding, the effect of dominance vanishes, and we show that for selfing species, a better estimate of Q(ST) is obtained from selfed families than from half-sib families. We also compare several sampling designs and find that it is always best to sample many populations (>20) with few families (five) rather than few populations with many families. Provided that estimates of Q(ST) are derived from individuals originating from many populations, we conclude that the pattern Q(ST) > F(ST), and hence the inference of directional selection for different local optima, is robust to the effect of nonadditive gene actions.     

Q(St) meets the G matrix: the dimensionality of adaptive divergence in multiple correlated quantitative traits.

The Q(ST)-F(ST) comparison has become an increasingly common method for inferring adaptive quantitative trait divergence among populations. For cases in which there is divergence in multiple traits, most studies have applied the method by performing multiple univariate Q(ST)-F(ST) comparisons. However, because traits are often genetically correlated, such univariate analyses are likely to paint a simplified picture of adaptive divergence. Here we show how the multivariate analogue of Q(ST), F(STq), which accounts for genetic correlations among traits, can be used to supply a more detailed picture of multitrait divergence. We apply the method to naturally occurring genetic variation for a suite of sexually selected display traits in Drosophila serrata. The analyses suggest the operation of divergent multivariate selection that has influenced multiple independent axes of genetic variance in a sex-specific manner. Finally, we show how a comparison of the components of F(STq), the average within and among population genetic variance-covariance matrices, G(W) and G(B), can be used as an additional test of the null expectation of neutral divergence, and allows for an investigation of whether natural populations have diverged along major or minor axes of genetic variance.     

Genetic basis of adaptation in Arabidopsis thaliana: local adaptation at the seed dormancy QTL DOG1

Local adaptation provides an opportunity to study the genetic basis of adaptation and investigate the allelic architecture of adaptive genes. We study delay of germination 1 (DOG1), a gene controlling natural variation in seed dormancy in Arabidopsis thaliana and investigate evolution of dormancy in 41 populations distributed in four regions separated by natural barriers. Using F(ST) and Q(ST) comparisons, we compare variation at DOG1 with neutral markers and quantitative variation in seed dormancy. Patterns of genetic differentiation among populations suggest that the gene DOG1 contributes to local adaptation. Although Q(ST) for seed dormancy is not different from F(ST) for neutral markers, a correlation with variation in summer precipitation supports that seed dormancy is adaptive. We characterize dormancy variation in several F(2) -populations and show that a series of functionally distinct alleles segregate at the DOG1 locus. Theoretical models have shown that the number and effect of alleles segregatin at quantitative trait loci (QTL) have important consequences for adaptation. Our results provide support to models postulating a large number of alleles at quantitative trait loci involved in adaptation.     

Natural selection drives clinal life history patterns in the perennial sunflower species, Helianthus maximiliani

In plants, ecologically important life history traits often display clinal patterns of population divergence. Such patterns can provide strong evidence for spatially varying selection across environmental gradients but also may result from nonselective processes, such as genetic drift, population bottlenecks and spatially restricted gene flow. Comparison of population differentiation in quantitative traits (measured as Q(ST) ) with neutral molecular markers (measured as F(ST) ) provides a useful tool for understanding the relative importance of adaptive and nonadaptive processes in the formation and maintenance of clinal variation. Here, we demonstrate the existence of geographic variation in key life history traits in the diploid perennial sunflower species Helianthus maximiliani across a broad latitudinal transect in North America. Strong population differentiation was found for days to flowering, growth rate and multiple size-related traits. Differentiation in these traits greatly exceeds neutral predictions, as determined both by partial Mantel tests and by comparisons of global Q(ST) values with theoretical F(ST) distributions. These findings indicate that clinal variation in these life history traits likely results from local adaptation driven by spatially heterogeneous environments.     

Bias and precision in QST estimates: problems and some solutions

Comparison of population differentiation in neutral marker genes and in genes coding quantitative traits by means of F(ST) and Q(ST) indexes has become commonplace practice. While the properties and estimation of F(ST) have been the subject of much interest, little is known about the precision and possible bias in Q(ST) estimates. Using both simulated and real data, we investigated the precision and bias in Q(ST) estimates and various methods of estimating the precision. We found that precision of Q(ST) estimates for typical data sets (i.e., with <20 populations) was poor. Of the methods for estimating the precision, a simulation method, a parametric bootstrap, and the Bayesian approach returned the most precise estimates of the confidence intervals.     

Adaptive divergence in moor frog (Rana arvalis) populations along an acidification gradient: inferences from Q(st) -F(st) correlations

Microevolutionary responses to spatial variation in the environment seem ubiquitous, but the relative role of selection and neutral processes in driving phenotypic diversification remain often unknown. The moor frog (Rana arvalis) shows strong phenotypic divergence along an acidification gradient in Sweden. We here used correlations among population pairwise estimates of quantitative trait (P(ST) or Q(ST) from common garden estimates of embryonic acid tolerance and larval life-history traits) and neutral genetic divergence (F(ST) from neutral microsatellite markers), as well as environmental differences (pond pH, predator density, and latitude), to test whether this phenotypic divergence is more likely due to divergent selection or neutral processes. We found that trait divergence was more strongly correlated with environmental differences than the neutral marker divergence, suggesting that divergent natural selection has driven phenotypic divergence along the acidification gradient. Moreover, pairwise P(ST) s of embryonic acid tolerance and Q(ST) s of metamorphic size were strongly correlated with breeding pond pH, whereas pairwise Q(ST) s of larval period and growth rate were more strongly correlated with geographic distance/latitude and predator density, respectively. We suggest that incorporating measurements of environmental variation into Q(ST) -F(ST) studies can improve our inferential power about the agents of natural selection in natural populations.     

Maternal genetic effects on adaptive divergence between anadromous and resident brook charr during early life history

The importance of directional selection relative to neutral evolution may be determined by comparing quantitative genetic variation in phenotype (Q(ST)) to variation at neutral molecular markers (F(ST)). Quantitative divergence between salmonid life history types is often considerable, but ontogenetic changes in the significance of major sources of genetic variance during post-hatch development suggest that selective differentiation varies by developmental stage. In this study, we tested the hypothesis that maternal genetic differentiation between anadromous and resident brook charr (Salvelinus fontinalis Mitchill) populations for early quantitative traits (embryonic size/growth, survival, egg number and developmental time) would be greater than neutral genetic differentiation, but that the maternal genetic basis for differentiation would be higher for pre-resorption traits than post-resorption traits. Quantitative genetic divergence between anadromous (seawater migratory) and resident Laval River (Québec) brook charr based on maternal genetic variance was high (Q(ST) > 0.4) for embryonic length, yolk sac volume, embryonic growth rate and time to first response to feeding relative to neutral genetic differentiation [F(ST) = 0.153 (0.071-0.214)], with anadromous females having positive genetic coefficients for all of the above characters. However, Q(ST) was essentially zero for all traits post-resorption of the yolk sac. Our results indicate that the observed divergence between resident and anadromous brook charr has been driven by directional selection, and may therefore be adaptive. Moreover, they provide among the first evidence that the relative importance of selective differentiation may be highly context-specific, and varies by genetic contributions to phenotype by parental sex at specific points in offspring ontogeny. This in turn suggests that interpretations of Q(ST)-F(ST) comparisons may be improved by considering the structure of quantitative genetic architecture by age category and the sex of the parent used in estimation.     

Adaptive divergence for a fitness-related trait among invasive Ambrosia artemisiifolia populations in France

The impact of natural selection on the adaptive divergence of invasive populations can be assessed by testing the null hypothesis that the extent of quantitative genetic differentiation (Q(ST) ) would be similar to that of neutral molecular differentiation (F(ST) ). Using eight microsatellite loci and a common garden approach, we compared Q(ST) and F(ST) among ten populations of an invasive species Ambrosia artemisiifolia (common ragweed) in France. In a common garden study with varying water and nutrient levels, we measured Q(ST) for five traits (height, total biomass, reproductive allocation, above- to belowground biomass ratio, and days to flowering). Although low F(ST) indicated weak genetic structure and strong gene flow among populations, we found significant diversifying selection (Q(ST) > F(ST) ) for reproductive allocation that may be closely related to fitness. It suggests that abiotic conditions may have exerted selection pressure on A. artemisiifolia populations to differentiate adaptively, such that populations at higher altitude or latitude evolved greater reproductive allocation. As previous studies indicate multiple introductions from various source populations of A. artemisiifolia in North America, our results suggest that the admixture of introduced populations may have increased genetic diversity and additive genetic variance, and in turn, promoted the rapid evolution and adaptation of this invasive species.     

Comparing Bayesian estimates of genetic differentiation of molecular markers and quantitative traits: an application to Pinus sylvestris

Comparison of the level of differentiation at neutral molecular markers (estimated as F(ST) or G(ST)) with the level of differentiation at quantitative traits (estimated as Q(ST)) has become a standard tool for inferring that there is differential selection between populations. We estimated Q(ST) of timing of bud set from a latitudinal cline of Pinus sylvestris with a Bayesian hierarchical variance component method utilizing the information on the pre-estimated population structure from neutral molecular markers. Unfortunately, the between-family variances differed substantially between populations that resulted in a bimodal posterior of Q(ST) that could not be compared in any sensible way with the unimodal posterior of the microsatellite F(ST). In order to avoid publishing studies with flawed Q(ST) estimates, we recommend that future studies should present heritability estimates for each trait and population. Moreover, to detect variance heterogeneity in frequentist methods (ANOVA and REML), it is of essential importance to check also that the residuals are normally distributed and do not follow any systematically deviating trends.     

Does habitat fragmentation reduce fitness and adaptability? A case study of the common frog (Rana temporaria)

Studies examining the effects of anthropogenic habitat fragmentation on both neutral and adaptive genetic variability are still scarce. We compared tadpole fitness-related traits (viz. survival probability and body size) among populations of the common frog (Rana temporaria) from fragmented (F) and continuous (C) habitats that differed significantly in population sizes (C > F) and genetic diversity (C > F) in neutral genetic markers. Using data from common garden experiments, we found a significant positive relationship between the mean values of the fitness related traits and the amount of microsatellite variation in a given population. While genetic differentiation in neutral marker loci (F(ST)) tended to be more pronounced in the fragmented than in the continuous habitat, genetic differentiation in quantitative traits (Q(ST)) exceeded that in neutral marker traits in the continuous habitat (i.e. Q(ST) > F(ST)), but not in the fragmented habitat (i.e. Q(ST) approximately F(ST)). These results suggest that the impact of random genetic drift relative to natural selection was higher in the fragmented landscape where populations were small, and had lower genetic diversity and fitness as compared to populations in the more continuous landscape. The findings highlight the potential importance of habitat fragmentation in impairing future adaptive potential of natural populations.     

Divergent selection as revealed by P(ST) and QTL-based F(ST) in three-spined stickleback (Gasterosteus aculeatus) populations along a coastal-inland gradient

Three measures of divergence, estimated at nine putatively neutral microsatellite markers, 14 quantitative traits, and seven quantitative trait loci (QTL) were compared in eight populations of the three-spined stickleback (Gasterosteus aculeatus L.) living in the Scheldt river basin (Belgium). Lowland estuarine and polder populations were polymorphic for the number of lateral plates, whereas upland freshwater populations were low-plated. The number of short gill rakers and the length of dorsal and pelvic spines gradually declined along a coastal-inland gradient. Plate number, short gill rakers and spine length showed moderate to strong signals of divergent selection between lowland and upland populations in comparison between P(ST) (a phenotypic alternative for Q(ST)) and neutral F(ST). However, such comparisons rely on the unrealistic assumption that phenotypic variance equals additive genetic variance, and that nonadditive genetic effects and environmental effects can be minimized. In order to verify this assumption and to confirm the phenotypic signals of divergence, we tested for divergent selection at the underlying QTL. For plate number, strong genetic evidence for divergent selection between lowland and upland populations was obtained based on an intron marker of the Eda gene, of which the genotype was highly congruent with plate morph. Genetic evidence for divergent selection on short gill rakers was limited to some population pairs where F(ST) at only one of two QTL was detected as an outlier, although F(ST) at both loci correlated significantly with P(ST). No genetic confirmation was obtained for divergent selection on dorsal spine length, as no outlier F(ST)s were detected at dorsal spine QTL, and no significant correlations with P(ST) were observed.     

Population differentiation in G matrix structure due to natural selection in Rana temporaria

The additive genetic variance-covariance matrix (G) is a concept central to discussions about evolutionary change over time in a suite of traits. However, at the moment we do not know how fast G itself changes as a consequence of selection or how sensitive it is to environmental influences. We investigated possible evolutionary divergence and environmental influences on G using data from a factorial common-garden experiment where common frog (Rana temporaria) tadpoles from two divergent populations were exposed to three different environmental treatments. G-matrices were estimated using an animal model approach applied to data from a NCII breeding design. Matrix comparisons using both Flury and multivariate analysis of variance methods revealed significant differences in G matrices both between populations and between treatments within populations, the former being generally larger than the latter. Comparison of levels of population differentiation in trait means using Q(ST) indices with that observed in microsatellite markers (F(ST)) revealed that the former values generally exceeded the neutral expectation set by F(ST). Hence, the results suggest that intraspecific divergence in G matrix structure has occurred mainly due to natural selection.     

Patterns of differentiation in a colour polymorphism and in neutral markers reveal rapid genetic changes in natural damselfly populations

The existence and mode of selection operating on heritable adaptive traits can be inferred by comparing population differentiation in neutral genetic variation between populations (often using F(ST) values) with the corresponding estimates for adaptive traits. Such comparisons indicate if selection acts in a diversifying way between populations, in which case differentiation in selected traits is expected to exceed differentiation in neutral markers [F(ST )(selected) > F(ST )(neutral)], or if negative frequency-dependent selection maintains genetic polymorphisms and pulls populations towards a common stable equilibrium [F(ST) (selected) < F(ST) (neutral)]. Here, we compared F(ST) values for putatively neutral data (obtained using amplified fragment length polymorphism) with estimates of differentiation in morph frequencies in the colour-polymorphic damselfly Ischnura elegans. We found that in the first year (2000), population differentiation in morph frequencies was significantly greater than differentiation in neutral loci, while in 2002 (only 2 years and 2 generations later), population differentiation in morph frequencies had decreased to a level significantly lower than differentiation in neutral loci. Genetic drift as an explanation for population differentiation in morph frequencies could thus be rejected in both years. These results indicate that the type and/or strength of selection on morph frequencies in this system can change substantially between years. We suggest that an approach to a common equilibrium morph frequency across all populations, driven by negative frequency-dependent selection, is the cause of these temporal changes. We conclude that inferences about selection obtained by comparing F(ST) values from neutral and adaptive genetic variation are most useful when spatial and temporal data are available from several populations and time points and when such information is combined with other ecological sources of data.