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Pim e del aar,* pablo burrac o and ivan gomez-mestre*†


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Comparisons between QST and



FST—how wrong have we been?
PIM E DEL AAR,* PABLO BURRAC O * and

IVAN GOMEZ-MESTRE*†

*Estacio´n Biolo´gica de Don˜ ana (EBD-CSIC). Avda. Ame´rico Vespucio s ⁄ n, Sevilla E-41092, Spain, †Biodiversity Research Group (CSIC-UO-PA). c ⁄ Catedra´tico Rodrigo Ur´ıa s ⁄ n, Oviedo E-33071, Spain

Abstract
The comparison between quantitative genetic divergence (QST) and neutral genetic divergence (FST) among popula- tions has become the standard test for historical signa- tures of selection on quantitative traits. However, when


Introduction


Determining the relative role of neutral vs. selective pro- cesses in the divergence of populations is a major research topic in evolutionary and conservation biology. Several methods have been developed to this end, and one that is commonly applied is the comparison between population divergence in neutral molecular markers (as estimated by FST) and genetic divergence in functional, quantitative traits (as estimated by QST) (reviewed in Whitlock 2008; see Ovas- kainen et al. 2011 for methodological amendments). Both parameters can vary between 0 and 1 and express variation among populations relative to the total variation. Assuming all genes underlying the phenotypic traits of interest (here-

after, quantitative genetic loci) have equal, additive and

the mutation rate of neutral markers is relatively high in

independent effects, then QST

should equal FST

when popu-

comparison with gene flow, estimates of FST will

decrease, resulting in upwardly biased comparisons of

lation divergence is driven only by neutral genetic drift

(Merila¨ & Crnokrak 2001; McKay & Latta 2002; Whitlock

QST vs. FST. Reviewing empirical studies, the difference

2008). In contrast, QST

will be larger than FST

if quantitative

between QST and FST is positively related to marker het-

traits are exposed to diversifying selection across popula-

erozygosity. After refuting alternative explanations for

this pattern, we conclude that marker mutation rate

tions, whereas QST

will be smaller than FST

if selection is



indeed has had a biasing effect on published QST–FST

stabilizing. FST estimation is straightforward using fre-

quency data of neutral genetic markers (reviewed in Hol-

comparisons. Hence, it is no longer clear that populations

have commonly diverged in response to divergent selec-

singer & Weir 2009). QST

is calculated from estimates of

tion. We present and discuss potential solutions to this bias. Comparing QST with recent indices of neutral diver- gence that statistically correct for marker heterozygosity

within- and between-population additive genetic variance

components, preferably obtained from controlled breeding and rearing of large numbers of offspring in a biologically relevant common garden setting. By now, dozens of articles

(Hedrick’s G¢st and Jost’s D) is not advised, because these

have applied this comparison of QST

and F

ST. Based on

indices are not theoretically equivalent to QST. One valid

meta-analysis, the average and most frequent finding is that

solution is to estimate FST from neutral markers with

Q > F

, so it appears that study populations are com-

mutation rates comparable to those of the loci underlying quantitative traits (e.g. SNPs). QST can also be compared

ST ST


monly exposed to divergent selection (Leinonen et al. 2008).

There has been ample discussion regarding the potential

to FST (PhiST) of AMOVA, as long as the genetic distance

problems and biases in the estimation of QST

and its SE

among allelic variants used to estimate FST reflects evolu-

tionary history: in that case, neutral divergence is inde-

(e.g. Merila¨ & Crnokrak 2001; O¢Hara & Merila¨ 2005; Lei- nonen et al. 2008; Whitlock 2008). From this, it clearly

pendent of mutation rate. In contrast to their common

emerges that a critical assumption in QST

estimation is that

usage in comparisons of QST and FST, microsatellites typ-

ically have high mutation rates and do not evolve accord- ing to a simple evolutionary model, so are best avoided in QST–FST comparisons.

Keywords: divergent selection, FST, microsatellites, neutral marker mutation rate, QST, FST

Correspondence: Pim Edelaar or Ivan Gomez-Mestre, Fax: +34 954 621 125; E-mails: edelaar@ebd.csic.es, igmestre@ebd.csic.es

within- and among-population variance components be good estimators of additive genetic variance. In practice, few studies do in fact report purely additive genetic vari- ance components, but instead often include some combina- tion of maternal, environmental and ⁄ or non-additive genetic effects, inflating the resulting QST values. Moreover, epistasis can decrease QST values, whereas dominance can substantially increase or decrease QST estimates relative to FST, depending on the model of evolution underlying a given study system (reviewed in Whitlock 2008). Life-his- tory traits, which are often connected to fitness, commonly bear considerable epistatic and dominance components.




Furthermore, the environmental effects on gene expression are often disregarded in this context, assuming that there is little if any genotype by environment interaction. This, however, is not the case, and QST estimates strongly depend on the environment in which they are being taken, even if derived from additive genetic variance components under experimental settings (e.g. Gomez-Mestre & Tejedo

2004).


Problems with FST?
Comparatively less attention has been given to sources of bias in FST calculation. However, recent studies have raised the concern that the comparison of FST and QST might be compromised because of problems with the interpretation of FST (Hedrick 1999, 2005; Hendry 2002; Jost 2008; Heller

& Siegismund 2009; Gerlach et al. 2010; Kronholm et al.

2010; Meirmans & Hedrick 2010). This is best shown when using GST, an estimator similar to FST that is used for mul- tilocus genetic markers (from now on, FST and GST will be used interchangeably). GST = (HTOTAL)HWITHIN) ⁄ HTOTAL, where HTOTAL is the expected heterozygosity of the pooled populations, and HWITHIN is the average expected hetero- zygosity within populations. Both HTOTAL and HWITHIN have a maximum of 1 (when all individuals are expected heterozygotes). For a highly variable marker, it is not uncommon to find HWITHIN values of, e.g., 0.85. Even assuming that populations are entirely composed of private alleles and HTOTAL approaches its theoretical maximum of

1, then GST still only has a maximum value of

(1)0.85) ⁄ 1 = 0.15. Such a value is frequently interpreted as indicating only mild to moderate differentiation, even though in this case the populations do not share any alleles at all and in that sense are completely genetically differen- tiated. Hence, for variable markers, FST does not provide a

However, when the quantitative genetic loci have a higher mutation rate, this also results in a decline of QST: more genetic variation will now reside within populations rela- tive to variation among populations, and QST = VAMONG ⁄ (VAMONG + 2 VWITHIN) (for a diploid outbreeding species: McKay & Latta 2002; Whitlock 2008). By means of simula- tions, Edelaar & Bjo¨ rklund (2011) showed that the quantita- tive expectation of FST = QST under genetic drift holds, independent of mutation rate.

However, there is one important caveat: this is only true when the effects of mutation rate on FST and QST are com- parable, and these effects depend on migration rate. It should be noted that under the island model at equilib- rium


FST ¼ 1=½4N * ðm þ lÞþ 1]; ð2Þ
where N is the population size of each deme, m is migra- tion rate and l is the mutation rate (Hartl & Clark 1997). When m >> l, FST is virtually determined by migration only and mutation rate can be neglected. Hence, FST is vir- tually independent of mutation rate until the mutation rate becomes high relative to migration. The same is true for QST (Edelaar & Bjo¨ rklund 2011). Quantitative genetic loci are thought to have a low mutation rate of around 10)6

10)9 (Drake et al. 1998; Nachman & Crowell 2000; Roach

et al. 2010), which will virtually guarantee that in the absence of selection QST will be determined by genetic drift and migration alone. In contrast, some neutral genetic markers have much higher mutation rates, up to 10)2 (Elle- gren 2004), and this may decrease the value of FST.

To visualize this, we have plotted in Fig. 1 how FST

depends on mutation rate and migration rate, using eqn 2 and assuming a constant population size of N = 1000. It is



good measure of genetic differentiation of populations in

allelic composition (Jost 2008; Meirmans & Hedrick 2010). It is more useful as a fixation index, which measures differ- entiation among alleles in population affiliation (when pop- ulations are very variable, individual alleles are hardly uniquely associated with particular populations: see Grego- rius 2010). If FST values decrease because of higher HWITHIN, its comparison with QST may be highly question- able.

Fortunately, this is not necessarily the case, because QST is in fact also a kind of fixation index and responds simi- larly to FST to the variability of underlying loci (Edelaar & Bjo¨ rklund 2011). One reason why a genetic locus might be more variable, is that its mutation rate is higher. Under the infinite allele model, in a single isolated population

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m = 10–4

m = 10–3

m = 10–2



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HWITHIN ¼ 4Ne * l =ð4Ne * l þ 1Þ; ð1Þ
where Ne is the effective population size, and l is the mutation rate (Hartl & Clark 1997). When l is very low, HWITHIN will approach zero (fixation), whereas for a very large l, HWITHIN will approach one (high marker variabil- ity). Hence, FST will decline as mutation rate increases, and correctly so because there will be less fixation of alleles.

Mutation rate


Fig. 1 FST goes down (continuous line, left Y-axis), and hetero- zygosity goes up (dashed line, right Y-axis) with increasing mutation rate. The decline of FST strongly depends on how high the mutation rate is relative to the migration rate m. Equi- librium values were calculated using eqns 1 and 2, and assum- ing a population size N of 1000.




clear that a lower migration rate results in a higher FST. More importantly here, FST declines when mutation rate becomes relatively high compared to migration rate. Also plotted (Fig. 1) is the positive effect of mutation rate on heterozygosity (using eqn 1), independent of migration rate. Hence, a high mutation rate is indicated by a higher heterozygosity, which empirically is estimated much more easily than mutation rate. Therefore, in Fig. 2, we plotted FST against heterozygosity using the same equations and parameter values. A high heterozygosity (because of a high mutation rate) does not result in a decline in the estimate of FST if migration rate is high relative to mutation rate (Fig. 2, lower line). However, for the same high heterozy- gosity (and same underlying high mutation rate), a serious decline in FST is observed if migration rate is low relative to mutation rate (Fig. 2, upper line).

Thus, if we compare QST with FST estimates obtained from markers whose mutation rate is too high relative to migration rate, we will obtain a result that is biased towards QST > FST (see Ritland 2000; Hendry 2002; Leinon- en et al. 2008). Over the years, researchers have actively sought highly variable markers for population genetics studies because these yield more discriminatory power per unit of effort (Kalinowski 2002), resulting in a steady increase in average heterozygosity over time (Fig. 3). In consequence, there is a real possibility that published empirical QST–FST comparisons are biased, and increasingly so (Kronholm et al. 2010; Edelaar & Bjo¨ rklund 2011). How- ever, in the absence of empirical estimates of population size, migration rates and mutation rates for each study, we



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cannot establish theoretically whether such a bias has occurred or not.

Therefore, to determine whether, and to what extent, a bias has occurred, we review here the published empirical comparisons of neutral and quantitative genetic differentia- tion among populations using a ‘QST vs. FST’ framework. Because the exact marker mutation rates are not known, we used marker heterozygosity as a proxy for mutation rate (see eqn 1) and test for the expected positive relation- ship between heterozygosity and the difference QST–FST. Such a positive relationship would support our hypothesis that selecting markers with a high mutation rate and hence high heterozygosity will result in lower estimates of FST, and subsequently larger, biased values for QST–FST. In addition, we determine whether a quantitative prediction of our hypothesis actually provides a good fit to the observed pattern of QST–FST reported in the literature.

However, some alternative explanations may also fit

such a pattern. First, estimates of QST and ⁄ or FST could have changed over time for reasons other than increased marker heterozygosity, in which case the correlation would not be causal. For example, the choice of study populations or traits may have been increasingly steered towards those a priori known to be phenotypically divergent and where local adaptation was suspected (another serious and prob- lematic kind of bias, inflating QST: see Leinonen et al. 2008; Whitlock 2008). We therefore also tested statistically whether the factor ¢year¢ explained part of the variation in QST–FST, independent of the variation in heterozygosity among studies. Second, variation in population size and ⁄ or migration rate among studies could create a positive corre- lation between heterozygosity and QST–FST, as both popu- lation size and migration rate could simultaneously

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Heterozygosity
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