Pim e del aar,* pablo burrac o and ivan gomez-mestre*†
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          Heterozygosity
cloud of data points of the microsatellites on the right-hand   side of Fig. 4 towards the left along the regression slope, until it overlaps with the range of heterozygosity of the al- lozymes (which generally have mutation rates much more comparable to those of quantitative genetic loci so are probably not biased). The result is quite startling. If less variable neutral markers had been used in these studies, it is very likely that many would have found QST < FST. Many others might have lost their statistical support for the conclusion that QST > FST, because QST estimates nor- mally have wide confidence intervals (O¢Hara & Merila¨
2005; Whitlock 2008). Similarly, the results of the meta-analyses are compro- mised, as these did not adequately take this bias into account. Leinonen et al. 2008 did recognize the possibility that differences between neutral markers in mutation rate could result in biased FST values and included the variable ‘marker type’ in their analyses. They did not find a signifi- cant effect on FST estimates (although their Fig. 4c does
Fig. 4 The difference between QST and FST is positively related to the heterozygosity of the neutral markers used to estimate FST. White dots are studies using allozymes, black dots are studies using microsatellites. Values above the horizontal dot- ted line indicate divergent selection on quantitative traits. The continuous line is the regression slope of QST–FST on heterozy- gosity; the dashed line is the predicted relationship between these same variables assuming that quantitative and neutral divergence are constant across studies, but FST declines linearly with heterozygosity (see Fig. 2). of the utilized markers. However, allozymes and microsat- ellites generally differ in mutation rate (Hartl & Clark 1997; Ellegren 2004). For the studies reviewed here, we found the expected large difference in heterozygosity between these markers, indicating that at least some of the variation in heterozygosity among studies is indeed because of variation in mutation rate, and not just because of variation in demography. Although variation in demography may add to the pattern of Fig. 4, we refute it as being a sufficient explanation. Similarly, any alternative explanation we have not considered here would have to explain why heterozy- gosity differs systematically between microsatellites and al- lozymes, and why that alternative is more likely than a difference in mutation rate between them. It seems thus clear that the usage of more variable neu- tral markers with higher mutation rates has biased the esti- mated differences between QST and FST, and that this bias has tended to become increasingly strong over the years. Apparently, by selecting markers with a high heterozygos- ity, researchers have violated the assumption that migra- tion rates are two or more orders of magnitude larger than mutation rates, such that mutation rate could no longer be ignored and deflated estimates of FST (see Figs 1 and 2). Implications
show a trend that microsatellites give lower FST estimates than other markers). We suspect that this is because a fair proportion of the microsatellites used in earlier studies actually have low mutation rates (resulting in low hetero- zygosities, see Figs 3 and 4), and thus overlapped with al- lozymes in their effect. In addition, many of the studies using highly variable microsatellites have been published after Leinonen et al. (2008), giving our study more statisti- cal power to observe the bias because of marker mutation rate. Overall, the general conclusion from these studies, that populations have commonly diverged because of exposure to divergent selection, has to be substantially moderated. Neutral genetic drift or even stabilizing selec- tion is likely to have a higher relevance for population dif- ferentiation than previously inferred. Potential solutions to biased QST–FST comparisons
Potential solution 1: correcting for marker heterozygosity. A first solution to biased QST–FST comparisons might be to correct the effect of marker heterozygosity on FST, which could be applied to both past and future estimates of divergence in neutral markers. Hedrick (Hedrick 2005; Meirmans & Hedrick 2010) and Jost (2008) have derived estimators of population differentiation that are indepen- dent of marker variability, suggesting that perhaps one could avoid bias by calculating the difference between QST and these estimators. However, Hedrick’s G¢st and Jost’s D are not theoretically equivalent to FST and measure differ- ent aspects of population genetics than FST and QST do (see examples in Meirmans & Hedrick 2010). In addition, G¢st and D are not independent of mutation rate when this is high relative to migration rate (Jost 2008; Whitlock 2011), so it is not clear that values of G¢st and D for markers with high mutation rates are comparable to divergence at quan- titative genetic loci with low mutation rates (Kronholm et al. 2010; Whitlock 2011). Moreover, any statistical correc- tion for marker heterozygosity such as G¢st has the prob- lem of deciding for each individual study which proportion of marker heterozygosity is attributable to vari- ation in mutation rate that needs to be corrected for and which part is attributable to variation in population size and migration rate, which have independent effects on QST, FST and heterozygosity and which should not be cor- rected for. Hence, neither G¢st nor Jost’s D seem to be use- ful as estimators of neutral divergence in the context of comparison with QST. Potential solution 2: using markers with lower mutation rates. A second solution is to abandon the use of highly variable markers, such as microsatellites, for comparisons of QST and FST and use markers with low mutation rates instead, such as SNPs (Edelaar & Bjo¨ rklund 2011). More- over, the vast majority of SNPs are bi-allelic and can be analysed within the classical FST framework, because bi- allelic loci can reach their theoretical maximum FST of 1. Because the information content of single SNPs is rather low, and because evolutionary stochasticity can result in very different FST estimates for individual SNPs, a decent number of unlinked SNPs would be needed to get a reli- able estimate of the mean and variance of FST across the genome (Whitlock 2008; Edelaar & Bjo¨ rklund 2011). Scoring large numbers of SNPs is now becoming increasingly feasi- ble for any kind of organism (Ouborg et al. 2010; Tautz et al. 2010). It is even possible to take into account that a small percentage of SNPs might be under divergent selec- tion (Brumfield et al. 2003; Glover et al. 2010), which other- wise tends to yield higher FST values (but a more conservative test for divergent selection on the quantitative trait of interest). Similar suggestions of moving back to markers with low variation have recently been made in the general context of using FST for the estimation of the demographic parameters driving population differentiation (Meirmans & Hedrick 2010; Whitlock 2011). While highly variable markers can be very useful for some applications, such as assignment of individuals to parents or populations, they appear to be problematic for the interpretation of the demographic his- tory of populations. A more pluralistic usage of marker variability, where marker choice is tailored to the aims of each study, seems called for. Potential solution 3: calculating a measure of neutral population divergence that is not affected by mutation rate. A third solu- tion would be to compare quantitative genetic divergence of quantitative traits (QST) with an equally quantitative approach to neutral genetic divergence. It should be noted that virtually all estimators of neutral genetic divergence treat alleles as different by identity only, e.g. in the calcula- tion of heterozygosity. This neglects information about genetic distances among alleles (if this is known). In con- trast, QST does take the distance among individuals (their genetic breeding values) into account when calculating var- iance components. As such, QST is really a kind of relative genetic distance measure, which expresses the difference among populations relative to the difference among indi- viduals within populations. Hence, the best comparison with this seems to be a conceptually similar genetic dis- tance measure for neutral markers that takes into account the genetic distance among alleles. Such a distance mea- sure was described by Excoffier et al. (1992) for haplotypes (FST). Likewise, Slatkin (1995) introduced RST, based on differences in microsatellites allele size, which was later shown by Michalakis & Excoffier (1996) to be comparable to FST. Recently, Kronholm et al. (2010) and Whitlock (2011) have shown by simulation that divergence measures which take into account the genetic distance among alleles are independent of mutation rate for any kind of marker, if the mutation process leaves a reliable traceable history of the coancestry of alleles (coalescence information). This condition is not fulfilled by all commonly used neutral markers. For allozymes, it is hard to derive a valid genetic distance among the different alleles. For microsatellites, it is hard to argue that mutations involving several repeats are negligible. The percentage of multistep mutations has been estimated to vary between 11–63% in humans, and between 5–75% in other organisms (Ellegren 2004), so that microsatellite allele size similarity appears to be a poor measure of ancestral similarity (see Balloux & Lugon-Mou- lin 2002; Li et al. 2002; Ellegren 2004). Simulations by Kron- holm et al. (2010) showed that when 20% of microsatellite mutations were not stepwise, FST did not correct properly for mutation rate. Therefore, only those microsatellite loci that have been confirmed in the study system to adhere to the stepwise mutation model by checking the process of mutation in a large number of pedigreed offspring (Elle- gren 2004) could be confidently used to calculate RST as a measure of neutral genetic divergence. So in practice, this restricts the choice of markers to sequence data of regions other than SSR. Here, the signature of old mutations is only likely to be erased by additional mutations after a long period of evolutionary time and would rarely happen among populations within species. Therefore, any two alleles differing by a greater number of sites are likely to have been evolving independently for longer. In practical terms, such a relative neutral genetic distance measure can be for instance calculated via AMOVA, when implementing a matrix of genetic distances (not identities) among non- recombining haplotypes (Excoffier et al. 1992; see also Kronholm et al. 2010). The resulting estimate of FST is then the appropriate quantitative measure of relative neutral genetic divergence among populations with which to com- pare QST. (Note that this estimate does not need the correc- tion of Meirmans (2006), which was only proposed for AMOVA based on allele identities). Because multiple unlinked loci would be required to estimate evolutionary stochasticity among loci (Whitlock 2008), the use of mtDNA would be disqualified because mtDNA normally acts as a single locus. Moreover, mtDNA has a smaller effective population size, has a different mode of inheri- tance and is exposed to selection. As far as we could estab- lish, a comparison between QST and FST using non-SSR sequence data has not yet been made, which is surprising given that AMOVA has been around since the first empirical QST–FST comparisons. There are two caveats, however, in comparing QST with distance-based neutral divergence measures. The first one is that the loci underlying neutral or quantitative genetic divergence may not follow the same mutation model. Ear- lier, we argued that distance-based measures are indepen- dent of mutation rate, if we use the genetic distances among alleles and if these alleles contain sufficient coales- cence information. However, for a valid comparison in principle, the same must be true for QST. Kronholm et al. (2010) and Edelaar & Bjo¨ rklund (2011) showed that when the mutations of quantitative genetic loci are independent (i.e. they do not resemble their ancestral states), QST decreases at high mutation rates. In that case, comparing QST with a distance-based neutral divergence measure would be inappropriate (although it would provide a con- servative test for the hypothesis of selection-driven popula- tion divergence). However, at the moment, it appears that the mutation rate of quantitative genetic loci is sufficiently low relative to migration rate that this complication in practice can be ignored, and we do not have to know how quantitative genetic loci mutate. [To the extent that non- Mendelian epigenetic mechanisms of inheritance play a role in divergence (Gilbert & Epel 2009; Herrera & Bazaga 2010), this assumption may need to be reconsidered]. The second caveat is that genetic differentiation estima- tors based on allele distances can have larger variances than those based on allele identities (Hardy et al. 2003). However, Excoffier (2007) suggests this is essentially only true if distances among alleles evolve according to the stepwise mutation model. This is by and large the case for microsatellites: a new mutation may either add or remove a repeat (Li et al. 2002; Ellegren 2004). This means that a microsatellite allele of a given length may have evolved from a shorter or from a longer ancestral allele, i.e. iden- tity-by-state is not exactly identity-by-descent, and the coa- lescent information in allele length variation is reduced. If so, for neutral markers that are closer to the infinite alleles model (multiple mutations at the same site do not occur), the variance in distance-based divergence measures should not be affected. Conclusions
studies cannot be determined nor corrected. To obtain unbiased future QST–FST estimates, we suggest the use of neutral markers with mutation rates that are comparable to those of quantitative genetic loci (in the order of 10)6 or lower), because this makes it less likely that mutation rate biases neutral genetic divergence. SNPs generally have low mutation rates and can be analysed within the classical FST framework, so these are a good option. When the neutral marker can be argued to contain much coalescent informa- tion (allele distance reliably conveys the degree of shared evolutionary history), we suggest comparing QST not to FST (or its relatives such as GST or h) but to measures of genetic divergence such as FST that are based on genetic distances among alleles, because of their conceptual similarity to QST. In addition, distance-based measures of neutral genetic divergence are independent of mutation rate, so allow for the use of neutral markers with any mutation rate. Non- recombining stretches of nuclear DNA contain much coa- lescent information and should be suitable. Microsatellites typically have high mutation rates and contain questionable coalescent information and should be avoided. The use of mtDNA is not advised in view of multiple issues. Other kinds of neutral markers should be judged similarly on their mutation rate and coalescent information content to assess their suitability for QST–FST comparisons. Acknowledgements
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