Bias and Precision in QST Estimates: Problems and Some Solutions

Abstract

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.

The roles of genetic drift and natural selection in quantitative trait divergence along an altitudinal gradient in Arabidopsis thaliana

“…We extracted variance components from mixed models with responses transformed as described above and obtained 95% CIs for Q ST and H 2 using parametric bootstrapping 10 000 bootstrap samples (bootMer function) using the lme4 package (Bates et al, 2013). This method has been shown to be one of the least biased methods for CI calculations of Q ST (O'Hara and Merilä, 2005).…”

“…We inferred statistical differences between overall Q ST (for PCs and individual traits) and F ST when there was no overlap between their CIs (Merilä and Crnokrak, 2001;O'Hara and Merilä, 2005). Using pair-wise (between population) data and Mantel tests with 10 000 permutations with the vegan package for R (Oksanen et al, 2009) we assessed (i) whether neutral genetic differentiation between populations (F ST ) correlated with differences in their altitude of origin (similar to an isolation by distance pattern), (ii) whether Q ST correlated with F ST as would be expected if trait differentiation is due to selectively neutral processes and (iii) whether Q ST correlated with altitude differences as would be expected if trait differentiation results from adaptive divergence along altitude.…”

“…Clinal variation can further be analyzed using correlations of pair-wise (between population pairs) Q ST , F ST and geographic distances or environmental differences (e.g., Kawakami et al, 2011). Q ST -F ST comparisons have been criticized based on theoretical grounds but recent method improvements (O'Hara and Merilä, 2005;Whitlock, 2008;Karhunen et al, 2013) as well as empirical support (Porcher et al, 2006) suggest that Q ST -F ST comparisons remain one of the best exploratory methods to identify potentially adaptive traits (Karrenberg and Widmer, 2008;Leinonen et al, 2013).…”

Testing for Spatially Divergent Selection: Comparing QST to FST

“…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).…”

Genetic distance predicts trait differentiation at the subpopulation but not the individual level in eelgrass,Zostera marina

“…Significant deviation from the null expectation indicates that traits are under selection and local adaptation is occurring. We tested whether Q ST was significantly different from the mean F ST among subpopulations using a method developed by Whitlock and Guillaume (2009), which uses a parametric resampling approach (O'Hara & Merilä, 2005). In brief, this method predicts the null distribution of the difference between Q ST and F ST ( Q ST ‐ F ST ) using a mixture of parametric simulations and bootstrapping.…”