Qst 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.