Chenoweth SF and Blows MW 2008. QST meets the G matrix: The dimensionality of adaptive divergence in multiple correlated quantitative traits. Evolution online early doi:10.1111/j.1558-5646.2008.00374.x.
Traits under selection may be genetically correlated. Therefore, univariate analysis of quantitative trait and neutral genetic divergence may potentially yield an incomplete picture of multi-trait selection. In this paper, the authors use the method of Kremer et al. (1997) to obtain a matrix of QST for genetic variances and covariances. Qualitatively, the results obtained with the univariate and multivariate approach were similar selection is acting on most of the traits studied (i.e. set of sexually selected traits in Drosophila serrata). The magnitude of quantitative genetic divergence was higher in the multivariate estimates as compared to the univariate estimates. However, the biological implications of the differences in magnitude are unclear. First, for purely mathematical reasons, the leading eigenvalues of a matrix will be larger than the variances for any of the individual components of the matrix. Second, the eigenvalues of the multivariate QST matrix represent genetically independent linear combinations of traits and (to me) it is unclear how to informative are about the actual genetic architecture of the traits.
I’ve found interesting that the authors incorporated the idea of Lande (1979) of comparing the eigenstructure of Gwithin-populations with Gamong-populations. The rationale is that non-proportionality between these matrices can be interpreted as support for selection (i.e. proportionality would be the expectation under drift).
Surprisingly easy was the way of dealing with the multilocus FST. In brief, if the loci are in Hardy-Weinberg equilibrium they can be considered as independent and the traditional estimate (i.e. averaging across loci) can be used.
-Kremer, A., A. Zanetto, and A. Ducousso. 1997. Multilocus and multitrait measures of differentiation for gene markers and phenotypic traits. Genetics 145:1229–1241.
-Lande, R. 1979. Quantitative genetic analysis of multivariate evolution, applied to brain-body size allometry. Evolution 33:402–416.