There is more than one way to skin a G matrix

Because of its importance in directing evolutionary trajectories there has been considerable interest in comparing variation among genetic variance-covariance ( G) matrices. Numerous statistical approaches have been suggested but no general analysis of the relationship among these methods has previously been published. In this paper we used data from a half-sib experiment and simulations to explore the results of applying eight tests (T method, modified Mantel test, Bartlett’s test, Flury hierarchy, Jackknife-MANOVA, Jackknife-eigenvalue test, random skewers, selection skewers). Whereas a randomization approach produced acceptable estimates those from a bootstrap were typically unacceptable and we recommend randomization as the preferred method. All methods except the Jackknife-eigenvalue test gave similar results although a fine scale analysis suggested that the former group can be subdivided into two or possibly three groups, hierarchical tests, skewers, and the rest (Jackknife-MANOVA...