Comparing G matrices: a MANOVA approach

There is considerable interest in comparing genetic variance-covariances matrices (G matrix). However, present methods are difficult to implement and cannot readily be extended to incorporate effects of other variables such as habitat, sex, or location. In this paper I present a method based on MANOVA that can be done using only standard statistical packages (coding for the method using SPLUS is available from the author). The crux of the approach is to use the jackknife method to estimate the pseudovalues of the estimates; these estimates can then be used as datapoints in a MANOVA. I illustrate the method using two published datasets: (1) variation in G matrices resulting from differences in rearing condition, species, and sex in the crickets Gryllus firmus and G. pennsylvanicus; and (2) variation in G matrices associated with habitat and history in the amphipod Gammarus minus.