Developmental regulation of skull morphology II: ontogenetic dynamics of covariance.
Principal Component Analysis
Canalization may play a critical role in molding patterns of integration when variability is regulated by the balance between processes that generate and remove variation. Under these conditions, the interaction among those processes may produce a dynamic structure of integration even when the level of variability is constant. To determine whether the constancy of variance in skull shape throughout most of postnatal growth results from a balance between processes generating and removing variation, we compare covariance structures from age to age in two rodent species, cotton rats (Sigmodon fulviventer) and house mice (Mus musculus domesticus). We assess the overall similarity of covariance matrices by the matrix correlation, and compare the structures of covariance matrices using common subspace analysis, a method related to common principal components (PCs) analysis but suited to cases in which variation is so nearly spherical that PCs are ambiguous. We find significant differences from age to age in covariance structure and the more effectively canalized ones tend to be least stable in covariance structure. We find no evidence that canalization gradually and preferentially removes deviations arising early in development as we might expect if canalization results from compensatory differential growth. Our results suggest that (co)variation patterns are continually restructured by processes that equilibrate variance, and thus that canalization plays a critical role in molding patterns of integration.