How much can the orientation of G's eigenvectors tell us about genetic constraints?

A key goal in evolutionary quantitative genetics is to understand how evolutionary trajectories are constrained by pleiotropic coupling among multiple traits. Because studying pleiotropic constraints directly at the molecular genetic level remains very difficult, several analytical approaches attempt to draw conclusions about constraints by relating the orientation of the eigenvectors of the traits' (co)variance matrix to vectors of multivariate selection. On the basis of explicit models of genetic architecture, I here argue that the value of such approaches is greatly overestimated. The reason is that eigenvector orientation can be highly unstable and lack a biologically meaningful relationship with the underlying traits' genetic architecture. Genetic constraints are more profitably explored through experimental approaches avoiding the mathematical abstraction inherent in eigenanalysis.