Interspecific allometry for sexual shape dimorphism: macroevolution of multivariate sexual phenotypes with application to Rensch's rule

Allometric trends in the degree of sexual dimorphism with body size have long fascinated evolutionary biologists. Many male-biased clades display more prominent sexual dimorphism in larger taxa (Rensch’s rule), with most examples documenting this pattern for body size dimorphism. While sexual dimorphism in traits other than body size is equally functionally relevant, characterizing allometric patterns of sexual dimorphism in such traits is hampered by lack of an analytical framework that can accommodate multivariate phenotypes. In this paper we derive a multivariate equivalency for investigating trends in sexual dimorphism – relative to overall body size – across taxa and provide a generalized test to determine whether such allometric patterns correspond with Rensch's rule. For univariate linear traits like body size, our approach yields equivalent results to those from standard procedures, but our test is also capable of detecting trends in multivariate datasets like shape. Computer si...