Methods for studying allometry in geometric morphometrics: a comparison of performance

Allometry has been the focus of growing interest in studies using geometric
morphometric methods to address a wide range of research questions at the interface of ecology and evolution. This study uses computer simulations to compare four methods for estimating allometric vectors from landmark data: the multivariate regression of shape on a measure of size, the first principal component (PC1) of shape, the PC1 in conformation space, and a recently proposed method, the PC1 of Boas coordinates. Simulations with no residual variation around the allometric relationship showed that all four methods are logically consistent with one another, up to minor nonlinearities in the mapping between conformation space and shape tangent space. In simulations that included residual variation, either isotropic or with a pattern independent of allometry, regression of shape on size performed consistently better than the PC1 of shape. The PC1s of conformation and of Boas coordinates were very
similar and very close to the simulated allometric vectors under all conditions. An extra series of simulations to elucidate the relation between conformation and Boas coordinates indicated that they are almost identical, with a marginal advantage for conformation. Empirical examples of ontogenetic allometry in rat skulls and rockfish body shape illustrate simple biological applications of the methods. The paper concludes with recommendations how these methods for estimating allometry can be used in studies of evolution and ecology.