Morphometrics and evolution: the challenge of crossing rugged phenotypic landscapes with straight paths

Abstract

Geometric morphometrics is widely used to study underlying causal factors in phenotypic evolution and to reconstruct evolutionary history of phenotypes. However, non-linearities in the phenotypic landscape may exist such that analytical solutions derived from comparison of phenotypes in morphospace may have complex or contradictory relationships in the space of the underlying factors. Ancestral reconstruction of horn morphology based on two mammalian ungulates illustrates how biologically improbable results can arise from the mathematical properties of geometric morphometric morphospaces. Raup’s shell coiling equations are used to illustrate the potential for contradictory conclusions to be drawn from ancestral reconstructions in parameter spaces (such as measurements of levels of gene expression or allele frequencies) versus shape spaces (such as morphospaces based on phenotypic analysis). These examples are generalizable to many real morphometric studies, suggesting that care should be taken when drawing conclusions about genetic, developmental, or environmental processes based on morphometric analyses. Dense sampling of shape space and the use of fully multivariate and, perhaps, nonlinear methods can help forestall potential problems.