Deconstructing Symmetry

For over half a century biologists have investigated departures from perfect symmetry in organisms as a means to explore the nature of biological development and effects of stresses on developmental stability. More recently (and more contentiously), morphological symmetry has been hypothesized to be an important signal of quality used in social interactions such as mate selection. Current approaches for quantifying asymmetries depend almost entirely on "fluctuating asymmetry" (FA), defined as the distribution of differences between bilateral traits. FA has a number of well-known problems, however. We propose a new approach based on estimating (1) a latent distribution for the underlying trait, and (2) a distribution of developmental noise that is superimposed on the trait in the expression of each side. The method yields maximum likelihood estimates for the parameters of both distributions. Extensions of the method allow for simultaneous estimation of other types of anymmetries (directional asymmetry and antisymmetry), as well as the means to quantify covariate effects on different components of the model. The new method is explored using morphological and chronometric traits.