Analysis of character divergence along environmental gradients and other covariates.

Character displacement is typically identified by comparing phenotypic differences in sympatry and allopatry. Recently, however, Goldberg and Lande (2006) pointed out that when phenotypic characters vary along an environmental gradient, the standard approach may fail to identify sympatric character divergence. Here we present a general analytical procedure for identifying sympatric character divergence while accounting for phenotypic changes that covary with environmental variables. Our approach uses residual randomization from a generalized linear model, and allows the statistical comparison of sympatric phenotypic divergence to allopatric phenotypic divergence while accounting for phenotypic variation along a gradient. Through simulation we demonstrate that our approach correctly identifies patterns of sympatric character divergence when they are present, and does not identify such patterns when they are not. Our analytical approach complements and extends the suggestions of Goldberg and Lande (2006), by allowing a full statistical assessment of the varied patterns of character displacement along environmental gradients, or while accounting for other covariates and sources of variation.