Procedures for the Analysis of Comparative Data Using Phylogenetically Independent Contrasts

Abstract

We discuss and clarify several aspects of applying Felsenstein's (1985, Am. Nat. 125: 1–15) procedures to test for correlated evolution of continuous traits. This is one of several available comparative methods that maps data for phenotypic traits onto an existing phylogenetic tree (derived from independent information). Application of Felsenstein's method does not require an entirely dichotomous topology. It also does not require an assumption of gradual, clocklike character evolution, as might be modeled by Brownian motion. Almost any available information can be used to estimate branch lengths (e.g., genetic distances, divergence times estimated from the fossil record or from molecular clocks, numbers of character changes from a cladistic analysis). However, the adequacy for statistical purposes of any proposed branch lengths must be verified empirically for each phytogeny and for each character. We suggest a simple way of doing this, based on graphical analysis of plots of standardized independent contrasts versus their standard deviations (i.e., the square roots of the sums of their branch lengths). In some cases, the branch lengths and/or the values of traits being studied will require transformation. An example involving the scaling of mammalian home range area is presented. Once adequately standardized, sets of independent contrasts can be analyzed using either linear or nonlinear (multiple) regression. In all cases, however, regressions (or correlations) must be computed through the origin. We also discuss ways of correcting for body size effects and how this relates to making graphical representations of relationships of standardized independent contrasts. We close with a consideration of the types of traits that can be analyzed with independent contrasts procedures and conclude that any (continuous) trait that is inherited from ancestors is appropriate for analysis, regardless of the mechanism of inheritance (e.g., genetic or cultural).