Seeking the evolutionary regression coefficient: an analysis of what comparative methods measure.

Two alternative classes of comparative statistical method differ in the way that the comparative data are used to test for an association between two quantitative traits. Directional comparative methods use reconstructions of the ancestral character states to calculate the changes between ancestral and descendant conditions along the branches of the phylogenetic tree. The set of changes in two or more traits is used to test for evidence of correlated evolution. Cross-sectional techniques do not estimate changes along the branches of the tree, but rather make comparisons across the tips of a phylogeny, or between pairs of extant taxa (or between their higher nodes). These methods, then, study the association between pairs of traits representing the contemporary endpoints of evolution. The best known of the cross-sectional techniques, the species regression, simply regresses the species values of one variable onto those of another. However, it is shown here analytically that directional and cross-sectional methods, despite making very different use of the data, estimate precisely the same evolutionary parameter: the association between the changes in two variables along the branches of the phylogenetic tree. Thus, comparative statistical techniques are able to recover the historical trends of evolution, that is, the ways in which evolution has proceeded along the branches of the phylogenetic tree, from analysis of the variation among the contemporary species of a phylogeny. This means that the choice between the two alternative traditions of comparative study cannot be based upon what the different methods purport to measure, but rather must be based upon the statistical properties of particular methods. In the light of this result, it is discussed here whether there are statistical reasons to prefer some methods over others.