Phylogeny shape and the phylogenetic comparative method

We explored the impact of phylogeny shape on the results of interspecific statistical analyses incorporating phylogenetic information. In most phylogenetic comparative methods (PCMs), the phylogeny can be represented as a relationship matrix, and the hierarchical nature of interspecific phylogenies translates into a distinctive blocklike matrix that can be described by its eigenvectors (topology) and eigenvalues (branch lengths). Thus, differences in the eigenvectors and eigenvalues of different relationship matrices can be used to gauge the impact of possible phylogeny errors by comparing the actual phylogeny used in a PCM analysis with a second phylogenetic hypothesis that may be more accurate. For example, we can use the sum of inverse eigenvalues as a rough index to compare the impact of phylogenies with different branch lengths. Topological differences are better described by the eigenvectors. In general, phylogeny errors that involve deep splits in the phylogeny (e.g., moving a taxon across the base of the phylogeny) are likely to have much greater impact than will those involving small perturbations in the fine structure near the tips. Small perturbations, however, may have more of an impact if the phylogeny structure is highly dependent (with many recent splits near the tips of the tree). Unfortunately, the impact of any phylogeny difference on the results of a PCM depends on the details of the data being considered. Recommendations regarding the choice, design, and statistical power of interspecific analyses are also made.