On the selection of phylogenetic eigenvectors for ecological analyses

Among the statistical methods available to control for phylogenetic autocorrelation in ecological data, those based on eigenfunction analysis of the phylogenetic distance matrix among the species are becoming increasingly important tools. Here, we evaluate a range of criteria to select eigenvectors extracted from a phylogenetic distance matrix (using phylogenetic eigenvector regression, PVR) that can be used to measure the level of phylogenetic signal in ecological data and to study correlated evolution. We used a principal coordinate analysis to represent the phylogenetic relationships among 209 species of Carnivora by a series of eigenvectors, which were then used to model log-transformed body size. We first conducted a series of PVRs in which we increased the number of eigenvectors from 1 to 70, following the sequence of their associated eigenvalues. Second, we also investigated three non-sequential approaches based on the selection of 1) eigenvectors significantly correlated with body size, 2) eigenvectors selected by a standard stepwise algorithm, and 3) the combination of eigenvectors that minimizes the residual phylogenetic autocorrelation. We mapped the mean specific component of body size to evaluate how these selection criteria affect the interpretation of non-phylogenetic signal in Bergmann's rule. For comparison, the same patterns were analyzed using autoregressive model (ARM) and phylogenetic generalized least-squares (PGLS). Despite the robustness of PVR to the specific approaches used to select eigenvectors, using a relatively small number of eigenvectors may be insufficient to control phylogenetic autocorrelation, leading to flawed conclusions about patterns and processes. The method that minimizes residual autocorrelation seems to be the best choice according to different criteria. Thus, our analyses show that, when the best criterion is used to control phylogenetic structure, PVR can be a valuable tool for testing hypotheses related to heritability at the species level, phylogenetic niche conservatism and correlated evolution between ecological traits.