Taxon sampling, correlated evolution, and independent contrasts.

Independent contrasts are widely used to incorporate phylogenetic information into studies of continuous traits, particularly analyses of evolutionary trait correlations, but the effects of taxon sampling on these analyses have received little attention. In this paper, simulations were used to investigate the effects of taxon sampling patterns and alternative branch length assignments on the statistical performance of correlation coefficients and sign tests; "full-tree" analyses based on contrasts at all nodes and "paired-comparisons" based only on contrasts of terminal taxon pairs were also compared. The simulations showed that random samples, with respect to the traits under consideration, provide statistically robust estimates of trait correlations. However, exact significance tests are highly dependent on appropriate branch length information; equal branch lengths maintain lower Type I error than alternative topological approaches, and adjusted critical values of the independent contrast correlation coefficient are provided for use with equal branch lengths. Nonrandom samples, with respect to univariate or bivariate trait distributions, introduce discrepancies between interspecific and phylogenetically structured analyses and bias estimates of underlying evolutionary correlations. Examples of nonrandom sampling processes may include community assembly processes, convergent evolution under local adaptive pressures, selection of a nonrandom sample of species from a habitat or life-history group, or investigator bias. Correlation analyses based on species pairs comparisons, while ignoring deeper relationships, entail significant loss of statistical power and as a result provide a conservative test of trait associations. Paired comparisons in which species differ by a large amount in one trait, a method introduced in comparative plant ecology, have appropriate Type I error rates and high statistical power, but do not correctly estimate the magnitude of trait correlations. Sign tests, based on full-tree or paired-comparison approaches, are highly reliable across a wide range of sampling scenarios, in terms of Type I error rates, but have very low power. These results provide guidance for selecting species and applying comparative methods to optimize the performance of statistical tests of trait associations.