| Popis: |
Over the last three and a half decades the analysis of relationships between traits in comparative data has come to be dominated by the least-squares regression approach, mainly as implemented in the phylogenetic generalized least-squares (PGLS) regression. Though powerful and straightforward, this approach has two main drawbacks: it requires assumptions about the shape of the data, and it is limited to addressing questions about the conditional mean of one variable as a function of other variables. Here I develop frequentist non-parametric constructs for the analysis of a broader range of comparative questions: two phylogenetic permutation tests based respectively on cyclic permutations and permutations that conserve phylogenetic signal. The cyclic permutation test, an extension of the restricted permutation test that performs exchanges via cyclic permutations of the phylogeny, is conceptually straightforward and performs well both within and outside the bounds where PGLS is applicable, but it can only be used for balanced trees. The signal-based permutation test has identical statistical properties and works with any kind of tree. The statistical power and size of these two tests compares favorably with independent contrasts and surpasses that of a previously developed phylogenetic permutation test that exchanges pairs of observations with probability proportional to their phylogenetic proximity. Three case studies illustrate the use of phylogenetic permutations for detecting relationships in non-normal and heteroscedastic data, for quantile regression, for testing hypotheses about trait space occupation, and for comparative biological problems in which the data points are not tips in the phylogeny. |
