A generalized permutation model for the analysis of cross-species data

Many fields of biology employ cross-species comparisons. However, because species descend with modification from common ancestors, and rates of evolution may vary among branches of an evolutionary tree, problems of nonindependence and nonidentical distributions may occur in comparative data sets. Several phylogenetically based statistical methods have been developed to deal with these issues, but two are most commonly used. Independent contrasts attempts to transform the data to meet the i.i.d, assumption of conventional statistical methods. Monte Carlo computer simulations attempt to produce phylogenetically informed null distributions of test statistics. A disadvantage of the former is its ultimate reliance on conventional distributional assumptions, whereas the latter may require excessive information on biological parameters that are rarely known. We propose a phylogenetic permutation method that is akin to the simulation approach but requires less biological input information. We show that the conventional, equally likely (EL) randomization model is a special case of our phylogenetic permutations (PP). An application of the method is presented to test the correlation between two traits with cross-species data.