Whole-tree methods for detecting differential diversification rates

Prolific cladogenesis, adaptive radiation, species selection, key innovations, and mass extinctions are a few examples of biological phenomena that lead to differential diversification among lineages. Central to the study of differential diversification rates is the ability to distinguish chance variation from that which requires deterministic explanation. To detect diversification rate variation among lineages, we propose a number of methods that incorporate information on the topological distribution of species diversity from all internal nodes of a phylogenetic tree. These whole-tree methods (M-Pi, M-Sigma, and M-R) are explicitly connected to a null model of random diversification-the equal-rates Markov (ERM) random branching model-and an alternative model of differential diversification: M-Pi is based on the product of individual nodal ERM probabilities; M-Sigma is based on the sum of individual nodal ERM probabilities, and M-R is based on a transformation of ERM probabilities that corresponds to a formalized system that orders trees by their relative symmetry. These methods have been implemented in a freely available computer program, SYMMETREE, to detect clades with variable diversification rates, thereby allowing the study of biological processes correlated with and possibly causal to shifts in diversification rate. Application of these methods to several published phylogenies demonstrates their ability to contend with relatively large, incompletely resolved trees. These topology-based methods do not require estimates of relative branch lengths, which should facilitate the analysis of phylogenies, such as supertrees, for which such data are unreliable or unavailable.