Power of eight tree shape statistics to detect nonrandom diversification: a comparison by simulation of two models of cladogenesis.

We used simulations to compare the relative power of eight statistical tests to detect imbalance in phylogenies that is too great to be ascribed to an equal-rates Markov null model. Three of these tests have never had their power assessed before. Our simulations are the first to assess performance under scenarios in which the speciation rates of various lineages can evolve independently. In one of the scenarios explored, rates depend upon the value of an evolving trait, whereas in the other the probability that a species will speciate declines with the time since it last did so. The results indicate that the relative performance of the methods depends upon how the imbalance is generated. Different types of processes lead to different imbalance signatures, i.e., different patterns of imbalance at different depths in the phylogeny, and the measures of tree shape differ in the depth of phylogeny at which they are most sensitive. Relative performance is also affected by tree size but does not appear to depend greatly upon the degree of speciation rate variation among lineages. Two of the indices (Colless's index I(c) and Shao and Sokal's Nmacr;) show reasonable performance throughout, but another (Shao and Sokal's B(2)) is never indicated to be a preferred method. Two tests that do not require completely resolved phylogenies, mean I' and mean I'(10), have reasonable power.