Recognizing the forest for the trees: testing temporal patterns of cladogenesis using a null model of stochastic diversification

Computer simulations are developed and employed to examine the expected temporal distributions of nodes under a null model of stochastic lineage bifurcation and extinction. These Markovian models of phylogenetic process were constructed so as to permit direct comparisons against empirical phylogenetic trees generated from molecular or other information available solely from extant species. For replicate simulated phylads with n extant species, cumulative distribution functions (cdf's) of branching times were calculated, and compared (using the Kolmogorov-Smirnov test statistic D) to those from three published empirical trees. Molecular phylogenies for columbine plants and avian cranes showed statistically significant departures from the null expectations, in directions indicating recent and ancient species' radiations, respectively, whereas a molecular phylogeny for the Drosophila virilis species group showed no apparent historical clustering of branching events. Effects of outgroup choice and phylogenetic frame of reference were investigated for the columbines and found to have a predictable influence on the types of conclusions to be drawn from such analyses. To enable other investigators to statistically test for nonrandomness in temporal cladogenetic pattern in empirical trees generated from data on extant species, we present tables of mean cdf's and associated probabilities under the null model for expected branching times in phylads of varying size. The approaches developed in this report complement and extend those of other recent methods for employing null models to assess the statistical significance of pattern in evolutionary trees.