Properties of phylogenetic trees generated by Yule-type speciation models

We investigate some discrete structural properties of evolutionary trees ge nerated under simple null models of speciation, such as the Yule model. The se models have been used as priors in Bayesian approaches to phylogenetic a nalysis, and also to test hypotheses concerning the speciation process. In this paper we describe new results for three properties of trees generated under such models. Firstly, for a rooted tree generated by the Yule model w e describe the probability distribution on the depth (number of edges from the root) of the most recent common ancestor of a random subset of k specie s. Next we show that, for trees generated under the Yule model, the approxi mate position of the root can be estimated from the associated unrooted tre e, even for trees with a large number of leaves. Finally, we analyse a biol ogically motivated extension of the Yule model and describe its distributio n on tree shapes when speciation occurs in rapid bursts. (C) 2001 Elsevier Science Inc. All rights reserved.