Distributions of cherries for two models of trees

Null models for generating binary phylogenetic trees are useful for testing evolutionary hypotheses and reconstructing phylogenies. We consider two such null models - the Yule and uniform models - and in particular the induced distribution they generate on the number C-n of cherries in the tree, where a cherry is a pair of leaves each of which is adjacent to a common ancestor. By realizing the process of cherry formation in these two models by extended Polya urn models we show that C-n is asymptotically normal. We also give exact formulas for the mean and standard deviation of the C-n in these two models. This allows simple statistical tests for the Yule and uniform null hypotheses. (C) 2000 Elsevier Science Inc. All rights reserved.