Clades, clans, and reciprocal monophyly under neutral evolutionary models

The Yule model and the coalescent model are two neutral stochastic models for generating trees in phylogenetics and population genetics, respectively. Although these models are quite different, they lead to identical distributions concerning the probability that pre-specified groups of taxa form monophyletic groups (clades) in the tree. We extend earlier work to derive exact formulae for the probability of finding one or more groups of taxa as clades in a rooted tree, or as 'clans' in an unrooted tree. Our findings are relevant for calculating the statistical significance of observed monophyly and reciprocal monophyly in phylogenetics.