Minimal clade size and external branch length under the neutral coalescent

Michael G. B. Blum, Olivier François
2002 Advances in Applied Probability  
Given a sample of genes taken from a large population, we consider the neutral coalescent genealogy and study the theoretical and empirical distributions of the size of the smallest clade containing a fixed gene. We show that the theoretical distribution is strongly related to a Yule distribution of parameter 2, and that the empirical count statistics are asymptotically Gaussian as the number of genes grows to infinity. Then we consider external branches of the coalescent tree, and describe
more » ... e, and describe their lengths. Using the infinitely many sites model of mutation, we also describe the conditional distribution of the external branch lengths, given the number of pairwise differences between a reference DNA sequence and the sequence of one closest relative in the sample.
doi:10.1239/aap/1127483740 fatcat:bdvmi5xcxzetnbh4dngts3ij2e