James Degnan

University of Canterbury

Bimodal distributions of coalescent times given a gene tree in a species tree

In evolutionary biology, trees of species relationships are often used to depict which species are most closely related, and such species trees can be used as a basis for classifying species. Genes sampled from different species also have tree-like evolutionary histories (gene trees) that often have similar branching patterns to that of the species tree. Relationships between gene trees and species can be modeled probabilistically to determine quantities such as the expected time to coalescence (i.e., common ancestry) for two gene lineages given the species-level divergence times and population sizes for the species being sampled. In this talk, I show how the distribution of a coalescent time can be obtained by integrating over a joint distribution of gene trees and coalescent times for cases with more than two lineages. This marginal distribution for the coalescent time can be regarded as a mixture distribution and can be multimodal when population sizes are not constant.