The time back to the most recent common ancestor in exchangeable population models

Abstract

A class of haploid population models with population sizeN, nonoverlapping generations and exchangeable offspring distribution is considered. Based on an analysis of the discrete ancestral process, we present solutions, algorithms and strong upper bounds for the expected time back to the most recent common ancestor which hold for arbitrary sample sizen∈ {1,…,N}. New insights into the asymptotic behaviour of the expected time back to the most recent common ancestor for large population size are presented relating the results to coalescent theory.