Evolution of Coalescence Times, Genetic Diversity and Structure during Colonization

Abstract

We consider the impact of a colonization process on the genetic diversity and spatial structure of a geographically subdivided population. A stepping-stone model combined with coalescence theory is used to predict the evolution of sequence divergence and genetic parameters. We first derive analytical results for coalescence times in a population undergoing logistic growth. We next consider a stepping-stone model in which demes are successively colonized, starting from a first deme at one of the borders of the metapopulation. We use recurrence equations to calculate coalescence times for two genes chosen either inside the same deme or in different demes. This allows us to obtain the distribution and the expectation of the coalescence times, and to deduce from them the distribution of the average pairwise differences and the evolution ofFst. Our results reflect the impact of the founder effect, which becomes stronger as the distance of the deme from the first deme increases. An increase in migration rate or growth rate generally leads to a decrease of the founder effect.Fst(i) increases during the beginning of the colonization, (ii) decreases when migration creates homogenization and (iii) increases again towards an equilibrium value. The distributions of pairwise coalescence times or differences between sequences show a peak corresponding to the colonization period. These results could help detect former colonization events in natural populations.