Journal of Mathematical Biology

, Volume 29, Issue 1, pp 59-75

First online:

The coalescent and the genealogical process in geographically structured population

  • M. NotoharaAffiliated withDepartment of Biology, Faculty of Science, Kyushu University

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We shall extend Kingman's coalescent to the geographically structured population model with migration among colonies. It is described by a continuous-time Markov chain, which is proved to be a dual process of the diffusion process of stepping-stone model. We shall derive a system of equations for the spatial distribution of a common ancestor of sampled genes from colonies and the mean time to getting to one common ancestor. These equations are solved in three particular models; a two-population model, the island model and the one-dimensional stepping-stone model with symmetric nearest-neighbour migration.

Key words

Coalescent Genealogical process Geographical structure Migration Markov chain