The coalescent and the genealogical process in geographically structured population

J Math Biol. 1990;29(1):59-75. doi: 10.1007/BF00173909.


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.

MeSH terms

  • Genetics, Population*
  • Geography
  • Mathematics
  • Models, Genetic*
  • Probability