Journal of Mathematical Biology

, Volume 29, Issue 1, pp 59–75

The coalescent and the genealogical process in geographically structured population

  • M. Notohara

DOI: 10.1007/BF00173909

Cite this article as:
Notohara, M. J. Math. Biol. (1990) 29: 59. 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.

Key words

CoalescentGenealogical processGeographical structureMigrationMarkov chain

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • M. Notohara
    • 1
  1. 1.Department of Biology, Faculty of ScienceKyushu UniversityFukuokaJapan