Journal of Mathematical Biology

, Volume 48, Issue 3, pp 275–292

The two-locus ancestral graph in a subdivided population: convergence as the number of demes grows in the island model


DOI: 10.1007/s00285-003-0230-x

Cite this article as:
Lessard, S. & Wakeley, J. J. Math. Biol. (2004) 48: 275. doi:10.1007/s00285-003-0230-x


We study the ancestral recombination graph for a pair of sites in a geographically structured population. In particular, we consider the limiting behavior of the graph, under Wright’s island model, as the number of subpopulations, or demes, goes to infinity. After an instantaneous sample-size adjustment, the graph becomes identical to the two-locus graph in an unstructured population, but with a time scale that depends on the migration rate and the deme size. Interestingly, when migration is gametic, this rescaling of time increases the population mutation rate but does not affect the population recombination rate. We compare this to the case of a partially-selfing population, in which both mutation and recombination depend on the selfing rate. Our result for gametic migration holds both for finite-sized demes, and in the limit as the deme size goes to infinity. However, when migration occurs during the diploid phase of the life cycle and demes are finite in size, the population recombination rate does depend on the migration rate, in a way that is reminiscent of partial selfing. Simulations imply that convergence to a rescaled panmictic ancestral recombination graph occurs for any number of sites as the number of demes approaches infinity.


Coalescent Island model Migration Recombination 

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Département de mathématiques et de statistique
  2. 2.Department of Organismic and Evolutionary Biology

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