Citation:
Lessard S, Wakeley J. The two-locus ancestral graph in a subdivided population: convergence as the number of demes grows in the island model. J. Math. Biol. 2004;48 (3) :275-292.
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Abstract:
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.