The stepping stone model. II: Genealogies and the infinite sites model

Abstract

This paper extends earlier work by Cox and Durrett, who studied the coalescence times for two lineages in the stepping stone model on the two-dimensional torus. We show that the genealogy of a sample of size n is given by a time change of Kingman's coalescent. With DNA sequence data in mind, we investigate mutation patterns under the infinite sites model, which assumes that each mutation occurs at a new site. Our results suggest that the spatial structure of the human population contributes to the haplotype structure and a slower than expected decay of genetic correlation with distance revealed by recent studies of the human genome.

Published at http://dx.doi.org/10.1214/105051604000000701 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• The spatial Λ-Fleming-Viot process on a large torus: Genealogies in the presence of recombination
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• Intermediate range migration in the two-dimensional stepping stone model
• From coalescing random walks on a torus to Kingman's coalescent
• Ancestral lineages in spatial population models with local regulation