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

Iljana Zahle·J. Theodore Cox·Richard Durrett
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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.

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Iljana Zahle, J. Theodore Cox, Richard Durrett. 2005-03-24. The stepping stone model. II: Genealogies and the infinite sites model. https://doi.org/10.1214/105051604000000701

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