Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 15, Number 1B (2005), 671-699.
The stepping stone model. II: Genealogies and the infinite sites model
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.
Ann. Appl. Probab., Volume 15, Number 1B (2005), 671-699.
First available in Project Euclid: 1 February 2005
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Zähle, Iljana; Cox, J. Theodore; Durrett, Richard. The stepping stone model. II: Genealogies and the infinite sites model. Ann. Appl. Probab. 15 (2005), no. 1B, 671--699. doi:10.1214/105051604000000701. https://projecteuclid.org/euclid.aoap/1107271664