Math @ Duke

Publications [#243543] of Richard T. Durrett
Papers Published
 Z�hle, I; Cox, JT; Durrett, R, The stepping stone model. II: Genealogies and the infinite sites model,
The Annals of Applied Probability, vol. 15 no. 1B
(February, 2005),
pp. 671699, Institute of Mathematical Statistics, ISSN 10505164 [MR2114986 (2006d:60157)], [doi]
(last updated on 2019/04/24)
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 twodimensional 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. © Institute of Mathematical Statistics, 2005.


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