The Annals of Applied Probability

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

Iljana Zähle, J. Theodore Cox, and 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.

Article information

Source
Ann. Appl. Probab., Volume 15, Number 1B (2005), 671-699.

Dates
First available in Project Euclid: 1 February 2005

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1107271664

Digital Object Identifier
doi:10.1214/105051604000000701

Mathematical Reviews number (MathSciNet)
MR2114986

Zentralblatt MATH identifier
1082.60097

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 92D10: Genetics {For genetic algebras, see 17D92}

Keywords
Voter model stepping stone model genealogy recombination linkage disequilibrium haplotype structure

Citation

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


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