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

Publication ,  Journal Article
Zähle, I; Cox, JT; Durrett, R
Published in: Annals of Applied Probability
February 1, 2005

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. © Institute of Mathematical Statistics, 2005.

Duke Scholars

Published In

Annals of Applied Probability

DOI

ISSN

1050-5164

Publication Date

February 1, 2005

Volume

15

Issue

1 B

Start / End Page

671 / 699

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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Zähle, I., Cox, J. T., & Durrett, R. (2005). The stepping stone model. II: Genealogies and the infinite sites model. Annals of Applied Probability, 15(1 B), 671–699. https://doi.org/10.1214/105051604000000701
Zähle, I., J. T. Cox, and R. Durrett. “The stepping stone model. II: Genealogies and the infinite sites model.” Annals of Applied Probability 15, no. 1 B (February 1, 2005): 671–99. https://doi.org/10.1214/105051604000000701.
Zähle I, Cox JT, Durrett R. The stepping stone model. II: Genealogies and the infinite sites model. Annals of Applied Probability. 2005 Feb 1;15(1 B):671–99.
Zähle, I., et al. “The stepping stone model. II: Genealogies and the infinite sites model.” Annals of Applied Probability, vol. 15, no. 1 B, Feb. 2005, pp. 671–99. Scopus, doi:10.1214/105051604000000701.
Zähle I, Cox JT, Durrett R. The stepping stone model. II: Genealogies and the infinite sites model. Annals of Applied Probability. 2005 Feb 1;15(1 B):671–699.

Published In

Annals of Applied Probability

DOI

ISSN

1050-5164

Publication Date

February 1, 2005

Volume

15

Issue

1 B

Start / End Page

671 / 699

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 4901 Applied mathematics
  • 0104 Statistics
  • 0102 Applied Mathematics