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.
Publié le : 2005-02-14
Classification:
Voter model,
stepping stone model,
genealogy,
recombination,
linkage disequilibrium,
haplotype structure,
60K35,
92D10
@article{1107271664,
author = {Z\"ahle, Iljana and Cox, J. Theodore and Durrett, Richard},
title = {The stepping stone model. II: Genealogies and the infinite sites model},
journal = {Ann. Appl. Probab.},
volume = {15},
number = {1A},
year = {2005},
pages = { 671-699},
language = {en},
url = {http://dml.mathdoc.fr/item/1107271664}
}
Zähle, Iljana; Cox, J. Theodore; Durrett, Richard. The stepping stone model. II: Genealogies and the infinite sites model. Ann. Appl. Probab., Tome 15 (2005) no. 1A, pp. 671-699. http://gdmltest.u-ga.fr/item/1107271664/