%0 Journal Article %1 MR2114986 %A Zähle, Iljana %A Cox, J. Theodore %A Durrett, Richard %D 2005 %J Ann. Appl. Probab. %K Kingmans_coalescent coalescent_theory spatial_coalescent spatial_structure %N 1B %P 671--699 %R 10.1214/105051604000000701 %T The stepping stone model. II. Genealogies and the infinite sites model %U http://dx.doi.org/10.1214/105051604000000701 %V 15 %X 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{MR2114986, 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. }, added-at = {2012-08-24T19:36:01.000+0200}, author = {Z{\"a}hle, Iljana and Cox, J. Theodore and Durrett, Richard}, biburl = {https://www.bibsonomy.org/bibtex/296d57a94486651a774b8f2e500f2cb81/peter.ralph}, doi = {10.1214/105051604000000701}, fjournal = {The Annals of Applied Probability}, interhash = {6f4ea5039f0ac8d34bfcf851acafdd38}, intrahash = {96d57a94486651a774b8f2e500f2cb81}, issn = {1050-5164}, journal = {Ann. Appl. Probab.}, keywords = {Kingmans_coalescent coalescent_theory spatial_coalescent spatial_structure}, mrclass = {60K35 (92D10)}, mrnumber = {2114986 (2006d:60157)}, mrreviewer = {Mu Fa Chen}, number = {1B}, pages = {671--699}, timestamp = {2015-06-15T03:18:45.000+0200}, title = {The stepping stone model. {II}. {G}enealogies and the infinite sites model}, url = {http://dx.doi.org/10.1214/105051604000000701}, volume = 15, year = 2005 }