Stepping stone model, Kingman's coalescent, Mutation patterns, Infinite sites model, Genetics, Geonomics
Genetics and Genomics | Mathematics
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.
Zähle, Iljana; Cox, J. Theodore; and Durrett, Richard, "The Stepping Stone Model, II: Genealogies and the Infinite Sites Model, Submitted" (2005). Mathematics Faculty Scholarship. Paper 7.
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