  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.
