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

Iljana Zähle, J. Theodore Cox, Richard Durrett

Research output: Contribution to journalArticle

23 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)671-699
Number of pages29
JournalAnnals of Applied Probability
Issue number1 B
StatePublished - Feb 1 2005


  • Genealogy
  • Haplotype structure
  • Linkage disequilibrium
  • Recombination
  • Stepping stone model
  • Voter model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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