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

Iljana Zähle, J. Theodore Cox, Richard Durrett

Research output: Contribution to journalArticlepeer-review

24 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 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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