The stepping stone model: New formulas expose old myths

J. Theodore Cox, Richard Durrett

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


We study the stepping stone model on the two-dimensional torus. We prove several new hitting time results for random walks from which we derive some simple approximation formulas for the homozygosity in the stepping stone model as a function of the separation of the colonies and for Wright's genetic distance FST. These results confirm a result of Crow and Aoki (1984) found by simulation: in the usual biological range of parameters FST grows like the log of the number of colonies. In the other direction, our formulas show that there is significant spatial structure in parts of parameter space where Maruyama and Nei (1971) and Slatkin and Barton (1989) have called the stepping model "effectively panmictic".

Original languageEnglish (US)
Pages (from-to)1348-1377
Number of pages30
JournalAnnals of Applied Probability
Issue number4
StatePublished - Nov 2002


  • Coalescent
  • Fixation indices
  • Heterozygosity
  • Identity by descent
  • Stepping stone model
  • Voter model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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