The stepping stone model: New formulas expose old myths

Journal Article (Journal Article)

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".

Full Text

Duke Authors

Cited Authors

  • Cox, JT; Durrett, R

Published Date

  • November 1, 2002

Published In

Volume / Issue

  • 12 / 4

Start / End Page

  • 1348 - 1377

International Standard Serial Number (ISSN)

  • 1050-5164

Digital Object Identifier (DOI)

  • 10.1214/aoap/1037125866

Citation Source

  • Scopus