Intermediate range migration in the two-dimensional stepping stone model

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3 Scopus citations

Abstract

We consider the stepping stone model on the torus of side L in ℤ2 in the limit L → ∞, and study the time it takes two lineages tracing backward in time to coalesce. Our work fills a gap between the finite range migration case of [Ann. Appl. Probab. 15 (2005) 671-699] and the long range case of [Genetics 172 (2006) 701-708], where the migration range is a positive fraction of L. We obtain limit theorems for the intermediate case, and verify a conjecture in [Probability Models for DNA Sequence Evolution (2008) Springer] that the model is homogeneously mixing if and only if the migration range is of larger order than (log L)1/2.

Original languageEnglish (US)
Pages (from-to)785-805
Number of pages21
JournalAnnals of Applied Probability
Volume20
Issue number3
DOIs
StatePublished - Jun 1 2010

Keywords

  • Coalescence times
  • Hitting times
  • Stepping stone model
  • Torus random walk

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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