INTERMEDIATE RANGE MIGRATION IN THE TWO-DIMENSIONAL STEPPING STONE MODEL

• 成果类型: Article
• 署名作者: Cox, J. Theodore
• 署名单位: Syracuse University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP639
• 发表日期: 2010
• 页码: 785-805
• 关键词: random-walks; population; coalescent; genetics; times

摘要

We consider the stepping stone model on the torus of side L in Z(2) in the limit L -> infinity, 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).