Clustering Behavior of a Continuous-Sites Stepping-Stone Model with Brownian Migration

Xiaowen Zhou (Department of Mathematics and Statistics, Concordia university)

Abstract


Clustering behavior is studied for a continuous-sites stepping-stone model with Brownian migration. It is shown that, if the model starts with the same mixture of different types of individuals over each site, then it will evolve in a way such that the site space is divided into disjoint intervals where only one type of individuals appear in each interval. Those intervals (clusters) are growing as time $t$ goes to infinity. The average size of the clusters at a fixed time $t$ is of the order of square root of $t$. Clusters at different times or sites are asymptotically independent as the difference of either the times or the sites goes to infinity.

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Pages: 1-15

Publication Date: July 3, 2003

DOI: 10.1214/EJP.v8-141

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