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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