Rates of Consolidation in a Selectively Neutral Migration Model

Abstract

Assume a population is distributed in an infinite lattice of colonies in a migration and random-mating model in which all creatures are selectively equivalent. In one and two dimensions, the population tends to consolidate into larger and larger blocks, each of which is composed of the descendents of a single initial individual. The purpose here is to describe the variation of the size and shape of these blocks with time. Specifically, we obtain asymptotic results for (1) the expected number of individuals in, (2) the approximate radius of, and (3) the distribution of the individuals within a typical block for large time. These results depend on the dimension, and most extend to three or more dimensions.