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June, 1977 Rates of Consolidation in a Selectively Neutral Migration Model
Stanley Sawyer
Ann. Probab. 5(3): 486-493 (June, 1977). DOI: 10.1214/aop/1176995811


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.


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Stanley Sawyer. "Rates of Consolidation in a Selectively Neutral Migration Model." Ann. Probab. 5 (3) 486 - 493, June, 1977.


Published: June, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0363.92006
MathSciNet: MR446585
Digital Object Identifier: 10.1214/aop/1176995811

Primary: 92A10
Secondary: 60J15 , 60J20 , 60K99 , 92A15

Keywords: migration , population structure , rates of consolidation , selective neutrality , stepping stone

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 3 • June, 1977
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