Rate of Decrease of Genetic Variability in a Two-Dimensional Continuous Population of Finite Size

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The rate of decay of genetic variability was investigated for two-dimensional continuous populations of finite size. The exact value of the rate involves a rather complicated expression (formula (4-1)). However, numerical examples indicate that in a population habitat size L x L and density D, the rate is approximately equal to (see PDF) where σ2 is the variance of dispersion distance assuming isotropical migration. The value given in (2) is equal to that of a panmictic population of size DL2. It is remarkable that whether the rate assumes the value given by (1) or by (2) depends only on Dσ2 (a local property), which is independent of the habitat size. Since, in a one-dimensional population, this depends on both Dσ2 and the habitat size, there is an essential difference between the two types of population structure.—The function giving the probability of two homologous genes separated by a given distance being different alleles was also obtained, (formula (5-1)).

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