Stepping stone models of finite length

Author:

Maruyama Takeo

Abstract

The stepping stone model of population structure, of finite length, is analysed with special reference to the variance, and correlation coefficients of gene frequencies. Explicit formulas for these quantities are obtained. The model is also analysed for the genetic variability maintained in the population. In order to check the validity of the analytical results, several numerical computations were carried out using two different methods: iterations and Monte Carlo experiments. The values obtained by these numerical methods agree well with the theoretical values obtained by formulas derived analytically.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

Reference9 articles.

1. The number of alleles that can be maintained in a finite population;Kimura;Genetics,1964

2. The stepping stone model of population structure and the decrease of genetic correlation with distance;Kimura;Genetics,1964

3. “Stepping stone” model of population;Kimura;Ann. Rept. Nat. Inst. Genetics, Japan,1953

4. Lectures in Abstract Algebra

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