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A mathematical analysis of the stepping stone model of genetic correlation

Published online by Cambridge University Press:  14 July 2016

George H. Weiss  and
Motoo Kimura
George H. Weiss
Affiliation:
National Cancer Institute, Bethesda, Maryland
Motoo Kimura
Affiliation:
National Institute of Genetics, Mishima-shi, Japan
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Abstract

In this paper we analyze the correlation coefficient between members of any two colonies out of an infinite ensemble of colonies. It is assumed that each colony has the same number of members, that migration takes place between the different colonies, and that there is a constant rate of mutation in each colony. An explicit formula is derived for the correlation function and the long distance form of this function is derived. It is shown that under rather weak restrictions on the pattern of migration the asymptotic form of the correlation function is characteristic of the dimension of the model.

Type
Research Papers
Information
Journal of Applied Probability , Volume 2 , Issue 1 , June 1965 , pp. 129 - 149
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

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