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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1979 Aug;76(8):4001–4005. doi: 10.1073/pnas.76.8.4001

Population genetics of multigene family with special reference to decrease of genetic correlation with distance between gene members on a chromosome.

M Kimura, T Ohta
PMCID: PMC383964  PMID: 291060

Abstract

A mathematical method is developed which enables us to treat exactly the process of coincidental evolution under mutation, unequal intrachromosomal crossing-over as well as ordinary crossing-over between homologous chromosomes in a finite population of the effective size N. It makes use of finite difference equations involving two quantities denoted by fi and phi i, in which fi is the identity coefficient of two gene members that are i steps apart on the same chromosome and phi i is that of two members i steps apart on two homologous chromosomes. When the number of genes (n) per family is large, the finite difference equations can be approximately by ordinary second-order differential equations which can then be solved analytically. Results obtained by the present method are compared with the corresponding results previously obtained by one of us (T.O.) using conventional diffusion models of gene frequency changes in population genetics. It is shown that the previous results obtained by T.O. regarding second-order statistics are essentially valid, and they give good approximations particularly when N beta is small, where beta is the rate of ordinary interchromosomal crossing-over within the multigene family.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

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