标题：Population genetics of multigene family with special reference to decrease of genetic correlation with distance between gene members on a chromosome
期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1979
卷号：76
期号：8
页码：4001-4005
DOI：10.1073/pnas.76.8.4001
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：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.
