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Linkage disequilibrium between neutral genes in finite populations

Published online by Cambridge University Press:  01 July 2016

William G. Hill
William G. Hill*
Affiliation:
Institute of Animal Genetics, Edinburgh
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Extract

There is now a large literature on linkage disequilibrium between pairs of loci, both for selection in infinite populations and for neutral genes in finite populations, but there have been few studies with more loci. Bennett (1954) showed how the frequencies of chromosomes with any number of neutral genes would change in an infinite population, and the author (unpublished) has extended Bennett's results to find expected changes in chromosome frequencies with up to six loci in finite populations. For two linked neutral genes in finite populations the expected disequilibrium is zero, but the variance of the disequilibrium or the correlation of gene frequencies in segregating populations has been found. This has been done by Monte Carlo simulation (Hill and Robertson (1968)), but an approximation can be obtained by diffusion methods (Ohta and Kimura (1969)) and the asymptotic values using inbreeding theory (Sved (1971)). In this note we discuss the case of disequilibrium between three neutral loci and show how it relates to that between two loci.

Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 1 , March 1974 , pp. 13 - 15
Copyright
Copyright © Applied Probability Trust 1974 

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References

Bennett, J. H. (1954) On the theory of random mating. Ann. Eugen. 184, 311–317.Google Scholar
Hill, W. G. and Robertson, A. (1968) Linkage disequilibrium in finite populations. Theor. Appl. Genet. 38, 226–231.Google Scholar
Ohta, T. and Kimura, M. (1969) Linkage disequilibrium due to random genetic drift. Genet. Res. 13, 47–55.CrossRefGoogle Scholar
Sved, J. A. (1971) Linkage disequilibrium and homozygosity of chromosome segments in finite populations. Theor. Pop. Biol. 2, 125–141.CrossRefGoogle ScholarPubMed