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The Hardy-Weinberg law with overlapping generations

Published online by Cambridge University Press:  01 July 2016

Brian Charlesworth
Brian Charlesworth*
Affiliation:
Department of Genetics, University of Liverpool
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Extract

The Hardy-Weinberg law is generally regarded as one of the most important results of population genetics. It was originally proved for the case of populations with distinct generations (Hardy (1908), Weinberg (1908)); a general proof for populations with overlapping generations has apparently not been given before. The case of a single autosomal locus with an arbitrary number of alleles is considered here. Births and deaths are assumed to occur in continuous time. The weak ergodicity property of the birth rate and age structure of such a population, first derived by Norton (1928), is used to establish the fact that allele frequencies tend to constant limits in the absence of mutation, migration, selection and genetic drift.

Type
Research Article
Information
Advances in Applied Probability , Volume 6 , Issue 1 , March 1974 , pp. 4 - 6
Copyright
Copyright © Applied Probability Trust 1974 

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References

Hardy, G. H. (1908) Mendelian proportions in a mixed population. Science 28, 49–50.CrossRefGoogle Scholar
Norton, H. T. J. (1928) Natural selection and Mendelian variation. Proc. Lond. Math. Soc. 28, 1–45.CrossRefGoogle Scholar
Weinberg, W. (1908) Über den Nachweis der Vererbung beim Menschen. Jh. Ver. vaterl. Naturk. Württ. 64, 368–382.Google Scholar