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The effect of population subdivision on two loci without selection

Published online by Cambridge University Press:  14 April 2009

Marcus W. Feldman  and
Freddy Bugge Christiansen
Marcus W. Feldman
Affiliation:
Department of Biological Sciences, Stanford University, Stanford, California 94305
Freddy Bugge Christiansen
Affiliation:
Department of Biological Sciences, Stanford University, Stanford, California 94305

Summary

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This paper is devoted to the study of the effects of population subdivision on the evolution of two linked loci. Two simple deterministic models of population subdivision without selection are investigated. One is a finite linear ‘stepping stone’ model and the other is a finite linear stepping stone chain of populations stretching between two large populations of constant genetic constitution. At equilibrium in the first model the gene frequencies in each population are equal and there is linkage equilibrium in each population. The rate of decay to zero of the linkage disequilibrium functions is the larger of (1 – c) and , where λ1 is the rate of convergence of the gene frequencies to equilibrium and c is the recombination frequency. In the second model at equilibrium there will be a linear cline in gene frequencies connecting the two large constant populations. This cline will be accompanied by a ‘cline’ of linkage disequilibria. The rate of convergence to this equilibrium cline is independent of the recombination frequency, and, in fact, the gene frequencies and the linkage disequilibria converge to equilibrium at the same rate.

Type
Research Article
Information
Genetics Research , Volume 24 , Issue 2 , October 1974 , pp. 151 - 162
Copyright
Copyright © Cambridge University Press 1974

References

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