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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
. 1969 Jan;62(1):70–74. doi: 10.1073/pnas.62.1.70

LINKAGE AND SELECTION: NEW EQUILIBRIUM PROPERTIES OF THE TWO-LOCUS SYMMETRIC VIABILITY MODEL*

Samuel Karlin 1, Marcus W Feldman 1
PMCID: PMC285956  PMID: 5253665

Abstract

In the two-locus symmetric viability model with recombination, conditions for the existence and stability of a new class of polymorphic equilibria are given. These „unsymmetric” equilibria, which exist for relatively loose linkage, can be explicitly obtained, in contrast to the previously known symmetric equilibria which are generally given by the solutions of a cubic equation.

For sufficiently tight linkage, there is always at least one stable symmetric equilibrium. Seven is the precise maximum for the number of interior equilibria. The qualitative consequences of these results are briefly examined. In particular it is pointed out that since for some linkage values no stable polymorphic equilibria exist, there is no „overdominance theorem” comparable to the single-locus case.

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Selected References

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

  1. Bodmer W. F., Felsenstein J. Linkage and selection: theoretical analysis of the deterministic two locus random mating model. Genetics. 1967 Oct;57(2):237–265. doi: 10.1093/genetics/57.2.237. [DOI] [PMC free article] [PubMed] [Google Scholar]
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