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Analysis of central equilibrium configurations for certain multi-locus systems in subdivided populations

Published online by Cambridge University Press:  14 April 2009

Samuel Karlin  and
R. B. Campbell
Samuel Karlin
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, U.S.A.
R. B. Campbell
Affiliation:
Department of Mathematics, Stanford University, Stanford, CA 94305, U.S.A.
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The multi-locus systems expressing non-epistatic and generalized symmetric selection lend themselves to the study of the stability of certain central polymorphic equilibria. These equilibria persist when any form of migration connects demes which share a common equilibrium. The analysis of the stability of the equilibrium in the global system is tractable, thus supplementing known protection results for two alleles at one locus with stability conditions on an internal equilibrium involving an arbitrary number of loci, each with an arbitrary number of alleles. Two of the principal findings are that stability of central Hardy–Weinberg type equilibria increase with ‘more’ migration and ‘more’ recombination. As a corollary, local stability in each deme implies stability in a system with migration superimposed; but instability in each deme when isolated does not imply instability when migration is superimposed.

Type
Research Article
Information
Genetics Research , Volume 32 , Issue 2 , October 1978 , pp. 151 - 169
Copyright
Copyright © Cambridge University Press 1978

References

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