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SELECTION IN COMPLEX GENETIC SYSTEMS I. THE SYMMETRIC EQUILIBRIA OF THE THREE-LOCUS SYMMETRIC VIABILITY MODEL
Marcus W. Feldman 1, Ian Franklin 2, and Glenys J. Thomson 3
1 Department of Biological Sciences, Stanford University, Stanford, California 94305
2 Division of Animal Genetics, Commonwealth Scientific and Industrial Research Organization, Epping, New South Wales 2121, Australia
3 Department of Statistics, Melbourne University, Melbourne, Australia
The symmetric equilibria of the three-locus symmetric viability model are determined and their stability analyzed. For tight linkage there may be four stable equilibria, each characterized by having one pair of complementary chromosomes in high frequencies, with all others low. For looser linkage the only stable symmetric equilibrium is that with complete linkage equilibrium. For intermediate recombination values both types of equilibria may be stable. A new class of equilibria with all pairwise linkage disequilibria zero, but with third order linkage disequilibrium, has been discovered. It may be stable for tight linkage.
Submitted on February 8, 1973Revised on July 30, 1973
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