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REGIONS OF STABLE EQUILIBRIA FOR MODELS OF DIFFERENTIAL SELECTION IN THE TWO SEXES UNDER RANDOM MATING
J. F. Kidwell 1, M. T. Clegg 1, F. M. Stewart 2, and T. Prout 3
1 Division of Biological and Medical Sciences, Brown University,
Providence, Rhode Island 02912
2 Department of Mathematics, Brown University, Providence, Rhode
Island 02912
3 Department of Genetics, University of California, Davis, California
95616
The equilibrium structure of models of differential selection in the sexes is investigated. It is shown that opposing additive selection leads to stable polymorphic equilibria for only a restricted set of selection intensities, and that for weak selection the selection intensities must be of approximately the same magnitude in the sexes. General models of opposing directional selection, with arbitrary dominance, are investigated by considering simultaneously the stability properties of the trivial equilibria and the curve along which multiple roots appear. Numerical calculations lead us to infer that the average degree of dominance determines the equilibrium characteristics of models of opposing selection. It appears that if the favored alleles are, on the average, recessive, there may be multiple polymorphic equilibria, whereas only a single polymorphic equilibrium can occur when the favored alleles are, on the average, dominant. The principle that the average degree of dominance controls equilibrium behavior is then extended to models allowing directional selection in one sex with overdominance in the other sex, by showing that polymorphism is maintained if and only if the average fitness in heterozygotes exceeds one.
Submitted on April 27, 1976Revised on August 10, 1976
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