Regions of Stable Equilibria for Models of Differential Selection in the Two Sexes Under Random Mating

Abstract

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.

Experimental evolution reveals sex-specific dominance for surviving bacterial infection in laboratory populations ofDrosophila melanogaster

“…SSDRs can greatly broaden the parameter space for which SA selection can maintain balanced polymorphisms (Kidwell et al. 1977 ; Fry 2010 ; Connallon and Clark 2011 , 2012 ). SSDRs can arise through two distinct mechanisms, either as a by‐product of concavity of fitness landscapes and SA selection (see fig.…”

An unbiased test reveals no enrichment of sexually antagonistic polymorphisms on the human X chromosome

“…When fitness effects of SA alleles are small [ 19 , 51 ], single-generation allele frequency changes at X-linked and autosomal loci (respectively) are well-approximated by and (see the electronic supplementary material). SA selection is expected to maintain genetic variation (i.e.…”

Random and non-random mating populations: Evolutionary dynamics in meiotic drive

“…And hence if we let the frequency of gametes A 1 , A 2 be x t , 1 − x t in sperm and y t , 1 − y t in eggs, then in the mating pool for the following generation the frequencies of male allele A 1 s and female allele A 1 s are [7,43] x…”

“…To plot the figures we have considered that different alleles are favored in the two sexes. If, in spite of different alleles, same alleles are favored in the two sexes, then it can be shown that the possibility of existence of equilibrium at the Mendelian segregation is low where in most of the cases the Mendelian segregation point becomes a boundary point of the stable or unstable regions [43,45]. Here, it is noticeable observation that when alleles A 1 are favored in the both sexes, the shaded region relating to feasible solution in (k, κ) space tries to spread toward the (0, 0) corner and on the contrary when the both sexes favor alleles A 2 , the shaded region tries to spread toward the opposite corner, (1,1).…”