The geometry of dominance shows broad potential for stable polymorphism under antagonistic pleiotropy

Abstract Alleles with opposing effects on fitness characters are said to exhibit selectional antagonistic pleiotropy (broadly construed so that effects are not necessarily confined to the same individual). A number of theoretical investigations considered the case where a pair of alleles at a locus influences two fitness components and derived the conditions giving rise to stable polymorphism under various assumptions about the mode of trait-interaction. Strikingly, many of these analyses concluded that the potential for maintaining polymorphism is strongly constrained by the joint influence of two factors: (1) the prevalence of weak selection coefficients over coefficients of large magnitude, and (2) the absence of beneficial dominance reversals (where the deleterious effects of each allele are partially or completely masked in the heterozygous genotype). Consequently, the conclusion that selective polymorphism is unlikely to be maintained by intralocus mechanisms of antagonistic pleiotropy has achieved widespread acceptance. Here we argue that such conclusions do not apply to any of the following models of antagonism: (i) additive trait-interaction, (ii) multiplicative trait-interaction, (iii) bivoltine selection, (iv) soft selection, (v) hard selection, and (vi) sexual antagonism. We demonstrate that the parameter space giving rise to stable allelic variation is quite large throughout, and moreover, the plenitude of suitable parameters neither depends on the strength of selection nor requires dominance reversal. Dominance coefficients associated with stringent conditions for stable polymorphism are shown to be atypical as compared to all feasible parameters, and best regarded as an outcome of adherence to a special relation: dominance with a constant magnitude and direction, which includes the case of additive allelic effects at a locus. Properties of single-locus equilibria (heterozygosity, allele frequency differentiation) are investigated, as well as the contribution of dominance schemes to the genetic variance in fitness characters in populations at multilocus linkage equilibrium. Author summary Allelic variants at a locus with opposing effects on multiple fitness components (antagonistic fitness pleiotropy) have long been appreciated as a possible source of balancing selection. The prevalence of polymorphism owing to this form of natural selection, however, has been doubted on theoretical grounds due to the fact that standard assumptions of genetic models (namely, constant magnitudes for the dominance coefficients) are hardly conducive to the maintenance of polymorphism. The major exception to this conclusion lies with schemes that exhibit dominance reversal (where the direction of dominance for antagonistic alleles flips across fitness components). Here we conduct a geometric analysis of the space of polymorphism-promoting dominance parameters and conclude that the conditions for maintaining balanced alleles is unrestrictive, with non-reversals playing an underappreciated role. Competing Interest Statement The authors have declared no competing interest. Footnotes Corrections to Figure 2B (rightmost panel) and the equations in Appendix B.