A polymorphic effect of sexually differential production costs when one parent controls the sex ratio

R. A. Fisher's sex ratio theory predicts that if sons and daughters cost fixed amounts of resources to raise and parents have fixed amounts to invest, then the numerical sex ratio of a panmictic population will evolve to be inversely proportional to relative cost. However, the theory assumes control by both parents. We show that allowing one parent to control the sex ratio biases it further from parity than Fisher's theory predicts. Quantitatively, the additional bias towards the cheaper sex depends only very weakly on which sex is in control. Qualitatively, however, the effect is very strong: a monomorphic, mixed-brood strategy evolves only if the more expensive sex is in control. If the controlling sex is cheaper to raise, then the sex ratio is instead achieved through a polymorphism of single-sex broods. Such polymorphisms are seldom observed in nature, generating the prediction that wherever the sexes are not equally costly, sex ratio is usually either under biparental control or under uniparental control by the more expensive sex. However, such polymorphisms do occur, and some of them may be explained by our model.