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 fi xed 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 i nversely proportional to relative cost. However, the theory assumes control by bother parents. We show that allowing one parent to control the sex rat io biases it further from parity that fisher's theory predicts. Quantitativ ely, the additional bias towards the cheaper sex depends only ver 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 se x is in control. If the controlling sex is cheaper to raise, than the sex r atio 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 und er biparental control or under uniparental control by the more expensive se x. However, such polymorphisms do occur, and some of them may be explained by our mode.