Towards a genetic theory for the evolution of the sex ratio II. Haplodiploid and diploid models with sibling and parental control of the brood sex ratio and brood size

Population genetic models involving sister, brother, and father control of the brood sex ratio and brood size in both the haplodiploid and diploid cases are constructed and analyzed. The results are interpreted in light of the verbal theories which predict the evolution of the sex ratio to a value which is proportional to the ratio of relatedness of the controlling members of the family to males and to females produced in the brood. In our models, the sex ratio in a certain class of polymorphic equilibria evolves to equal investment in males and females in those cases where the controlling members of the family are symmetrically related to males and females as predicted by the verbal theory. However, the sex ratio in the case of sister control in haploidiploids does not evolve to 1:3, but rather to a value proportional to the ratio of the regression coefficients of additive genotypes. Even so, the predicted sex ratio, which is proportional to 1:3, is in fact an “ESS” in the sense that fixation of a genotype specifying that sex ratio is resistant to the initial increase of all other genotypes.