Factors influencing the optimum sex ratio in a structured population.

W. D. Hamilton (1967, Science 156, 477-488) calculated the optimum sex-ratio strategy for a population subdivided into local mating groups. He made three important assumptions: that the females founding each group responded precisely to the number of them initiating the group; that ail broods within a group matured synchronously; and that males were incapable of dispersing between groups. We have examined the effects of relaxing each of these assumptions and obtained the following results: (1) When broods mature asynchronously the optimum sex ratio is considerably more female biased than the Hamiltonian prediction. (2) Increasing male dispersal always decreases the optimum female bias to the sex ratio, but it is of particular interest that when moderate levels of dispersal are coupled with asynchrony of brood maturation then the optimum strategy is relatively insensitive to changes in foundress number. (3) When females cannot precisely determine the number of other foundresses initiating the group then the optimum strategy is almost exactly the strategy appropriate to a group of average size. These effects can be most easily understood in terms of local parental control (LPC) of the sex ratio. Through LPC a founding female can alter the mating success of her sons by altering the sex ratio of her brood. Asynchrony in the maturation of broods within a group increases the control that a founding female has over the mating success of her sons, whereas male dispersal reduces it. We have shown that the role of LPC and the role of inbreeding, which favors a female-biased sex ratio in haploidiploid species, are independent and that their effects can be combined into a single general formula r = (1-(r2/z2) E(alpha z/alpha r]/(1 + I). The concept of LPC can also be used to interpret two factors which have been proposed to select for the Hamiltonian sex ratios: local mate competition is LPC acting through sons; and sib mating is LPC acting through daughters.