Evolution of sex ratios in social hymenoptera: Consequences of finite brood size

Evolutionarily stable sex ratios are determined for social hymenoptera under local mate competition (LMC) and when the brood size is finite. LMC is modelled by the parameterd. Of the reproductive progeny from a single foundress nest, a fractiond disperses (outbreeding), while (l-d) mate amongst themselves (sibmating). When the brood size is finite,d is taken to be the probability of an offspring dispersing, and similarly,r, the proportion of male offspring, the probability of a haploid egg being laid. Under the joint influence of these two stochastic processes, there is a nonzero probability that some females remain unmated in the nest. As a result, the optimal proportion of males (corresponding to the evolutionarily stable strategy, ESS) is higher than that obtained when the brood size is infinite. When the queen controls the sex ratio, the ESS becomes more female biased under increased inbreeding (lowerd). However, the ESS under worker control shows an unexpected pattern, including anincrease in the proportion ofmales withincreased inbreeding. This effect is traced to the complex interaction between inbreeding and local mate competition.