A sex ratio theory of gregarious parasitoids

A mathematical model is constructed to explain a density-dependent increase in the progeny sex ratios of gregarious parasitoids. In the model we considered non-cooperative game between females concerned with their own inclusive fitness. Equilibrium progeny sex ratios of the first and second females ovipositing on the same host are expressed in terms of the probability of double parasitism (p), the ratio of a male to a female in contribution to resource competition (α), the clutch size ratio between the two females (β), the crowding effect on female reproductive success (γ), and the inbreeding coefficient (f). Major predictions from the model are: 1) the progeny sex ratios of both the first and second females increase with p, 2) as β becomes smaller, the progeny sex ratios of the first females decrease, while those of the second females dramatically increases, 3) when a host is attacked by at most two wasps, the sex ratio of the total number of eggs laid on the host does not exceed 0.25. The effects of α and preferential death by female progeny in doubly parasitized hosts are considered as factors responsible for an excess number of males at emergence. Some possible modes of density-dependent increase in the sex ratios of the overall progeny populations is also discussed on the basis of the present model.