Superparasitism as a differential game

Superparasitism refers to a female parasitoid laying an egg in a host already parasitized by a conspecific. In solitary species, only one offspring per host is expected to complete development, hence the game. Hosts are often clumped in patches and several females exploiting such an aggregate of resource make its state change over time, hence the dynamical character of the game. Two coupled questions arise: (i) Is it worth accepting a parasitized host? (ii) When to leave the host patch? Through these decisions (i) the competition for healthy hosts and (ii) the trade-off between leaving in quest of a better patch and staying to make the patch less profitable for other parasitoids (this is a way to lower superparasitism likely to occur after having left the patch) are addressed. The aim of this work is to characterize a strategy that would be evolutionarily relevant in such a situation, as it directly concerns females' reproductive success. Investigating a (synchronous) nonzero-sum two-player differential game allows us to characterize candidate dynamic evolutionarily stable policies in terms of both oviposition and patch-leaving decisions. For that matter, the game is (in the most part of the parameter space) completely solved if the probability that superparasitism succeeds is assumed to be close to one-half, a fair value under direct competition. The strategic equilibrium consists, for each females, in (i) superparasitizing consistently upon arrival on the patch, and (ii) leaving when the loss of fitness due to superparasitism likely to occur after its departure is reduced to zero. The competing females are thus expected to leave the patch as they arrived: synchronously. Superparasitism does not necessarily lead to a war of attrition.