The optimal strategy for brood-parasitism: how many eggs should be laid in the host's nest?

We consider the optimal strategy for intra-specific brood-parasitism, especially with respect to the number of eggs laid by the parasitic individual in the nest of non-parasitic individual, in particular, a host that does not reject the parasite's eggs. With a fundamental mathematical model, assuming that the survival probability of the parasite's offspring in the nest of the host is significantly smaller than that in parasite's own nest, we determine the optimal number of eggs laid in the nest of host that maximizes the expected reproductive fitness of the parasite. We show that the invasion success of brood-parasitism could significantly depend on the total number of eggs laid by the parasite in a breeding season, and that the successfully invading brood-parasitism could realize maximum fitness with a specific number of parasite's eggs laid in the nest of the host.