Mutualisms in a parasitism-predation system consisting of crows, cuckoos and cats

An avian brood parasite usually places its eggs in the nest of other birds by stealth, which raise the unrelated chicks. Since the chicks compete food with the host offsprings, the host typically suffers serious loss of its own brood. However, an over 16-year study on cuckoos and their host (crows) demonstrates that the parasites may provide a benefit to the host by deterring predators (e.g., quasi-feral cats). In order to better understand these changes, we propose a mathematical model to describe the crow-cuckoo-predator system. Dynamics of the model demonstrate mechanism by which the crow-cuckoo interaction can change among parasitism, commensalism, mutualism and neutralism in a smooth fashion. Our results not only consolidate empirical observations, but also reveal some new phenomena: the crow-cuckoo interaction will return from mutualism to parasitism when the predation is extremely strong, and periodic oscillations of the populations may occur in certain range of the parameters.