Global dynamics of a competition-parasitism-mutualism model characterizing plant-pollinator-robber interactions

This paper studies global dynamics of a class of plant-pollinator-robber systems, in which plant is the resource while the pollinator and nectar robber are two competing consumers. The nectar robber is a parasite of plant while the pollinator is the mutualist. Based on the competition-parasitism-mutualism interactions, we established a plant-pollinator-robber model by nectar-mediated consumer-resource theory. By complete analysis on the model, we demonstrate necessary and sufficient conditions for the principle of competitive exclusion to hold and give the global dynamical behavior of the three species in the first octant, in which a three-dimensional saddle-node bifurcation is exhibited. It is shown that pollination-mutualisms promote survival of the nectar robber, the invasion of nectar robber would mean extinction of both the pollinator and the nectar robber itself, while the pollinator (resp. robber) can drive the robber (resp. pollinator) into extinction. Initial population densities of the species are exhibited to play a role in persistence of the systems. This analysis demonstrates mechanisms by which the pollinator and nectar robber can stably coexist, which is observed in real situations.