Pollination-mutualisms in a two-patch system with dispersal

Abstract

In this paper, we consider a two-patch pollination-mutualism model with dispersal, which is derived from resource-service exchange between the plant and pollinator. The pollinator is assumed to persist in one patch in the presence of pollination-mutualisms, while it can (or cannot) survive alone in the other. Rigorous study on the model exhibits that solutions of the equations are nonnegative and bounded, and there exist stable positive equilibria under conditions. Theoretical analysis on the equilibria demonstrates that if the pollinator can survive alone in the other patch, a small dispersal can make the pollinator approach higher total population abundance than if non-dispersing. If the pollinator cannot survive alone in the other patch, a small or large dispersal can make the pollinator approach higher size than if non-dispersing, which is not intuitive. A novel prediction of this work is that the pollinator with dispersal can reach high population abundance even though the mutualistic plant approaches a low density, while constructing a high-quality patch for pollinator can lead to extra individuals for both plant and pollinator via dispersal. Numerical simulations confirm and extend our results.