Abstract

An ODE system modeling the competition between two species in a two-patch environment is studied. How do diffusion affect the competition outcomes of two competing species that have the same birth rate on average? It has previously been conjectured by Gourley and Kuang in 2005 that the species that can concentrate its birth in a single patch wins if the diffusion rate is large enough, and two species will coexist if the diffusion rate is small. In short, the winning strategy is simply to focus as much birth in a single patch as possible. We solve the conjectures and establish new results, which include the conjectures as special cases. This may provide us with insight into how species learn to compete and may point out species evolution directions.

This is a joint work with Yuan Lou and Chih-Wen Shih.