Global dynamics and evolutionarily stable strategies in a two-species competition patch model

In this paper, we consider a two-species competition patch model in advective heterogeneous environments, where the two species are ecologically identical except for their dispersal rates. It is shown that there exist two critical values such that the species with slower dispersal rate wins the competition if the drift rate is smaller than one critical value, whereas the species with faster dispersal rate is selected if the drift rate is larger than the other critical value. Moreover, treating one species as a resident species and the other one as a mutant species, and viewing dispersal rates as strategies, we show that the dispersal rate of the resident species can be an evolutionarily stable strategy for some intermediate drift rate between the above two critical values.