In this paper, we are concerned with a general reaction–diffusion–advection model which characterizes the interactions between two competing species in river environments. By regarding advection rates of two species as variable parameters, we provide an efficient way to completely understand the local dynamics. It turns out that there always exist two critical curves which may separate competition outcomes into competitive exclusion, bistability, and coexistence. As a further development, under the assumption that the ratio of advection and diffusion rates of one species is greater than or equal to that of the other species, we give a specific classification on the global dynamics, which shows that bistability does not happen, but coexistence and competitive exclusion may occur. These interesting results indicate that advective movements play a key role in determining the dynamical behaviors.
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