POPULATION DYNAMICS OF TWO COMPETING SPECIES IN AN ADVECTIVE HETEROGENEOUS TWO-PATCH ENVIRONMENT

We investigate the population dynamics in an advective heterogeneous two-patch environment with general boundary conditions. We give a criterion for the persistence of a single species in such an environment in terms of the dispersal rate d, the drift rate q, the upstream-end flow rate alpha, and the downstream-end flow rate beta. For two competing species which have distinct dispersal rates d and D but are identical in all the other respects, we study the global dynamics of their populations under alpha = 0. The evolution outcome of the two species depends not only on these parameters but also on the ratio of the carrying capacities of the two patches. It turns out that a coexistent equilibrium must be globally asymptotically stable if 0 < beta < q. However, it could be either globally asymptotically stable or unstable if beta > q, and in the latter case, there are two stable semi-trivial equilibria. For beta = q, we give a complete and explicit classification of the dynamics, provide a formula of an evolutionarily stable dispersal strategy, and answer some open questions pro-posed by Lou (J. Nonlinear Modeling and Analysis 1 (2019), 151-166) regarding the competition between the faster and the slower diffusers.