Population dynamics and evolution in river ecosystems

Abstract

In this paper, we consider a single species model and a two-species competition model arising in river ecology. An interesting feature of these models lies in the boundary conditions, where there may appear a net loss of individuals from the habitat ends, as measured by two parameters bu and bd. We first determine various sufficient conditions for the persistence of a single species, in terms of the critical habitat size and critical advection rate. Then we turn to study a competition system, where two populations are supposed to differ only in their advection speeds. By using the theory of monotone dynamical systems and principal spectrum, we achieve a complete understanding on the global dynamics, which suggests that weaker advective movement is more beneficial for species to win the competition, extending several existing work (Lou et al., 2016; Xu and Gan, 2019; Zhou and Zhao, 2018).