On a Lotka–Volterra type competition model from river ecology

Abstract

We revisit a stream population model which was formulated to study the evolution of passive movement in advective environments and has been discussed by Lou et al. in a homogeneous situation (Lou et al., 2016) and later by Zhou and Zhao, (2018) in a spatially heterogeneous situation but with a restriction that the resource is distributed non-increasingly across space. In this paper, by employing a different and more direct argument, we remove the technical condition imposed in Zhou and Zhao, (2018) and obtain a more general result, which suggests that the outcome of evolution does not depend on the shape of the resource distribution for most situations. Biologically, our main result puts new insights into the understanding of the mechanism behind the evolution of dispersal.