The Role of Diffusion Rate in the Persistence of Species in Advective Homogeneous Environment

Abstract

We study a few single species models in a one-dimensional advective homogeneous environment. One interesting feature in these models concerns the boundary condition at the downstream end, where the species might be subject to a net loss of individuals, as measured by the parameter $b$ which accounts for the magnitude of the loss. We investigate conditions for the persistence of a single species for general value of $b$, in terms of the critical habitat size and the critical diffusion rate $d$. Our primary objective is to investigate the relationship between the diffusion rate d and the critical habitat size $L^*$, specifically for $b=\infty$ and $b=1$ and, more broadly, for $b>3/2$ and $b<3/2$. The findings imply that for $1\leq b<3/2$, the essential habitat size is a decreasing function of diffusion rate, which means the diffusion rate is more larger, the species are more persister; When $3/2<b\leq \infty $, the critical habitat size first decreases and then increases with diffusion rate increases, additionally, the species persist just on the moderate area of the diffusion rate.