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

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 which accounts for the magnitude of the loss.We investigate conditions for the persistence of a single species for general value of , in terms of the critical habitat size and the critical diffusion rate .Our primary objective is to investigate the relationship between the diffusion rate d and the critical habitat size , specifically for and and, more broadly, for and .The findings imply that for , 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 , 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.