Abstract
It is widely accepted that diffusive dispersal can permit persistence in an advective environment. This paper studies in some sense the optimal diffusion rate of species in a flowing habitat with hostile downstream boundary conditions. Firstly, we study the dependence of the critical length of the habitat on the dispersal rate d. It is shown that the critical length first decreases and then increases and asymptotically tends to infinity. Then there is a unique optimal diffusion rate d_{0} for a single species to evolve. Then, by using this observation, we study the competition system of two species which are the same but only with different dispersal rates. We get an open finite interval, which is a neighborhood of d_{0}, such that, if one of the dispersal rates lies within the interval but the other rate falls outside, then competition exclusion occurs. If the two dispersal rates both lie within the interval, the one with an intermediate dispersal rate can always invade the other with its dispersal rate near the ends of the interval.
Highlights
There are many species residing in flowing habitats, such as streams and rivers
We give a rigorous analytical proof that there exists a unique optimal diffusion rate, in the sense that a species adopting this diffusion rate will need the smallest length of critical habitat for persistence
3 Concluding remarks This paper explores the optimal strategy of diffusion of a single-species model and a twospecies competition model in a -dimensional flowing homogeneous habitat with hostile downstream boundary conditions
Summary
There are many species residing in flowing habitats, such as streams and rivers. As a result, the unidirectional water movement constantly drives the species out of the habitat. We give a rigorous analytical proof that there exists a unique optimal diffusion rate, in the sense that a species adopting this diffusion rate will need the smallest length of critical habitat for persistence. A species with diffusion rate d > q /( r) can persist if and only if the habitat length L is bigger than the critical length L∗(d).
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