Evolution of Dispersal in Advective Patchy Environments

We study a two-species competition model in patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches there losses of individuals downstream end (e.g., due flow into lake or ocean). The two competing assumed have same growth rates but different advection rates. focus our studies on properties an associated eigenvalue problem which characterizes extinction/persistence dynamics underlying patch population model. also derive conditions under mutating can cannot invade resident species.