| Summary: | In this paper, we consider the effect of dispersal on the permanence of single and interacting populations modelled by systems of integro differential equations. Different from former studies, our discussion here includes the important situation when species live in a weak patchy environment; i.e., species in some isolated patches will become extinct without the contribution from other patches. For the single population model considered in this paper, we show that the same species can persist for some dispersal rates and the species will vanish in some isolated patches. Based on the results for a single population model, we derive sufficient conditions for the permanence of two interacting competitive and predator-prey dispersing systems.
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