The effects of habitat fragmentation and ecological invasion on population sizes

In this paper, we consider the effects of habitat fragmentation and ecological invasion of exotic species on the survival of a native endangered species, respectively. Different from the former studies, we pay attention on the more important situation in conservation biology that species live in a weak patchy environment in the sense that species in some of the isolated patches will become extinct without the contribution from other patches. We establish some foundmental permanence and extinction results on the basic and important nonautonomous diffusive Logistic model. In addition, by using these results, we consider the effect of an introduced species on the survival of a native species through competition. Biological implications of these results are discussed.