Abstract
We study two discrete predator-prey models in patchy environment, one without dispersal corridors and one with dispersal corridors. Dispersal corridors are passes that allow the migration of species from one patch to another and their existence may influence the permanence of the model. We will offer sufficient conditions to guarantee the permanence of the two predator-prey models. By comparing the two permanence criteria, we discuss the effects of dispersal corridors on the permanence of the predator-prey model. It is found that the dispersion of the prey from one patch to another is helpful to the permanence of the prey if the population growth of the prey is density dependent; however, this dispersion of the prey could be disadvantageous or advantageous to the permanence of the predator. Five numerical examples are presented to confirm the theoretical results obtained and to illustrate the effects of dispersal corridors on the permanence of the predator-prey model.
Highlights
The conception of permanence in ecological communities is first discussed in [1]
The paper is mainly involved with the effects of dispersal corridors on the permanence of discrete predator-prey models in patchy environment
We have introduced two models of Ricker type undergoing the effect of density dependency— model (3) is in patchy environment without dispersal corridors and model (4) is with dispersal corridors
Summary
The conception of permanence in ecological communities is first discussed in [1]. This notion of permanence is known under different aliases, such as permanent coexistence or uniform persistence. It is common that in the real world today the habitats of the species are separated into isolated patches due to spatial heterogeneity or the development of mankind, such as the construction of highways or railways [9,10,11,12,13,14,15,16] This patchy environment may restrict the activities of the species and lead to adverse effects on the permanence of the ecological communities; some dispersal corridors may be built to allow movement between the patches. We remark that in the literature the numerous research papers on continuous/discrete predator-prey models in patchy environment have focused mainly on the permanence criteria and/or the existence of periodic solutions of the models; the effects of dispersal corridors on the permanence of the models are rarely studied until the present paper.
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