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arXiv · 1102.5563

Permanence of a general discrete-time two-species-interaction model with non-monotonic per capita growth rates

Yun Kang
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Abstract

Combined with all density-dependent factors, the per capita growth rate of a species may be non-monotonic. One important consequence is that species may suffer from weak Allee effects or strong Allee effects. In this paper, we study the permanence of a discrete-time two-species-interaction model with non-monotonic per capita growth rates for the first time. By using the average Lyapunov functions and extending the ecological concept of the relative nonlinearity, we find a simple sufficient condition for guaranteeing the permanence of systems that can model complicated two-species interactions. The extended relative nonlinearity allows us to fully characterize the effects of nonlinearities in the per capita growth functions with non-monotonicity. These results are illustrated with specific two species competition and predator-prey models of generic forms with non-monotone per capita growth rates.

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Yun Kang. 2011-02-28. Permanence of a general discrete-time two-species-interaction model with non-monotonic per capita growth rates. https://arxiv.org/abs/1102.5563

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