Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA.
Department of Mathematics, SUNY Cortland, Cortland, NY, 13045, USA.
J Math Biol. 2024 Mar 1;88(3):35. doi: 10.1007/s00285-024-02048-1.
We study an integro-difference equation model that describes the spatial dynamics of a species with a strong Allee effect in a shifting habitat. We examine the case of a shifting semi-infinite bad habitat connected to a semi-infinite good habitat. In this case we rigorously establish species persistence (non-persistence) if the habitat shift speed is less (greater) than the asymptotic spreading speed of the species in the good habitat. We also examine the case of a finite shifting patch of hospitable habitat, and find that the habitat shift speed must be less than the asymptotic spreading speed associated with the habitat and there is a critical patch size for species persistence. Spreading speeds and traveling waves are established to address species persistence. Our numerical simulations demonstrate the theoretical results and show the dependence of the critical patch size on the shift speed.
我们研究了一个积分差分方程模型，该模型描述了在不断变化的栖息地中具有强烈阿利效应的物种的空间动态。我们研究了一个与半无限良好栖息地相连的半无限不良栖息地不断变化的情况。在这种情况下，如果栖息地变化速度小于（大于）物种在良好栖息地中的渐近扩散速度，则严格确定物种的持久性（非持久性）。我们还研究了一个有限的适宜栖息地的变化斑块的情况，并发现栖息地的变化速度必须小于与栖息地相关的渐近扩散速度，并且存在物种持久性的临界斑块大小。传播速度和传播波的建立是为了确定物种的持久性。我们的数值模拟验证了理论结果，并显示了临界斑块大小对变化速度的依赖性。
