School of Mathematics and Information Technology, Yuncheng University, Yuncheng, Shanxi, 044000, P. R. China.
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada.
J Theor Biol. 2019 Feb 7;462:455-465. doi: 10.1016/j.jtbi.2018.11.035. Epub 2018 Nov 29.
A predator-prey metapopulation model over arbitrary number of patches is considered in this paper. The model assumes that only prey move (with a dispersal delay) between all connected patches. Two cases of dispersal patterns are considered. For the case the dispersal of prey is due to random effect only (independent of predator density), we show that either the dispersal delay is harmless in the sense that it does not affect the stability of the metacommunity, or the dispersal delay can induce stability switches with finite number of stability intervals. For the case the dispersal of prey is due to predator-avoidance (dependent on predator density), we show that the interplay of density-dependent dispersal and dispersal delay may also induce finite number of stability switches. This indicates that the combination of the density-dependent dispersal and dispersal delay can exhibit both stabilizing and destabilizing effects on the stability of the coexistence equilibrium. Our results show that the delay and the patterns of prey dispersal jointly affect the stability of predator-prey metacommunities and can induce multiple stability switches.
本文研究了任意数量斑块上的捕食者-猎物化学生态种群模型。该模型假设只有猎物（存在扩散延迟）在所有连通斑块之间移动。考虑了两种扩散模式。对于由于随机效应（与捕食者密度无关）导致猎物扩散的情况，我们表明，扩散延迟在不影响化学生态种群稳定性的意义上是无害的，或者扩散延迟可以通过有限数量的稳定性间隔引起稳定性转变。对于由于逃避捕食者（依赖于捕食者密度）导致猎物扩散的情况，我们表明，密度依赖的扩散和扩散延迟的相互作用也可能引起有限数量的稳定性转变。这表明，密度依赖的扩散和扩散延迟的组合可以对共存平衡的稳定性产生稳定和不稳定的影响。我们的结果表明，延迟和猎物扩散模式共同影响捕食者-猎物化学生态种群的稳定性，并可以引起多个稳定性转变。
