具有Allee效应的捕食者-食饵模型的进化动力系统
Evolutionary Dynamics of Predator-Prey Systems Subject to Allee Effects
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摘要: 研究了具有 Allee 效应的捕食者-食饵种群显性特征的共同进化动力系统.得到了在对称作用下连续稳定策略和进化分支的生态条件和进化条件,食饵的分支能导致捕食者分支;证明了在对称作用下进化动力系统经历超临界Hopf分支和次临界Hopf分支,周期进化是随机突变和选择过程的可能结果.在对称作用下进化自杀不可能发生,然而,在非对称作用下当种群遭受Allee效应时,进化自杀可能发生.Abstract: In this paper, we discuss the coevolution of phenotypic traits in a community comprising the populations of predator and prey subject to Allee effects. We obtain the ecological and evolutionary conditions that allow for continuously stable strategy and evolutionary branching under symmetric interactions. It is shown that the branching in the prey can induce a secondary branching in the predator. We show that the evolutionary dynamics undergoes a supercritical Hopf bifurcation and a subcritical Hopf bifurcation under symmetric interactions. Evolutionary cycle is a likely outcome of the process. Evolutionary suicide is impossible if the interaction coefficients are symmetric;however, evolutionary suicide can occur for the prey populations when they are subject to Allee effects and the interaction coefficients are asymmetric.
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