Li Ao, Zou Xingfu
Department of Applied Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada.
Bull Math Biol. 2021 Apr 15;83(5):59. doi: 10.1007/s11538-021-00893-5.
When perceiving a risk from predators, a prey may respond by reducing its reproduction and decreasing or increasing (depending on the species) its mobility. We formulate a patch model to investigate the aforementioned fear effect which is indirect, in contrast to the predation as a direct effect, of the predator on the prey population. We consider not only cost but also benefit of anti-predation response of the prey, and explore their trade-offs together as well as the impact of the fear effect mediated dispersals of the prey. In the case of constant response level, if there is no dispersal and for some given response functions, the model indicates the existence of an evolutionary stable strategy which is also a convergence stable strategy for the response level; and if there is dispersal, the analysis of the model shows that it will enhance the co-persistence of the prey on both patches. Considering the trait as another variable, we continue to study the evolution of anti-predation strategy for the model with dispersal, which leads to a three-dimensional system of ordinary differential equations. We perform some numerical simulations, which demonstrate global convergence to a positive equilibrium with the response level evolving towards a positive constant level, implying the existence of an optimal anti-predation response level.
当察觉到来自捕食者的风险时，猎物可能会通过减少繁殖以及降低或增加（取决于物种）其活动能力来做出反应。我们构建了一个斑块模型，以研究上述恐惧效应，这种效应与捕食者对猎物种群的直接捕食效应不同，是间接的。我们不仅考虑了猎物反捕食反应的成本，还考虑了其收益，并共同探讨它们之间的权衡以及恐惧效应介导的猎物扩散的影响。在反应水平恒定的情况下，如果没有扩散且对于某些给定的反应函数，该模型表明存在一种进化稳定策略，它也是反应水平的收敛稳定策略；如果存在扩散，模型分析表明这将增强猎物在两个斑块上的共同持久性。将性状视为另一个变量，我们继续研究具有扩散的模型的反捕食策略的进化，这导致了一个三维常微分方程组。我们进行了一些数值模拟，这些模拟表明全局收敛到一个正平衡点，反应水平朝着一个正的恒定水平演化，这意味着存在一个最优的反捕食反应水平。
