Wang Xiaoying, Zou Xingfu
Department of Applied Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada.
Bull Math Biol. 2017 Jun;79(6):1325-1359. doi: 10.1007/s11538-017-0287-0. Epub 2017 May 15.
Recent field experiments on vertebrates showed that the mere presence of a predator would cause a dramatic change of prey demography. Fear of predators increases the survival probability of prey, but leads to a cost of prey reproduction. Based on the experimental findings, we propose a predator-prey model with the cost of fear and adaptive avoidance of predators. Mathematical analyses show that the fear effect can interplay with maturation delay between juvenile prey and adult prey in determining the long-term population dynamics. A positive equilibrium may lose stability with an intermediate value of delay and regain stability if the delay is large. Numerical simulations show that both strong adaptation of adult prey and the large cost of fear have destabilizing effect while large population of predators has a stabilizing effect on the predator-prey interactions. Numerical simulations also imply that adult prey demonstrates stronger anti-predator behaviors if the population of predators is larger and shows weaker anti-predator behaviors if the cost of fear is larger.
近期对脊椎动物进行的野外实验表明，仅仅是捕食者的存在就会导致猎物种群统计学特征发生显著变化。对捕食者的恐惧增加了猎物的生存概率，但会导致猎物繁殖成本增加。基于实验结果，我们提出了一个具有恐惧成本和捕食者适应性回避的捕食者-猎物模型。数学分析表明，在决定长期种群动态方面，恐惧效应可以与幼年猎物和成年猎物之间的成熟延迟相互作用。一个正平衡点可能会在延迟处于中间值时失去稳定性，而在延迟较大时重新获得稳定性。数值模拟表明，成年猎物的强适应性和恐惧的高成本都有破坏稳定的作用，而大量的捕食者种群对捕食者-猎物相互作用有稳定作用。数值模拟还表明，如果捕食者种群数量较大，成年猎物会表现出更强的反捕食行为；如果恐惧成本较大，成年猎物会表现出较弱的反捕食行为。
