Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700108, India.
Department of Mathematics, Visva-Bharati, Santiniketan 731235, India.
J Theor Biol. 2021 Nov 7;528:110846. doi: 10.1016/j.jtbi.2021.110846. Epub 2021 Jul 24.
In the predator-prey system, predators can affect the prey population (1) by direct killing and (2) by inducing predation fear, which ultimately force preys to adopt some anti-predator strategies. However, the anti-predator strategy is not the same for all individual preys of different life stages. Also, anti-predator behavior has both cost and benefit, but most of the mathematical models observed the dynamics by incorporating its cost only. In the present study, we formulate a predator-prey model dividing the prey population into two stages: juvenile and adult. We assume that adult preys are only adapting group defense as an anti-predator strategy when they are sensitive to predation. Group defense plays a positive role for adult prey by reducing their predation, but, on the negative side, it simultaneously decreases their reproductive potential. A parameter, anti-predator sensitivity is introduced to interlink both the benefit and cost of group defense. Our result shows that when adult preys are not showing anti-predator behavior, with an increase of maturation rate, the system exhibits a population cycle of abruptly increasing amplitude, which may drive all species of the system to extinction. Anti-predator sensitivity may exclude oscillation through homoclinic bifurcation and avert the prey population for any possible random extinction. Anti-predator sensitivity also decreases the predator population density and produces bistable dynamics. Higher values of anti-predator sensitivity may lead to the extinction of the predator population and benefit adult preys to persist with large population density. Below a threshold value of anti-predator sensitivity, it may possible to retain the predator population in the system by increasing the fear level of the predator. We also observe our fear-induced stage-structured model exhibits interesting and rich dynamical behaviors, various types of bistabilities in different bi-parameter planes. Finally, we discuss the potential impact of our findings.
在捕食者-猎物系统中，捕食者可以通过直接捕杀和（2）通过诱导捕食恐惧来影响猎物种群，这最终迫使猎物采取一些反捕食策略。然而，不同生命阶段的所有个体猎物的反捕食策略并不相同。此外，反捕食行为既有成本又有收益，但大多数数学模型在观察动态时仅考虑了其成本。在本研究中，我们将猎物种群分为两个阶段：幼体和成年体，构建了一个捕食者-猎物模型。我们假设，当成年猎物对捕食敏感时，它们只采用群体防御作为一种反捕食策略。群体防御对成年猎物有积极的作用，因为它可以降低被捕食的风险，但另一方面，它同时降低了它们的繁殖潜力。引入一个参数，即抗捕食敏感性，将群体防御的收益和成本联系起来。我们的结果表明，当成年猎物不表现出反捕食行为时，随着成熟率的增加，系统表现出急剧增加幅度的种群周期，这可能导致系统中的所有物种灭绝。抗捕食敏感性可以通过同宿分岔排除振荡，并避免猎物种群发生任何可能的随机灭绝。抗捕食敏感性还降低了捕食者的种群密度，并产生双稳动态。较高的抗捕食敏感性值可能导致捕食者种群灭绝，并有利于成年猎物以较大的种群密度持续存在。低于抗捕食敏感性的阈值值，通过增加捕食者的恐惧水平，可能使系统中的捕食者种群得以保留。我们还观察到，我们的基于恐惧的阶段结构模型表现出有趣和丰富的动力学行为，在不同的双参数平面上存在各种类型的双稳性。最后，我们讨论了我们发现的潜在影响。
