Modeling the Allee effects induced by cost of predation fear and its carry-over effects

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:505

Article

Sasmal, Sourav Kumar¹  Takeuchi, Yasuhiro² 

[1] Birla Inst Technol & Sci, Dept Math, Pilani 333031, Rajasthan, India

[2] Aoyama Gakuin Univ, Dept Phys & Math, Sagamihara, Kanagawa 2525258, Japan

关键词: Allee effect;    Fear effect;    Carry-over effect;    Predator-prey interactions;    Global stability;   

DOI  :  10.1016/j.jmaa.2021.125485

来源: Elsevier

【 摘 要 】

Predation-driven Allee effects play an important role in the dynamics of a small prey population; however, such effects cannot occur for the model with type I functional response. Predator-driven Allee effects generally occur when a generalist predator targets some specific prey. However, apart from the lethal effects of predation, there are some non-lethal effects in the presence of a predator. Due to the fear of predation, positive density dependence growth of prey may be observed at low population density because of reduced foraging activities. Moreover, such a non-lethal effect can be carried over through generations or seasons. In the present manuscript, we investigate the role of predation fear and its carry-over effects in the prey-predator model. First, we study the single-species model from a global perspective. We have shown that depending on the birth rate; our single-species model describes three types of growth dynamics, namely, strong Allee dynamics, weak Allee dynamics, and logistic dynamics. Then we include the explicit dynamics of the predator, with type I functional response. Basic dynamical properties, as well as the global stability of each equilibrium, have been discussed. From our analysis, we can observe that both the fear and its carry-over effects have a significant role in the stability of the coexistence equilibrium, even for the model with type I functional response. The phenomenon 'paradox of enrichment' can be observed in our model, which cannot be observed in the classical prey-predator model with type I functional response. However, we can see that such a phenomenon can be ruled out by choosing suitable non-lethal effect parameters. Therefore, our study shows how non-lethal effects change the dynamics of a prey-predator model and has powerful biological insights, especially for understanding the dynamics of small populations. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free