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Modeling the Fear Effect in Predator–Prey Interactions with Adaptive Avoidance of Predators

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Abstract

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.

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Acknowledgements

We benefitted a lot from the consultation and discussion with Dr. Liana Zanette in setting up the model, and we would like to thank Dr. Zanette for her friendly and generous help. We thank the two anonymous reviewers for their valuable suggestions and comments, which have led to a substantial improvement in the presentation of this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada

    Xiaoying Wang & Xingfu Zou

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  1. Xiaoying Wang
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  2. Xingfu Zou
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Correspondence to Xingfu Zou.

Additional information

Research was partially supported by the Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN-2016-04665).

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Wang, X., Zou, X. Modeling the Fear Effect in Predator–Prey Interactions with Adaptive Avoidance of Predators. Bull Math Biol 79, 1325–1359 (2017). https://doi.org/10.1007/s11538-017-0287-0

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  • DOI: https://doi.org/10.1007/s11538-017-0287-0

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