Fear effect in a three-species food chain model with generalist predator

Soumitra Pal; Pankaj Kumar Tiwari; Arvind Kumar Misra; Hao Wang; Soumitra Pal; Pankaj Kumar Tiwari; Arvind Kumar Misra; Hao Wang

doi:10.3934/mbe.2024001

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 1-33. doi: 10.3934/mbe.2024001

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Research article

Fear effect in a three-species food chain model with generalist predator

1.
Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
2.
Department of Basic Science and Humanities, Indian Institute of Information Technology, Bhagalpur 813210, India
3.
Department of Mathematical and Statistical Science, University of Alberta, Edmonton AB T6G 2G1, Canada

Received: 18 October 2023 Revised: 19 November 2023 Accepted: 27 November 2023 Published: 08 December 2023

Within the framework of a food web, the foraging behavior of meso-carnivorous species is influenced by fear responses elicited by higher trophic level species, consequently diminishing the fecundity of these species. In this study, we investigate a three-species food chain model comprising of prey, an intermediate predator, and a top predator. We assume that both the birth rate and intraspecies competition of prey are impacted by fear induced by the intermediate predator. Additionally, the foraging behavior of the intermediate predator is constrained due to the presence of the top predator. It is essential to note that the top predators exhibit a generalist feeding behavior, encompassing food sources beyond the intermediate predators. The study systematically determines all feasible equilibria of the proposed model and conducts a comprehensive stability analysis of these equilibria. The investigation reveals that the system undergoes Hopf bifurcation concerning various model parameters. Notably, when other food sources significantly contribute to the growth of the top predators, the system exhibits stable behavior around the interior equilibrium. Our findings indicate that the dynamic influence of fear plays a robust role in stabilizing the system. Furthermore, a cascading effect within the system, stemming from the fear instigated by top predators, is observed and analyzed. Overall, this research sheds light on the intricate dynamics of fear-induced responses in shaping the stability and behavior of multi-species food web systems, highlighting the profound cascading effects triggered by fear mechanisms in the ecosystem.
- food chain model,
- generalist predator,
- fear effect, Hopf bifurcation,
- stability region
Citation: Soumitra Pal, Pankaj Kumar Tiwari, Arvind Kumar Misra, Hao Wang. Fear effect in a three-species food chain model with generalist predator[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 1-33. doi: 10.3934/mbe.2024001

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Abstract

Within the framework of a food web, the foraging behavior of meso-carnivorous species is influenced by fear responses elicited by higher trophic level species, consequently diminishing the fecundity of these species. In this study, we investigate a three-species food chain model comprising of prey, an intermediate predator, and a top predator. We assume that both the birth rate and intraspecies competition of prey are impacted by fear induced by the intermediate predator. Additionally, the foraging behavior of the intermediate predator is constrained due to the presence of the top predator. It is essential to note that the top predators exhibit a generalist feeding behavior, encompassing food sources beyond the intermediate predators. The study systematically determines all feasible equilibria of the proposed model and conducts a comprehensive stability analysis of these equilibria. The investigation reveals that the system undergoes Hopf bifurcation concerning various model parameters. Notably, when other food sources significantly contribute to the growth of the top predators, the system exhibits stable behavior around the interior equilibrium. Our findings indicate that the dynamic influence of fear plays a robust role in stabilizing the system. Furthermore, a cascading effect within the system, stemming from the fear instigated by top predators, is observed and analyzed. Overall, this research sheds light on the intricate dynamics of fear-induced responses in shaping the stability and behavior of multi-species food web systems, highlighting the profound cascading effects triggered by fear mechanisms in the ecosystem.

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