A Three Species Food Chain Model with Fear Induced Trophic Cascade

Article Type

Research Article

Publication Title

International Journal of Applied and Computational Mathematics


In ecology, predator–prey interaction is one of the most important factors. The effects of predators on prey population can be direct and deadly, or it may be indirect and non-consumptive. Recent experimental findings have explored that fear of predator (indirect effect) alone can change prey’s behavior including reproduction and foraging. Suraci et al. (Nature Communications, 7, 10698, 2016) experimentally showed that fear of large carnivore reduces mesocarnivore foraging, which benefits the mesocarnivore’s prey. They also showed that fear of large carnivore mediates a cascading effect in lower trophic level. In the present study, our aim is to observe how the cascading effects of fear in a tri-trophic food chain model influence the dynamics of the model. We propose a three-species food chain model incorporating the cost of fear into the predation rate of middle predator. We consider the fact that due to fear of the top predator, middle predator forage less. As a result, the predation rate of middle predator decreases which reduces the predation pressure on basal prey. Mathematical properties such as boundedness, persistence, equilibria analysis, local and global stability analysis of the model are investigated. We perform bifurcation analysis around interior equilibrium point of the system. We notice that cost of the fear in middle predator can stabilize an otherwise chaotic system. We also investigate the robustness of the stabilizing role of the fear parameter. We observe that system initiating from the different dynamical regime, fear ultimately drives the system towards stability. It is also found that for increasing the level of fear, the system enters into a stable state through multiple switching of dynamics. Our results suggest that cost of the fear in middle predator can stabilize the system and enhances persistence of the system. We illustrate our analytical results numerically. Finally our results qualitatively reflect the experimental findings of Suraci et al.



Publication Date