Stoichiometry-Dependent Fear Effect in a Food Chain Model

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 783-807, June 2024.
Abstract. Evidence shows that resource quality can determine the costs and benefits of the fear effect on consumer dynamics. However, mechanistic modeling and analysis are lacking. This paper formulates a tritrophic level food chain model that integrates both stoichiometric food quality and fear effect. We establish the well-posedness of the model and examine the existence and stability of equilibria. Through extensive numerical simulations, we validate our findings and visually explore the interactive effects of fear and food quality. Our results reveal that the fear effect from predators stabilizes the system. Furthermore, we demonstrate that the fear effect amplifies the influence of food quality on consumers. When food quality is favorable, the fear effect enhances consumer production efficiency, whereas, in the case of poor food quality, the fear effect exacerbates the decline in production efficiency caused by low-nutrient food.