Dynamics of a Tri-Trophic Level Model With Excess Food Nutrient Content and Intraguild Predation Structure

The dynamics of consumers can be affected by both nutrient-deficient food (low phosphorus (P) to carbon (C) ratio) and nutrient-excessive (high P:C) food, which is known as the stoichiometric knife-edge phenomenon. In this study, aiming to illustrate the responses of herbivores and omnivores to food with excessive P content, we present and analyze a tri-trophic level stoichiometric knife-edge model incorporating the intraguild predation structure. The model dynamics are theoretically examined, including the boundedness and positivity of solutions, the existence and stability of boundary equilibria, and the existence of positive equilibria. Numerical simulations show that the model has complex dynamics, encompassing chaotic-like oscillations, multiple types of bifurcations, long transients, and regime shifts. Moderate P levels facilitate the coexistence of the three species, whereas both lower and higher P levels result in the extinction of herbivores and omnivores. Specifically, the energy enrichment paradox occurs at low P levels. In contrast, the nutrient enrichment paradox occurs at high P levels, both of which are detrimental to the survival of herbivores and omnivores. Furthermore, the high-intensity predation of producers by omnivores helps to restrain the occurrence of chaotic dynamics. These findings contribute to a deeper understanding of the mechanisms of multi-species coexistence.