The effects of excess food nutrient content on a tritrophic food chain model in the aquatic ecosystem.

Affiliation

Department of Mathematics and Statistics, Texas Tech University, Lubbock, USA. Electronic address: [Email]

Abstract

Ecological stoichiometry is an approach that focuses on the balance of energy and elements in environmental interactions, and it leads to new insights and a better understanding of ecological processes and outcomes. Modeling under this framework enables us to investigate the effects of nutrient content (i.e., food quality) on organisms, whether the imbalance involves insufficient or excess nutrient content. In this paper, we develop and analyze a tritrophic food chain model that captures the phenomenon known as the "stoichiometric knife-edge", where consumer growth is limited under conditions of excess nutrients. The model tracks two essential elements, carbon and phosphorus, in each species. The dynamics of the system such as boundedness and positivity of the solutions, existence and stability conditions of boundary and internal equilibria are analyzed. Through numerical simulations and bifurcation analyses, we observe the dynamics of the system switching between periodic oscillations and chaos. Our findings also show that nutrient-rich food consumption can cause adverse effects on species.

Keywords

Chaos,Ecological stoichiometry,Maximum Lyapunov exponent,Stoichiometric knife-edge,Tritrophic food chain model,

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