The effects of excess food nutrient content on a tritrophic food chain model in the aquatic ecosystem. 2020

Lale Asik, and Ming Chen, and Angela Peace
Department of Mathematics and Statistics, Texas Tech University, Lubbock, USA. Electronic address: lale.asik@ttu.edu.

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.

UI MeSH Term Description Entries
D010758 Phosphorus A non-metal element that has the atomic symbol P, atomic number 15, and atomic weight 31. It is an essential element that takes part in a broad variety of biochemical reactions. Black Phosphorus,Phosphorus-31,Red Phosphorus,White Phosphorus,Yellow Phosphorus,Phosphorus 31,Phosphorus, Black,Phosphorus, Red,Phosphorus, White,Phosphorus, Yellow
D002244 Carbon A nonmetallic element with atomic symbol C, atomic number 6, and atomic weight [12.0096; 12.0116]. It may occur as several different allotropes including DIAMOND; CHARCOAL; and GRAPHITE; and as SOOT from incompletely burned fuel. Carbon-12,Vitreous Carbon,Carbon 12,Carbon, Vitreous
D000078622 Nutrients Various components of food that are required for nourishment. Macronutrients,Macronutrient,Nutrient
D017753 Ecosystem A functional system which includes the organisms of a natural community together with their environment. (McGraw Hill Dictionary of Scientific and Technical Terms, 4th ed) Ecosystems,Biome,Ecologic System,Ecologic Systems,Ecological System,Habitat,Niche, Ecological,System, Ecological,Systems, Ecological,Biomes,Ecological Niche,Ecological Systems,Habitats,System, Ecologic,Systems, Ecologic
D020387 Food Chain The sequence of transfers of matter and energy from organism to organism in the form of FOOD. Food chains intertwine locally into a food web because most organisms consume more than one type of animal or plant. PLANTS, which convert SOLAR ENERGY to food by PHOTOSYNTHESIS, are the primary food source. In a predator chain, a plant-eating animal is eaten by a larger animal. In a parasite chain, a smaller organism consumes part of a larger host and may itself be parasitized by smaller organisms. In a saprophytic chain, microorganisms live on dead organic matter. Food Web,Parasite Chain,Predator Chain,Saprophytic Chain,Chain, Food,Chain, Parasite,Chain, Predator,Chain, Saprophytic,Chains, Food,Chains, Parasite,Chains, Predator,Chains, Saprophytic,Food Chains,Food Webs,Parasite Chains,Predator Chains,Saprophytic Chains,Web, Food,Webs, Food

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