Food Chains in the Chemostat: Relationships Between Mean Yield and Complex Dynamics

A tritrophic food-chain chemostat model composed of a prey with Monod-type nutrient uptake, a Holling Type II predator and a Holling Type II exploited superpredator is considered in this paper. The bifurcations of the model show that dynamic complexity first increases and then decreases with the nutrient supplied to the bottom of the food chain. Extensive simulations prove that the same holds for food yield, i.e., there exists an optimum nutrient supply which maximizes mean food yield. Finally, a comparative analysis of the results points out that the optimum nutrient supply practically coincides with the nutrient supply separating chaotic dynamics from high-frequency cyclic dynamics. This reinforces the idea, already known for simpler models, that food yield maximization requires that the system behaves on the edge of chaos.