Dynamics of a Producer–Grazer Model Incorporating the Effects of Excess Food Nutrient Content on Grazer’s Growth

Modeling under the framework of ecological stoichiometric allows the investigation of the effects of food quality on food web population dynamics. Recent discoveries in ecological stoichiometry suggest that grazer dynamics are affected by insufficient food nutrient content (low phosphorus (P)/carbon (C) ratio) as well as excess food nutrient content (high P:C). This phenomenon is known as the “stoichiometric knife edge.” While previous models have captured this phenomenon, they do not explicitly track P in the producer or in the media that supports the producer, which brings questions to the validity of their predictions. Here, we extend a Lotka–Volterra-type stoichiometric model by mechanistically deriving and tracking P in the producer and free P in the environment in order to investigate the growth response of Daphnia to algae of varying P:C ratios. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, lead to quantitative different predictions than previous models that neglect to track free nutrients. The full model shows that the fate of the grazer population can be very sensitive to excess nutrient concentrations. Dynamical free nutrient pool seems to induce extreme grazer population density changes when total nutrient is in an intermediate range.