It is well known that deficiencies in key chemical elements (such as phosphorus, P) can reduce animal growth; however, recent empirical data have shown that high levels of dietary nutrients can also reduce animal growth. In ecological stoichiometry, this phenomenon is known as the "stoichiometric knife edge," but its underlying mechanisms are not well-known. Previous work has suggested that the crustacean zooplankter Daphnia reduces its feeding rates on phosphorus-rich food, causing low growth due to insufficient C (energy) intake. To test for this mechanism, feeding rates of Daphnia magna on algae (Scenedesmus acutus) differing in C:P ratio (P content) were determined. Overall, there was a significant difference among all treatments for feeding rate (p < 0.05) with generally higher feeding rates on P-rich algae. These data indicate that both high and low food C:P ratio do affect Daphnia feeding rate but are in contradiction with previous work that showed that P-rich food led to strong reductions in feeding rate. Additional experiments are needed to gain further insights.

There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.