Stoichiometry and food-chain dynamics

Traditional models of chemostat systems looking at interactions between predator, prey and nutrients have used only a single currency, such as energy or nitrogen. In reality, growth of autotrophs and heterotrophs may be limited by various elements, e.g. carbon, nitrogen, phosphorous or iron. In this study we develop a dynamic energy budget model chemostat which has both carbon and nitrogen as currencies, and examine how the dual availability of these elements affects the growth of phytoplankton, trophic transfer to zooplankton, and the resulting stability of the chemostat ecosystem. Both species have two reserve pools to obtain a larger metabolic flexibility with respect to changing external environments. Mineral nitrogen and carbon form the base of the food chain, and they are supplied at a constant rate. In addition, the biota in the chemostat recycle nutrients by means of respiration and excretion, and organic detritus is recycled at a fixed rate. We use numerical bifurcation analysis to assess the model's dynamic behavior. In the model, phytoplankton is nitrogen limited, and nitrogen enrichment can lead to oscillations and multiple stable states. Moreover, we found that recycling has a destabilizing effect on the food chain due to the increased repletion of mineral nutrients. We found that both carbon and nitrogen enrichment stimulate zooplankton growth. Therefore, we conclude that the concept of single-element limitation may not be applicable in an ecosystem context.