Stoichiometric food quality and herbivore dynamics

Herbivores may grow with nutrient or energy limitation, depending on food a bundance and the chemical composition of their food. We present a model tha t describes herbivore growth as a continuous function of two limiting facto rs. This function uses the synthesizing unit concept, has the hyperbolic Mo nod model as a limiting case, and has the same number of parameters as the Monod model coupled to Liebig's discontinuous minimum rule. We use the mode l to explore nutrient-limited herbivore growth in a closed system with alga e, Daphnia and phosphorus as the limiting nutrient. Phosphorus in algae. ma y substantially influence Daphnia growth. This influence changes over time and is most pronounced when algae and Daphnia populations fluctuate strongl y. Relative to classic models that only consider food quantity as a determi nant of Daphnia growth, our model shows richer dynamical behaviour. In addi tion to the standard positive equilibrium, which may be stable or unstable depending on nutrient availability a new positive equilibrium may arise in our model when mortality rates are relatively high. This equilibrium is uns table and reduces the likelihood of long-term persistence of Daphnia in the system.