Existence and Stability of Microbial Prey-Predator Systems

A model for food uptake, energy conversion and allocation is proposed for individuals that propagate by fission. When simple assumptions for the environment and interactions between substrate, prey and predator in a chemostat are made, the conservation laws for energy and biomass determine a structured population model. This model is compared with lumped models from the literature, such as the "Double Monod model". Individual-based models consistent with these lumped models, are derived and compared. Expressions for the parameters of the lumped model are found as functions of parameters in the model for the individuals making up the population. To reduce the number of parameters body-size scaling relations are used. The existence and stability of equilibria under chemostat conditions are studied. The dynamics of the substrate, bacterial prey and protozoan predator depend substantially on the underlying model for the individuals.