Mathematical models for continuous culture growth dynamics of mixed populations subsisting on a heterogeneous resource base. II. Predation and trophic structure

Abstract

Models are presented for the joint dynamics of predators and prey, maintained in continuous flow chemostat culture. The predators are visualized as subsisting on one or more prey organisms, which in turn are visualized as subsisting on one or more substrate resources supplied by the investigator. The dynamic equations are translated into an analogous Lotka-Volterra predation model, and the criteria for the existence and stability of various equilibria are indicated. Denoting the number of different predator organisms as NH, the number of different prey organisms by NI and the number of different substrates as NJ, it is shown that the joint coexistence of all components requires 0 [les] NI - NH [les] NJ. The model is extended to more complex situations by including additional trophic layers and by allowing trophic layer "leap-frogging." The model may always be translated into an approximately quadratic differential equation of the Lotka-Volterra type. The [alpha]- and [beta]-coefficients of these latter are really variables, and become quite complex for some of the multi-layered models.