Mathematical models for continuous culture growth dynamics of mixed populations subsisting on a heterogeneous resource Base: I. Simple competition

Abstract

The classical Monod model for bacterial growth in a chemostat, based on a Michaelis-Menten kinetic analog, is restated in terms of an approximate Lotka-Volterra formulation. The parameters of these two formulations are explicitly related; the new model is easier to work with, but yields the same results as the original. The model is then extended to the case where multiple alternate substrates may be growth limiting, using the corresponding kinetic analogs for multiple-substrate enzymes. Again, one is led to a Lotka-Volterra analog. In the multiple-substrate model, however, coexistence of multiple genotypes is possible, in contrast to the single-substrate model. The usual Lotka-Volterra conditions for existence and stability of pure or mixed equilibria may all be translated into corresponding statements about the parameters of the chemostat system. Possible extensions to deal with metabolic inhibition, cross-feeding, and predation are indicated.