Exploitative Competition in the Chemostat for Two Perfectly Substitutable Resources

Abstract

A model of the chemostat involving two populations of microorganisms competing for two perfectly substitutable, growth limiting nutrients is developed. To describe nutrient uptake, a general class of functions is used which allows for the effects that the consumption of one resource may have on the consumption of the other. It includes as a special case the model studied by Waltman, Hubbell and HSu [21] in which they generalize Michaelis-Menten functional response for a single resource to two perfectly substitutable resources. It also generalizes the model studied by Leon and Tumpson [12] where the consumption of each resource is unaffected by the consumption of the other. Analytical methods are used to obtain information about the qualitative behaviour of the model. Interesting similarities are found between both the local and global behaviour in this model and in the model for perfectly complementary resources.