Pure competition of multiple species during mixed-substrate microbial   growth: Extending the resource-based theory
  The simultaneous growth of multiple microbial species is a problem of fundamental ecological interest. In media containing more than one growth-limiting substrate, multiple species can coexist. The question then arises: Can single-species data predict the existence and stability of mixed-culture steady states in mixed-substrate environments? This question has been extensively studied with the help of resource-based models. These studies have shown that the single-species data required to predict mixed-culture behavior consists of the growth isoclines and consumption vectors, which in turn are determined from single-substrate data by making specific assumptions about the kinetics of mixed-substrate growth. Here, we show that these assumptions are not valid for microbial growth on mixtures of substitutable substrates. However, the theory can be developed by determining the growth isoclines and consumption vectors directly from the mixed-substrate data, thus obviating the need for specific assumptions about the kinetics of mixed-substrate growth. We show furthermore that in addition to the growth isoclines and consumption vectors, the single-species, mixed-substrate data yields a new family of curves, which we call the consumption curves. Consideration of the growth isoclines and the consumption curves yields deeper insights into the behavior of the mixed cultures. It yields a priori bounds on the substrate concentrations achieved during coexistence, permits the extension of the theory to systems in which the growth isoclines are non-monotonic, and clarifies earlier results obtained by considering only the growth isoclines. 
Atul Narang & Sergei S. Pilyugin