A Mathematical Theory for Single-Nutrient Competition in Continuous Cultures of Micro-Organisms

The continuous culture of micro-organisms using the chemostat is an important research technique in microbiology and population biology. It offers advantages in the form of economical production of micro-organisms for the industrial microbiologist and is a laboratory idealization of nature for population studies. The paper studies a mathematical model, based on Michaelis-Menten kinetics, for one substrate and n competing species. Given the parameters of the system, we answer the basic question as to which species survive and which do not, and determine the limiting behaviors. The primary conclusion is that the species will survive whose Michaelis-Menten constant is smallest in comparison with its intrinsic rate of natural increase.