Competition for a single limiting resource in continuous culture: The variable-yield model

The global asymptotic behavior of solutions of the so-called variable yield model of competition between two microbial populations for a single growth-limiting nutrient is determined. This model, also referred to as the variable-internal stores or Caperon-Droop model, is a generalization of the classical Monod model. It assumes that the growth rate of a population depends on the amount of nutrient stored by the organism, taken to be the same for all organisms, rather than the concentration of ambient nutrient in the culture. It is shown that competitive exclusion holds, the winner being the organism that can grow at the lower ambient nutrient concentration.