Nonlinear population dynamics in the chemostat

tinuous stirred tank bioreactor, was independently invented by Jacques Monod1 and by Aaron Novick and Leo Szilard,2,3 who also coined the term chemostat. Its inventors conceived that this device provided a convenient way to study a bacterial population in the steady state, letting the experimenter adjust growth rate and external parameters, such as temperature or pH level. Novick and Szilard were mostly interested in the effects of mutations on a population’s long-range behavior, while Monod’s interest centered on the regulation mechanisms operating within the cells under nutrient-limited conditions. Since its invention, the chemostat has become a ubiquitous tool for studying microbial physiology and metabolism.4 Over the years, researchers have come to appreciate that chemostat theory could apply to studies of microbial ecology and, more generally, of population dynamics.5 Early formulations used time-invariant differential equations to model the chemostat. More recently, the models have expanded to include delayed nutrient recycling, as could occur in a lake where slow sediment decomposition takes place.6,7 In this article, I wish to give an elementary account of the chemostat, introduce the model’s equations, and describe some typical cases of population dynamics. Although the chemostat does not enjoy the Lotka–Volterra predator–prey model’s widespread popularity, this system is worthy of the interest of science educators. I’ve used it for several years as a theme for a computational physics project.