A modified chemostat exhibiting competitive exclusion "reversal"

Abstract

The classical chemostat is an intensely investigated model in ecology and bio/chemical engineering, where n-species, say $x_{1}, x_{2}...x_{n}$ compete for a single growth limiting nutrient. Classical theory predicts that depending on model parameters, one species competitively excludes all others. Furthermore, this ''order'' of strongest to weakest is preserved, $x_{1} >> x_{2} >> ...x_{n}$, for say $D_{1} < D_{2} <...D_{n}$, where $D_{i}$ is the net removal of species $x_{i}$. Meaning $x_{1}$ is the strongest or most dominant species and $x_{n}$ is the weakest or least dominant. We propose a modified version of the classical chemostat, exhibiting certain counterintuitive dynamics. Herein we show that if only a certain proportion of the weakest species $x_{n}$'s population is removed at a ''very'' fast density dependent rate, it will in fact be able to competitively exclude all other species, for certain initial conditions. Numerical simulations are carried out to visualize these dynamics in the three species case.