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Abstract

For microbial species competing for one limiting resource in a chemostat, mathematical models lead to the competitive exclusion principle (CEP) predicting survival of only one species in any case. Quantitative experimental data from our three-species model system related to the genetic disease Cystic Fibrosis allude to coexistence of two or even three competing species such that the CEP does not seem to hold. We developed a mathematical model to comply with the experimental phenomena by including species specific properties of the microorganisms into a classical chemostat model. We discuss the experimental data serving as the basis for the assumptions. These are a) one species produces a secondary metabolite, b) the metabolite has a growth-inhibiting effect, but can also be exploited as a secondary carbon source, c) some of the species could compete directly (e.g. via toxin production), and d) a lethal inhibitor is introduced that cannot be eliminated by one of the species and is selective for the strongest competitor. We present the analysis of the mathematical model, consisting of a system of nonlinear ordinary differential equations, as well as simulations for experimental parameter values. We found that the dynamic of the system changes in a fundamental way, if interspecific competition is included; a Hopf bifurcation occurs for an appropriate choice of parameters. This close connection between experiment and mathematical analysis to our knowledge has not yet been realized for a more than two-species system.