Impossibility of coexistence of three pure and simple competitors in configurations of three interconnected chemostats.

It is well established that pure and simple microbial competitors cannot coexist at a steady state if their environment is homogeneous. For the case of two microbial populations competing purely and simply in two interconnected chemostats having time-invariant input(s), it is known from the literature that a stable steady state of coexistence arises in domains of the operating parameters space and is attributed to the spatial heterogeneities of the system, which allow a different species to have the competitive advantage in each one of the two sub-environments. This article investigates whether the aforementioned result can be extended to the case of three species competing in three interconnected vessels. By studying all possible alternate configurations of the three-chemostat system, it is shown that coexistence of the three species is impossible, except possibly for some discrete values of the operating parameters. Some potential explanations for the results are discussed.