Competition of two microbial populations for a single resource in a chemostat when one of them exhibits wall attachment

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Abstract
It is known that two microbial populations competing for a single resource in a homogeneous environment with time‐invariant inputs cannot coexist in a steady state. The case where two microbial populations compete for a single resource in a chemostat but one of them exhibits attachment to the chemostat walls is studied theoretically. Because of the cells' attachment to the walls, the environment is no longer homogeneous. The present article considers the case where the attached cells form no more than a monolayer. Other situations occur, often frequently, but we do not consider them here. Two models are used to represent the attachment to the walls: the Topiwala‐Hamer model and a model which assumes that the attachment of microbial cells to the solid surfaces is a reversible process. The first model does not allow the population that exhibits wall attachment to wash out from the chemostat, in contrast to the second model (which nevertheless reduces to the first one in the limit). It has been found that in most of the possible cases for both models, the two competitors can coexist in a stable steady state for a wide range of the operating parameters space. The results of the stability analysis are discussed and analytical expressions for the conditions and the boundaries of the domains of stable coexistence are given for all the possible situations that may arise.

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