Coexistence of two competitors on one resource and one inhibitor: a chemostat model based on bacteria and antibiotics.

We present a continuous time model of the dynamics of two species competing for a single limiting resource in the presence of a substance that inhibits the growth of one of the species. Resource and inhibitor are both derived from external sources. These inputs, and all other model parameters, are assumed to be constant in space and time. There exist conditions that permit the stable coexistence of the competitors, provided that the sensitive species is more efficient in exploiting the limiting resource, and the resistant species removes the inhibitor from the environment. There exists a subset of these conditions wherein the sensitive species can become established if and only if the resistant species is already established. If the resistant species does not remove the inhibitor from the environment, then coexistence of sensitive and resistant species is structurally unstable. If the resistant species produces the inhibitor, then coexistence is dynamically unstable. We review several studies of bacterial competition in the presence of antibiotics that support these conclusions.