Analysis of stability to cheaters in models of antibiotic degrading microbial communities

Antibiotic resistance carried out by antibiotic degradation has been suggested recently as a new mechanism to maintain coexistence of microbial species competing on a single limiting resource, even in well-mixed homogeneous environments. Species diversity and community stability, however, critically depend on resistance against social cheaters, mutants that do not invest in production, but still enjoy the benefits provided by others. Here we investigate how different mutant cheaters affect the stability of antibiotic producing and degrading microbial communities. We consider two cheater types, production and degradation cheaters. We generalize the mixed inhibition-zone and chemostat models introduced previously [Kelsic, E. D., Zhao, J., Vetsigian, K., Kishony, R., 2015. Counteraction of an tibiotic production and degradation stabilizes microbial communities. Nature521, 516-519.] to study the population dynamics of microbial communities in well-mixed environment, and analyze the invasion of different cheaters in these models. We show that production cheaters, mutants that cease producing antibiotics, always destroy coexistence whenever there is a cost of producing these antibiotics. Degradation cheaters, mutants that loose their function of producing extracellular antibiotic degrading molecules, induce community collapse only if the cost of producing the degradation factors is above a critical level. Our analytical studies, supported by numerical simulations, highlight the sensitivity of antibiotic producing and degrading communities to loss-of-function mutants.