Stability Criteria for Complex Microbial Communities

Abstract

Competition and mutualism are inevitable processes in microbial ecology, and a central question is which and how many taxa will persist in the face of these interactions. Ecological theory has demonstrated that when direct, pairwise interactions among a group of species are too numerous, or too strong, then the coexistence of these species will be unstable to any slight perturbation. This instability worsens when mutualistic interactions complement competition. Here, we refine and to some extent overturn that understanding, by considering explicitly the resources that microbes consume and produce. In contrast to more complex organisms, microbial cells consume primarily abiotic resources, and mutualistic interactions are often mediated by these same abiotic resources through the mechanism of cross-feeding. Our model therefore considers the consumption and production of a set of abiotic resources by a group of microbial species. We show that if microbes consume, but do not produce resources, then any positive equilibrium will always be stable to small perturbations. We go on to show that in the presence of crossfeeding, stability is no longer guaranteed. However, stability still holds when mutualistic interations are either symmetric, or sufficiently weak.