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.

The balance of interaction types determines the assembly and stability of ecological communities

“…We add to these results by showing that saturating responses with ecological selection is enough to almost guarantee internal stability in both the in the unique and interchangeable interaction models. Another recent line of work by Butler and O'Dwyer [46,47] explicitly modeled species limited by resources that can be produced by other species. This model allows saturating functional responses in mutualisms to emerge endogenously from resource limitation.…”

Cooperation and Stability for Complex Systems in Resource-Limited Environments

“…Our approach builds on classic consumer-resource dynamics (1,11,(49)(50)(51), but incorporates the possibility of arbitrary exchanges of resources between consumers, which could be thought of in terms of the recycling of biomass into usable matter following mortality. Using this framework, we first generalized an earlier connection between pairwise reciprocity in the exchange of resources and community stability for a complex ecological system (8). Specifically, reciprocity of resource exchange is a sufficient condition for the local stability of a positive equilibrium, even when consumption requirements of species are a complicated combination of distinct resource types.…”

“…Consumer-resource models meet this need by explicitly considering the consumption and preferences of individuals for resources (1,10,11,34,44,(49)(50)(51), and can lead to dynamics that differ from models based on direct species interactions (39,52). Recent work has extended these analyses to large, open systems with extensive exchange of resources (8,15,16,20,21,36), and incorporating resource exchange as the mechanism underlying mutualistic interactions already leads to contradictions with the classical analyses using pairwise interactions. For example, if each species in a community specializes on a single resource, then local stability is guaranteed when each pair of species exchanges resources symmetri-cally (8), independent of how strong those interactions are.…”

“…Recent work has extended these analyses to large, open systems with extensive exchange of resources (8,15,16,20,21,36), and incorporating resource exchange as the mechanism underlying mutualistic interactions already leads to contradictions with the classical analyses using pairwise interactions. For example, if each species in a community specializes on a single resource, then local stability is guaranteed when each pair of species exchanges resources symmetri-cally (8), independent of how strong those interactions are. This counters both the idea that there is a limit on the strength and prevalence of interactions, and the result that asymmetry enhances stability in the case of mutualistic interactions, leveraged in both biological (6) and social systems (38).…”

“…These earlier results establish the importance of incorporating explicit resource exchange even when tackling basic questions related to equilibria and stability, but were limited in their scope to specific modes of consumption. For example (8) focused on consumers exchanging resources, while each specialized on consuming one particular resource. But in moving from models of direct species interactions to more mechanistic models of competition and mutualism, there is a tradeoff.…”