Stability criteria for complex microbial communities

Stacey Butler,James P O’Dwyer

doi:10.1038/s41467-018-05308-z

Stacey Butler, James P O’Dwyer

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https://doi.org/10.1038/s41467-018-05308-z

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Journal: Nature Communications	Publication Date: Jul 30, 2018
Citations: 132	License type: open-access

Affiliation: University of Illinois Urbana-Champaign

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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. 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 through the mechanism of crossfeeding. 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, positive equilibria remain stable whenever mutualistic interactions are either sufficiently weak, or when all pairs of taxa reciprocate each other’s assistance.

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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
We find that if mutualistic interactions are completely symmetric, stability is again guaranteed for feasible equilibria, a result at odds with earlier pairwise analyses
We consider solely the mass action terms above in the spirit of the vast range of Lotka–Volterra analyses undertaken for pairwise interactions: if we can understand the properties of these idealized communities, we have a baseline on which to layer further biological complexity

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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. 1234567890():,; Early ecological intuition suggested that tightly woven networks of interactions would lead to more stable and robust communities[1,2,3] This intuition was later overthrown by the realization that large, complex, interacting systems will tend to become unstable to small perturbations once either the number or strength of interactions passes a certain threshold[4,5]. We introduce a model for the exchange of resources, where microbes can both consume and produce resources, and choose a form for these equations that is interpretable as either a species-specific leakage of resources, or as a kind of recycling of biomass following mortality In this model, we find a similar result in our consumer–producer–resource system, and for a range of cases bound the possible strength and prevalence of resource production. We find that if mutualistic interactions are completely symmetric, stability is again guaranteed for feasible equilibria, a result at odds with earlier pairwise analyses

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