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Stability Criteria for Complex Microbial Communities

Stacey Butler, James O’Dwyer
doi: https://doi.org/10.1101/293605
Stacey Butler
1Department of Mathematics, University of Illinois,Urbana, IL 61801, USA
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James O’Dwyer
2Department of Plant Biology, University of Illinois, Urbana, IL 61801, USA
3Carl R. Woese Institute for Genomic Biology, University of Illinois, Urbana, IL 61801, USA
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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.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted April 02, 2018.
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Stability Criteria for Complex Microbial Communities
Stacey Butler, James O’Dwyer
bioRxiv 293605; doi: https://doi.org/10.1101/293605
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Stability Criteria for Complex Microbial Communities
Stacey Butler, James O’Dwyer
bioRxiv 293605; doi: https://doi.org/10.1101/293605

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