A major challenge in theoretical ecology is understanding how natural microbial communities support species diversity1,2,3,4,5,6,7,8, and in particular how antibiotic-producing, -sensitive and -resistant species coexist9,10,11,12,13,14,15. While cyclic ‘rock–paper–scissors’ interactions can stabilize communities in spatial environments9,10,11, coexistence in unstructured environments remains unexplained12,16. Here, using simulations and analytical models, we show that the opposing actions of antibiotic production and degradation enable coexistence even in well-mixed environments. Coexistence depends on three-way interactions in which an antibiotic-degrading species attenuates the inhibitory interactions between two other species. These interactions enable coexistence that is robust to substantial differences in inherent species growth rates and to invasion by ‘cheating’ species that cease to produce or degrade antibiotics. At least two antibiotics are required for stability, with greater numbers of antibiotics enabling more complex communities and diverse dynamic behaviours ranging from stable fixed points to limit cycles and chaos. Together, these results show how multi-species antibiotic interactions can generate ecological stability in both spatially structured and mixed microbial communities, suggesting strategies for engineering synthetic ecosystems and highlighting the importance of toxin production and degradation for microbial biodiversity.
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We thank R. Ward, S. Levin, M. Elowitz, G. Bunin, A. Amir, S. Kryazhimskiy, Y. Gerardin, J. Meyer, N. Yin, E. Bairey, H. Chung and A. Palmer for critical feedback and discussions; M. Baym, M. Fischbach, M. Traxler, R. Chait, L. Stone and E. Gontag for strains. E.D.K. acknowledges government support under and awarded by the Department of Defense, Office of Naval Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a. J.Z. acknowledges support from the Research Science Institute at MIT during the summer of 2011. K.V. acknowledges start-up funds from University of Wisconsin-Madison. R.K. acknowledges the support of a James S. McDonnell Foundation 21st Century Science Initiative in Studying Complex Systems Research Award 220020169, National Institutes of Health Grant R01GM081617, European Research Council Seventh Framework Programme ERC Grant 281891, Israeli Centers of Research Excellence I-CORE Program ISF Grant No. 152/11.
The authors declare no competing financial interests.
Extended data figures and tables
Extended Data Figure 1 Antibiotic attenuation is widespread among natural antibiotic producing species isolated from soil.
a, Diagram of three-species assays: measuring the antibiotic inhibition zone of E. coli around a producer strain enables quantification of three-species interactions caused by a modulator strain. b, Attenuating interactions dominate among a set of 54 Streptomyces producer–modulator combinations. Triangle and square markers show scoring from example images in Fig. 1b, left and right respectively. c, Antibiotic modulation assays: attenuating interactions dominate among combinations of soil species with a panel of ten pure antibiotics. Combinations are coloured by modulation index as in b and marked with a dot where the modulation index is significantly different from zero (n = 3, Methods). Strains 1 and 2 are the strongest modulators from the three-species assays, strain three is Streptomyces coelicolor, strains 4–18 are additional soil isolates (Extended Data Table 1). DOX, doxycycline; CMP, chloramphenicol; TOB, tobramycin; CPR, ciprofloxacin; FOX, cefoxitin; PIP, piperacillin; PEN, penicillin; NIT, nitrofurantoin; RIF, rifampicin; TMP, trimethoprim. d, Scatter plots of average modulation index M for 12 species from panel c, with and without β-lactamase inhibitors. Points occur off the diagonal for the β-lactams piperacillin and penicillin but near the diagonal for the structurally unrelated antibiotics rifampin and nitrofurantoin, consistent with attenuation of the β-lactams through a mechanism of antibiotic degradation. Error bars are standard error of the mean for technical replicas with inhibitor (n = 3) or without inhibitor (control, n = 6). Control is addition of H2O instead of inhibitor. Clav, clavulanic acid; tazB, tazobactum; sulB, sulbactam.
a, Images and scoring for three-species interaction assays from Extended Data Fig. 1b. p indicates producer species, m indicates potential modulator species. b, Example images and scoring from the antibiotic modulation assays from Extended Data Fig. 1c. Each plate shows tests for modulation of antibiotic inhibition for three different species against a different antibiotic. Colour lines show the size of the inhibition zone at the location of the radially positioned modulator species; the white circles show the radius of the zone of inhibition as inferred from the left side of the plate that contains no modulators. c, Example images from an antibiotic modulation assay with β-lactamase inhibitors and the β-lactam antibiotic cefoxitin. Left and right side of each plate is inoculated with a line of species four from Extended Data Fig. 1c. Attenuation is significantly reduced by the β-lactamase inhibitors (especially clavulanic acid and tazobactam) when compared to controls (H2O).
The simulation is performed on a grid of size L × L. A single individual occupies each grid location. During each generation: (1) Individuals from species of type P produce antibiotics within a circle of radius rproduction; (2) individuals of type RD remove antibiotics within a circle of radius rdegradation. This process is repeated for each of the different antibiotics; (3) all sensitive individuals (type S) are killed at any locations that still contain the corresponding antibiotics (crossed out S; antibiotic values at each location are calculated at centre positions); (4) empty locations of a new grid are filled by randomly choosing from any surviving individuals within a radius rdispersal. If there are no surviving individuals within rdispersal then an empty location remains empty.
a, Stability analysis of the full parameter space in the mixed inhibition-zone model. Using simulations, we tested the stability of cyclic three-species, three-antibiotic communities with dense sampling of all possible parameters for the inhibition-zone model, varying strengths of KP and KD, initial abundances of species 1–3 and growth ratios g2/g1 and g3/g1. As in Fig. 2b, each grid shows a 100-fold range of growth rate ratios from 0.1 to 10. Large basins of attraction exist across a wide range of parameter values, with maximal stability at high levels of antibiotic production and intermediate levels of degradation. b–d, Intuition for why coexistence depends on degradation. b, The inhibition-zone model calculates the probability of a given sensitive species being inhibited by an antibiotic producer (blue), or being protected by a degrading species (red), given the relative strengths of production (KP) and degradation (KD). The expected area covered by the overlapping circles (left) is used to calculate the corresponding inhibition and attenuation probabilities (percentage area of filled boxes, right; Methods). c, Focusing on one antibiotic in a stable three-species community, increasing the abundance of the yellow species creates negative feedback by decreasing the abundance of blue and red, which results in more inhibition of yellow. d, Communities are not stable at low levels of degradation due to positive feedback, whereby increasing the abundance of the yellow species results in a decrease of inhibition.
Extended Data Figure 5 Coexistence of antibiotic degrading communities in a well-mixed chemostat model with three antibiotics.
a, Stability of the three-species, three-antibiotic community in a single resource chemostat model in which species and antibiotics are completely homogeneous. Communities in the chemostat model may coexist through fixed points or limit cycles. For parameter sets in which the fixed point of the chemostat model was unstable, we started simulations close to the fixed point to determine if the community coexists through a limit cycle. Limit cycles occur in the areas between the dashed and solid black lines. Chemostat parameters: g1 = 3, g2 = 6, g3 = 9, kz = 0.5, P = 1. b, Communities coexist in the chemostat for a wide range of assumptions regarding antibiotic mechanisms. We simulated the chemostat model while changing how the action of the antibiotics is modelled and observed robust coexistence across all models. For each simulation we started all species at equal concentration (Xi = 0.2), ran the simulation until t = 100 generations and calculated the Shannon diversity of the final species levels. The default chemostat model assumes exponential inhibition of species by antibiotics, but similar coexistence is observed for Monod-like inhibition, for linear inhibition (for Gi < 0 we set Gi = 0), when species are only partially inhibited or when each species is sensitive at some level to all antibiotics. G1 is the growth rate of species 1 under inhibition, while g1 is its maximal rate of growth; R(x) captures resource dependence on current species levels; C1, C2 and C3 are the concentrations of antibiotics produced by species 1–3 respectively (Methods). Equations for the growth of species 2 and 3 have the same form as G1. All other parameters are the same as for panel a.
a, Comparing community diversity in the mixed inhibition-zone model and the chemostat model. For each simulation we started all species at equal concentration (Xi = 1/3 for the inhibition-zone model, Xi = 0.2 for the chemostat model), ran the simulation for until t = 100 generations and calculated the Shannon diversity of the final species levels. Other parameters are the same as in Fig. 2 for the inhibition-zone model or Extended Data Fig. 5 for the chemostat model. b, Three species communities require two antibiotics for stability. When only one antibiotic is degraded the community either lacks stability (first panel), or is stable only for a small number of growth rates and initial conditions (second panel). When two antibiotics are degraded the community is robustly stable to differences in species growth rates and initial conditions (third panel), provided that the antibiotics inhibit the faster-growing species (species 2 and 3). Basin colours as in Fig. 2b; grey shows parameters for which no initial conditions were stable; KP = 40, KD = 4.
Extended Data Figure 7 Robustness of three species communities to invasion by cheaters in the mixed inhibition-zone model.
Analysis of production cheaters (P→RI, left) and degradation cheaters (RD→S, right). As in Fig. 3, we plot the final abundance of each cheater as a function of its growth advantage ε over its parent species. a, Cheaters cannot invade the three-species, three-antibiotic network when their growth advantage is small, except for the production cheater of the species with the fastest inherent growth rate (species 3, green line), which replaces its parent generating a new stable community of three species interacting through two antibiotics. b, This resulting three-species, two-antibiotic community is resilient to invasion by all cheaters; cheaters must have a substantial growth advantage to invade and take over. Parameters for both networks are the same as Fig. 3. Shaded areas indicate the maximum and minimum abundance when the community reaches stable oscillations. Note, the analysis above is for networks with g1 < g2 < g3. The alternative network of g1 > g2 > g3, is less robust to invasion by production cheaters. Two cheaters can invade this community even with small ε: the production cheater for species 2 invades the network in a and gives rise to a stable three-species two-antibiotic community, while the production cheater for species 1 can take over the communities shown in a and b. For degradation cheaters this alternative network is similarly robust to cheaters as shown.
Extended Data Figure 8 Complex network topologies support coexistence of larger numbers of species in the mixed inhibition-zone model.
For given initial numbers of species and antibiotics, sets of up to 106 communities with random networks were simulated and the final number of surviving species recorded. The number inside each square shows how many networks resulted in the specified number of final species (after removing networks that did not use all of the initial antibiotics, Methods). Colours show the frequency of each outcome within all simulated networks, with grey where no stable networks were found. We sparsely sampled parameters for species growth rates and antibiotic production and degradation levels (Methods). The sparse sampling means that a given network topology may exhibit stability for parameter combinations that were not tested.
Plotting the abundance of species 1–3 for the network from Fig. 4b. We show the last 30,000 steps of a simulation with 40,000 total generations, coloured with a slowly changing gradient. The trajectories form a strange attractor.
Spatial inhibition-zone simulations, intrinsically resistant communities, dispersal radius = 3. (AVI 5928 kb)
Spatial inhibition-zone simulations, intrinsically resistant communities, dispersal radius = 6. (AVI 2996 kb)
Spatial inhibition-zone simulations, intrinsically resistant communities, dispersal radius = 20. (AVI 2996 kb)
Spatial inhibition-zone simulations, intrinsically resistant communities, dispersal radius = 80. (AVI 1041 kb)
Spatial inhibition-zone simulations, intrinsically resistant communities, dispersal radius = 200. (AVI 1041 kb)
Spatial inhibition-zone simulations, antibiotic degrading communities, dispersal radius = 3. (AVI 5928 kb)
Spatial inhibition-zone simulations, antibiotic degrading communities, dispersal radius = 6. (AVI 2996 kb)
Spatial inhibition-zone simulations, antibiotic degrading communities, dispersal radius = 20. (AVI 2996 kb)
Spatial inhibition-zone simulations, antibiotic degrading communities, dispersal radius = 80. (AVI 1041 kb)
Spatial inhibition-zone simulations, antibiotic degrading communities, dispersal radius = 200. (AVI 1041 kb)
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Kelsic, E., Zhao, J., Vetsigian, K. et al. Counteraction of antibiotic production and degradation stabilizes microbial communities. Nature 521, 516–519 (2015). https://doi.org/10.1038/nature14485
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