Robustness of three species communities to invasion by production and degradation cheaters. a, Analysis of production cheaters and degradation cheaters in the mixed inhibition-zone model for the symmetric motif. Final species abundances are shown as a function of the cheater growth advantage e over its parent species (cheater: blue; original species: red, yellow, green). Left column shows production cheaters: the production cheater of the species with the fastest inherent growth rate (species 3) replaces its parent generating a new stable community of three species interacting through two antibiotics. The other production cheaters are selected against (final abundance zero) when their growth advantage is small, but result in collapse of the community (a different producer species dominates). Second column shows degradation cheaters: the community is evolutionarily stable for all degradation cheaters with small growth advantage over their parent species. Parameters as in original Fig. 3. Split lines show the maximum and minimum abundance when the community reaches stable oscillations. b, Robustness to cheaters in the three-species, two-antibiotic community for the mixed inhibition-zone model. Again, the community is evolutionarily stable to degradation cheaters, while production cheaters cannot take over yet lead to community collapse. Parameters as in original Fig. 3. c, Analysis of production cheaters and degradation cheaters using the complete model as depicted in Extended Data Fig. 3, in which complete mixing is introduced after the short range colonization step. The community is evolutionarily stable to all production and degradation cheaters (at low growth advantage, the final cheater abundance is zero and the community is maintained). Growth parameters as in Fig. 3, simulated on a grid with rproduction = 8, rdegradation = 7, rcolonization = 8 and density of 4.5% with complete mixing after each time step. d, Robustness to cheaters in the three-species, two-antibiotic community for the complete model from Extended Data Fig. 3. Again, the community is evolutionarily stable for all production and degradation cheaters with small growth advantage. Parameters as in panel c.