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. 2020 May 25;10:8628. doi: 10.1038/s41598-020-65076-z

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Auto-regulation extends the window of QS-controlled cooperation to greater genetic mixing. For both constitutive cooperation and QS-controlled cooperation, we used a fixed cost of cooperation. We also used a fixed cost of signaling in QS-controlled regimes. In all cases, we evolved a population of 5,000 individuals for 5,000 generations. Each dot represents the evolved mean results (averaged over the last 50 generations) for different average number of genotypes per group $\bar{G}$ . The horizontal and vertical error bars represent the standard deviation over 30 replications. (A) Overall cooperation payoff. The black dashed line represents the baseline payoff. (B) Co-evolved production rate and signal threshold for QS-controlled cooperation with auto-regulation. The red star represents the clonal population (G = 1). Examples of evolution trajectories as well as population diversity from (B) can be found in Supplemental Material, Fig. S8, S6, respectively. The remaining parameters used in the simulations can be found in Supplemental Material, Table S1.