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. 2018 Jul 30;9:2969. doi: 10.1038/s41467-018-05424-w

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© The Author(s) 2018

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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Fig. 1 — Heterogeneous metapopulation structure increases the fraction of producers. a Schematic of the public-goods game. Producers (green) produce a public good (triangles), keeping a small fraction (~1%) for themselves and releasing the rest, which also benefits non-producers (red). Left inset: Illustration of the time evolution of the fraction of producers (F_p) in a well-mixed population. Right inset: Illustration of the dependency of the equilibrium fraction of producers (F_eq) on the density of a well-mixed population. Both illustrations were computed using the model in Fig. 2. b Migration scheme for isolated nodes (no migration), star networks (all side nodes send a fraction m of migrants towards the central node, which in turn sends a fraction m/9 towards each side node), and fully connected networks (every node sends a fraction m/9 of migrants towards each other node). c Experimental results showing the fraction of producers (computed as total number of producers over total number of cells for the whole network) as a function of time for the three network topologies, starting from three initial conditions. Each line corresponds to one 10-node network (or 10 isolated nodes)