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. 2018 Mar 6;8:4068. doi: 10.1038/s41598-018-22062-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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Fixation probability as a function of connectivity. Varying the interaction radius interpolates between neutral selection and the theory based on complete graphs. The fast-flow theory applies throughout, provided the flow mixes the particles well. The markers represent simulation results for different flows and different interaction radii, resulting in different connectivities, q. Predictions of the fast-flow theory [Eq. (2)] are shown as the solid black line. The conventional well-mixed theory [complete graph, Eq. (1)] is indicated by the filled circle at q = 1. The dashed gray line is for guidance only, and shows the result for neutral selection, ϕ = 1/N. (Mutant fitness r = 1.05, population size N = 100).