Kaveh, Kamran; McAvoy, Alex; Chatterjee, KrishnenduIST Austria ; Nowak, Martin A.
Resources are rarely distributed uniformly within a population. Heterogeneity in the concentration of a drug, the quality of breeding sites, or wealth can all affect evolutionary dynamics. In this study, we represent a collection of properties affecting the fitness at a given location using a color. A green node is rich in resources while a red node is poorer. More colors can represent a broader spectrum of resource qualities. For a population evolving according to the birth-death Moran model, the first question we address is which structures, identified by graph connectivity and graph coloring, are evolutionarily equivalent. We prove that all properly two-colored, undirected, regular graphs are evolutionarily equivalent (where “properly colored” means that no two neighbors have the same color). We then compare the effects of background heterogeneity on properly two-colored graphs to those with alternative schemes in which the colors are permuted. Finally, we discuss dynamic coloring as a model for spatiotemporal resource fluctuations, and we illustrate that random dynamic colorings often diminish the effects of background heterogeneity relative to a proper two-coloring.
PLOS Computational Biology
We thank Igor Erovenko for many helpful comments on an earlier version of this paper. : Army Research Laboratory (grant W911NF-18-2-0265) (M.A.N.); the Bill & Melinda Gates Foundation (grant OPP1148627) (M.A.N.); the NVIDIA Corporation (A.M.). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Kaveh K, McAvoy A, Chatterjee K, Nowak MA. The Moran process on 2-chromatic graphs. PLOS Computational Biology. 2020;16(11). doi:10.1371/journal.pcbi.1008402
Kaveh, K., McAvoy, A., Chatterjee, K., & Nowak, M. A. (2020). The Moran process on 2-chromatic graphs. PLOS Computational Biology, 16(11). https://doi.org/10.1371/journal.pcbi.1008402
Kaveh, Kamran, Alex McAvoy, Krishnendu Chatterjee, and Martin A. Nowak. “The Moran Process on 2-Chromatic Graphs.” PLOS Computational Biology 16, no. 11 (2020). https://doi.org/10.1371/journal.pcbi.1008402.
K. Kaveh, A. McAvoy, K. Chatterjee, and M. A. Nowak, “The Moran process on 2-chromatic graphs,” PLOS Computational Biology, vol. 16, no. 11, 2020.
Kaveh K, McAvoy A, Chatterjee K, Nowak MA. 2020. The Moran process on 2-chromatic graphs. PLOS Computational Biology. 16(11).
Kaveh, Kamran, et al. “The Moran Process on 2-Chromatic Graphs.” PLOS Computational Biology, vol. 16, no. 11, e1008402, Public Library of Science, 2020, doi:10.1371/journal.pcbi.1008402.
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