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. 2017 Sep 25;8:685. doi: 10.1038/s41467-017-00828-6

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© The Author(s) 2017

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. 3 — Our model generates multiple evolutionary outcomes and complex networks of mutational paths. Qualitative properties of the dynamics of adaptation can be visualized and conveyed through graphing the networks of mutational paths. a We hierarchically classify adaptation processes according to their evolutionary outcome using the number and type of recurrent states. Labels show each outcome’s frequency obtained by sampling of environmental parameters. b–e The networks of mutational paths from four sets of environmental parameters demonstrate the scope of the model’s dynamic and stationary behavior. The maximum size of mutation (ΔS _max) affects the mutational paths and long-term outcomes of adaptation (compare the recurrent states between the left and right networks). Circles are transient states; squares are recurrent states; colors denote the number, and type of metabolic phenotypes in each state following a. Red and blue traces are examples of mutational paths, which start from an ancestral initial state (always a monomorphic state) and end at a recurrent state. We indicate the phenotype values of residents in some vertices to aid interpretation. b The invasibility relationship between a pair of phenotypes may reverse in the presence of co-residents as a consequence of frequency-dependent modification of the environment. For example, an s = = 0.8 metabolic generalist can invade an s = 1.0 specialist but the converse is not possible in pairwise competition. When an s = 0.6 generalist is a co-resident, however, the s = 1.0 specialist can invade the dimorphic community of s = 0.8 and s = 0.6 generalists——and drive s = 0.8 to extinction. c A process with multiple, non-connected recurrent states has more than one evolutionarily stable state, each of which is reached with some probability. d A process where multiple recurrent states are connected exhibits quasi-periodic evolutionary cycling. e An example of a potentially bottle-necked process. The network consists of two highly-connected (top and bottom) subgraphs, which are themselves connected via only a few mutation and invasion transitions