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The authors study how the outcome of evolutionary dynamics on graphs depends on randomness on the graph structure. They gradually change the underlying graph from completely regular (e.g. a square lattice) to completely random. They find that the fixation probability increases as the randomness increases; nevertheless, the increase is not significant and thus the fixation probability could be estimated by the known formulas for underlying regular graphs. Evolutionary dynamics has been traditionally studied in infinite homogenous, infinite spatial, populations. Recently, the dynamics was studied in finite and spatially structured populations (i.e. graphs).
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