@MISC{Lieberman_1evolutionary, author = {Erez Lieberman and Christoph Hauert and Martin A. Nowak}, title = {1 Evolutionary Dynamics on Graphs}, year = {} }

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Abstract

Evolutionary dynamics have been traditionally studied in the context of homogeneous or spatially-extended populations1−3. Here we generalize population structure by arranging individuals on a graph. Each vertex represents an individual. The weighted edges denote reproductive rates which govern how often individuals place offspring into adjacent vertices. The homogeneous population, described by the Moran process4, is the special case of a fully connected graph with evenly-weighted edges. Spatial structures are described by graphs where vertices are connected with their nearest neighbors. We also explore evolution on random and scalefree networks5−6. We determine the fixation probability of mutants, and characterize those graphs whose fixation behavior is identical to that of a homogeneous population7. Furthermore, some graphs act as suppressors and others as amplifiers of selection. It is even possible to find graphs that guarantee the fixation of any advantageous mutant. We also study frequency dependent selection and show that the outcome of evolutionary