title: How mutation affects evolutionary games on graphs.
abstract: Evolutionary dynamics are affected by population structure, mutation rates and update rules. Spatial or network structure facilitates the clustering of strategies, which represents a mechanism for the evolution of cooperation. Mutation dilutes this effect. Here we analyze how mutation influences evolutionary clustering on graphs. We introduce new mathematical methods to evolutionary game theory, specifically the analysis of coalescing random walks via generating functions. These techniques allow us to derive exact identity-by-descent (IBD) probabilities, which characterize spatial assortment on lattices and Cayley trees. From these IBD probabilities we obtain exact conditions for the evolution of cooperation and other game strategies, showing the dual effects of graph topology and mutation rate. High mutation rates diminish the clustering of cooperators, hindering their evolutionary success. Our model can represent either genetic evolution with mutation, or social imitation processes with random strategy exploration.
authors.affiliation: Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, One Brattle Square, Cambridge, MA 02138, United States. benjcallen@gmail.com
authors.forename: Benjamin
authors.initials: B
authors.lastname: Allen
authors.forename: Arne
authors.initials: A
authors.lastname: Traulsen
authors.forename: Corina E
authors.initials: CE
authors.lastname: Tarnita
authors.forename: Martin A
authors.initials: MA
authors.lastname: Nowak
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003299:Cooperative Behavior; D005716:Game Theory; D008957:Models, Genetic; D059645:Mutation Rate; D012641:Selection, Genetic