How mutation affects evolutionary games on graphs

JOURNAL OF THEORETICAL BIOLOGY

卷:299

Article

Allen, Benjamin^1,2  Traulsen, Arne³  Tarnita, Corina E.^1,2,4  Nowak, Martin A.^1,2 

[1] Harvard Univ, Program Evolutionary Dynam, Dept Math, Cambridge, MA 02138 USA

[2] Harvard Univ, Dept Organism & Evolutionary Biol, Cambridge, MA 02138 USA

[3] Max Planck Inst Evolutionary Biol, D-24306 Plon, Germany

[4] Harvard Univ, Harvard Soc Fellows, Cambridge, MA 02138 USA

关键词: Evolutionary game theory;    Mutation;    Cooperation;    Evolutionary graph theory;    Population structure;   

DOI  :  10.1016/j.jtbi.2011.03.034

来源: Elsevier

【 摘 要 】

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. (c) 2011 Elsevier Ltd. All rights reserved.

【 授权许可】

Free