How mutation affects evolutionary games on graphs

Benjamin Allen, Arne Traulsen, Corina E. Tarnita, Martin A. Nowak

Research output: Contribution to journalArticle

49 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)97-105
Number of pages9
JournalJournal of Theoretical Biology
Volume299
DOIs
StatePublished - Apr 21 2012

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Keywords

  • Cooperation
  • Evolutionary game theory
  • Evolutionary graph theory
  • Mutation
  • Population structure

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