How mutation alters the evolutionary dynamics of cooperation on networks

Genki Ichinose, Yoshiki Satotani, Hiroki Sayama

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Cooperation is ubiquitous at every level of living organisms. It is known that spatial (network) structure is a viable mechanism for cooperation to evolve. A recently proposed numerical metric, average gradient of selection (AGoS), a useful tool for interpreting and visualizing evolutionary dynamics on networks, allows simulation results to be visualized on a one-dimensional phase space. However, stochastic mutation of strategies was not considered in the analysis of AGoS. Here we extend AGoS so that it can analyze the evolution of cooperation where mutation may alter strategies of individuals on networks. We show that our extended AGoS correctly visualizes the final states of cooperation with mutation in the individual-based simulations. Our analyses revealed that mutation always has a negative effect on the evolution of cooperation regardless of the payoff functions, fraction of cooperators, and network structures. Moreover, we found that scale-free networks are the most vulnerable to mutation and thus the dynamics of cooperation are altered from bistability to coexistence on those networks, undergoing an imperfect pitchfork bifurcation.

Original languageEnglish
Article number053049
JournalNew Journal of Physics
Issue number5
Publication statusPublished - 2018 May
Externally publishedYes


  • average gradient of selection
  • bifurcation
  • equilibrium point
  • evolution of cooperation
  • network structure
  • prisoner's dilemma game

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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