Breaking the Symmetry between Interaction and Replacement in Evolutionary Dynamics on Graphs

Hisashi Ohtsuki, Martin A. Nowak, and Jorge M. Pacheco
Phys. Rev. Lett. 98, 108106 – Published 8 March 2007

Abstract

We study the evolution of cooperation modeled as symmetric 2×2 games in a population whose structure is split into an interaction graph defining who plays with whom and a replacement graph specifying evolutionary competition. We find it is always harder for cooperators to evolve whenever the two graphs do not coincide. In the thermodynamic limit, the dynamics on both graphs is given by a replicator equation with a rescaled payoff matrix in a rescaled time. Analytical results are obtained in the pair approximation and for weak selection. Their validity is confirmed by computer simulations.

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  • Received 3 January 2007

DOI:https://doi.org/10.1103/PhysRevLett.98.108106

©2007 American Physical Society

Authors & Affiliations

Hisashi Ohtsuki1,2, Martin A. Nowak1,3, and Jorge M. Pacheco4

  • 1Program for Evolutionary Dynamics, Harvard University, Cambridge Massachusetts 02138, USA
  • 2Department of Biology, Faculty of Sciences, Kyushu University, 6-10-1 Hakozaki, Fukuoka 812-8581, Japan
  • 3Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 4Centro de Física Teórica e Computacional, Departamento de Física da Faculdade de Ciências, P-1649-003 Lisboa Codex, Portugal

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Issue

Vol. 98, Iss. 10 — 9 March 2007

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