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Evolutionary games on isothermal graphs

Author

Listed:
  • Benjamin Allen

    (Emmanuel College)

  • Gabor Lippner

    (Northeastern University)

  • Martin A. Nowak

    (Harvard University
    Harvard University
    Harvard University)

Abstract

Population structure affects the outcome of natural selection. These effects can be modeled using evolutionary games on graphs. Recently, conditions were derived for a trait to be favored under weak selection, on any weighted graph, in terms of coalescence times of random walks. Here we consider isothermal graphs, which have the same total edge weight at each node. The conditions for success on isothermal graphs take a simple form, in which the effects of graph structure are captured in the ‘effective degree’—a measure of the effective number of neighbors per individual. For two update rules (death-Birth and birth-Death), cooperative behavior is favored on a large isothermal graph if the benefit-to-cost ratio exceeds the effective degree. For two other update rules (Birth-death and Death-birth), cooperation is never favored. We relate the effective degree of a graph to its spectral gap, thereby linking evolutionary dynamics to the theory of expander graphs. Surprisingly, we find graphs of infinite average degree that nonetheless provide strong support for cooperation.

Suggested Citation

  • Benjamin Allen & Gabor Lippner & Martin A. Nowak, 2019. "Evolutionary games on isothermal graphs," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:10:y:2019:i:1:d:10.1038_s41467-019-13006-7
    DOI: 10.1038/s41467-019-13006-7
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    Cited by:

    1. Benjamin Allen & Christine Sample & Robert Jencks & James Withers & Patricia Steinhagen & Lori Brizuela & Joshua Kolodny & Darren Parke & Gabor Lippner & Yulia A Dementieva, 2020. "Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-20, January.
    2. Alex McAvoy & Andrew Rao & Christoph Hauert, 2021. "Intriguing effects of selection intensity on the evolution of prosocial behaviors," PLOS Computational Biology, Public Library of Science, vol. 17(11), pages 1-21, November.

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