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Calculating Evolutionary Dynamics in Structured Populations

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  • Charles G Nathanson
  • Corina E Tarnita
  • Martin A Nowak

Abstract

Evolution is shaping the world around us. At the core of every evolutionary process is a population of reproducing individuals. The outcome of an evolutionary process depends on population structure. Here we provide a general formula for calculating evolutionary dynamics in a wide class of structured populations. This class includes the recently introduced “games in phenotype space” and “evolutionary set theory.” There can be local interactions for determining the relative fitness of individuals, but we require global updating, which means all individuals compete uniformly for reproduction. We study the competition of two strategies in the context of an evolutionary game and determine which strategy is favored in the limit of weak selection. We derive an intuitive formula for the structure coefficient, σ, and provide a method for efficient numerical calculation.Author Summary: At the center of any evolutionary process is a population of reproducing individuals. The structure of this population can greatly affect the outcome of evolution. If the fitness of an individual is determined by its interactions with others, then we are in the world of evolutionary game theory. The population structure specifies who interacts with whom. We derive a simple formula that holds for a wide class of such evolutionary processes. This formula provides an efficient computational method for studying evolutionary dynamics in structured populations.

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  • Charles G Nathanson & Corina E Tarnita & Martin A Nowak, 2009. "Calculating Evolutionary Dynamics in Structured Populations," PLOS Computational Biology, Public Library of Science, vol. 5(12), pages 1-7, December.
    • Handle: RePEc:plo:pcbi00:1000615
    DOI: 10.1371/journal.pcbi.1000615
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    References listed on IDEAS

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    Cited by:

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    3. Bin Wu & Arne Traulsen & Chaitanya S. Gokhale, 2013. "Dynamic Properties of Evolutionary Multi-player Games in Finite Populations," Games, MDPI, vol. 4(2), pages 1-18, May.
    4. Tekwa, Edward W. & Gonzalez, Andrew & Loreau, Michel, 2019. "Spatial evolutionary dynamics produce a negative cooperation–population size relationship," Theoretical Population Biology, Elsevier, vol. 125(C), pages 94-101.
    5. Jorge Peña & Bin Wu & Jordi Arranz & Arne Traulsen, 2016. "Evolutionary Games of Multiplayer Cooperation on Graphs," PLOS Computational Biology, Public Library of Science, vol. 12(8), pages 1-15, August.
    6. Dirk Helbing & Attila Szolnoki & Matjaž Perc & György Szabó, 2010. "Evolutionary Establishment of Moral and Double Moral Standards through Spatial Interactions," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-9, April.

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