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Fixation properties of multiple cooperator configurations on regular graphs.

Hendrik Richter1

  • 1Faculty of Electrical Engineering and Information Technology, HTWK Leipzig University of Applied Sciences, Postfach 301166, 04251, Leipzig, Germany. hendrik.richter@htwk-leipzig.de.

Theory in Biosciences = Theorie in Den Biowissenschaften
|March 23, 2019
PubMed
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Cooperation in evolutionary games on graphs depends on network structure. Configuration-based structure coefficients link fixation properties of multiple cooperators to their average path length on evolutionary graphs.

Keywords:
Evolutionary graph theoryFixationMultiple mutantsRegular graphsStructure coefficients

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Area of Science:

  • Evolutionary game theory
  • Network science
  • Mathematical biology

Background:

  • Cooperation dynamics in evolutionary games are influenced by population structure and spatial network properties.
  • Understanding these dynamics is crucial for explaining cooperation's emergence in various biological and social systems.

Purpose of the Study:

  • To analyze how population structure, specifically configurations of cooperators and defectors, affects cooperation in evolutionary games on graphs.
  • To introduce and utilize configuration-based structure coefficients for assessing cooperation emergence and fixation properties.
  • To investigate the relationship between structure coefficients and spatial properties like path lengths between cooperators.

Main Methods:

  • Modeling interaction networks as regular graphs.
  • Employing configuration-based structure coefficients to analyze scenarios with varying numbers and arrangements of cooperators.
  • Analyzing the correlation between structure coefficients and the average shortest path length between cooperators under weak selection.

Main Results:

  • Structure coefficients provide a method to assess cooperation emergence for any configuration of cooperators and defectors.
  • These coefficients generalize the analysis of a single cooperator (lone mutant) to multiple cooperators.
  • A strong correlation was found between structure coefficients and the average shortest path length between cooperators under specific conditions.

Conclusions:

  • Fixation properties of multiple cooperators on regular evolutionary graphs can be linked to the spatial arrangement and path lengths between cooperators.
  • Configuration-based structure coefficients offer a powerful tool for understanding cooperation in structured populations.
  • The study highlights the importance of network topology in the evolution of cooperation.