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Evolution of cooperation in a multidimensional phenotype space.

Dhaker Kroumi1, Sabin Lessard1

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Cooperation evolves more readily in higher-dimensional phenotype spaces, especially with high phenotype mutation rates and low strategy mutation rates. This occurs because higher dimensions limit defector migration, favoring cooperative strategies.

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Area of Science:

  • Evolutionary game theory
  • Theoretical population genetics

Background:

  • The emergence of cooperation among selfish individuals is a key question in evolutionary theory.
  • The phenotypic model, where strategies depend on observable traits, is crucial for studying cooperation.
  • Previous work analyzed cooperation in one-dimensional and infinite-dimensional phenotype spaces under weak selection.

Purpose of the Study:

  • To derive the condition for cooperation prevalence in finite-dimensional phenotype spaces.
  • To extend previous findings from 1D and infinite-D to intermediate dimensions.
  • To investigate the impact of phenotype space dimension on cooperation dynamics.

Main Methods:

  • Application of perturbation methods to analyze mutation-selection equilibrium.
  • Utilizing ancestral processes in the limit of large population size.
  • Studying the Prisoner's Dilemma under weak selection.

Main Results:

  • A condition for cooperation to be favored by selection in finite-dimensional phenotype spaces was derived.
  • The best scenario for cooperation involves high population-scaled phenotype mutation rate and low population-scaled strategy mutation rate.
  • Higher phenotype space dimensions facilitate cooperation, with significant effects from 1D to 3D.

Conclusions:

  • Phenotype space dimension is a critical factor influencing the evolution of cooperation.
  • Mutation rates play a significant role, with specific combinations favoring cooperation.
  • The findings bridge the gap between theoretical models and more realistic, multi-dimensional scenarios.