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Truncation selection and payoff distributions applied to the replicator equation.

B Morsky1, C T Bauch2

  • 1Department of Mathematics and Statistics, 50 Stone Road East, Room 437 MacNaughton Building, University of Guelph, Guelph, Ontario, Canada N1G 2W1.

Journal of Theoretical Biology
|June 26, 2016
PubMed
Summary

The replicator equation simplifies biological dynamics. This study introduces payoff distributions and truncation selection, revealing complex dynamics not captured by standard models, highlighting the impact of simplifying assumptions.

Keywords:
CooperationESSEvolutionary game theoryReplicator dynamicsTruncation selection

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Area of Science:

  • Evolutionary Game Theory
  • Theoretical Ecology
  • Mathematical Biology

Background:

  • The replicator equation is a cornerstone in theoretical biology for modeling evolutionary dynamics.
  • It relies on simplifying assumptions like mean payoffs and proportional selection, which may limit its applicability.
  • These assumptions can obscure complex behaviors observed in real biological systems.

Purpose of the Study:

  • To investigate the impact of relaxing mean payoffs and proportional selection assumptions in the replicator equation.
  • To explore the dynamics introduced by payoff distributions and truncation selection.
  • To compare the outcomes of extended replicator equations and agent-based models with standard models.

Main Methods:

  • Developed extensions of the replicator equation incorporating payoff distributions.
  • Implemented agent-based models with truncation selection (independent and dependent).
  • Analyzed the stability of fixed points under different payoff variance conditions.

Main Results:

  • Recovered the standard replicator equation when payoff variances were uniform under independent truncation.
  • Demonstrated that non-uniform payoff variances allow for tunable stability of boundary fixed points.
  • Observed transient and complex dynamics in extended models, absent in standard replicator equations.

Conclusions:

  • The assumptions of mean payoffs and proportional selection significantly influence replicator dynamics.
  • Incorporating payoff distributions and truncation selection reveals richer evolutionary behaviors.
  • Extended models offer a more nuanced understanding of biological phenomena compared to the standard replicator equation.