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The replicator dynamics with n players and population structure.

Matthijs van Veelen1

  • 1CREED, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands. c.m.vanveelen@uva.nl

Journal of Theoretical Biology
|February 8, 2011
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Summary
This summary is machine-generated.

This study generalizes replicator dynamics for n-player games and structured populations, revealing inclusive fitness predicts selection direction and speed in additive games with constant relatedness.

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Area of Science:

  • Evolutionary Game Theory
  • Population Genetics
  • Mathematical Biology

Background:

  • Replicator dynamics typically models 2-player games with random interactions.
  • Understanding evolutionary dynamics in structured populations is crucial.

Purpose of the Study:

  • To generalize replicator dynamics for n-player games and non-random population structures.
  • To explore the role of population structure in evolutionary dynamics.
  • To reformulate and extend inclusive fitness theory.

Main Methods:

  • Generalized replicator dynamics formulation.
  • Analysis of games with equal and unequal gains from switching.
  • Incorporation of population structure and relatedness.

Main Results:

  • The generalized replicator dynamics encompasses standard models as a special case.
  • Inclusive fitness accurately predicts selection for additive games (equal gains from switching).
  • Constant relatedness makes inclusive fitness a predictor of selection speed and direction.

Conclusions:

  • Generalized replicator dynamics provides a powerful framework for studying evolution in structured populations.
  • Inclusive fitness is a robust predictor under specific conditions (additive effects, constant relatedness).
  • The value of inclusive fitness is meaningful beyond just its sign in additive games.