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Following the Dynamics of Structural Variants in Experimentally Evolved Populations
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Deterministic evolutionary game dynamics in finite populations.

Philipp M Altrock1, Arne Traulsen

  • 1Emmy-Noether Group of Evolutionary Dynamics, Department of Evolutionary Ecology, Max-Planck-Institute for Evolutionary Biology, 24306 Plön, Germany. altrock@evolbio.mpg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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PubMed
Summary
This summary is machine-generated.

This study introduces a new birth-death process for evolutionary game dynamics, offering a deterministic model for strategy spreading in any population size. It extends existing models and provides simple formulas for fixation probabilities and times.

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Population Dynamics

Background:

  • Evolutionary game dynamics models strategy spread in reproducing populations.
  • Traditional models are often stochastic, becoming deterministic only in infinite populations.
  • Existing models lack a universally applicable deterministic limit for finite populations.

Purpose of the Study:

  • To present a novel microscopic birth-death process with a deterministic strong selection limit.
  • To extend evolutionary dynamics under weak selection by recovering the frequency-dependent Moran process.
  • To derive simple expressions for fixation probabilities and average fixation times.

Main Methods:

  • Development of a microscopic birth-death process.
  • Analysis of the strong selection limit in well-mixed populations of any size.
  • Investigation of the weak selection limit to recover the Moran process.
  • Derivation of analytical expressions for fixation probabilities and times in two-strategy games.

Main Results:

  • A new birth-death process yields a fully deterministic strong selection limit for any population size.
  • The process naturally extends weak selection dynamics, recovering the frequency-dependent Moran process.
  • Simple formulas for fixation probabilities and average fixation times are obtained for two-player, two-strategy games.
  • For cyclic games (two players, three strategies), deterministic dynamics show nontrivial initial condition dependence.

Conclusions:

  • The proposed birth-death process offers a robust and deterministic framework for evolutionary game dynamics.
  • This model provides a unified approach, bridging strong and weak selection regimes.
  • The findings offer new analytical tools for understanding strategy evolution in finite populations.