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Continuous stability and evolutionary convergence

I Eshel1, U Motro, E Sansone

  • 1Department of Statistics, School of Mathematical Sciences, Tel Aviv University, Ramat-Aviv, Israel.

Journal of Theoretical Biology
|April 7, 1997
PubMed
Summary
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Long-term evolutionary dynamics in asexual populations are governed by mutation and selection. Small mutations ensure evolutionary stability aligns with continuous stability in population games, regardless of mutation distribution for one-dimensional strategies.

Area of Science:

  • Evolutionary biology
  • Game theory
  • Mathematical modeling

Background:

  • Understanding long-term evolutionary dynamics requires integrating mutation and selection processes.
  • Population games model strategic interactions within populations, influencing evolutionary trajectories.
  • Asexual reproduction simplifies evolutionary models by removing genetic recombination.

Purpose of the Study:

  • To define and analyze a stochastic process for long-term evolution in asexual populations.
  • To investigate the relationship between evolutionary stability and game-theoretic stability under mutation and selection.
  • To determine the influence of mutation characteristics on evolutionary stability.

Main Methods:

  • Defined a stochastic evolutionary process incorporating mutation and selection.

Related Experiment Videos

  • Analyzed population dynamics using a one-dimensional continuous strategy space in a population game.
  • Focused on the impact of small-effect mutations on evolutionary stability.

    • Main Results:

    • Established an equivalence between long-term dynamic stability in the evolutionary process and continuous stability in the population game.
    • Demonstrated that for one-dimensional strategy sets, this equivalence is largely independent of mutation distribution.
    • Showcased the critical role of mutation size in linking evolutionary and game-theoretic stability.

    Conclusions:

    • Continuous stability in population games is a key predictor of long-term evolutionary stability for asexual populations with small mutations.
    • The dimensionality of the strategy set is crucial for the robustness of this stability relationship.
    • Mutation distribution has minimal impact on evolutionary stability when strategies are one-dimensional, simplifying evolutionary predictions.