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Dynamics and evolution: evolutionarily stable attractors, invasion exponents and phenotype dynamics

D A Rand1, H B Wilson, J M McGlade

  • 1Nonlinear Systems Laboratory, Mathematics Institute, University of Warwick, Coventry CV4 7AL, U.K.

Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
|February 28, 1994
PubMed
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This study introduces evolutionary stable attractors (ESAs) and the invasion exponent for analyzing complex evolutionary dynamics in biological and economic systems. The research provides a new mathematical framework for understanding evolutionary stability beyond traditional game theory.

Area of Science:

  • Evolutionary dynamics
  • Mathematical biology
  • Dynamical systems theory

Background:

  • Classical evolutionary game theory focuses on evolutionary stable strategies (ESSs).
  • Extending these concepts to broader dynamical systems requires new mathematical frameworks.
  • Understanding stability in complex biological and economic systems is crucial.

Purpose of the Study:

  • To generalize evolutionary dynamics and stability to a wide range of systems.
  • To introduce and define the concept of an evolutionary stable attractor (ESA).
  • To develop the invasion exponent as a key analytical tool.

Main Methods:

  • Formulation of general dynamics for biological and other systems.
  • Definition and analysis of evolutionary stable attractors (ESAs).

Related Experiment Videos

  • Development and application of the invasion exponent for complex systems analysis.
  • Introduction of phenotype dynamics to model population changes over time.

    • Main Results:

    • Defined evolutionary stable attractors (ESAs) for systems with simple and complex dynamics.
    • Introduced the invasion exponent, enabling analysis of coevolution and chaotic dynamics.
    • Characterized internal ESAs using differential selective pressure.
    • Analyzed non-reproductive evolution, including learning rule competition and economic applications.

    Conclusions:

    • The developed theory and tools, including the invasion exponent, offer a powerful framework for analyzing evolutionary stability in diverse systems.
    • Evolutionary stable attractors (ESAs) provide a generalized concept for long-term stability in evolutionary dynamics.
    • The framework has potential applications in biology, economics, and understanding non-reproductive evolution.