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The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.

Jussi Lehtonen

    The American Naturalist
    |December 16, 2017
    PubMed
    Summary

    The Price equation, a fundamental theorem of evolution, is extended to game theory and continuous trait dynamics. This unifying framework reveals connections between evolutionary game theory and adaptive dynamics.

    Keywords:
    Price equationadaptive dynamicsgame theorygradientinvasion analysisquantitative genetics

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    Area of Science:

    • Evolutionary Biology
    • Theoretical Ecology
    • Game Theory

    Background:

    • The Price equation is a foundational theorem in evolutionary biology.
    • Previous work has not extensively applied it to game theory or continuous trait dynamics with frequency-dependent fitness.

    Purpose of the Study:

    • To unify evolutionary game theory and gradient dynamics under the Price equation framework.
    • To derive fundamental results in these areas using a consistent approach.

    Main Methods:

    • Application of the Price equation with Taylor polynomials.
    • Analysis of multivariable Taylor polynomials within the Price equation framework.

    Main Results:

    • Derivation of a dynamic measure of evolutionary change.
    • Identification of conditions for singular points and convergence stability.
    • An alternative interpretation of evolutionary stability.
    • Emergence of the direct fitness approach to kin selection.
    • Comparison with quantitative genetics and adaptive dynamics equations.

    Conclusions:

    • The Price equation provides a powerful unifying framework for diverse evolutionary concepts.
    • This approach illuminates similarities and differences between game-theoretical and dynamic perspectives.
    • It offers a simplified and unified view of evolutionary processes.