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Models of darwinian processes and evolutionary principles

R Feistel, W Ebeling

    Bio Systems
    |January 1, 1982
    PubMed
    Summary

    Evolutionary processes are modeled as stochastic movements on adaptive landscapes. A diffusion approximation for phenotypic evolution yields mathematical challenges akin to the Schrödinger equation.

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    Area of Science:

    • Evolutionary biology
    • Theoretical biology
    • Mathematical modeling

    Background:

    • Evolutionary processes can be conceptualized as movements within genotype and phenotype spaces.
    • Adaptive landscapes, defined by real-valued functions, guide these evolutionary trajectories.
    • Understanding these dynamics is crucial for predicting evolutionary outcomes.

    Purpose of the Study:

    • To model evolutionary processes as stochastic motions in genotype and phenotype spaces.
    • To introduce real-valued functions forming landscapes over these spaces.
    • To propose a diffusion approximation for phenotypic processes.

    Main Methods:

    • Describing evolution as stochastic motions in genotype and phenotype spaces.
    • Formulating smoothness postulates for real-valued landscape functions.
    • Proposing a diffusion approximation for phenotypic evolutionary processes.

    Main Results:

    • Evolution is conceptualized as a hill-climbing process on adaptive landscapes.
    • The proposed diffusion approximation for phenotypic processes results in mathematical problems similar to those found with the Schrödinger equation for disordered potentials.
    • This provides a novel mathematical framework for studying evolution.

    Conclusions:

    • The study offers a mathematical framework for understanding evolution as a landscape-driven process.
    • The diffusion approximation provides a tractable model for phenotypic evolution.
    • The connection to the Schrödinger equation opens avenues for advanced mathematical analysis in evolutionary biology.

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