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Related Experiment Videos

Generalizing Fisher's "reproductive value": overlapping and nonoverlapping generations with competing genotypes.

P A Samuelson

    Proceedings of the National Academy of Sciences of the United States of America
    |August 1, 1978
    PubMed
    Summary

    This study extends Fisher's reproductive value concept to Mendelian genetics. General systems are nonlinear, requiring infinite steps to calculate reproductive value, unlike simple dilute systems.

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    Area of Science:

    • Population Genetics
    • Mathematical Biology

    Background:

    • Fisher's 1930 linear eigenvector definition of reproductive value is limited to dilute systems with scale-free intensive ratios.
    • Extending this definition is crucial for understanding complex genetic dynamics.

    Purpose of the Study:

    • To extend Fisher's reproductive value concept beyond linear, dilute systems.
    • To apply this extension to standard Mendelian models.

    Main Methods:

    • Application of an established extension of reproductive value to Mendelian models.
    • Analysis of dynamic relations as first-degree-homogeneous functions.

    Main Results:

    • General Mendelian systems are irreducibly nonlinear.
    • Reproductive value functions for these systems are calculable only in an infinite number of steps.

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  • Exceptions include singular cases like the Hardy-Weinberg equilibrium.

    • Conclusions:

    • The generalized reproductive value is applicable to standard Mendelian models.
    • Nonlinearity necessitates iterative calculation for reproductive value in complex genetic systems.