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Demographic parameters and natural selection.

L Demetrius

    Proceedings of the National Academy of Sciences of the United States of America
    |December 1, 1974
    PubMed
    Summary
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    This study introduces population entropy and reproductive potential, revealing entropy change equals genetic variance minus covariance, analogous to Fisher's theorem.

    Area of Science:

    • Demography
    • Population Genetics
    • Mathematical Biology

    Background:

    • Traditional demographic models focus on population growth rates.
    • Understanding the genetic underpinnings of population structure and dynamics is crucial.

    Purpose of the Study:

    • Introduce novel demographic parameters: population entropy and reproductive potential.
    • Analyze the relationship between these parameters and population growth.
    • Investigate the rate of change of population entropy under specific genetic conditions.

    Main Methods:

    • Defined population entropy as variability in age class contributions to stationary distribution.
    • Defined reproductive potential as the mean contribution of age classes to growth rate.
    • Derived a relationship between entropy, reproductive potential, and the Malthusian parameter.

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    Main Results:

    • Established an equation for the rate of change of entropy in random mating, Hardy-Weinberg populations under slow selection.
    • Showed the rate of change of entropy equals genetic variance in entropy minus genetic covariance of entropy and reproductive potential.
    • Demonstrated this result as an analogue of Fisher's fundamental theorem of natural selection.

    Conclusions:

    • The new demographic parameters offer insights into population structure and dynamics.
    • The derived relationship provides a genetic interpretation of entropy change in populations.
    • This work extends fundamental principles of natural selection to demographic processes.