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[Allometry and the original and generalized Gompertz function (author's transl)]

G Sager

    Anatomischer Anzeiger
    |January 1, 1980
    PubMed
    Summary
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    This study explores the Gompertz function for organic growth, examining mathematical consequences when applying the allometry principle. A generalized Gompertz function offers greater flexibility for growth curves and inflection points.

    Area of Science:

    • Mathematical biology
    • Growth modeling

    Context:

    • The traditional Gompertz function is a standard model for organic growth.
    • Allometry describes the relationship between body size and other biological traits.

    Purpose:

    • To investigate the mathematical implications of applying the allometry principle to the Gompertz function.
    • To introduce and analyze a generalized Gompertz function with an additional parameter for enhanced flexibility.

    Summary:

    • The study reviews the Gompertz function and its relationship with allometry, presenting graphical examples.
    • A generalized Gompertz function (dW/dt = kWme-rt) is introduced, offering more flexibility in growth curves and inflection points.
    • Allometric relations are re-examined using the generalized function and applied to existing examples.

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    Impact:

    • Provides a more flexible mathematical model for organic growth analysis.
    • Enhances understanding of the interplay between growth functions and allometric principles.
    • Offers improved curve fitting and analysis of biological growth patterns.