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A simple but flexible growth function

J France1, J Dijkstra, J H Thornley

  • 1Institute of Grassland and Environmental Research North Wyke Research Station, Okehampton Devon U.K.

Growth, Development, and Aging : GDA
|January 1, 1996
PubMed
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A new flexible growth equation is introduced, accurately describing sigmoidal and hyperbolic growth patterns in animals. This generalized Gompertz equation offers a valuable tool for analyzing biological growth data.

Area of Science:

  • * Mathematical modeling
  • * Animal growth dynamics
  • * Biological growth functions

Background:

  • * Existing growth functions like Gompertz and logistic have limitations in describing diverse growth patterns.
  • * There is a need for flexible mathematical models to accurately represent biological growth across species.
  • * Sigmoidal and diminishing returns behaviors are common in animal growth.

Purpose of the Study:

  • * To derive and evaluate a novel flexible growth equation.
  • * To compare the new function with established growth models (Gompertz, logistic, monomolecular, Richards).
  • * To assess the applicability of the new equation to empirical animal growth data.

Main Methods:

  • * Derivation of a new functional form: W(t) = Wf - (Wf - Wo) exp[-k * (t - T) + 2c(sqrt(t) - sqrt(T))].

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  • * Evaluation against standard growth functions using mathematical criteria.
  • * Application to diverse animal growth datasets, from mice to horses.

    • Main Results:

    • * The new function effectively describes both sigmoidal and hyperbolic growth shapes.
    • * It accurately models sigmoidal patterns with rapid early growth and variable inflection points, akin to a generalized Gompertz equation.
    • * The equation demonstrates flexibility in capturing diminishing returns behavior and hyperbolic growth without inflection points.

    Conclusions:

    • * The proposed growth equation is a versatile and valuable addition to existing biological growth models.
    • * Its ability to describe varied growth patterns makes it suitable for a wide range of animal species.
    • * The simplicity and flexibility of the new function enhance its utility in growth analysis.