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Allometry and multivariate growth revisited

D A Griffiths, R L Sandland

    Growth
    |January 1, 1982
    PubMed
    Summary
    This summary is machine-generated.

    This study critiques Turner's (1978) deterministic models for multivariate growth, finding them flawed. It proposes superior stochastic models using maximum likelihood for accurate ecological data analysis, including lynx and hare populations.

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    Area of Science:

    • Ecology
    • Mathematical Biology
    • Statistical Modeling

    Background:

    • Turner (1978) proposed deterministic models and a least squares fitting procedure for multivariate growth processes.
    • The validity and inferential methods of Turner's approach have been questioned.
    • Existing models may not adequately capture the complexities of biological growth.

    Purpose of the Study:

    • To identify fundamental flaws in Turner's (1978) deterministic growth models and fitting procedures.
    • To introduce a novel class of stochastic models for multivariate growth processes.
    • To demonstrate the superiority of the proposed stochastic models and maximum likelihood fitting.

    Main Methods:

    • Critique of the least squares fitting procedure introduced by Turner (1978).

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  • Development of a new class of stochastic models, building upon Turner's generalization of allometry and Lotka-Volterra equations.
  • Application of the method of maximum likelihood for parameter estimation and inference.

    • Main Results:

    • Turner's fitting procedure is demonstrated to be ill-founded, leading to misleading inferences.
    • The proposed stochastic models provide a more robust framework for analyzing multivariate growth.
    • Re-analysis of a dataset previously studied by Turner highlights the improved performance of the new methodology.

    Conclusions:

    • The deterministic models and fitting methods proposed by Turner (1978) are inadequate for reliable multivariate growth analysis.
    • Stochastic models combined with maximum likelihood estimation offer a valid and superior approach for ecological modeling.
    • The findings have implications for the analysis of population dynamics, such as the classic lynx and hare data.