A Versatile Growth Model with Statistically Stable Parameters

Abstract

This paper presents a new comprehensive growth model which includes numerous historical models as special cases. The new model is derived from a concise biological principle which, unlike earlier theories, relates to growth acceleration. Properties of growth curves, such as asymptotic limits or inflection points, are shown to be incidental in this new context. Possible submodels include not only asymptotic growth (such as von Bertalanffy, Richards, Gompertz, or logistic growth) but also linear, quadratic, or exponential growth. By simple analysis of variance, the observed data can be used directly in deciding which type of model is most appropriate. The new model is cast in terms of parameters which have stable statistical estimates. From this perspective, it is shown how earlier formulations sometimes result in an endless computer search for optimal parameter estimates.Key words: Growth, asymptotic growth, von Bertalanffy, Richards, Gompertz, logistic, length at age, weight at age, nonlinear parameter estimation