Parameterizations of the Von Bertalanffy model for description of growth curves

Abstract

The growth curves of animals, in general, have an “S” shape, also known as sigmoidal curves. This type of curve is well fitted by nonlinear regression models, including von Bertalanffy’s model, which has been widely applied in several areas, being presented in literature through different parameterizations, which in practice, can complicate its understanding, affect nonlinearity measures and inferences about parameters. To quantify the nonlinearity present in a Bates and Watts model, a geometric concept of curvature has been used. The aim of this work was to analytically develop three parameterizations of the von Bertalanffy’s nonlinear model referring to its nonlinearity, implications for inferences and to establish relationships between parameters in the different ways of expressing the models. These parameterizations were adjusted to the growth data of sheep. For each parameterization, the intrinsic and parametric curvature measurements described by Bates and Watts were calculated. The parameterization choice affects nonlinearity measures, consequently, influences the reliability and inferences about estimated parameters. The forms most used in literature showed the greatest deviations from linearity, showing the importance of analyzing these measures in any growth curve study. Parameterization should be used in which the b estimate represents the abscissa of the inflection point, as it presents minor linearity deviations and direct biological interpretation for all parameters.