PARAMETRIZAÇÕES DO MODELO DE VON BERTALANFFY PARA A DESCRIÇÃO DE CURVAS DE CRESCIMENTO

Resumo

Animal growth curves are generally "S" shaped, also known as sigmoidal curves. This type of curve is well adjusted by nonlinear regression models, among them the von Bertalanffy which has been widely applied in several areas, being presented in the literature through different parameterizations, which in practice can complicate their understanding, affect non-linearity measurements and inferences about parameters. To quantify the nonlinearity present in a Bates and Watts model, they used a geometric concept of curvature. The objective of this paper was to analytically develop three parameterizations of von Bertalanffy's nonlinear model, regarding its nonlinearity, the implications on inferences and to establish relationships between the parameters in the different ways of expressing the models. These parameters were adjusted to the sheep growth data. For each parameterization, the intrinsic and parametric curvature measurements described by Bates and Watts were calculated. The choice of parameterization affects the nonlinearity measurements, consequently influences the reliability and inferences about the estimated parameters. The most used forms in the literature presented the largest deviations from linearity, highlighting the importance of analyzing these measurements in any growth curve study. Parameterization should be used in which the estimate of b represents the inflection point abscissa because it has smaller linearity deviations and direct biological interpretation for all parameters.