Theoretical modeling of pre and postnatal growth

Abstract

A simultaneous analysis of the pre and postnatal growth data obtained for five exemplary animals (zebra, rat, guinea pig, chicken, tilapia) is performed. To this aim, the generalized von Bertalanffy (VB) model is employed in which one of the fitted parameters is related to the gestation or incubation period of the system under consideration. The results obtained reveal a descriptive power of the VB model in both the pre and postnatal stages for a wide range of the data analyzed using several goodness-of-fit metrics and biologically meaningful parameters fitted. It has been proved that generalized VB function with one parameter constrained to the experimental value of the gestation (incubation) period and other parameters fitted only to the postnatal data predicts with high accuracy the growth of animals in the developmental prenatal stages. Hence, the VB model features not only descriptive but also retro-predictive power to reproduce the prenatal growth patterns of the animals considered. Three main sources of the problems with the fit stability reported for the VB function are identified: nonlinear nature of the scaling n-exponent, its strong correlation with remaining parameters defining the model and n-value placed in the vicinity of the discontinuity point n = 1 or outside the standard range 0 ≤ n < 1 usually applied in the data analysis.