Métodos geradores de modelos de crescimento e decrescimento aplicados às ciências agrárias

Abstract

The objectives of this work were: to propose methods that generate models of growth and decrease applied in the agrarian sciences and to propose models from these methods. This thesis is divided into five chapters. The first chapter consists of a bibliographical review of the themes related to growth curves and a collection of the most used nonlinear models. In the second chapter, the method that generates growth and decay models is presented, and a new non linear model was developed from the method presented for the first article of the thesis. In addition, a new non-linear model is proposed for describing the growth of goats and sheep from the method. For the applications of the new proposed model, the SRD goat database presented in the work of Cavalcante et al. (2013) and data of Santa Inês sheep from the work of Sarmento et al. (2006a). The proposed model was compared, statistically, with the nonlinear models Logistic, Von Bertalanffy, Brody, Gompertz and Richards. The parameter estimation for the models was done by least squares methods and the Levenberg-Marquardt iterative process of the IBM SPSS Statistics 1.0 program. Afterwards, the selection of the best model to describe the growth curves was based on the mean square of the residue (QMR), Akaike information criterion (AIC), Bayesian information criterion (BIC), absolute mean deviation (DMA) and adjusted determination coefficient R2 aj.. For the third chapter, we present a new model-generating method, obtained from combinations of existing models, called constructor methods. In addition, we propose a model to describe the kinetic curve of gas production by the technique vitro of different accessions of ten genotypes of forage peanuts. The gas production readings were two, four, six, eight, ten, 12, 14, 17, 20, 24, 28, 32, 48, 72, and 96 hours of incubation. The adjusted coefficient of determination (R2 aj.), mean square of residue (QMR), mean absolute deviation (DMA), Akaike information criterion (AIC) and Bayesian Schwarz criterion (BIC ) were used to select the best fit model of the curves. It is understood that this chapter is of fundamental importance for the support of the article presented in the fourth chapter of this thesis. Chapter four consists of a proposal for a new model based on the combination of the Logistic and Von Bertalanffy models, using the constructor method (VII) of chapter three, in order to compare and or identify with the bicompartmental logistic model the one with the highest quality of fit to the cumulative gas production (GWP) kinetics curve of sunflower, corn and mixtures of silages. The parameters were estimated using the least squares method using the Gauss-Newton algorithm implemented in the nls function of the R software. The fit quality of the models was measured by the adjusted coefficient of determination R2 aj., mean square of the residue (QMR), absolute mean deviation (DMA), Akaike information criterion (AIC), Bayesian Schwarz criterion (BIC), and relative efficiency (ER). Chapter 5 presents the final considerations about the work. The results show that the proposed models were superior to the other models commonly used to study animal growth curves and or to describe kinetics of in vitro gas production.