Modelos não lineares duplo sigmoidais: uma aplicação para descrição do crescimento de frutos do pessegueiro

Abstract

Brazil is the twelfth largest producer of peach in the world, with the highest concentration located in Rio Grande do Sul. The way of handling the fruit after harvest is one of the most important stages of the production process since in this phase the greatest losses occur . Thus, it is necessary to study its stages of development to help producers make decisions regarding management in the field and especially the harvest. The peach growth curve is divided into three different stages, featuring a double sigmoid shape. The first phase is characterized by the accelerated growth of the seed and the development of the endocarp. Then, the fruit starts to grow more slowly due to physiological and anatomical changes. Finally, in the third phase of growth, the cell volume increases along with the maturation process. In order to describe this behavior, some non-linear models with double sigmoid characteristics were adjusted to the height and polar diameter data, measured in millimeters (mm) of peach fruits “ Aurora 1”. The models used were: Brody + Brody, Brody + Gompertz, Brody + Logistics, Gompertz + Brody, Gompertz + Gompertz, Gompertz + Logistics, Logistics + Logistics, Logistics + Brody, Logistics + Gompertz, Generalized Brody, Generalized Gompertz and Generalized Logistics. In addition, models were also adjusted considering the incorporation of the heterogeneity of the measures, including different weights in the forms of simple power, logarithmic or exponential power. The estimation was performed using the least squares method with the aid of the Gauss- Newton algorithm, implemented in software R version 4.0.2. For the analysis of residues the tests of Shapiro Wilk, Breusch Pagan, Durbin Watson and some graphic analyzes were used. The quality of the fit of the models was verified based on the analysis of the adjusted determination coefficient, information criterion if corrected Akaike, residual standard error, asymptote adjustment index and non-linearity measures. The results found show that the adjusted nonlinear models make it possible to describe the growth curve for peaches “Aurora 1”, contributing with important information to optimize production.