Modelos não lineares na comparação de fertilizantes de liberação controlada aplicados ao cafeeiro

Abstract

Coffee is a very important culture for Brazil, it creates economic and social development to the country. The success in cultivating the grain is related to the increase of productivity, that may be influenced by many factors, among them, deserving a highlight is the handling of soil fertility. Many nutrients are needed for fertilizing, an indispensable one is the Nitrogen (𝑁) and one of the most used fertilizers to supply this demand is urea, because it possesses high amounts of the nutrient and a low price per unit. Nonetheless, this fertilizer presents high rates of 𝑁 loss, mainly by volatilization of ammonia (𝑁𝐻3). Aiming to reduce these losses new technological innovation emerged, among them the controlled release fertilizer. The pattern of nutrient release, in the controlled release technology, shows the behavior of a sigmoid, that resembles the absorption curve of N in coffee and sigmoid are well adjusted by non linear regression models. The goal of this research is to select the most suitable non-linear regression model to describe the loss of nitrogen by volatilization of ammonia (𝑁𝐻3) in controlled-release fertilizers applied to coffee and to compare the different fertilizers based on the parameters of the selected model. The data studied are the controlled release of fertilizers urea + sulfur + polymer, urea + plastic resin, urea formaldehyde, urea + water-insoluble polymer, applied to coffee. The parameters of the Logistic, Gompertz, Brody and von Bertalanffy models were estimated by the least squares method using the Gauss-Newton algorithm, considering the independent or autoregressive residual structures. The quality of the adjustment was evaluated based on the fit coefficient of determination, mean absolute deviation and Akaike's information criterion. All models showed good fits, but based on the quality evaluators used, the Von Bertalanffy model proved to be, in most cases, the best to describe the average accumulated loss of nitrogen by ammonia volatilization in controlled-release fertilizers used in coffee. Individual adjustments of the Von Bertalanffy model were performed for each repetition and analysis of variance was applied to the parameter estimates and the results compared considering the completely randomized design, applying the F test and the Tukey test. The F test was significant in all parameters indicating that the treatments have a different effect on the response, the Tukey test showed that the urea formaldehyde fertilizer reaches the asymptote faster and has the lowest accumulated loss of 𝑁 in the coffee plant. The fertilizers urea + sulfur + polymers and urea + insoluble polymer have the latest inflection point among those studied.