Modelos não lineares no estudo do acúmulo de matéria seca de plantas de soja sob o efeito de diferentes tratamentos

Abstract

Brazil is currently the world's largest producer of soybeans. The grain is the most economically important part of the plant, being a commodity. In the early stages of soybean use in Brazil, the entire aerial part of the plant, including the grains, was used as feed for ruminants. Like other plants, soybean growth over time follows a sigmoidal curve, which can be well described using nonlinear regression models. This study aimed to compare the fit of three nonlinear models — Logistic, Gompertz, and von Bertalanffy — to data on the accumulation of total dry matter (TDM), stem dry matter (SDM), leaf dry matter (LDM), and root dry matter (RDM), in grams per square meter, under four treatments: fully irrigated throughout the entire period (IPTP), irrigated and shaded during the vegetative stage (ISFV), non-irrigated during the vegetative stage (NIFV), and non-irrigated during the flowering stage (NIFF), in relation to days after plant emergence. The data analyzed were obtained from Pereira (2002). The experiment was conducted during the 1998/1999 growing season at the Vila Chaves Experimental Station, on the campus of the Federal University of Viçosa, located in Viçosa, Minas Gerais, Brazil. The assumptions of normality, homoscedasticity, and residual independence were verified using the Shapiro-Wilk (SW), Breusch-Pagan (BP), and Durbin-Watson (DW) tests, respectively. The models were fitted by the least squares method using the Gauss-Newton algorithm implemented in R software. Model selection was based on the lowest Akaike Information Criterion (AIC), and model quality was assessed using the coefficient of determination (R2), the residual standard deviation (RSD). Parameter estimates and confidence intervals were calculated for each model that best fit the data. Plots were also generated for each variable with the fitted models for each treatment. For TDM under the IPTP treatment, the von Bertalanffy model was the most suitable, while the Logistic model best fit the other treatments. For SDM under the IPTP and ISFV treatments, the Logistic model was most appropriate, whereas for the NIFV and NIFF treatments, the Gompertz model performed better. Regarding LDM, the von Bertalanffy model best fit the IPTP and NIFV treatments; for ISFV, the Logistic model was more suitable, and for NIFF, the Gompertz model was preferred. For RDM, the Logistic model provided the best fit across all treatments.