Uso de modelos mistos e pontos críticos em dados de crescimento de frutos

Abstract

Since the emergence of the new Coronavirus in late 2019, nonlinear growth models have gained prominence both in national and international media. This is due to the sigmoidal trend observed in the moving average of the number of cases, which has led many researchers to employ these models to understand this behavior. This same sigmoidal growth pattern is observed in various living organisms. While some authors chose to use linear models to describe this growth, they ended up missing out on the inherent advantages of nonlinear models. Although linear models were easier to estimate since they did not require iterative methods, nonlinear growth models offered several advantages, including simplicity, biological interpretation of parameters, and the ability to extrapolate inferences beyond the range of variables. Additionally, other interesting aspects have been explored, such as the so-called "critical points”. These points were determined by taking derivatives of the growth functions, from the first to the fourth order, with respect to the independent variable (usually time). The critical points included the point of maximum acceleration, inflection point, point of maximum deceleration, and asymptotic deceleration point. Beyond the critical points, it was possible to explore variability among individuals by analyzing how each one grew over time, considering the inclusion of random effects in the model para- meters, characterizing it as a mixed-effects model. With this approach, the aim of this study was to estimate the critical points of nonlinear growth models and investigate variability among individuals using mixed-effects models. This was done for a single stage of development and for two stages of development, applying the models to the growth data of Blackberry and Dwarf Green Coconut. The critical points were obtained through derivatives and were represented on a graph that showed the growth rate, allowing the location of each critical point to be visualized. The mixed-effects modeling for the Choctaw cultivar was performed using the simple logistic model with random effects on parameters β1 and β2 for length, as well as the mixed-effects double logistic model with random effects on parameters β1 and β4 in relation to diameter.