No abstract

We proposed a workflow for nonlinear modeling of data from multiple‐harvest crops. We demonstrated why the nonlinearity measures should be used to select nonlinear models. We demonstrated as the critical points describe the multiple‐harvest crops production. Logistic model parameters determine the precocity and the concentration of production. Growth models are alternative to ANOVA in analyzing data from multiple‐harvest crops. Nonlinear growth models have been widely used for analyzing production curves with a sigmoidal pattern; however, all benefits that these models provide are not being fully exploited. Our aim here is to provide a step‐by‐step guide on how to choose a nonlinear model with parameters close to being unbiased, and to show how to estimate and interpret the critical points of a model aimed at determining the precocity and concentration of the production. Data on two uniformity trials conducted with eggplant (Solanum melongena L.) was used for this purpose. The Brody, Gompertz, logistic, and von Bertalanffy models were fitted to predict the number and fresh mass of fruits per plant. The model with lower nonlinearity measures and lower bias of the parameter estimates was selected. All the tested models presented satisfactory goodness‐of‐fit measures, but they differed regarding nonlinearity measures. The logistic model was selected because it had lower intrinsic and parametric nonlinearity and lower bias in parameter estimates. The inflection point and maximum acceleration/deceleration points of this model provide detailed pieces of information of the production through the productive cycle. Finally, using the logistic model as an example, we demonstrate that lower values of β2 are related to an earlier maximum production rate, and higher values of β3 are related to an earlier production that is concentrated in fewer days. The nonlinearity measures were important for the model selection. Thus, it is strongly recommended that nonlinearity is estimated and used to select nonlinear models in future studies.

RESUMO O objetivo do trabalho foi estudar o ajuste dos modelos não-lineares, gompertz e logístico, na descrição do desenvolvimento de frutos de coqueiro da variedade anão

RESUMO -o objetivo do trabalho foi avaliar o ajuste dos modelos gompertz e logístico, com estrutura de erros independentes e autorregressivos, no desenvolvimento de frutos de caju, com base em medidas de comprimento e largura do fruto, tomados ao longo do tempo. a estimação dos parâmetros foi feita por meio de rotinas no software R, utilizando-se do método dos mínimos quadrados e o processo iterativo de gaussNewton. Os modelos foram comparados pelos critérios: coeficiente de determinação ajustado (R 2 aj ), desvio padrão residual (DPR), critério de informação Akaike (AIC) e critério bayesiano de Schwarz (BIC). Para os dois modelos, os dados apresentaram autocorrelação residual positiva, tanto para a variável comprimento como para a largura do fruto, descrita por processo autorregressivo de primeira ordem. em geral, por todos critérios de avaliação da qualidade de ajuste, os dados se ajustaram ao modelo logístico com uma estrutura autorregressiva da primeira ordem, havendo no entanto superestimação do tamanho do fruto nas últimas idades, tanto no crescimento em comprimento (cm) como em largura (cm). termos para indexação: Modelo de crescimento. Medidas biométricas. Regressão não linear. Cajú. DESCRIPTION OF THE GROWTH CURVE OF CASHEW FRUITS IN NONLINEAR MODELSABSTRACT -The objective of this study was to evaluate the adjustment of gompertz and logistic models, with independent and autoregressive error structure in cashew fruits growth, based on the length and width measurements of the fruit, taken through the time. The estimation of the parameters was done in R software routines using the method of minimal squares and the interactive process of gauss-newton. the models were compared by the following criteria: the adjusted coefficient of determination, residual standard deviation, Akaike information criterion and Schwarz Bayesian criterion. For both models, the data showed positive residual autocorrelation for both variables: length and width of the fruit, described in autoregressive process of order one. in general, both models adjusted to the data, however there was an overestimation of the fruit size at the late stages. the logistic model was the most adequate to describe the cashew fruit growth in length and width.