Description of blackberry fruit growth by nonlinear regression models

Abstract

Blackberry is a small fruit with several properties beneficial to human health and its cultivation is an alternative for small producers due to its fast and high financial return. Studying the growth of fruits over time is extremely important to understand their development, helping in the most appropriate crop management, avoiding post-harvest losses, which is one of the aggravating factors of blackberry cultivation, being a short shelf life fruit. Thus, growth curves are highlighted in this type of study and modeling through statistical models helps understanding how such growth occurs. Data from this study were obtained from an experiment conducted at the Federal University of Lavras in 2015. The aim of this study was to adjust nonlinear, double Logistic and double Gompertz models to describe the diameter growth of four blackberry cultivars (‘Brazos’, ‘Choctaw’, ‘Guarani’ and ‘Tupy’). Estimations of parameters were obtained using the least squares method and the Gauss-Newton algorithm, with the “nls” and “glns” functions of the R statistical software. The comparison of adjustments was made by the Akaike information criterion (AICc), residual standard deviation (RSD) and adjusted determination coefficient (R2 aj). The models satisfactorily described data, choosing the Logistic double model for ‘Brazos’ and ‘Guarani’ cultivars and the double Gompertz model for ‘Tupy’ and ‘Choctaw’ cultivars.

Nonlinear models in the study of the cedar diametric growth in a seasonally dry tropical forest

“…(φ 1 ), because according to Ribeiro et al (2018b), in presence of autocorrelated errors, it is important to model this autocorrelation and incorporate it into the model to ensure greater precision in the estimates. Muianga et al (2016), Muniz et al (2017), Silva et al (2020) and Jane et al (2020) all found similar results when observing autocorrelated errors in the fitting of nonlinear models applied to the growth data in cashew, cacao, blackberry and sugar cane varieties, respectively.…”

Evaluation of the critical points of the most adequate nonlinear model in adjusting growth data of ‘green dwarf’ coconut fruits

“…Since models are adjusted, it is necessary to verify the residual vector to guarantee the results of hypothesis tests applied in studies. There are several hypothesis tests in literature to verify the validation of residual vector assumptions which can also be verified by the graphic analysis (RIBEIRO et al, 2018b;SILVA et al, 2020). For models to be considered fit to describe the functional relationship in study, in addition to the analysis of residues, it is essential to verify the significance of the parameters of models.…”

“…With all these steps completed, the various tested models can be reduced to a single model, said to be the "most adequate" (ARCHONTOULIS; MIGUEZ, 2015). For the selection of the "most adequate" model, some criteria are used to assess the quality of fit, which are used in several growth studies (RIBEIRO et al, 2018aSILVA et al, 2020), such as the Akaike information criterion (AIC) (AKAIKE, 1974), the Bayesian information criterion (BIC) (SCHWARZ, 1978), adjusted determination coefficient (R 2 a j ), residual standard deviation (RSD) and the intrinsic (C l ) and parametric (C q ) nonlinearity measures.…”

“…Several authors have used these steps to study fruit growth (MUIANGA et al, 2016;FERNANDES et al, 2017;MUNIZ, J. A. et al, 2017;DIEL et al, 2019;JANE et al 2019, RIBEIRO et al, 2018a, RIBEIRO et al , 2018b, SARI et al, 2019b, SILVA et al 2020JANE et al, 2020a).…”

“…Critical points have been satisfactorily studied by the following authors in the growth of different types of fruits (SARI et al, 2019a;SARI et al, 2019b;DIEL et al, 2020;SILVA et al, 2020). In this context, the aim of this work was to describe steps in adjusting Gompertz and Logistics models to growth data of the longitudinal diameter of 'Green Dwarf' coconut fruits, estimating the critical points of models.…”