Nonlinear Modeling for Analyzing Data from Multiple Harvest Crops

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.

Production of biquinho pepper in different growing seasons characterized by the logistic model and its critical points

“…The low non-linearity reported in the estimated model for the cultivars BRS Moema and Airetama Biquinho at E1 and E2 seasons indicated that the model parameters estimates are close to being non-biased (RATKOWSKY, 1993;SARI et al, 2018) and can satisfactorily explain the productive performance of the crop. In addition to low parametric and intrinsic nonlinearity, the models presented normality and homogeneity of variances.…”

“…The reproductive period of the biquinho pepper fruits, described by the Logistic model, could be well characterized, because the parameters allowed biological interpretation, and the critical points of the model provide the trend of the production along the crop cycle (MISCHAN et al, 2011); which, for example, indicated precocity and rate of fruit production (DIEL et al, 2019;SARI et al, 2018;. In addition, nonlinear growth models such as logistic are flexible enough to explain the variable performance of plants (PAINE et al, 2012) over the cycle.…”

“…The logistic model was selected a priori since it presents lower intrinsic and parametric nonlinearity values when compared with other nonlinear growth models. In addition, the logistic model was selected in other researches with multipleharvested crops (LÚCIO et al, 2015;DIEL et al, 2019;SARI et al, 2018). The logistic model for the cultivars in the E1 and E2 seasons was specified as…”

“…Plant growth responds non-linearly to temperature (PAINE et al, 2012) and, thus, the use of non-linear models is promising for modeling the growth of plants (YIN et al, 1995;PAINE et al, 2012), allowing biological interpretations of the critical points of the adjusted function (MISCHAN et al, 2011;SARI et al, 2018;. Peppers respond to the accumulated thermal sum, and the crop cycle is associated with the amount of degree-days for each stage of development (FILGUEIRA, 2003).…”

“…For multiple-harvest crops, logistic regression models can efficiently describe fruit production which is the appropriate for crops such as Capsicum annuum, Cucurbita pepo, Solanum melongena, Phaseolus vulgaris and Fragaria ananassa (DIEL et al, 2019;LUCIO et al, 2016;LÚCIO;NUNES;REGO, 2015;SARI, et al, 2018;. For Fragaria ananassa, DIEL et al (2019) modeled the fruit production as a function of STa (accumulated thermal sum) for the logistic, Gompertz and von Bertalanffy models in different parameterizations and concluded that the Logisitic model described fruit production best while the models of Gompertz and von Bertalanffy overestimate the parameter that represent the production.…”