Abbreviations: AMMI, additive main effects and multiplicative interaction; ASV, additive main effects and multiplicative interaction stability value; AUDPC, area under the disease progress curve; BLUP, best linear unbiased prediction; CW, caryopses weight; GEI, genotype × environment interaction; GSI, genotype stability index; GW, grain weight; GWP, grain weight per panicle; GY, grain yield; HI, hulling index; HW, hectoliter weight; IGY, industrial grain yield; IPCA, interaction principal component axis; LMM, linear mixed-effect model; MET, multi-environment trial; MPE, mean performance and stability; MTSI, multi-trait stability index; NEP, number of spikelets per panicle; NG2, number of grains >2 mm; NGP, number of grains per panicle; PL, panicle length; PM, panicle mass; TGW, thousand-grain weight; WAASB, weighted average of absolute scores from the singular value decomposition of the matrix of best linear unbiased predictions for the genotype × environment interaction effects generated by an linear mixed-effect model; WAASBY, weighted average of WAASB and response variable. bIoMetrY, ModeLInG, And stAtIstIcsPublished in Agron.
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.
The statistical interpretation of experimental results is inherent to the research process. Therefore, every researcher is expected to have basic understanding on the subject. In vegetable crops, the planning, implementing and data gathering is more complex due to specific aspects related to this group of plants, such as intensive management and high labor requirement to carry out the experiments, uneven fruit maturation and heterogeneity of the experimental area. Since all these factors are sources of variability within the experiment, circumventing them in the experiment planning and implementing phases is fundamental to reduce the experimental error. Furthermore, the knowledge of statistical tests and the assumptions for their use is equally critical to make the research statistically valid. The present work presents the problems of unwanted variability within an experiment with vegetables and the possibilities to reduce and manage it. We discuss alternatives to reduce the variability due to uncontrolled effects within an experiment; the most common experimental designs; recommendation of appropriate statistical tests for each type of treatment; and techniques for the diagnosis of residues. We expect to contribute with researchers dealing with vegetable crops, offering subsidies to aid researchers in the planning and implementation of experiments and in the analysis and interpretation of experimental results.
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