Background: Commonly, several traits are assessed in agronomic experiments to better understand the factors under study. However, it is also common to see that even when several traits are available, researchers opt to follow the easiest way by applying univariate analyses and post-hoc tests for mean comparison for each trait, which arouses the hypothesis that the benefits of a multi-trait framework analysis may have not been fully exploited in this area. Results: In this paper, we extended the theoretical foundations of the multi-trait genotype-ideotype distance index (MGIDI) to analyze multivariate data either in simple experiments (e.g., one-way layout with few treatments and traits) or complex experiments (e.g., with a factorial treatment structure). We proposed an optional weighting process that makes the ranking of treatments that stands out in traits with higher weights more likely. Its application is illustrated using (1) simulated data and (2) real data from a strawberry experiment that aims to select better factor combinations (namely, cultivar, transplant origin, and substrate mixture) based on the desired performance of 22 phenological, productive, physiological, and qualitative traits. Our results show that most of the strawberry traits are influenced by the cultivar, transplant origin, cultivation substrates, as well as by the interaction between cultivar and transplant origin. The MGIDI ranked the Albion cultivar originated from Imported transplants and the Camarosa cultivar originated from National transplants as the better factor combinations. The substrates with burned rice husk as the main component (70%) showed satisfactory physical proprieties, providing higher water use efficiency. The strengths and weakness view provided by the MGIDI revealed that looking for an ideal treatment should direct the efforts on increasing fruit production of Albion transplants from Imported origin. On the other hand, this treatment has strengths related to productive precocity, total soluble solids, and flesh firmness. Conclusions: Overall, this study opens the door to the use of MGIDI beyond the plant breeding context, providing a unique, practical, robust, and easy-to-handle multi-trait-based framework to analyze multivariate data. There is an exciting possibility for this to open up new avenues of research, mainly because using the MGIDI in future studies will dramatically reduce the number of tables/figures needed, serving as a powerful tool to guide researchers toward better treatment recommendations.

The aim of this study was to select growth models to describe strawberry (Fragaria x ananassa)fruit production. To do this, data on 16 treatments (combination of 2 cultivars [Albion and Camarosa], 2 origins [National and Imported], and 4 organic substrates mixed [70% crushed sugar cane residue + 30% organic compost, 70% crushed sugar cane residue + 30% commercial substrate, 70% burnt rice husk + 30% organic compost, and 70% burnt rice husk + 30% commercial substrate]) conducted in a Randomized Complete Block Design (RCBD) with 4 replicates were used. Different parameterizations of the Logistic, Gompertz, and von Bertalanffy models were adjusted for number and weight of fruits per plant (g) accumulated in multiple harvests. The model adjustment and parameter estimation were obtained by ordinary least squares, using a Gauss Newton algorithm. The selection of the best model was chosen by intrinsic and parametric nonlinearity. Among the adjusted nonlinear models, the best adjustment for both variables was achieved by the parameterization 2 of the Logistic model and parameterization 1 of the Gompertz model, because they had lower results with less parametric and intrinsic nonlinearity. However, care should be taken when using the Gompertz model because it tends to overestimate the production estimate and may cause misunderstandings in interpretation.

The multi-trait genotype-ideotype distance index (MGIDI) was used to select superior treatments in experiments with strawberries. Twenty-three productive, qualitative, physiological, and phenological traits with negative and positive desired gains were accessed in 16 treatments, a combination of two cultivars (Albion-neutral days, and Camarosa-short days), two transplants origins (National and Imported), and four organic substrates mixes (Crushed sugarcane bagasse, burnt rice husk, organic substrate, and Carolina commercial substrate). Our results suggest that most of the strawberry traits are influenced by the cultivar, transplant origin, cultivation substrates, as well as by the interaction between cultivar and transplant origin. The MGIDI index indicated that the Albion cultivar originated from imported transplants grown in substrates where the main component (70%) is burnt rice husk provides desired values for 20 of a total of 22 traits, which represents a success rate of ~ 91% in selecting traits with desired values. The strengths and weakness view provided by the MGIDI index revealed that the looking for an ideal treatment should direct the efforts on improving the water efficiency use and reducing total acidy of fruits. On the other hand, the strengths of selected treatments are mainly related to productive precocity, total soluble solids, and flesh firmness. The MGIDI index provides a unique, robust, and easy-to-handle process, standing out as a powerful tool to develop better treatment recommendations for experiments with strawberries when multiple traits are assessed.

The objective of this study was to characterize the production of biquinho pepper through the interpretation of parameter estimates from the logistic model and its critical points obtained by the partial derivatives of the function, and to indicate the best cultivar and growing season for subtropical climate sites. For this, a 2x3 factorial experiment was conducted with two cultivars of biquinho pepper (BRS Moema and Airetama biquinho) in three growing seasons (E1: October 2015, E2: November 2015, E3: January 2016). The logistic non-linear model for fruit mass was specified as a function of the accumulated thermal sum, and the critical points were calculated through the partial derivatives of the model, in order to characterize the productive performance of the crop by the biological interpretation of the estimates of the three set parameters. In E3, temperatures close to 0 ºC during the experiment were lethal to the plants, and a linear regression model was used in this case. The production of the cultivars in E1 and E2 were well characterized by the estimated logistic models, and the most productive cultivar was Airetama biquinho in all evaluated seasons. This cultivar also presented higher concentration of production. The two cultivars did not differ significantly with regards to productive precocity. For E3, it was not possible to interpret the parameters in the same way as for E1 and E2, since the use of the linear model did not allow the same interpretations performed for the nonlinear model, reaffirming its applicability horticultural crops of multiple harvests.

Strawberry is an economically and socially important crop in several regions worldwide. Thus, studies that provide information on topics in strawberry growth are important and must be constantly updated. The aims of this study were to fit a logistic growth model to describe strawberry fruit production and to estimate the partial derivatives of the fitted model in order to estimate and interpret the critical points, in addition to using multivariate analyses. To do this, data on 16 treatments [combinations of two cultivars (Albion and Camarosa), two origins (national and imported), and four mixed organic substrates (70% crushed sugar cane residue + 30% organic compost, 70% crushed sugar cane residue + 30% commercial substrate, 70% burnt rice husk + 30% organic compost, and 70% burnt rice husk + 30% commercial substrate)] conducted in a randomized complete block design (RCBD) with four replicates were used. A logistic model was fitted to the accumulated fruit production stratified by treatment and replication. Partial derivatives related to the accumulated thermal sum were estimated in order to quantify the critical points of the model. Subsequently, a principal component analysis was performed. The results show that the use of growth models substantially increases the inferences that can be made about crop growth, and the multivariate analysis summarizes this information, simplifying its interpretation. Approaches such as those carried out in this study are still rarely used, but, compared to simpler models, they increase the amount of inferences that can be made and provide greater elucidation of the results.