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There is a need to strengthen maize (Zea mays L.) breeding strategies based on multivariate selection to obtain high-yielding hybrids that are more stable and resilient to contrasting environmental conditions. Here, we show how the multi-trait stability index (MTSI) can be used to select maize hybrids for mean performance and stability of multiple traits. A set of 10 traits, including grain yield (GY), yield components, and plant-related traits with negative and positive desired selection gains (SGs), were accessed in 90 F 1 hybrids conducted in multi-environment trials. Hybrid and hybrid × location interaction effects were significant (p ≤ .001) for all analyzed traits. The MTSI provided positive gains for all the four traits that were wanted to increase (2.52% ≤ SG ≤ 4.86; mean, 3.28%), including GY (SG, 4.86%), and negative gains for all the six traits that were wanted to decrease (-20.28% ≤ SG ≤ -0.09%; mean, -6.70%), including tassel branch number (SG, -20.28%) and plant height (SG, -1.2%). We also observed desired gains for the stability of all traits. Direct and univariate selection for GY solely was not efficient to provide desired gains for all traits. The MTSI provides a unique, robust, and easy-to-handle selection process that allows identifying the strengths and weaknesses of hybrids. The index was found to be a powerful tool to develop better selection strategies, optimizing the use of resources and time, thus contributing to the sustainability of maize breeding programs worldwide.Abbreviations: DFL, distance from the flag leaf to the first branch of the tassel; DLN, distance for the last node to the first branch of the tassel; EH, ear height; GTB, genotype-by-trait biplot; GY, grain yield; KD, kernel depth; MET, multi-environment trial; MPE, mean performance and stability; MTSI, multi-trait stability index; NKE, number of kernels per ear; PH, plant height; SG, selection gains; TBN, tassel branch number; TKW, thousand-kernel weight; TL, tassel length; 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 a linear mixed-effect model; WAASBY, superiority index that weights between mean performance and stability.

Recently developed selection indexes provide solutions for plant breeding, using linear‐bilinear models that consider factors as fixed or random. This work aimed to compare the multitrait selection indexes based on factor analysis and ideotype‐design (FAI‐BLUP), GGE biplot, and grain yield × trait index (GYT), and proposes the use of predicted genetic values together with the GYT index (best linear unbiased prediction used in grain yield*trait index, GYT‐BLUP). In addition, this work indicates the best index to select superior soybean [Glycine max (L.) Merr.] genotypes, closer to the ideotype. Data from 35 homozygous soybean lines and four checks, were obtained from trials conducted in six locations in the southern region of Brazil in the 2014/2015 crop season. The grain yield, yield components, morphological and grain composition were evaluated. Phenotypic data were used for GGE biplot and GYT analysis, using the software GGE biplot. Genetic values were predicted with mixed models considering genotype and location as random and fixed effects, respectively. Thus, genetic values were used in GYT‐BLUP and FAI‐BLUP indexes. These methods were compared by Spearman's rank correlation. Genetic gains obtained by indexes and traits were estimated. Soybean lines L1 and L22, and cultivars C3 and C4 were selected based on their performance for multiple traits, for indexes used. Thus, we suggest to combined FAI‐BLUP and GYT‐BLUP indexes. The GYT‐BLUP has a high importance for grain yield, which was related to all other traits. FAI‐BLUP gave similar weights for all traits. So, combining different approaches can provide better answers to breeders.

This work aimed to estimate the variance components and genetic parameters, the selection gain, and the cause and effect relationships among traits in order to identify important traits for direct and indirect selection of wheat (Triticum aestivum L.) lines. Three strategies were used to obtain selection gains: direct and indirect selection, an index based on "ranks," and the Smith and Hazel index. In the 2017 crop season in Brazil, 420 wheat lines from the F 5 generation were conducted in families with intercalary controls. High heritability of spike weight, number of kernels, and total kernel weight resulted in the best direct selection gains. The selection of plants with a high number of tillers resulted in grain yield improvement. The use of selection indexes is important in advanced wheat lines; they promote genetic gains distributed among agronomic traits.

Core Ideas The confidence interval (CI) of Pearson’s correlation coefficient (r) was investigated.Confidence interval width is inversely proportional to r and sample size (n).It is recommended to use 1000 or more bootstrap replicates in order to not underestimate CI width (CIw).A model to estimate CIw as a function of n and r is proposed. The nonparametric bootstrap percentile method has been widely used to estimate confidence intervals (CI) for Pearson’s product‐moment correlation coefficient (r). However, because most studies provide results for specific crops and pre‐stablished CIs, an innovative approach to CI estimation is needed. The aim of this study was to propose a model that predicts CI width (CIw) as a function of the sample size (n) and the strength of association among traits. Additionally, we also investigated the extent to which the number of bootstrap replicates (BRs) influences CI estimation. Seventy‐eight different r magnitudes from a maize field experiment were used. The 95% CI half‐width for each trait combination was estimated based on 991 different sample sizes and seven different numbers of BRs. A simple nonlinear model with n and r as predictors is proposed for estimating the CIw: , where δ, β0, and β1 are the model coefficients. Based on our data, the fitted model was: . This model exhibited excellent goodness of fit (R2 = 0.988; root mean square error [RMSE] = 0.011). Considering an assumed magnitude of association (r), the n for a desired CIw can then be calculated as: . We also recommend using ≥1000 BRs, to prevent underestimating CIw. Finally, we present an intuitive table that provides previously estimated n for 9 levels of half‐widths for 95% CIs (0.05, 0.1,... 0.45) and 19 magnitudes for r (0.05, 0.10,..., 0.95).

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Experimental design without replication, such as Federer's augmented block design, allows us to determine productivity, adaptability and stability in multi-environment trials. This work aimed to select productive wheat lines with high adaptability and stability in preliminary trials. The grain yield of 140 homozygous wheat lines was measured in 2015 at three locations. The cultivar TBIO Mestre was used as a check. Genetic parameters were evaluated by mixed models, and selection was based on the harmonic mean of the relative performance of the genetic values (HMRPGV) using models 74 (individual analysis) and 75 (joint analysis) of Selegen software. In the joint analysis, 33 wheat lines stood out in terms of productivity, adaptability and stability. These lines have the potential to be evaluated in Value for Cultivation and Use (VCU) trials for future release of new wheat cultivars.