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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.

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Soybean [Glycine max (L.) Merril] is one of the main crops produced worldwide, and on‐farm yields have increased considerably in the last decades in Brazil. We evaluated the genetic gain for agronomic, phenological, and end‐use quality traits in 29 cultivars in the South Region, and in 38 cultivars in the Midwest Region in Brazil, released from 1966 to 2011. Field trials were conducted in Macroregions 1, 2, and 4, in 2016–2017, 2017–2018, and 2018–2019 crop seasons. The best linear unbiased predictors (BLUP) of the cultivars were obtained for each trait using a linear model. The BLUPs were regressed with the year of release using linear and quadratic regression models. The rates of genetic gain for seed yield ranged from 11.98 to 15.31 kg ha–1 yr–1 (0.33 to 0.42% yr–1) in the South Region, and from 13.58 to 21.84 kg ha–1 yr–1 (0.47 to 0.77% yr–1) in the Midwest Region. New cultivars presented taller plants and more seed oil content, oil and protein yield, and lower seed weight, days to flowering, days to maturity, and seed protein content than old cultivars in the South Region, although with differences between the Macroregions. In the Midwest Region, new cultivars showed higher seed oil content, oil and protein yield, and lower bottom pod height and seed protein content than old cultivars. Our results showed that breeding programs have been efficient to improve soybean yield and other traits across the years, without yield plateaus in sight.

Asian soybean rust (ASR) causes large reductions in soybean yield, affecting the entire grain market. With low fungicide e ciency, the use of resistant cultivars can be an economical, safe, e cient, and sustainable control alternative. However, the great variability and aggressiveness of ASR and the use of Rpp genes are limited. Thus, gene pyramiding is a promising strategy for the development of cultivars with high resistance to a greater number of isolates. Thus, the aim of this study was to evaluate sister lines with different pyramided Rpp gene for resistance to Phakopsora pachyrhizi and identify which combination of Rpp genes had higher levels of resistance under eld conditions. All Rpp-pyramided lines showed higher levels of resistance, with signi cant reductions in sporulation levels (SL), number of uredinia per lesion (NoU), and frequency of lesions with uredinia (%LU), compared to the resistance sources PI200487 (Rpp5), PI200492 (Rpp1), PI230970 (Rpp2), PI459025A (Rpp4), PI506764 (Rpp3, 5), PI587880A (Rpp1-b), PI594538A (Rpp1-b), and PI594723 (Rpp1-b). Rpp-pyramided lines carrying Rpp1-b + Rpp1-b, Rpp2 + Rpp1-b, Rpp4 + Rpp1-b, and single gene Rpp1-b were classi ed as "highly resistant". Furthermore, one sister line, 52117-57 (Rpp2 + Rpp1-b), showed immunity under eld conditions. The Rpppyramided genes are an alternative for achieving high resistance levels against ASR.