Motivation Multivariate data are common in biological experiments and using the information on multiple traits is crucial to make better decisions for treatment recommendations or genotype selection. However, identifying genotypes/treatments that combine high performance across many traits has been a challenger task. Classical linear multi-trait selection indexes are available, but the presence of multicollinearity and the arbitrary choosing of weighting coefficients may erode the genetic gains. Results We propose a novel approach for genotype selection and treatment recommendation based on multiple traits that overcome the fragility of classical linear indexes. Here, we use the distance between the genotypes/treatment with an ideotype defined a priori as a multi-trait genotype-ideotype distance index (MGIDI) to provide a selection process that is unique, easy-to-interpret, free from weighting coefficients and multicollinearity issues. The performance of the MGIDI index is assessed through a Monte Carlo simulation study where the percentage of success in selecting traits with desired gains is compared with classical and modern indexes under different scenarios. Two real plant datasets are used to illustrate the application of the index from breeders and agronomists’ points of view. Our experimental results indicate that MGIDI can effectively select superior treatments/genotypes based on multi-trait data, outperforming state-of-the-art methods, and helping practitioners to make better strategic decisions towards an effective multivariate selection in biological experiments. Availability and implementation The source code is available in the R package metan (https://github.com/TiagoOlivoto/metan) under the function mgidi(). Supplementary information Supplementary data are available at Bioinformatics online.

The multicollinearity in path analysis was investigated in different scenarios. A biometrical approach identified the multicollinearity‐generating traits. Data derived from averages overestimated the correlation coefficients. The use of all sampled observations increased the accuracy in path analysis. A simple sample tracking method that reduces multicollinearity is proposed. Some data arrangement methods often used may mask correlation coefficients among explanatory traits, increasing multicollinearity in multiple regression analysis. This study was performed to determine if the harmful effects of multicollinearity might be reduced in the estimation of the X′X correlation matrix among explanatory traits. For this, data on 45 treatments (15 maize [Zea mays L.] hybrids sown in three places) were used. Three path analysis methods (traditional, with k inclusion, and traditional with trait exclusion) were tested in two scenarios: with X′X matrix estimated with all sampled observations (ASO, n = 900) and with the X′X matrix estimated with the average values of each plot (AVP, n = 180). The condition number (CN) was reduced from 3395 to 2004 when the matrix was estimated with all observations. On average, the factors that inflate the variance of regression coefficients were increased by 61% in the AVP scenario. The addition of the k coefficient reduced the CN to 85.40 and 51.17 for the ASO and AVP scenarios, respectively. Exclusion of multicollinearity‐generating traits was more effective in the ASO than the AVP scenario, resulting in CNs of 29.62 and 63.66, respectively. The largest coefficient of determination (0.977) and the smallest noise (0.150) were obtained in the ASO scenario after the exclusion of the multicollinearity‐generating traits. The use of all sampled observations does not mask the individual variances and reduces the magnitude of the correlations among explanatory traits in 90% of cases, improving the accuracy of biological studies involving path analysis.

Irrigated rice (Oryza sativa L.) is a crop of extreme social and economic importance in Brazil, and the state of Rio Grande do Sul accounts for >70% of the national production. The Brazilian Agricultural Research Corporation (Embrapa) is focused on rice breeding, with the aim of developing cultivars with significantly increased grain yield and improved sustainability. The objective of this study was to estimate the genetic progress of 45 yr of the irrigated rice breeding program of Embrapa in Southern Brazil from 1972 to 2016 by conducting a comparative analysis of cultivars in the same environment and by meta‐analysis of line yield assays. The estimates were results from a meta‐analysis obtained by evaluating 455 genotypes in 145 trials of regional line yield and value for cultivation and use of 44 agricultural crop seasons, and by comparing cultivars obtained by evaluating 25 cultivars in 10 agricultural crop seasons. Genetic gains were evaluated for grain yield, plant height, and days to flowering. The cultivars released by the breeding program were also evaluated for important agronomic characters. The genetic estimates determined a genetic progress for grain yield via meta‐analysis and via comparison of cultivars of 0.62 (37.91 kg yr−1) and 0.73% (47.78 kg yr−1), respectively. It was also verified that during the period there was a reduction in plant height and days to flowering. Three distinct historical phases that defined changes in research focus and in genetic gains can be described: (i) 1972 to 1983, before the rice Green Revolution; (ii) 1983 to 2000, after the rice Green Revolution; and (iii) 2000 to 2016, selection intensification for industrial grain quality attributes. Other relevant genetic aspects, selection strategies, and phases of the breeding program were discussed.

Resumo -O objetivo deste trabalho foi identificar correlações canônicas entre caracteres morfológicos e componentes da produção de genótipos de trigo de duplo propósito, sob diferentes manejos de corte. Os experimentos foram realizados em 2013 e 2014, no delineamento de blocos ao acaso, em arranjo fatorial com cinco genótipos (BRS Tarumã, BRS Umbu, BRS Figueira, BRS Guatambu e BRS 277), quatro manejos de corte (sem corte, um corte, dois cortes e três cortes) e três repetições. Os grupos canônicos foram estabelecidos entre os caracteres morfológicos (grupo 1) e os componentes de produção (grupo 2). No grupo 1, foram avaliados número de perfilhos, diâmetro do colmo principal e dos perfilhos, e número de perfilhos férteis; no grupo 2, foram avaliados número de grãos por espiga e de espigas por metro quadrado, massa de grãos por espiga e de mil grãos, produtividade de grãos e peso hectolítrico. A correlação entre os grupos 1 e 2 depende do manejo de corte adotado. O diâmetro do colmo principal (nos manejos sem e com um corte), o diâmetro dos perfilhos (dois cortes), e o número total de perfilhos e de perfilhos férteis por planta (três cortes) devem ser priorizados para seleção de genótipos superiores quanto à produtividade de grãos e ao peso hectolítrico.Termos para indexação: Triticum aestivum, análise multivariada, manejo de corte, seleção indireta. Canonical correlations between morphological traits and yield components in dual-purpose wheatAbstract -The objective of this work was to identify canonical correlations between morphological traits and yield components in dual-purpose wheat, under different cutting managements. The experiments were carried out in 2013 and 2014, under a complete block design, in a factorial arrangement with five genotypes (BRS Tarumã, BRS Umbu, BRS Figueira, BRS Guatambu, and BRS 277), four cutting managements (no cuts, one cut, two cuts, and three cuts), and three replicates. The canonical groups were established between morphological traits (group 1) and yield components (group 2). In group 1, number of tillers, diameter of the main stem and of the tillers, and number of fertile tillers were evaluated; in group 2, the number of grains per spike and of spikes per square meter, the mass of grains per spike and of a thousand grains, grain yield, and hectoliter weight were evaluated. The correlation between groups 1 and 2 depends on the adopted cutting management. The diameter of the main stem (in the managements without and with one cut), tiller diameter (two cuts), and the total number of tillers and of fertile tillers per plant (three cuts) should be prioritized for selection of superior genotypes as to grain yield and hectoliter weight.

The main aim of this study was to investigate the phenotypic correlation of yield component traits using several environmental stratifications methods. We also aimed to propose cause and effect of relationships for grain yield components in soybean genotypes under several environmental conditions. The tests were conducted in the agricultural year of 2013/2014 in four growing sites in Rio Grande do Sul, Brazil. The experimental arrangement was randomized blocks in factorial scheme (11 x 4), consisting eleven soybean genotypes in four environments with four repetitions each. All the growing environments Tapera-RS, Derrubadas-RS and Frederico Westphalen-RS were classified as favorable for soybean cultivation. The traits such as total number of pods per plant, number of branches and number of pods with 2-3 grains showed significant linear correlations with grain yield in both methods of analysis. The path analysis was applied under favorable and unfavorable environments to accurately estimate the direct and indirect effect of traits on soybean grain yield. The mass of a thousand grains and plant height were highly associated with grain yield but mostly influenced by environmental effects. The total number of pods should be prioritized for selecting superior soybean genotypes due to its direct and indirect effects on grain yield. It has shown constant in all environmental conditions. The direct effects of number of branches and number of pods (with one grain) presented distinct effects on yield in favorable and unfavorable environments.

The objective of this work was to evaluate the adaptability and multi-trait stability of wheat (Triticum aestivum) genotypes according to the phenotypic index of seed vigor (PIV). Thirty wheat genotypes were grown in seven environments in the state of Rio Grande do Sul, Brazil, during one crop season. In each environment, a randomized complete block design with three replicates was used. The PIV was elaborated from the following traits: first germination count, germination percentage, accelerated aging, and electrical conductivity. The evaluated phenotypic index makes it possible to define macroenvironments for the production of wheat seeds with high physiological potential and to understand the implications of the genotype x environment interaction. The phenotypic index of seed vigor is effective to rank genotypes considering multi-trait selection related to the vigor of wheat seeds produced in Southern Brazil.

ABSTRACT. Methodologies using restricted maximum likelihood/ best linear unbiased prediction (REML/BLUP) in combination with sequential path analysis in maize are still limited in the literature. Therefore, the aims of this study were: i) to use REML/BLUPbased procedures in order to estimate variance components, genetic parameters, and genotypic values of simple maize hybrids, and ii) to fit stepwise regressions considering genotypic values to form a path diagram with multi-order predictors and minimum multicollinearity that explains the relationships of cause and effect among grain yieldrelated traits. Fifteen commercial simple maize hybrids were evaluated in multi-environment trials in a randomized complete block design with four replications. The environmental variance (78.80%) and genotypevs-environment variance (20.83%) accounted for more than 99% of the phenotypic variance of grain yield, which difficult the direct selection of breeders for this trait. The sequential path analysis model allowed the selection of traits with high explanatory power and minimum multicollinearity, resulting in models with elevated fit (R 2 > 0.9 and ε < 0.3). The number of kernels per ear (NKE) and thousand-kernel weight (TKW) are the traits with the largest direct effects on grain yield (r = 0.66 and 0.73, respectively). The high accuracy of selection (0.86 and 0.89) associated with the high heritability of the average (0.732 and 0.794) for NKE and TKW, respectively, indicated good reliability and prospects of success in the indirect selection of hybrids with highyield potential through these traits. The negative direct effect of NKE on TKW (r = -0.856), however, must be considered. The joint use of mixed models and sequential path analysis is effective in the evaluation of maize-breeding trials.

ABSTRACT. The wheat crop presents sensitivity to the environmental conditions culminating in the genotype x environment interaction, being crucial the use of different methodologies to guide the positioning of genotypes to certain cultivation environments. The objective of this study was to estimate the adaptability and phenotypic stability of wheat genotypes grown in the State of Rio Grande do Sul using univariate and multivariate techniques and mixed models. The yield data of 42 2 V.J. Szareski et al. Genetics and Molecular Research 16 (3): gmr16039735wheat genotypes evaluated in five environments (Cachoeira do Sul, Passo Fundo, Santo Augusto, São Gabriel, and São Luiz Gonzaga) were used in the 2012 and 2013 crop seasons. In each experiment, a randomized complete block design was used, with three replicates. In the evaluation of the genotype x environment interaction, the sum of squares relative to contribution index, the methodology based on the univariate method of Annicchiarico (1992), the multivariate method (AMMI), and the mixed models (REML and MHPRVG) were used. The favorable environments expressed by the univariate method referred to São Gabriel, Cachoeira do Sul, Passo Fundo, Santo Augusto, and São Luiz Gonzaga; for the multivariate method, only Santo Augusto was favorable to the productivity character. The genotypes CD 121 and TBIO Tibagi were adapted and stable for the univariate and multivariate methods. The genotypes TBIO Sinuelo, Quartzo, BRS 327, Mirante, Topázio, Guamirim, TBIO Seleto, Ametista, TBIO Mestre, and BRS Louro were superior through the mixed model approach. The different strategies to estimate the adaptability and phenotypic stability allowed indicating and recommending the best environments and genotypes efficiently to obtain increases in wheat grain yield.