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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.

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 metabolic variability of fruit from Butia spp. (Arecaceae) genotypes from different geographical locations was characterized using untargeted metabolomics by liquid chromatography-mass spectrometry (LC-MS) followed by multivariate data analyses. Principal component analysis (PCA) and partial least-squares discriminant analysis (PLS-DA) from LC-MS data sets showed a clear distinction among Butia catarinensis, Butia odorata, Butia paraguayensis, and Butia yatay. The major metabolites that contributed to species discrimination were primary metabolites including sugars and organic acids and specialized metabolites such as tetrahydroxy-trans-stilbene and rutin. B. odorata fruit from Tapes, RS, Brazil, showed a high content of organic acids and flavonoids, whereas B. odorata fruits from Capão do Leão, RS, Brazil, showed a high sugar content. The results demonstrate that LC-ESI-qToF-MS-based metabolic profiling coupled with chemometric analysis can be used to discriminate among Butia species and between geographical origins of B. odorata and to identify primary and specialized metabolites responsible for the discrimination.

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.

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 was to identify phenotypic and genotypic associations, and cause-and-effect relations of secondary components on primary components to establish criteria in the indirect