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.

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.

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.

The aim of this study was to evaluate the phenotypic interrelation among agronomic characters associated with wheat grain yield of the main Brazilian cultivated genotypes through path analysis in two environments. The tests were conducted in Tenente Portela-RS and Braga-RS. The experimental design was randomized blocks arranged in factorial scheme, 2 locations × 17 genotypes and 3 repetitions. The evaluated characters were plant height, main stem spike mass, tiller spikes mass, main stem spike grains number, tiller spikes grains number, main stem spike grains mass, tiller spikes grains mass, mass of a thousand grains and grain yield. Path analysis was performed for characters associated with grain yield. The results show that main stem spike grains mass, main stem spike grains number, and tiller spikes grains mass have direct effects on grain yield. Larger main stem spike grains mass, main stem spike grains number, and tiller spikes grains mass should be considered for achieving genotypes of high grain yield potential.

R E S U M ONo Planalto do Rio Grande do Sul, Brasil, local de clima subtropical, o cultivo da segunda safra de verão com a cultura da soja (safrinha), semeada após o cultivo de milho, vem agregando importância econômica, aumentando progressivamente sua área de cultivo e possibilitando maior produção de grãos durante o período de verão. Estudos dos caracteres dos genótipos semeados nessa condição específica, com efeito da redução da luminosidade, podem auxiliar nas futuras seleções em programas de melhoramento vegetal da cultura. O objetivo do trabalho foi avaliar as relações lineares entre caracteres de soja (Glycine max L.) e identificar caracteres para a seleção indireta, em segunda safra de cultivo de verão, em região subtropical. Dezoito cultivares de soja foram avaliadas em três locais do Rio Grande do Sul. As semeaduras foram realizadas em 09/01/2013, 10/01/2013 e 24/01/2013, para os experimentos conduzidos em Barra do Guarita, Vista Gaúcha e Tenente Portela, respectivamente. Foi utilizado o delineamento de blocos ao acaso, com quatro repetições. Foram mensurados os caracteres altura de inserção do primeiro legume, altura de planta, massa de cem grãos e produtividade de grãos. Realizou-se a análise de variância dos caracteres. Foi investigada a relação entre os caracteres por meio de análises de correlação e de trilha. No cultivo de soja em época de safrinha (segunda safra de verão), em clima subtropical, a altura de planta tem relação linear positiva com produtividade de grãos e pode ser usada para seleção indireta de cultivares mais produtivas. Palavras-chave: Glycine max L., relações lineares, seleção indireta. A B S T R A C TIn the highlands of Rio Grande do Sul, Brazil, with subtropical climate, the cultivation of the second summer crop with soybean (off-season), sowed after maize, has been adding economic importance, increasing progressively its cultivation area, and allowing greater grain yield during the summer period. Studies of traits of genotypes sown in this particular condition, with reducing luminosity effect, can assist in future selections in soybean plant breeding programs. The objective of this study was to evaluate the linear relations among soybean traits (Glycine max L.) and identify traits for indirect selection in the second crop of summer cultivation, in subtropical region. Eighteen soybean cultivars were evaluated in three locations of Rio Grande do Sul. Sowing was performed on Jan/09/2013, Jan/10/2013, and Jan/24/2013 for the experiments carried out in Barra do Guarita, Vista Gaúcha, and Tenente Portela, respectively. The randomized block design with four replications was utilized. The traits insertion of the first pod height, plant height, one hundred grains weight, and grain yield were measured. The traits analysis of variance was performed. Relation among traits was investigated through correlation and path analysis. In off-season soybean cultivation (second summer crop) in subtropical climate, plant height has positive linear relation with grain yield and it can be used for in...