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.

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. 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.

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.