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Predicting maize single-crosses genotypic values under unbalanced number of genotypes and environments The more difficult phase and that demands more funding in a maize breeding program is the experimental evaluation of the hybrids, because usually a high number of hybrids needs to be evaluated in several environments. Then, both the number of environments and hybrids are limited by the resources available, which could lead to a reduction in the number of environments, and therefore, sets of hybrids are commonly tested in different environments leading to unbalanced comparisons among the hybrids. The statistical methodology known as REM/BLUP has been widely used in animal breeding, but in plant breeding programs its use has been restricted to perennial crops where unbalanced experiments are very common. There is limited information about the reliability of the REM/BLUP method using experimental data for the genotypic values prediction under unbalanced experiments for annual crops breeding programs. Thus, the objective of this research was to assess whether the REM/BLUP method could be useful to predict the genotypic values of maize single-crosses under unbalanced situations. A set of 256 single-crosses was evaluated in a 16 x 16 lattice design with two replications per environment in 13 environments, and the traits analyzed were grain yield, plant lodging and plant height. As the evaluation consisted of 26 observations for each single-cross, their adjusted overall means computed by the least squares method were considered as their genotypic values for the sake of comparisons with the genotypic predictions by REM/BLUP method. The predictions of the single-crosses were computed considering unbalanced sets of hybrids within environments and unbalanced sets of environments. The data were submitted to a random unbalance and each situation was simulated 1,000 times using the bootstrap method. Coefficients of correlation were then computed between the predicted genotypic values and the adjusted overall means, and their values were squared to obtain the R values; thus 1,000 R values were obtained for each considered situation. Also, selection were performed using the predict values and the adjusted overall means of the single-crosses, and the percentage of coincidence were computed. Regardless of the trait analyzed, the R values and the percentage of coincidence of the selected single-crosses showed that the REM/BLUP predict with high accuracy the genotypic values of the single-crosses up to 20% of losses of hybrids within environments and up to 23% of environments reduction. It should be noted that grain yield showed a significant cross-over interaction, and even so the REM/BLUP predicted the genotypic values of the hybrids with high accuracy. Thus, the REM/BLUP method can be considered as a valuable tool in maize breeding programs to predict the genotypic values of the hybrids under unbalanced data. However, the results also pointed out that there is a limit for its accuracy, which is around 20% of unbalanced data.

Predição de valores genotípicos de híbridos de milho com desbalanceamentos de genótipos e ambientes