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While sparse testing methods have been proposed by researchers to improve the efficiency of genomic selection (GS) in breeding programs, there are several factors that can hinder this. In this research, we evaluated four methods (M1-M4) for sparse testing allocation of lines to environments under multi-environmental trails for genomic prediction of unobserved lines. The sparse testing methods described in this study are applied in a two-stage analysis to build the genomic training and testing sets in a strategy that allows each location or environment to evaluate only a subset of all genotypes rather than all of them. To ensure a valid implementation, the sparse testing methods presented here require BLUEs (or BLUPs) of the lines to be computed at the first stage using an appropriate experimental design and statistical analyses in each location (or environment). The evaluation of the four cultivar allocation methods to environments of the second stage was done with four data sets (two large and two small) under a multi-trait and uni-trait framework. We found that the multi-trait model produced better genomic prediction (GP) accuracy than the uni-trait model and that methods M3 and M4 were slightly better than methods M1 and M2 for the allocation of lines to environments. Some of the most important findings, however, were that even under a scenario where we used a training-testing relation of 15-85%, the prediction accuracy of the four methods barely decreased. This indicates that genomic sparse testing methods for data sets under these scenarios can save considerable operational and financial resources with only a small loss in precision, which can be shown in our cost-benefit analysis.

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Grain yield and stay-green drought adaptation trait are important targets of selection in grain sorghum breeding for broad adaptation to a range of environments. Genomic prediction for these traits may be enhanced by joint multi-trait analysis. The objectives of this study were to assess the capacity of multi-trait models to improve genomic prediction of parental breeding values for grain yield and stay-green in sorghum by using information from correlated auxiliary traits, and to determine the combinations of traits that optimize predictive results in specific scenarios. The dataset included phenotypic performance of 2645 testcross hybrids across 26 environments as well as genomic and pedigree information on their female parental lines. The traits considered were grain yield (GY), stay-green (SG), plant height (PH), and flowering time (FT). We evaluated the improvement in predictive performance of multi-trait G-BLUP models relative to single-trait G-BLUP. The use of a blended kinship matrix exploiting pedigree and genomic information was also explored to optimize multi-trait predictions. Predictive ability for GY increased up to 16% when PH information on the training population was exploited through multi-trait genomic analysis. For SG prediction, full advantage from multi-trait G-BLUP was obtained only when GY information was also available on the predicted lines per se, with predictive ability improvements of up to 19%. Predictive ability, unbiasedness and accuracy of predictions from conventional multi-trait G-BLUP were further optimized by using a combined pedigree-genomic relationship matrix. Results of this study suggest that multi-trait genomic evaluation combining routinely measured traits may be used to improve prediction of crop productivity and drought adaptability in grain sorghum.

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KEY MESSAGE: The use of a kinship matrix integrating pedigree- and marker-based relationships optimized the performance of genomic prediction in sorghum, especially for traits of lower heritability. Selection based on genome-wide markers has become an active breeding strategy in crops. Genomic prediction models can make use of pedigree information to account for the residual polygenic effects not captured by markers. Our aim was to evaluate the impact of using pedigree and genomic information on prediction quality of breeding values for different traits in sorghum. We explored BLUP models that use weighted combinations of pedigree and genomic relationship matrices. The optimal weighting factor was empirically determined in order to maximize predictive ability after evaluating a range of candidate weights. The phenotypic data consisted of testcross evaluations of sorghum parental lines across multiple environments. All lines were genotyped, and full pedigree information was available. The performance of the best predictive combined matrix was compared to that of models fitting the component matrices independently. Model performance was assessed using cross-validation technique. Fitting a combined pedigree-genomic matrix with the optimal weight always yielded the largest increases in predictive ability and the largest reductions in prediction bias relative to the simple G-BLUP. However, the weight that optimized prediction varied across traits. The benefits of including pedigree information in the genomic model were more relevant for traits with lower heritability, such as grain yield and stay-green. Our results suggest that the combination of pedigree and genomic relatedness can be used to optimize predictions of complex traits in crops when the additive variation is not fully explained by markers.

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The study of QTL x environment interaction (QEI) is important for understanding genotype x environment interaction (GEI) in many quantitative traits. For modeling GEI and QEI, factorial regression (FR) models form a powerful class of models. In FR models, covariables (contrasts) defined on the levels of the genotypic and/or environmental factor(s) are used to describe main effects and interactions. In FR models for QTL expression, considerable numbers of genotypic covariables can occur as for each putative QTL an additional covariable needs to be introduced. For large numbers of genotypic and/or environmental covariables, least square estimation breaks down and partial least squares (PLS) estimation procedures become an attractive alternative. In this paper we develop methodology for analyzing QEI by FR for estimating effects and locations of QTLs and QEI and interpreting QEI in terms of environmental variables. A randomization test for the main effects of QTLs and QEI is presented. A population of F2 derived F3 families was evaluated in eight environments differing in drought stress and soil nitrogen content and the traits yield and anthesis silking interval (ASI) were measured. For grain yield, chromosomes 1 and 10 showed significant QEI, whereas in chromosomes 3 and 8 only main effect QTLs were observed. For ASI, QTL main effects were observed on chromosomes 1, 2, 6, 8, and 10, whereas QEI was observed only on chromosome 8. The assessment of the QEI at chromosome 1 for grain yield showed that the QTL main effect explained 35.8% of the QTL + QEI variability, while QEI explained 64.2%. Minimum temperature during flowering time explained 77.6% of the QEI. The QEI analysis at chromosome 10 showed that the QTL main effect explained 59.8% of the QTL + QEI variability, while QEI explained 40.2%. Maximum temperature during flowering time explained 23.8% of the QEI. Results of this study show the possibilities of using FR for mapping QTL and for dissecting QEI in terms of environmental variables. PLS regression is efficient in accounting for background noise produced by other QTLs.

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