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A genomic selection index (GSI) is a linear combination of genomic estimated breeding values that uses genomic markers to predict the net genetic merit and select parents from a nonphenotyped testing population. Some authors have proposed a GSI; however, they have not used simulated or real data to validate the GSI theory and have not explained how to estimate the GSI selection response and the GSI expected genetic gain per selection cycle for the unobserved traits after the first selection cycle to obtain information about the genetic gains in each subsequent selection cycle. In this paper, we develop the theory of a GSI and apply it to two simulated and four real data sets with four traits. Also, we numerically compare its efficiency with that of the phenotypic selection index (PSI) by using the ratio of the GSI response over the PSI response, and the PSI and GSI expected genetic gain per selection cycle for observed and unobserved traits, respectively. In addition, we used the Technow inequality to compare GSI vs. PSI efficiency. Results from the simulated data were confirmed by the real data, indicating that GSI was more efficient than PSI per unit of time.

Genotyping-by-sequencing (GBS) technologies have proven capacity for delivering large numbers of marker genotypes with potentially less ascertainment bias than standard single nucleotide polymorphism (SNP) arrays. Therefore, GBS has become an attractive alternative technology for genomic selection. However, the use of GBS data poses important challenges, and the accuracy of genomic prediction using GBS is currently undergoing investigation in several crops, including maize, wheat, and cassava. The main objective of this study was to evaluate various methods for incorporating GBS information and compare them with pedigree models for predicting genetic values of lines from two maize populations evaluated for different traits measured in different environments (experiments 1 and 2). Given that GBS data come with a large percentage of uncalled genotypes, we evaluated methods using nonimputed, imputed, and GBS-inferred haplotypes of different lengths (short or long). GBS and pedigree data were incorporated into statistical models using either the genomic best linear unbiased predictors (GBLUP) or the reproducing kernel Hilbert spaces (RKHS) regressions, and prediction accuracy was quantified using cross-validation methods. The following results were found: relative to pedigree or marker-only models, there were consistent gains in prediction accuracy by combining pedigree and GBS data; there was increased predictive ability when using imputed or nonimputed GBS data over inferred haplotype in experiment 1, or nonimputed GBS and information-based imputed short and long haplotypes, as compared to the other methods in experiment 2; the level of prediction accuracy achieved using GBS data in experiment 2 is comparable to those reported by previous authors who analyzed this data set using SNP arrays; and GBLUP and RKHS models with pedigree with nonimputed and imputed GBS data provided the best prediction correlations for the three traits in experiment 1, whereas for experiment 2 RKHS provided slightly better prediction than GBLUP for drought-stressed environments, and both models provided similar predictions in well-watered environments.

Genomic prediction is expected to considerably increase genetic gains by increasing selection intensity and accelerating the breeding cycle. In this study, marker effects estimated in 255 diverse maize (Zea mays L.) hybrids were used to predict grain yield, anthesis date, and anthesis-silking interval within the diversity panel and testcross progenies of 30 F2-derived lines from each of five populations. Although up to 25% of the genetic variance could be explained by cross validation within the diversity panel, the prediction of testcross performance of F2-derived lines using marker effects estimated in the diversity panel was on average zero. Hybrids in the diversity panel could be grouped into eight breeding populations differing in mean performance. When performance was predicted separately for each breeding population on the basis of marker effects estimated in the other populations, predictive ability was low (i.e., 0.12 for grain yield). These results suggest that prediction resulted mostly from differences in mean performance of the breeding populations and less from the relationship between the training and validation sets or linkage disequilibrium with causal variants underlying the predicted traits. Potential uses for genomic prediction in maize hybrid breeding are discussed emphasizing the need of (1) a clear definition of the breeding scenario in which genomic prediction should be applied (i.e., prediction among or within populations), (2) a detailed analysis of the population structure before performing cross validation, and (3) larger training sets with strong genetic relationship to the validation set.