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Sparse testing in genome‐enabled prediction in plant breeding can be emulated throughout different line allocations where some lines are observed in all environments (overlap) and others are observed in only one environment (nonoverlap). We studied three general cases of the composition of the sparse testing allocation design for genome‐enabled prediction of wheat (Triticum aestivum L.) breeding: (a) completely nonoverlapping wheat lines in environments, (b) completely overlapping wheat lines in all environments, and (c) a proportion of nonoverlapping/overlapping wheat lines allocated in the environments. We also studied several cases in which the size of the testing population was systematically decreased. The study used three extensive wheat data sets (W1, W2, and W3). Three different genome‐enabled prediction models (M1–M3) were used to study the effect of the sparse testing in terms of the genomic prediction accuracy. Model M1 included only main effects of environments and lines; M2 included main effects of environments, lines, and genomic effects; whereas the remaining model (M3) also incorporated the genomic × environment interaction (GE). The results show that the GE component of the genome‐based model M3 captures a larger genetic variability than the main genomic effects term from models M1 and M2. In addition, model M3 provides higher prediction accuracy than models M1 and M2 for the same allocation designs (different combinations of nonoverlapping/overlapping lines in environments and training set sizes). Overlapped sets of 30–50 lines in all the environments provided stable genomic‐enabled prediction accuracy. Reducing the size of the testing populations under all allocation designs decreases the prediction accuracy, which recovers when more lines are tested in all environments. Model M3 offers the possibility of maintaining the prediction accuracy throughout both extreme situations of all nonoverlapping lines and all overlapping lines.

In this study, we used genotype × environment interactions (G×E) models for hybrid prediction, where similarity between lines was assessed by pedigree and molecular markers, and similarity between environments was accounted for by environmental covariables. We use five genomic and pedigree models (M1-M5) under four cross-validation (CV) schemes: prediction of hybrids when the training set (i) includes hybrids of all males and females evaluated only in some environments (T2FM), (ii) excludes all progenies from a randomly selected male (T1M), (iii) includes all progenies from 20% randomly selected females in combination with all males (T1F), and (iv) includes one randomly selected male plus 40% randomly selected females that were crossed with it (T0FM). Models were tested on a total of 1888 wheat ( L.) hybrids including 18 males and 667 females in three consecutive years. For grain yield, the most complex model (M5) under T2FM had slightly higher prediction accuracy than the less complex model. For T1F, the prediction accuracy of hybrids for grain yield and other traits of the most complete model was 0.50 to 0.55. For T1M, Model M3 exhibited high prediction accuracies for flowering traits (0.71), whereas the more complex model (M5) demonstrated high accuracy for grain yield (0.5). For T0FM, the prediction accuracy for grain yield of Model M5 was 0.61. Including genomic and pedigree gave relatively high prediction accuracy even when both parents were untested. Results show that it is possible to predict unobserved hybrids when modeling genomic general combining ability (GCA) and specific combining ability (SCA) and their interactions with environments.

Genomic prediction models have been commonly used in plant breeding but only in reduced datasets comprising a few hundred genotyped individuals. However, pedigree information for an entire breeding population is frequently available, as are historical data on the performance of a large number of selection candidates. The single-step method extends the genomic relationship information from genotyped individuals to pedigree information from a larger number of phenotyped individuals in order to combine relationship information on all members of the breeding population. Furthermore, genomic prediction models that incorporate genotype x environment interactions (G x E) have produced substantial increases in prediction accuracy compared with single-environment genomic prediction models. Our main objective was to show how to use single- step genomic and pedigree models to assess the prediction accuracy of 58,798 CIMMYT wheat (Triticum aestivum L.) lines evaluated in several simulated environments in Ciudad Obregon, Mexico, and to predict the grain yield performance of some of them in several sites in South Asia (India, Pakistan, and Bangladesh) using a reaction norm model that incorporated G x E. Another objective was to describe the statistical and computational challenges encountered when developing the pedigree and single-step models in such large datasets. Results indicate that the genomic prediction accuracy achieved by models using pedigree only, markers only, or both pedigree and markers to predict various environments in India, Pakistan, and Bangladesh is higher (0.25-0.38) than prediction accuracy of models that use only phenotypic prediction (0.20) or do not include the G x E term.

The single most important decision in plant breeding programs is the selection of appropriate crosses. The ideal cross would provide superior predicted progeny performance and enough diversity to maintain genetic gain. The aim of this study was to compare the best crosses predicted using combinations of mid-parent value and variance prediction accounting for linkage disequilibrium (V) or assuming linkage equilibrium (V). After predicting the mean and the variance of each cross, we selected crosses based on mid-parent value, the top 10% of the progeny, and weighted mean and variance within progenies for grain yield, grain protein content, mixing time, and loaf volume in two applied wheat ( L.) breeding programs: Instituto Nacional de Investigacion Agropecuaria (INIA) Uruguay and CIMMYT Mexico. Although the variance of the progeny is important to increase the chances of finding superior individuals from transgressive segregation, we observed that the mid-parent values of the crosses drove the genetic gain but the variance of the progeny had a small impact on genetic gain for grain yield. However, the relative importance of the variance of the progeny was larger for quality traits. Overall, the genomic resources and the statistical models are now available to plant breeders to predict both the performance of breeding lines per se as well as the value of progeny from any potential crosses.

The leaf spotting diseases in wheat that include Septoria tritici blotch (STB) caused by , Stagonospora nodorum blotch (SNB) caused by , and tan spot (TS) caused by pose challenges to breeding programs in selecting for resistance. A promising approach that could enable selection prior to phenotyping is genomic selection that uses genome-wide markers to estimate breeding values (BVs) for quantitative traits. To evaluate this approach for seedling and/or adult plant resistance (APR) to STB, SNB, and TS, we compared the predictive ability of least-squares (LS) approach with genomic-enabled prediction models including genomic best linear unbiased predictor (GBLUP), Bayesian ridge regression (BRR), Bayes A (BA), Bayes B (BB), Bayes Cπ (BC), Bayesian least absolute shrinkage and selection operator (BL), and reproducing kernel Hilbert spaces markers (RKHS-M), a pedigree-based model (RKHS-P) and RKHS markers and pedigree (RKHS-MP). We observed that LS gave the lowest prediction accuracies and RKHS-MP, the highest. The genomic-enabled prediction models and RKHS-P gave similar accuracies. The increase in accuracy using genomic prediction models over LS was 48%. The mean genomic prediction accuracies were 0.45 for STB (APR), 0.55 for SNB (seedling), 0.66 for TS (seedling) and 0.48 for TS (APR). We also compared markers from two whole-genome profiling approaches: genotyping by sequencing (GBS) and diversity arrays technology sequencing (DArTseq) for prediction. While, GBS markers performed slightly better than DArTseq, combining markers from the two approaches did not improve accuracies. We conclude that implementing GS in breeding for these diseases would help to achieve higher accuracies and rapid gains from selection.

Wheat (Triticum aestivum L.) cultivars must possess suitable end- use quality for release and consumer acceptability. However, breeding for quality traits is often considered a secondary target relative to yield largely because of amount of seed needed and expense. Without testing and selection, many undesirable materi- als are advanced, expending additional resources. Here, we de- velop and validate whole-genome prediction models for end-use quality phenotypes in the CIMMYT bread wheat breeding pro- gram. Model accuracy was tested using forward prediction on breeding lines (n = 5520) tested in unbalanced yield trials from 2009 to 2015 at Ciudad Obregon, Sonora, Mexico. Quality parameters included test weight, 1000-kernel weight, hardness, grain and our protein, our yield, sodium dodecyl sulfate sedi- mentation, Mixograph and Alveograph performance, and loaf volume. In general, prediction accuracy substantially increased over time as more data was available to train the model. Re ect- ing practical implementation of genomic selection (GS) in the breeding program, forward prediction accuracies (r) for quality parameters were assessed in 2015 and ranged from 0.32 (grain hardness) to 0.62 (mixing time). Increased selection intensity was possible with GS since more entries can be genotyped than phe- notyped and expected genetic gain was 1.4 to 2.7 times higher across all traits than phenotypic selection. Given the limitationsin measuring many lines for quality, we conclude that GS is a powerful tool to facilitate early generation selection for end-use quality in wheat, leaving larger populations for selection on yield during advanced testing and leading to better gain for both qual- ity and yield in bread wheat breeding programs.

The partial rust resistance genes Lr34 and Sr2 have been used extensively in wheat (Triticum aestivum L.) improvement, as they confer exceptional durability. Interestingly, the resistance of Lr34 is associated with the expression of leaf tip necrosis (LTN) and Sr2 with pseudo-black chaff (PBC). Genome-wide association mapping using CIMMYT's stem rust resistance screening nursery (SRRSN) wheat lines was done to identify genotyping-by-sequencing (GBS) markers linked to LTN and PBC. Phenotyping for these traits was done in Ithaca, New York (fall 2011); Njoro, Kenya (main and off-seasons, 2012), and Wellington, India (winter, 2013). Using the mixed linear model (MLM), 18 GBS markers were significantly associated with LTN. While some markers were linked to loci where the durable leaf rust resistance genes Lr34 (7DS), Lr46 (1BL), and Lr68 (7BL) were mapped, significant associations were also detected with other loci on 2BL, 5B, 3BS, 4BS, and 7BS. Twelve GBS markers linked to the Sr2 locus (3BS) and loci on 2DS, 4AL, and 7DS were significantly associated with PBC. This study provides insight into the complex genetic control of LTN and PBC. Further efforts to validate and study these loci might aid in determining the nature of their association with durable resistance.

Genomic selection (GS) is a methodology that can improve crop breeding efficiency. To implement GS, a training population (TP) with phenotypic and genotypic data is required to train a statistical model used to predict genotyped selection candidates (SCs). A key factor impacting prediction accuracy is the relationship between the TP and the SCs. This study used empirical data for quantitative adult plant resistance to stem rust of wheat (Triticum aestivum L.) to investigate the utility of a historical TP (TPH ) compared with a population-specific TP (TPPS ), the potential for TPH optimization, and the utility of TPH data when close relative data is available for training. We found that, depending on the population size, a TPPS was 1.5 to 4.4 times more accurate than a TPH , and TPH optimization based on the mean of the generalized coefficient of determination or prediction error variance enabled the selection of subsets that led to significantly higher accuracy than randomly selected subsets. Retaining historical data when data on close relatives were available lead to a 11.9% increase in accuracy, at best, and a 12% decrease in accuracy, at worst, depending on the heritability. We conclude that historical data could be used successfully to initiate a GS program, especially if the dataset is very large and of high heritability. Training population optimization would be useful for the identification of TPH subsets to phenotype additional traits. However, after model updating, discarding historical data may be warranted. More studies are needed to determine if these observations represent general trends.

Quantitative adult plant resistance (APR) to stem rust (Puccinia graminis f. sp. tritici) is an important breeding target in wheat (Triticum aestivum L.) and a potential target for genomic selection (GS). To evaluate the relative importance of known APR loci in applying GS, we characterized a set of CIMMYT germplasm at important APR loci and on a genome-wide profile using genotyping-by-sequencing (GBS). Using this germplasm, we describe the genetic architecture and evaluate prediction models for APR using data from the international Ug99 stem rust screening nurseries. Prediction models incorporating markers linked to important APR loci and seedling phenotype scores as fixed effects were evaluated along with the classic prediction models: Multiple linear regression (MLR), Genomic best linear unbiased prediction (G-BLUP), Bayesian Lasso (BL), and Bayes Cp (BCp). We found the Sr2 region to play an important role in APR in this germplasm. A model using Sr2 linked markers as fixed effects in G-BLUP was more accurate than MLR with Sr2 linked markers (p-value = 0.12), and ordinary G-BLUP (p-value = 0.15). Incorporating seedling phenotype information as fixed effects in G-BLUP did not consistently increase accuracy. Overall, levels of prediction accuracy found in this study indicate that GS can be effectively applied to improve stem rust APR in this germplasm, and if genotypes at Sr2 linked markers are available, modeling these genotypes as fixed effects could lead to better predictions.