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Abstract Soybean [Glycine max (L.) Merr.] is a significant source of protein and oil and is also widely used as animal feed. Thus, developing lines that are superior in terms of yield, protein, and oil content is important to feed the ever‐growing population. As opposed to high‐cost phenotyping, genotyping is both cost and time efficient for breeders because evaluating new lines in different environments (location–year combinations) can be costly. Several genomic prediction (GP) methods have been developed to use the marker and environment data effectively to predict the yield or other relevant phenotypic traits of crops. Our study compares a conventional GP method (genomic best linear unbiased predictor [GBLUP]), a kernel method (Gaussian kernel [GK]), an artificial‐intelligence (AI) method (deep learning [DL]), and a hybrid method that corresponds to the emulation of a DL model using a kernel method (an arc‐cosine kernel [AK]) in terms of their prediction accuracies for predicting grain yield, oil, and protein using data from the soybean nested association mapping experiment (1,379 genotypes tested in six environments, all genotypes in all environments). The relative performance of the four methods varied with the response variable and whether the model includes the genotype × environmental interaction (G×E) effects or not. The GBLUP consistently showed better performances, whereas GK and AK followed a similar pattern to GBLUP and DL performed slightly worse than the other three methods in most of the cases; however, this may also be attributed to suboptimal hyperparameters. The DL method performed particularly worse than the other three methods in presence of the G×E effects.

Abstract 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.

Wheat ( L.) breeding programs test experimental lines in multiple locations over multiple years to get an accurate assessment of grain yield and yield stability. Selections in early generations of the breeding pipeline are based on information from only one or few locations and thus materials are advanced with little knowledge of the genotype × environment interaction (G × E) effects. Later, large trials are conducted in several locations to assess the performance of more advanced lines across environments. Genomic selection (GS) models that include G × E covariates allow us to borrow information not only from related materials, but also from historical and correlated environments to better predict performance within and across specific environments. We used reaction norm models with several cross-validation schemes to demonstrate the increased breeding efficiency of Kansas State University’s hard red winter wheat breeding program. The GS reaction norm models line effect (L) + environment effect (E), L + E + genotype environment (G), and L + E + G + (G × E) effects) showed high accuracy values (>0.4) when predicting the yield performance in untested environments, sites or both. The GS model L + E + G + (G × E) presented the highest prediction ability ( = 0.54) when predicting yield in incomplete field trials for locations with a moderate number of lines. The difficulty of predicting future years (forward prediction) is indicated by the relatively low accuracy ( = 0.171) seen even when environments with 300+ lines were included.