Prediction of single-cross hybrid performance for grain yield and grain dry matter content in maize using AFLP markers associated with QTL

Prediction methods to identify single-cross hybrids with superior yield performance have the potential to greatly improve the efficiency of commercial maize (Zea mays L.) hybrid breeding programs. Our objectives were to (1) identify marker loci associated with quantitative trait loci for hybrid performance or specific combining ability (SCA) in maize, (2) compare hybrid performance prediction by genotypic value estimates with that based on general combining ability (GCA) estimates, and (3) investigate a newly proposed combination of the GCA model with SCA predictions from genotypic value estimates. A total of 270 hybrids was evaluated for grain yield and grain dry matter content in four Dent × Flint factorial mating experiments, their parental inbred lines were genotyped with 20 AFLP primer-enzyme combinations. Markers associated significantly with hybrid performance and SCA were identified, genotypic values and SCA effects were estimated, and four hybrid performance prediction approaches were evaluated. For grain yield, between 38 and 98 significant markers were identified for hybrid performance and between zero and five for SCA. Estimates of prediction efficiency (R ²) ranged from 0.46 to 0.86 for grain yield and from 0.59 to 0.96 for grain dry matter content. Models enhancing the GCA approach with SCA estimates resulted in the highest prediction efficiency if the SCA to GCA ratio was high. We conclude that it is advantageous for prediction of single-cross hybrids to enhance a GCA-based model with SCA effects estimated from molecular marker data, if SCA variances are of similar or larger importance as GCA variances.     

Genome-wide prediction for maize single-cross hybrids using the GBLUP model and validation in different crop seasons

The aim of this study was to perform genome-wide selection using a set of Dart-seq markers associated to the additive-dominant genomic best linear unbiased prediction (GBLUP) model to predict maize grain yield in different crop seasons and locations. Genotyping was performed with Dart-seq markers from 447 lines coming from a germplasm bank of a private maize breeding company. Crossing these lines provided 838 single-cross hybrids evaluated in six locations in the winter crop season of 2013 and 797 single-cross hybrids evaluated in four locations in the summer crop season of 2013/2014. Four k-fold levels were applied on the full panel of 23,153 Dart genotyping-by-sequencing markers and samples of 50% of the available markers. The different crop seasons were used as training and validation populations to estimate the predictive accuracy. The magnitude of the correlations between predicted and observed hybrids ranged from 0.82 to 0.89 in the winter crop season and from 0.56 to 0.76 in the summer crop season. The correlations between combinations tested in different crop seasons and locations were encouraging (0.53). Predictive ability was highly influenced by the genetic background and also by the interaction between crop seasons. The coincidences between the genomic values of the summer crop and winter crop, in terms of discard, were 89 and 90%. This result shows the possibility of using genomic prediction in breeding programs for initial discard of low-yielding genotypes. The GBLUP method was able to generate high correlations between predicted and observed hybrids, even at high levels of missing in k-fold and in different locations and crop seasons.     

Genomewide predictions from maize single-cross data

Maize (Zea mays L.) breeders evaluate many single-cross hybrids each year in multiple environments. Our objective was to determine the usefulness of genomewide predictions, based on marker effects from maize single-cross data, for identifying the best untested single crosses and the best inbreds within a biparental cross. We considered 479 experimental maize single crosses between 59 Iowa Stiff Stalk Synthetic (BSSS) inbreds and 44 non-BSSS inbreds. The single crosses were evaluated in multilocation experiments from 2001 to 2009 and the BSSS and non-BSSS inbreds had genotypic data for 669 single nucleotide polymorphism (SNP) markers. Single-cross performance was predicted by a previous best linear unbiased prediction (BLUP) approach that utilized marker-based relatedness and information on relatives, and from genomewide marker effects calculated by ridge-regression BLUP (RR-BLUP). With BLUP, the mean prediction accuracy (r _MG) of single-cross performance was 0.87 for grain yield, 0.90 for grain moisture, 0.69 for stalk lodging, and 0.84 for root lodging. The BLUP and RR-BLUP models did not lead to r _MG values that differed significantly. We then used the RR-BLUP model, developed from single-cross data, to predict the performance of testcrosses within 14 biparental populations. The r _MG values within each testcross population were generally low and were often negative. These results were obtained despite the above-average level of linkage disequilibrium, i.e., r ² between adjacent markers of 0.35 in the BSSS inbreds and 0.26 in the non-BSSS inbreds. Overall, our results suggested that genomewide marker effects estimated from maize single crosses are not advantageous (compared with BLUP) for predicting single-cross performance and have erratic usefulness for predicting testcross performance within a biparental cross.     

Prediction of maize single-cross hybrid performance: support vector machine regression versus best linear prediction

Accurate prediction of the phenotypic performance of a hybrid plant based on the molecular fingerprints of its parents should lead to a more cost-effective breeding programme as it allows to reduce the number of expensive field evaluations. The construction of a reliable prediction model requires a representative sample of hybrids for which both molecular and phenotypic information are accessible. This phenotypic information is usually readily available as typical breeding programmes test numerous new hybrids in multi-location field trials on a yearly basis. Earlier studies indicated that a linear mixed model analysis of this typically unbalanced phenotypic data allows to construct ɛ-insensitive support vector machine regression and best linear prediction models for predicting the performance of single-cross maize hybrids. We compare these prediction methods using different subsets of the phenotypic and marker data of a commercial maize breeding programme and evaluate the resulting prediction accuracies by means of a specifically designed field experiment. This balanced field trial allows to assess the reliability of the cross-validation prediction accuracies reported here and in earlier studies. The limits of the predictive capabilities of both prediction methods are further examined by reducing the number of training hybrids and the size of the molecular fingerprints. The results indicate a considerable discrepancy between prediction accuracies obtained by cross-validation procedures and those obtained by correlating the predictions with the results of a validation field trial. The prediction accuracy of best linear prediction was less sensitive to a reduction of the number of training examples compared with that of support vector machine regression. The latter was, however, better at predicting hybrid performance when the size of the molecular fingerprints was reduced, especially if the initial set of markers had a low information content.     

Prediction of maize hybrid performance using similarity in state and similarity by descent information

We evaluated the efficiency of the best linear unbiased predictor (BLUP) and the influence of the use of similarity in state (SIS) and similarity by descent (SBD) in the prediction of untested maize hybrids. Nine inbred lines of maize were crossed using a randomized complete diallel method. These materials were genotyped with 48 microsatellite markers (SSR) associated with the QTL regions for grain yield. Estimates of four coefficients of SIS and four coefficients of SBD were used to construct the additive genetic and dominance matrices, which were later used in combination with the BLUP for predicting genotypic values and specific combining ability (SCA) in unanalyzed hybrids under simulated unbalance. The values of correlations between the genotypic values predicted and the means observed, depending on the degree of unbalance, ranged from 0.48 to 0.99 for SIS and 0.40 to 0.99 using information from SBD. The results obtained for the SCA ranged from 0.26 to 0.98 using the SIS and 0.001 to 0.990 using the SBD information. It was also observed that the predictions using SBD showed less biased than SIS predictions demonstrating that the predictions obtained by these coefficients (SBD) were closer to the observed value, but were less efficient in the ranking of genotypes. Although the SIS showed a bias due to overestimation of relatedness, this type of coefficient may be used where low values are detected in the SBD in the group of parents because of its greater efficiency in ranking the candidates hybrids.     

Progressive heterosis in genetically defined tetraploid maize

Progressive heterosis, i.e., the additional hybrid vigor in double-cross tetraploid hybrids not found in their single-cross tetraploid parents, has been documented in a number of species including alfalfa,potato, and maize. In this study, four artificially induced maize tetraploids, directly derived from standard inbred lines, were crossed in pairs to create two single-cross hybrids. These hybrids were then crossed to create double-cross hybrids containing genetic material from all four original lines. Replicated fieldbased phenotyping of the materials over four years indicated a strong progressive heterosis phenotype in tetraploids but not in their diploid counterparts. In particular, the above ground dry weight phenotype of double-cross tetraploid hybrids was on average 34% and 56% heavier than that of the single-cross tetraploid hybrids and the double-cross diploid counterparts, respectively. Additionally,whole-genome resequencing of the original inbred lines and further analysis of these data did not show the expected spectrum of alleles to explain tetraploid progressive heterosis under the complementation of complete recessive model. These results underscore the reality of the progressive heterosis phenotype,its potential utility for increasing crop biomass production, and the need for exploring alternative hypothesis to explain it at a molecular level.     

Prediction of single-cross hybrid performance in maize using haplotype blocks associated with QTL for grain yield

Marker-based prediction of hybrid performance facilitates the identification of untested single-cross hybrids with superior yield performance. Our objectives were to (1) determine the haplotype block structure of experimental germplasm from a hybrid maize breeding program, (2) develop models for hybrid performance prediction based on haplotype blocks, and (3) compare hybrid performance prediction based on haplotype blocks with other approaches, based on single AFLP markers or general combining ability (GCA), under a validation scenario relevant for practical breeding. In total, 270 hybrids were evaluated for grain yield in four Dent × Flint factorial mating experiments. Their parental inbred lines were genotyped with 20 AFLP primer–enzyme combinations. Adjacent marker loci were combined into haplotype blocks. Hybrid performance was predicted on basis of single marker loci and haplotype blocks. Prediction based on variable haplotype block length resulted in an improved prediction of hybrid performance compared with the use of single AFLP markers. Estimates of prediction efficiency (R ² ) ranged from 0.305 to 0.889 for marker-based prediction and from 0.465 to 0.898 for GCA-based prediction. For inter-group hybrids with predominance of general over specific combining ability, the hybrid prediction from GCA effects was efficient in identifying promising hybrids. Considering the advantage of haplotype block approaches over single marker approaches for the prediction of inter-group hybrids, we see a high potential to substantially improve the efficiency of hybrid breeding programs. Tobias A. Schrag and Hans Peter Maurer contributed equally to this work.     

Prediction of hybrid performance in maize using molecular markers and joint analyses of hybrids and parental inbreds

The identification of superior hybrids is important for the success of a hybrid breeding program. However, field evaluation of all possible crosses among inbred lines requires extremely large resources. Therefore, efforts have been made to predict hybrid performance (HP) by using field data of related genotypes and molecular markers. In the present study, the main objective was to assess the usefulness of pedigree information in combination with the covariance between general combining ability (GCA) and per se performance of parental lines for HP prediction. In addition, we compared the prediction efficiency of AFLP and SSR marker data, estimated marker effects separately for reciprocal allelic configurations (among heterotic groups) of heterozygous marker loci in hybrids, and imputed missing AFLP marker data for marker-based HP prediction. Unbalanced field data of 400 maize dent × flint hybrids from 9 factorials and of 79 inbred parents were subjected to joint analyses with mixed linear models. The inbreds were genotyped with 910 AFLP and 256 SSR markers. Efficiency of prediction (R ²) was estimated by cross-validation for hybrids having no or one parent evaluated in testcrosses. Best linear unbiased prediction of GCA and specific combining ability resulted in the highest efficiencies for HP prediction for both traits (R ² = 0.6–0.9), if pedigree and line per se data were used. However, without such data, HP for grain yield was more efficiently predicted using molecular markers. The additional modifications of the marker-based approaches had no clear effect. Our study showed the high potential of joint analyses of hybrids and parental inbred lines for the prediction of performance of untested hybrids.     

Support vector machine regression for the prediction of maize hybrid performance

Accurate prediction of the phenotypical performance of untested single-cross hybrids allows for a faster genetic progress of the breeding pool at a reduced cost. We propose a prediction method based on ɛ-insensitive support vector machine regression (ɛ-SVR). A brief overview of the theoretical background of this fairly new technique and the use of specific kernel functions based on commonly applied genetic similarity measures for dominant and co-dominant markers are presented. These different marker types can be integrated into a single regression model by means of simple kernel operations. Field trial data from the grain maize breeding programme of the private company RAGT R2n are used to assess the predictive capabilities of the proposed methodology. Prediction accuracies are compared to those of one of today’s best performing prediction methods based on best linear unbiased prediction. Results on our data indicate that both methods match each other’s prediction accuracies for several combinations of marker types and traits. The ɛ-SVR framework, however, allows for a greater flexibility in combining different kinds of predictor variables.     

Hybrid breeding of rice via genomic selection

Hybrid breeding is the main strategy for improving productivity in many crops, especially in rice and maize. Genomic hybrid breeding is a technology that uses whole‐genome markers to predict future hybrids. Predicted superior hybrids are then field evaluated and released as new hybrid cultivars after their superior performances are confirmed. This will increase the opportunity of selecting true superior hybrids with minimum costs. Here, we used genomic best linear unbiased prediction to perform hybrid performance prediction using an existing rice population of 1495 hybrids. Replicated 10‐fold cross‐validations showed that the prediction abilities on ten agronomic traits ranged from 0.35 to 0.92. Using the 1495 rice hybrids as a training sample, we predicted six agronomic traits of 100 hybrids derived from half diallel crosses involving 21 parents that are different from the parents of the hybrids in the training sample. The prediction abilities were relatively high, varying from 0.54 (yield) to 0.92 (grain length). We concluded that the current population of 1495 hybrids can be used to predict hybrids from seemingly unrelated parents. Eventually, we used this training population to predict all potential hybrids of cytoplasm male sterile lines from 3000 rice varieties from the 3K Rice Genome Project. Using a breeding index combining 10 traits, we identified the top and bottom 200 predicted hybrids. SNP genotypes of the training population and parameters estimated from this training population are available for general uses and further validation in genomic hybrid prediction of all potential hybrids generated from all varieties of rice.     

Comparative analysis of inbred and hybrid maize at the diploid and tetraploid levels

Heterosis often occurs in offspring derived from a cross between inbred or divergent parents and can be observed as the superior performance of these hybrids for a wide variety of characters. Heterosis was compared in maize lines at two ploidy levels, diploid and tetraploid, to gain a better understanding of the interaction of heterosis and ploidy level. Employing genetically identical diploid and tetraploid maize derived from four different inbred lines, we investigated heterosis for 11 morphological traits, including several plant height measures, as well as flowering time for both silks and anthers. We find that the heterotic response of a certain hybrid differs between diploid and tetraploid lines, and that the response at one ploidy cannot serve as a predictor for the other. Also, progressive heterosis was found for several of the characters in the tetraploid double-cross hybrid, which can have four different alleles at one locus, compared to the double-cross diploid hybrids, which can only possess two alleles per locus. Overall, the results indicate that the heterotic response of tetraploid maize lines differs significantly from that of the diploid. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Hybrid performance in taro (<Emphasis Type="Italic">Colocasia esculenta</Emphasis>) in relation to genetic dissimilarity of parents

Taro (Colocasia esculenta) breeding, as other root crop breeding, is based on the production and evaluation of large numbers of hybrids. The selection of parents is based on their phenotypic value in the absence of information concerning general combining ability (GCA), specific combining ability (SCA), or genetic distances between varieties. By combining data from heritability trials and from genetic diversity studies conducted with AFLP and SSR markers, we aimed at studying the relationship between hybrid vigour and genetic dissimilarity between parents. The traits studied included number of suckers, corm weight, corm dimensions, and dry matter content. Correlation coefficients between hybrid gain and dissimilarity values were calculated. The prediction of hybrid performance based on the mid-parent value was compared to the prediction based on a modified expression that takes into account the genetic relationships between parents. Correlations were all but one positive but not statistically significant for all traits, with the exception of the number of suckers, when using SSR markers for dissimilarity calculations. Accordingly, the genetic dissimilarities in the prediction of hybrid performances did not increase the correlation between predicted and observed hybrid vigour values. However, large differences were observed among the residual means from the regression between predicted and observed values when using AFLP or SSR markers, mainly due to the much higher polymorphism revealed by the latter. Models need to be further adapted to the type of molecular marker used, since their ability to reveal different rates of polymorphism will have a direct incidence on the calculation of genetic dissimilarities between genotypes. Nevertheless, since SSR markers are more polymorphic and more informative than AFLP markers, they should be preferentially used for these studies. Low genetic dissimilarity of parents yielded weak heterosis effects and future studies need to be conducted by using a broader genetic base. This is the first study assessing the relationship of hybrid vigour with the genetic distances between parents, conducted on a tropical root crop.     

Molecular marker-based prediction of hybrid performance in maize using unbalanced data from multiple experiments with factorial crosses

In hybrid breeding, the prediction of hybrid performance (HP) is extremely important as it is difficult to evaluate inbred lines in numerous cross combinations. Recent developments such as doubled haploid production and molecular marker technologies have enhanced the prospects of marker-based HP prediction to accelerate the breeding process. Our objectives were to (1) predict HP using a combined analysis of hybrids and parental lines from a breeding program, (2) evaluate the use of molecular markers in addition to phenotypic and pedigree data, (3) evaluate the combination of line per se data with marker-based estimates, (4) study the effect of the number of tested parents, and (5) assess the advantage of haplotype blocks. An unbalanced dataset of 400 hybrids from 9 factorial crosses tested in different experiments and data of 79 inbred parents were subjected to combined analyses with a mixed linear model. Marker data of the inbreds were obtained with 20 AFLP primer–enzyme combinations. Cross-validation was used to assess the performance prediction of hybrids of which no or only one parental line was testcross evaluated. For HP prediction, the highest proportion of explained variance (R ²), 46% for grain yield (GY) and 70% for grain dry matter content (GDMC), was obtained from line per se best linear unbiased prediction (BLUP) estimates plus marker effects associated with mid-parent heterosis (TEAM-LM). Our study demonstrated that HP was efficiently predicted using molecular markers even for GY when testcross data of both parents are not available. This can help in improving greatly the efficiency of commercial hybrid breeding programs.     

The strategy and potential utilization of temperate germplasm for tropical germplasm improvement: a case study of maize (<Emphasis Type="Italic">Zea mays</Emphasis> L.)

The organization of maize (Zea mays L.) germplasm into genetically divergent heterotic groups is the foundation of a successful hybrid maize breeding program. In this study, 94 CIMMYT maize lines (CMLs) and 54 United States germplasm enhancement of maize (GEM) lines were assembled and characterized using 1,266 single nucleotide polymorphisms (SNPs) with high quality. Based on principal component analysis (PCA), the GEM lines and CMLs were clearly separated. In the GEM lines, there were two groups classified by PCA corresponding to the heterotic groups “stiff stalk” and “non-stiff stalk”. CMLs did not form obvious subgroups by PCA. The allelic frequency of each SNP differed in GEM lines and CMLs. In total, 3.6% alleles (46/1,266) of CMLs are absent in GEM lines and 4.4% alleles (56/1,266) of GEM lines are absent in CMLs. The performance of F1 plants (n = 654) produced by crossing between different groups based on pedigree information was evaluated at the breeding nurseries of two CIMMYT stations. Genomic estimated phenotypic values of plant height and days to anthesis for a testing set of 45 F1 crosses were predicted based on the training data of 600 F1 crosses using a best linear unbiased prediction method. The prediction accuracy benefitted from the adoption of the markers associated with quantitative trait loci for both traits; however, it does not necessarily increase with an increase in marker density. It is suggested that genomic selection combined with association analysis could improve prediction efficiency and reduce cost. For hybrid maize breeding in the tropics, incorporating GEM lines which have unique alleles and clear heterotic patterns into tropically adapted lines could be beneficial for enhancing heterosis in grain yields.     

Genetic distance of inbred lines and prediction of maize single-cross performance using RAPD markers

 To evaluate the genetic diversity of 18 maize inbred lines, and to determine the correlation between genetic distance and single-cross hybrid performance, we have used random amplified polymorphic DNA (RAPD), a PCR-based technique. Eight of these lines came from a Thai synthetic population (BR-105), and the others derived from a Brazilian composite population (BR-106). Thirty two different primers were used giving a total of 325 reproducible amplification products, 262 of them being polymorphic. Genetic divergence was determinated using Jaccard’s similarity coefficient, and a final dendrogram was constructed using an unweighted pair-group method with arithmetical averages (UPGMA). Cluster analysis divided the samples into three distinct groups (GI, GII and GIII) that were confirmed by principal-coordinate analysis. The genetic distances (GD) were correlated with important agronomic traits for single-cross hybrids and heterosis. No correlation was found when group division was not considered, but significant correlations were detected between GI×GII and GI×GIII GDs with their respective single-cross hybrid grain-yield values. Three groups were identified; that is, the BR-106 population was divided in two different groups and the BR-105 population remained mostly as one group. The results indicated that RAPD can be used as a tool for determining the extent of genetic diversity among tropical maize inbred lines, for allocating genotypes into different groups, and also to aid in the choice of the superior crosses to be made among maize inbred lines, so reducing the number of crosses required under field evaluation. Received: 24 May 1996 / Accepted: 22 November 1996     

Genome-based prediction of testcross values in maize

This is the first large-scale experimental study on genome-based prediction of testcross values in an advanced cycle breeding population of maize. The study comprised testcross progenies of 1,380 doubled haploid lines of maize derived from 36 crosses and phenotyped for grain yield and grain dry matter content in seven locations. The lines were genotyped with 1,152 single nucleotide polymorphism markers. Pedigree data were available for three generations. We used best linear unbiased prediction and stratified cross-validation to evaluate the performance of prediction models differing in the modeling of relatedness between inbred lines and in the calculation of genome-based coefficients of similarity. The choice of similarity coefficient did not affect prediction accuracies. Models including genomic information yielded significantly higher prediction accuracies than the model based on pedigree information alone. Average prediction accuracies based on genomic data were high even for a complex trait like grain yield (0.72–0.74) when the cross-validation scheme allowed for a high degree of relatedness between the estimation and the test set. When predictions were performed across distantly related families, prediction accuracies decreased significantly (0.47–0.48). Prediction accuracies decreased with decreasing sample size but were still high when the population size was halved (0.67–0.69). The results from this study are encouraging with respect to genome-based prediction of the genetic value of untested lines in advanced cycle breeding populations and the implementation of genomic selection in the breeding process.     

Impact of plant resistance on southwestern corn borer (Lepidoptera: Crambidae) biology and plant damage

Southwestern corn borer, Diatraea grandiosella Dyar (Lepidoptera: Crambidae), is a major insect pest of corn, Zea mays L., in the southern United States. Germplasm lines with resistance to southwestern corn borer have been developed and released by the USDA-ARS. Two single-cross hybrids produced by crossing germplasm lines with resistance to southwestern corn borer and a susceptible single-cross hybrid were infested with southwestern corn borer larvae in a 2-yr field test conducted in Mississippi. The susceptible hybrid sustained significantly more leaf damage and stalk tunneling than either resistant hybrid. The number of tunnels and the length of tunneling were significantly lower on the resistant hybrids. In 2003, up to 15 times more tunneling was observed on the susceptible hybrid. Larvae feeding on the resistant hybrids were delayed in their movement from the whorl to the stalk and larval survival was 50% lower on the resistant hybrids than on the susceptible hybrid. Larvae recovered from the susceptible hybrid 7-14 d after infestation weighed twice as much as those recovered from the resistant hybrids. Similar differences in larval weight were observed in the laboratory when larvae were reared on diets prepared from lyophilized tissue from the three hybrids. These results provide a foundation for other investigations designed to identify and determine the roles of specific genes and gene families associated with southwestern corn borer resistance in corn.     

Bridging the gap between marker-assisted and genomic selection of heading time and plant height in hybrid wheat

Based on data from field trials with a large collection of 135 elite winter wheat inbred lines and 1604 F₁ hybrids derived from them, we compared the accuracy of prediction of marker-assisted selection and current genomic selection approaches for the model traits heading time and plant height in a cross-validation approach. For heading time, the high accuracy seen with marker-assisted selection severely dropped with genomic selection approaches RR-BLUP (ridge regression best linear unbiased prediction) and BayesCπ, whereas for plant height, accuracy was low with marker-assisted selection as well as RR-BLUP and BayesCπ. Differences in the linkage disequilibrium structure of the functional and single-nucleotide polymorphism markers relevant for the two traits were identified in a simulation study as a likely explanation for the different trends in accuracies of prediction. A new genomic selection approach, weighted best linear unbiased prediction (W-BLUP), designed to treat the effects of known functional markers more appropriately, proved to increase the accuracy of prediction for both traits and thus closes the gap between marker-assisted and genomic selection.     

Genomic models with genotype × environment interaction for predicting hybrid performance: an application in maize hybrids

Key message

A new genomic model that incorporates genotype?×?environment interaction gave increased prediction accuracy of untested hybrid response for traits such as percent starch content, percent dry matter content and silage yield of maize hybrids.

Abstract

The prediction of hybrid performance (HP) is very important in agricultural breeding programs. In plant breeding, multi-environment trials play an important role in the selection of important traits, such as stability across environments, grain yield and pest resistance. Environmental conditions modulate gene expression causing genotype?×?environment interaction (G?×?E), such that the estimated genetic correlations of the performance of individual lines across environments summarize the joint action of genes and environmental conditions. This article proposes a genomic statistical model that incorporates G?×?E for general and specific combining ability for predicting the performance of hybrids in environments. The proposed model can also be applied to any other hybrid species with distinct parental pools. In this study, we evaluated the predictive ability of two HP prediction models using a cross-validation approach applied in extensive maize hybrid data, comprising 2724 hybrids derived from 507 dent lines and 24 flint lines, which were evaluated for three traits in 58 environments over 12 years; analyses were performed for each year. On average, genomic models that include the interaction of general and specific combining ability with environments have greater predictive ability than genomic models without interaction with environments (ranging from 12 to 22%, depending on the trait). We concluded that including G?×?E in the prediction of untested maize hybrids increases the accuracy of genomic models.