Comparison of Three Genomic Prediction Models for Testcross Populations of U.S. Inbred Lines

Abstract

To evaluate the breeding potential of introduced maize germplasm, 152 introduced inbred lines were crossed with two testers (Chang 7-2 and Zheng 58) to generate 304 hybrids, which were tested in four environments (2014–2015). An independent validation population comprised 40 hybrids from 20 newly introduced lines crossed with the same testers. All 172 parental lines were genotyped with 28285 single nucleotide polymorphisms (SNPs). Within the genomic best linear unbiased prediction (GBLUP) framework, we analyzed the effects of training population size, marker density, and genotype-by-environment interaction on prediction accuracy assessed the role of genetic relatedness by varying parental overlap and tester consistency, and evaluated models incorporating general combining ability (GCA) and specific combining ability (SCA) effects. Using the 304 hybrids as the training set, we performed five-fold cross-validation and independent validation, comparing GBLUP, GBLUP + GCA, and GBLUP + GCA + SCA. Results showed that prediction accuracy under GBLUP increased with training proportion and plateaued at 75% (3:1 ratio); approximately 1400 SNPs achieved high accuracy. For grain yield, genotype-by-environment interaction significantly affected prediction accuracy. Genetic relatedness was the key factor: presence of validation parents in the training set mattered more than tester consistency. In cross-validation, the three models performed similarly. However, in independent validation with no parental overlap, GBLUP + GCA and GBLUP + GCA + SCA significantly outperformed GBLUP, achieving observed-predicted correlations of 0.51–0.55 for kernel number per row and kernel row number, and improving grain yield correlation by 0.29 and 0.25, respectively. Thus, GBLUP + GCA was identified as the most suitable model for predicting hybrids from newly introduced inbred lines under the condition of no parental overlap with the training set.

Keywords

maize / genomic prediction / inbred lines / genetic effect / introduced germplasm

1 INTRODUCTION

Maize (Zea mays L.) is one of the world’s three major crops and has the largest planting area in China (Zeng, 2022). As a key food crop and bioenergy feedstock, maize is central to global agriculture owing to its high yield potential, wide adaptability, and nutritional value. The extensive genetic diversity of maize provides opportunities for agricultural biotechnology. However, with increasing demand, developing high-yielding cultivars has become ever more important—and maize breeding faces multiple constraints.

A key constraint in China’s maize breeding is the narrow genetic base of available germplasm, resulting from the overreliance on a limited number of core inbred lines and their repeated use. This overreliance erodes genetic diversity, narrows the breeding pool, accelerates varietal homogenization, and weakens resilience to biotic and abiotic stresses, threatening sustainable agricultural production (Li et al., 2021; Pian et al., 2021). Introducing exotic germplasm, especially U.S. materials, has therefore become a key strategy to broaden the genetic base and enhance breeding efficiency (Li et al., 2020b; Li et al., 2005).

Although exotic germplasm has expanded breeding resources, converting them into elite cultivars with strong heterosis remains difficult under conventional breeding paradigms. Heterosis is widely exploited in maize; however, traditional breeding still depends heavily on breeders’ experience and long-term data accumulation. Constrained by trial scale and resources, the comprehensive evaluation of testcross combinations is often impractical, reducing the efficiency of identifying superior hybrids. Genomic prediction (GP), with its capacity to efficiently predict multiple traits across species, provides a promising approach to overcome these bottlenecks and is expected to further enhance breeding efficiency.

In 2001, Meuwissen et al. (2001) first proposed GP technology. As an advanced alternative to marker-assisted selection (MAS), GP leverages genome-wide single-nucleotide polymorphism (SNP) markers to capture the overall genetic merit of individuals, establish marker–phenotype prediction models, and estimate the genetic values of untested populations with improved accuracy. Since its introduction, GP has quickly become a research focus in quantitative genetics, offering strong methodological support for genetic improvement in both animals and plants. In 2006, Schaeffer applied GP in dairy cattle, achieving an estimated breeding value (EBV) accuracy of 0.8. This approach reportedly reduced breeding costs by 92% and doubled the rate of genetic improvement (Schaeffer, 2006). Experience from dairy breeding programs has shown that the prediction accuracy of genomic estimated breeding values (GEBVs) is 2%–20% higher than that of pedigree-based estimates (Hayes et al., 2009). Through simulations, Bernardo and Yu (2007) demonstrated that, for polygenic traits with low heritability in maize, the genetic gain from genomic selection is 43% higher than that from marker-assisted recurrent selection.

After extensive and successful application in livestock breeding, GP has been increasingly adopted in plant research and breeding programs. Since 2007, it has been introduced into plant breeding practice (Lorenzana et al., 2009). In 2013, Guo et al. (2013) used GP to predict the phenotypes of F₁ hybrids derived from recombinant inbred lines (RILs) constructed by maize inbred lines Zong 3 and 87-1, identifying 114 hybrid combinations that might outperform Yuyu 22. Liu et al. (2015) compared the predictive performance of kernel row number-associated markers with that of randomly selected markers, showing that trait-linked markers improved prediction accuracy. Li et al. (2020a) evaluated 8 GP methods (parametric: ridge regression, LASSO, Elastic Net, BayesB, BayesC, and RKHS; non-parametric: RF and SVM) using 10 traits of 486 single-cross combinations and observed that parametric methods outperformed non-parametric ones in most cases. With continuing advances in sequencing and genotyping technologies, GP has been widely adopted in crop improvement, with particularly clear advantages in maize breeding. Because hybrid genotypes can be inferred from parental genotypes, prediction can often be conducted using only parental genotypes together with phenotypic data from a subset of hybrids. To date, GP has been explored for a range of maize traits, including flowering time, ear traits in landraces, and hybrid yield/combining ability in testcross populations (Ma et al., 2023; Zhang et al., 2022). For low-heritability traits, such as yield, Wang et al. (2017) tested the genomic best linear unbiased prediction (GBLUP) model for rice hybrids via North Carolina Design II (NCII). Results showed that in multi-trait scenarios, multivariate models outperformed univariate ones for predicting low-heritability target traits, whereas univariate models were adequate for traits with higher heritability.

However, previous studies have not systematically evaluated GP for exotic maize germplasm crossed with local testers when validation lines lack parental overlap with the training set. It remains unclear what training population size and marker density are cost-effective, and whether incorporating GCA or SCA improves prediction accuracy for completely new lines. Moreover, the achievable accuracy for low-heritability traits like grain yield in cross-population prediction remains unknown.

To address these questions, we applied genomic prediction approaches to a panel of 304 F₁ hybrids generated from 152 exotic inbred lines crossed with two testers under the NCII mating design. Using 28285 SNP markers obtained from a 56K genotyping chip and a suite of statistical models, we predicted grain yield and related traits in the F₁ hybrids. In parallel, we evaluated the capacity of these models to predict the performance of hybrids formed by newly introduced exotic inbred lines—whose genetic backgrounds are completely distinct from those of the 152 lines in the training set—when crossed with the same testers. The results of this study are expected to provide critical empirical evidence and methodological guidance for identifying elite maize hybrid combinations and predicting heterotic potential of newly introduced inbred lines following germplasm introduction. More broadly, this work aims to address the current constraints on maize breeding efficiency and further expand the evidence base for the use of heterosis and genomic selection in maize.

2 RESULTS AND ANALYSIS

2.1 SNP markers and genetic relationships

The distribution of SNP density across each chromosome is shown in Fig. 1-A. After quality filtering, the markers showed an average heterozygosity of 1.2% and an average missing rate of 0.1%. The final genome-wide SNP panel comprised 28285 high-quality markers, with the number of SNPs per chromosome ranging from 1865 on chromosome 10 to 4624 on chromosome 1. The marker set had an average minor allele frequency (MAF) of 0.2539, a mean polymorphic information content (PIC) of 0.2667, and 88.09% of SNPs with MAF > 0.05, indicating substantial genetic diversity within the population. Fig. 1-B and 1-C illustrate the genetic relationships among the tested materials and testers, all of which have been genotyped. Principal component analysis (PCA) indicated that the first two principal components explained 11.8% and 8.2% of the total variation, respectively. A phylogenetic tree was then constructed using the neighbor-joining method, with Chang 7-2 and Zheng 58 as reference lines. Zheng 58 (SS-type) and Chang 7-2 (NSS-type) served as references for assigning the remaining inbred lines to two corresponding groups based on their genetic distance in the phylogenetic tree. The classification was primarily determined by the phylogenetic tree (Fig. 1-D), with PCA serving as a complementary validation of the grouping pattern. All inbred lines were clearly allocated to either the SS or NSS group, and no lines were assigned to a mixed or ambiguous group.

2.2 Combined analysis of variance and correlation analysis for yield-related traits

Analysis of variance (ANOVA) identified highly significant genotypic differences in yield-related traits among the 304 testcross combinations, indicating abundant genetic diversity. Except for ear length (EL) in Test 1 and 2 and kernel number per row (KNR) in Test 3, all traits showed highly significant location effects, and G × E variance accounted for approximately 15%–25% of total variance, supporting the use of BLUPs to integrate multi-environment data (Table 1). The coefficients of variation ranged from 15.56% to 31.09%, confirming adequate variability for screening elite hybrids (Table 2). Skewness and kurtosis diagnostics indicated approximate normality, with absolute skewness below 1 and absolute kurtosis below 1, except for seed yield rate (SY) in Test 1 (−5.847). The phenotypic values showed continuous variation across all traits, consistent with polygenic inheritance.

Broad-sense heritability estimates varied by trait, ranging from 0.31–0.72 for EL, 0.24–0.65 for ear diameter (ED), 0.24–0.75 for kernel row number (KRN), 0.55–0.84 for KNR, 0.13–0.94 for hundred-grain weight (HGW), 0.26–0.43 for SY, 0.35–0.81 for moisture content (MC), and 0.15–0.64 for grain yield (GY). Correlation analysis showed that KNR was significantly and positively associated with EL (r = 0.34–0.69), while ED was positively correlated with KRN (r = 0.25–0.74) across the four experiments. In addition, both KNR (r = 0.36–0.69) and KRN (r = 0.21–0.56) were positively correlated with GY (Fig. 2), suggesting that improving ear-related traits may contribute to higher grain yield. The wide range of heritability estimates across test groups can be largely attributed to environmental effects and genotype × environment (G × E) interactions. Each test group comprised two distinct year-by-location combinations, and the environmental contrast varied considerably within each group. Consequently, G × E variance relative to genetic variance differed across groups, leading to substantial variation in heritability estimates. As shown in Table 1, the significance levels of genotype × location interaction terms varied considerably across tests, supporting this interpretation.

In summary, these results demonstrated substantial variation in grain yield and its component traits within the testcross population, providing a solid foundation for identifying superior hybrids.

2.3 Effects of SNPs and training population size on prediction accuracy

We evaluated how training population size influences prediction accuracy using the GBLUP framework. As shown in Fig. 3, as the training proportion increased from 1/8 to 9/10, the mean prediction accuracy for grain yield increased from 0.3 to 0.85. When the training set accounted for 75% of the population, the prediction accuracies for most traits ranged from 0.7 to 0.81. Beyond 75%, the gains in accuracy diminished markedly, approaching a plateau.

Marker density significantly affected the prediction performance. As the SNP set increased from 88 to 5600, the prediction accuracy for grain yield increased from 0.23 to 0.83. Approximately 1400 SNPs yielded mean prediction accuracies of 0.6–0.85 across traits; further increasing marker density to 5600 SNPs provided only marginal improvements.

These results indicated that a training proportion of 75%–90% and approximately 1400 SNPs are optimal parameters for predicting yield-related traits in this study. In addition, high prediction accuracy can be achieved with approximately 1400 SNP markers. To address whether the observed variation in prediction accuracy across SNP densities is associated with SNP diversity, we analyzed this question based on the statistical principle of random sampling. Since all reduced SNP subsets were generated by systematic random sampling from the full panel, their expected genetic diversity, such as minor allele frequency (MAF) and polymorphism information content (PIC) is theoretically identical to the above genome-wide parameters. Therefore, under our sampling design, SNP diversity is not a variable that differs across density levels.

Given that the experimental materials were planted in different locations with significant G × E interaction effects confirmed in the present study, it is essential to further explore the specificity of genomic prediction accuracy under different environmental backgrounds, which provides a practical basis for the application of genomic prediction in multi-location field trials.

2.4 Specificity analysis of genomic prediction accuracy across different environments

To clarify the environmental regulation on genomic prediction efficiency and verify the feasibility of predicting the phenotypic performance of all materials by planting a subset of materials in separate environments, taking grain yield as an example, 10 independent random sampling validations were carried out in each experimental environment based on the GBLUP model. The Pearson correlation coefficient between observed and predicted phenotypic values was used to evaluate the environment-specific prediction accuracy of the model. The results showed that prediction accuracy of the model varied significantly across environments, exhibiting obvious environment-dependent characteristics (Fig. 4). Environment 1 achieved the best prediction performance, with an average correlation coefficient of 0.7222, and the 10 sampling validations showed good stability. Environment 4 ranked second, with an average correlation coefficient of 0.6835, indicating high prediction reliability. Environment 3 showed moderate prediction accuracy, with an average correlation coefficient of 0.3294, indicating limited predictive ability. In contrast, environment 2 had the poorest prediction performance, with an average correlation coefficient of −0.1207, meaning the model failed to achieve effective phenotypic prediction in this environment. Overall, in the multi-location planting experimental system of this study, the prediction efficiency of the GBLUP model was significantly modulated by environmental background, and efficient inference of materials with unknown phenotypes could be achieved by sampling prediction within suitable environments.

The poor prediction performance of Environment 2 (Yangling) can be attributed to the genetic parameters of the hybrid subsets evaluated at this location. As shown in Table 2, Environment 2 comprised hybrids from Tests 1 and 2, both of which had low heritability for GY (0.24 and 0.15, respectively), resulting in insufficient genetic signal for accurate prediction. In contrast, Environments 1 and 4 both included hybrids from Test 4, which had the highest heritability (0.51) and coefficient of variation (0.3109) for GY among all tests (Table 2), contributing to their higher prediction accuracy.

2.5 Comparison of genomic prediction accuracy under different prediction schemes

All comparisons were conducted using the NSS subgroup. Within this subgroup, prediction accuracy for grain yield ranged from 0.46 to 0.92, which was comparable to that obtained using the mixed population, indicating that pre-partitioning by genetic structure is unnecessary (Fig. 5).

Further analysis of parental overlap between training and validation sets revealed that under the CV1 strategy (validation parents present in the training set, only the tester differed), the prediction accuracies for all traits ranged from 0.7 to 0.95 (Fig. 6). Under the CV2 strategy (validation parents completely absent from the training set), prediction accuracies were consistently poor for all traits, ranging from 0.12 to 0.45 (Fig. 7). These results highlighted that the presence of validation set parents in the training set is a key determinant of prediction accuracy.

To exclude the influence of tester consistency, we further conducted tester-specific prediction (CV3 and CV4). In CV3 (tester fixed as Chang 7-2) and CV4 (tester fixed as Zheng 58), no parental lines overlapped between the training and validation sets. The prediction accuracy for grain yield was relatively low (0.16 and 0.26, respectively), lower than the value observed in CV2 (r = 0.43), presumably due to the training population size (Fig. 8 and 9). These results confirmed that the absence of parental overlap leads to very poor prediction accuracy even with the same tester.

2.6 Evaluation of the impact of genetic effects on prediction accuracy based on the GBLUP model

In addition to the effects of training population size and marker density, explicit modeling of genetic effects could further enhance the practical utility of genomic prediction. Using the full set of 304 hybrid combinations, we evaluated prediction performance for each trait under three models: the baseline GBLUP model, GBLUP augmented with general combining ability (GBLUP + GCA), and GBLUP augmented with both general and specific combining ability effects (GBLUP + GCA + SCA).

Using 304 hybrid combinations as the total population, three models (GBLUP, GBLUP + GCA, GBLUP + GCA + SCA) showed average prediction accuracies as follows: GY (0.63–0.92), MC (0.55–0.91), EL (0.52–0.91), ED (0.60–0.84), KRN (0.37–0.77), KNR (0.52–0.84), HGW (0.64–0.87), and SY (0.67–0.93) (Fig. 10). Compared with the baseline GBLUP model, both GBLUP + GCA and GBLUP + GCA + SCA improved prediction accuracy, albeit with modest magnitudes. In particular, the mean difference in GY prediction accuracies between GBLUP + GCA and GBLUP + GCA + SCA was less than 0.03, suggesting that SCA effects contributed only minimally under the conditions of this evaluation (Fig. 10). To provide statistical support for these observations, paired t-tests were performed on the prediction accuracies of the three models across all traits based on 50 repeated cross-validation runs (Table 3). The results showed that GBLUP + GCA and GBLUP + GCA + SCA significantly outperformed GBLUP for most traits (P < 0.05), whereas no significant differences were detected between GBLUP + GCA and GBLUP + GCA + SCA for any trait except GY (P = 0.0138). Given that the absolute differences in prediction accuracy among models were generally less than 0.03, despite a marginal statistical effect on GY, the addition of SCA effects provided little practical value beyond GCA. Collectively, these results indicated that incorporating GCA effects effectively improves prediction accuracy, while further including SCA effects offers no additional practical benefit.

2.7 Prediction and validation of the test population based on genetic effect models

Using 304 combinations as the training population and the 40 newly developed hybrids as an independent validation population, both GBLUP + GCA and GBLUP + GCA + SCA outperformed the baseline GBLUP model. Under GBLUP + GCA, prediction–observation correlations were relatively high for HGW (r = 0.5) and KNR (r = 0.61), whereas the correlation for GY reached 0.29. The GBLUP + GCA + SCA model also showed strong performance for KNR (r = 0.55) and KRN (r = 0.51), with correlations of 0.36 and 0.25 for EL and GY, respectively (Fig. 11 to 13).

The validation based on yield ranking further indicated that GBLUP + GCA and GBLUP + GCA + SCA produced more accurate yield estimates. For these two models, the mean yield of the top 20 predicted hybrids exceeded that of the bottom 20 hybrids by 5.4% and 15.08%, respectively. Moreover, under the GBLUP + GCA and GBLUP + GCA + SCA models, 13 and 12 hybrid combinations, respectively, were simultaneously ranked in the top 20 for both predicted and observed performance, whereas only eight such overlaps were observed for the GBLUP model (Table 4).

In summary, GBLUP + GCA and GBLUP + GCA + SCA exhibited comparable predictive performance and were both markedly superior to GBLUP for identifying elite hybrid combinations under independent validation. Thus, in cross-validation with parental overlap, all three models performed similarly. In independent validation with no parental overlap, GBLUP alone was inadequate, while the inclusion of GCA effects improved prediction; SCA did not add further value.

3 DISCUSSION

In crop breeding, genomic prediction has become an essential tool for enhancing breeding efficiency and accelerating variety improvement. This study systematically investigated genomic prediction by assessing the influence of training population size and SNP density on prediction accuracy and by evaluating GBLUP model performance under different genetic-effect specifications. The results showed that increasing the training population proportion improved prediction accuracy for traits such as grain yield, with an optimal proportion of 75%–90% for yield-related traits. In addition, a marker set of 1400 SNPs achieved high prediction accuracy, and further increases in marker number do not lead to significant gains. These findings provide a practical basis for the rational design of training populations and for balancing prediction performance against genotyping costs. Moreover, GBLUP models incorporating GCA and SCA effects exhibited superior performance in independent test-population validation, offering useful guidance for hybrid combination screening in practical breeding programs.

3.1 Effects of training population size and SNP marker density on prediction accuracy

Previous studies have placed greater emphasis on population size (Zhang et al., 2017; Zhang et al., 2023), whereas this study provides a more systematic evaluation of both the training-to-validation ratio and SNP density. Our results showed that a training proportion of 75% achieves high prediction accuracy. Adopting a 3:1 training-to-validation ratio balances cost and performance—particularly important for exotic germplasm, which is often expensive to genotype. A 75%–90% training proportion appeared to maximize the use of information without excessive resource demands.

Approximately 1400 markers achieved high prediction accuracy, with further increases to 5600 yielding only marginal gains. Although the specific thresholds differ from earlier reports (e.g., ~7000 SNPs in maize (Liu et al., 2018) and ~5000 in wheat (Norman et al., 2018)), the overall conclusion is consistent: once an optimal marker density is reached, prediction accuracy plateaus. The lower marker requirement here may reflect American inbred lines with concentrated genetic backgrounds and longer linkage disequilibrium (LD) blocks, which allows key genetic variation to be captured with fewer markers—a practical advantage for cost control in exotic germplasm prediction.

In relation to the actual analytical strategy employed in this study, it should be noted that the 1400 SNP threshold served only as a reference for cost-effectiveness analysis; all final model comparisons were based on the full set of 28285 SNPs. In the CV2 scenario, the bottleneck in prediction accuracy was the lack of genetic relatedness between the training and validation sets, rather than insufficient training proportion or marker density. Therefore, for predicting novel germplasm with no parental overlap, priority should be given to optimizing parental representativeness in the training set (Melchinger et al., 2023) rather than simply expanding population size or marker density.

3.2 Impacts of genetic effects and population genetic relationship on prediction results

In maize hybrids, performance is jointly determined by additive and dominance-related genetic effects. Using 304 hybrids generated from 152 American inbred lines and two testers, we evaluated GBLUP-based models incorporating parental GCA and SCA effects and observed clear scenario-dependent patterns.

In cross-validation within the training population, the baseline GBLUP model performed similarly to GBLUP + GCA and GBLUP + GCA + SCA, with differences in prediction accuracy below 0.03 for most traits. Adding SCA effects provided only marginal gains. In contrast, when predicting the 40 new hybrids (20 newly introduced inbred lines crossed with the same testers, with no parental overlap), the accuracy of GBLUP dropped sharply, whereas models incorporating GCA and/or SCA performed substantially better. Notably, GBLUP + GCA and GBLUP + GCA + SCA again showed comparable accuracy, indicating that SCA contributed little additional predictive value in independent validation.

Wang et al. (2024) reported that in a narrow-base immortalized F₂ population, an additive-dominance model outperformed GCA + SCA models, suggesting that the importance of SCA may depend on population structure. In their narrow-base population derived from two founders, additive variance dominated, making additive-dominance models highly effective. In contrast, our exotic germplasm possessed broader genetic diversity. Under independent validation with no parental overlap, additive effects (GCA) are more transferable across populations than non-additive effects (SCA), which are often population-specific. This likely explains why GCA effects became critical in the CV2, CV3, and CV4 scenarios.

Although all three models achieved high accuracy under cross-validation, prediction accuracy decreased sharply in the independent validation population. This decline is largely driven by reduced genetic relatedness between training and validation populations. Specifically, accuracy was highest when both parents of an untested hybrid were present in the training set and lowest when neither parent was present. This interpretation is consistent with previous reports. Technow et al. (2014) showed that prediction accuracy was highest for T2 hybrids (both parents in the training set), followed by T1 hybrids (one parent included), and lowest for T0 hybrids (neither parent included). Similarly, Zhao et al. (2024) reported reduced accuracy when predicting one foxtail millet subgroup using another subgroup, compared with predictions based on the full set of materials.

Supplementary analyses further support and extend this conclusion (Section “Comparison of genomic prediction accuracy under different prediction schemes”). Prediction accuracy within the NSS subgroup was comparable to that of the mixed population, indicating that pre-partitioning by population structure was unnecessary when the training population already possessed sufficient genetic diversity. When the tester was fixed but no parental overlap occurred (CV3/CV4), prediction accuracy for grain yield was extremely low (r = 0.16 and 0.26), further confirming that genetic relatedness among inbred lines was more critical than tester consistency. Consistent with Rogers et al. (2022), analyses from the GEM project using exotic germplasm showed that the prediction accuracy across programs and heterotic groups was generally poorer than within groups. Collectively, these findings underscore the critical role of genetic relatedness in genomic prediction and provide practical guidance for constructing training populations.

3.3 Perspectives for improving genomic prediction accuracy

Based on the findings and limitations of this study, several strategies could further improve genomic prediction accuracy.

First, genotype-by-environment (G × E) interactions must be explicitly modeled. Multi-environment linear mixed models accounting for environmental structure can more accurately predict unobserved performance (Zhang et al., 2015; Burgueño et al., 2012; Luo et al., 2023). We observed substantial variation in prediction accuracy across environments (Section “Specificity analysis of genomic prediction accuracy under different environments”). The extreme variation in prediction accuracy across environments (−0.12 to 0.72) was mainly attributable to sampling fluctuation due to the small validation set per environment and differential G × E interaction intensity across year-by-location combinations. Since the core conclusions of this study are based on BLUP values integrated across multiple environments, the fluctuation in single-environment accuracy does not affect their reliability, highlighting the strong influence of G × E. Cuevas et al. (2017) demonstrated that multi-environment models accounting for G × E interactions achieve higher prediction accuracy than single-environment models. Moreover, SCA effects became significant when GCA × E and SCA × E interactions were included in the model for predicting maize test-cross hybrids under drought and well-watered conditions (Bernardeli et al., 2025). Our model included only the main SCA effect without environmental interactions, which may explain why SCA contributed little predictive value in our study. Future work should therefore consider incorporating SCA × E interactions to capture genotype-specific responses across environments.

Second, incorporating significant genome-wide association study (GWAS) loci or population structure information can enhance predictive performance. Using significant GWAS loci as fixed effects consistently improves accuracy for agronomic traits (e.g., grain yield, ear traits), plant architecture traits, and disease resistance (Liu et al., 2015; Dang et al., 2023; Zhang et al., 2025; Cooper et al., 2019). Yu et al. (2024) showed that including the Q matrix as a fixed effect gave the highest predictive performance in cross-population genomic prediction.

Third, using multiple testers and optimizing training set design for no-parental-overlap scenarios are promising directions. Dong et al. (2024) reported that epistatic effects explained 26.2%–64.3% of phenotypic variation in maize hybrids. Our fixed two-tester design may have limited the detection of non-additive effects; future studies should consider using multiple testers to better capture SCA and epistatic effects. Furthermore, Melchinger et al. (2023) provided a solution for H₀ hybrids (no parental overlap) by optimizing training set design—maximizing the number of parent lines with each parent involved in only one cross—which could improve prediction accuracy for newly introduced germplasm.

Finally, joint modeling of additive and non-additive effects remains valuable. Zhang et al. (2022) reported that jointly modeling additive and non-additive effects can significantly improve prediction accuracy for yield-related traits in hybrid combinations. When predicting the yield GCA of tested lines, incorporating tester GCA information increased the average predictive ability to 0.49–0.55. Future studies may integrate this strategy with multi-environment and multi-tester designs to further boost prediction performance.

This study has two design limitations. First, the 304 training hybrids were divided into four groups, each evaluated in only two environments. This incomplete design introduced partial confounding between genetic group effects and environmental conditions, which primarily affects the precision of absolute BLUP estimates rather than the relative ranking of models. Because each genotype was tested in only two specific environments, the standard errors of across-environment BLUP estimates were relatively large, limiting the ability to precisely quantify the true genetic merit of individual hybrids on a perfectly comparable scale and potentially affecting the external generalizability of the reported absolute prediction accuracies. Nevertheless, because all model comparisons and cross-validation schemes were performed using the same set of BLUP estimates, the relative ranking of model performance is unlikely to be systematically biased, and the comparisons among models remain reliable. Second, the environmental conditions of the training population (tested at four sites in 2014–2015) and the independent validation population (tested at three sites in 2023) were only partially overlapping, with one location (Urumqi) shared. Therefore, the relatively low absolute prediction accuracies observed in independent validation (e.g., r = 0.29 for grain yield) could not be unequivocally attributed solely to the absence of parental overlap; environmental discrepancy is a confounding factor. However, because all three models were evaluated on the same validation population under the same 2023 environmental conditions, their relative performance—with GBLUP + GCA and GBLUP + GCA + SCA significantly outperforming GBLUP—remains robust.

To address these limitations, future studies could adopt fully balanced multi-environment trial designs or apply G × E-structured models (e.g., GBLUP-G × E) to improve the precision of genetic effect estimation. Additionally, incorporating more shared environments between training and validation sets would enable a cleaner assessment of the true impact of environmental factors on prediction accuracy.

4 CONCLUSIONS

This study examined the genomic prediction framework by quantifying the influence of training population size and SNP set size on trait prediction accuracy and by assessing the performance of GBLUP models under different genetic-effect specifications. Furthermore, parental genetic relatedness between the training and validation sets was the primary factor that determined prediction accuracy, and environmental background exerts a significant regulatory effect. The results indicated that both training population size and SNP set size had a significant impact on predictive accuracy. Increasing the proportion of the training population improved the accuracy of traits like grain yield, with an optimal range of 75%–90% for yield-related traits. Likewise, a panel of 1400 SNPs achieved high prediction accuracy, and expanding marker density beyond this level yielded only marginal gains. Independent validation further demonstrated that incorporating genetic effects into the GBLUP framework improved predictive performance. Models including GCA and SCA effects outperformed the baseline GBLUP model when predicting the test population. In particular, GBLUP + GCA and GBLUP + GCA + SCA showed comparable performance, and both were more effective than GBLUP for identifying elite hybrids derived from newly introduced inbred lines. Collectively, these findings provide practical guidance for deploying genomic prediction in breeding programs and offer key references for optimizing models and parameters to improve breeding efficiency.

5 MATERIALS AND METHODS

5.1 Test materials

A total of 304 hybrid combinations were developed by crossing 152 publicly released American inbred lines (used as female parents) with two testers, Chang 7-2 and Zheng 58. Additionally, 40 hybrid combinations were obtained by crossing 20 publicly released American inbred lines (introduced in 2019 as female parents) with the same two testers (Chang 7-2 and Zheng 58).

5.2 Experimental design

5.2.1 Training population

The training population comprised 304 hybrids derived from the 152 introduced inbred lines and the two testers. These combinations were evaluated in four location-by-year trials, as described below:

Test 1: Hybrids 1–72 were planted in Urumqi (Xinjiang) in 2014 and Yangling (Shaanxi) in 2015;

Test 2: Hybrids 73–146 were planted in Yangling (Shaanxi) in 2014 and Xinzhou (Shanxi) in 2015;

Test 3: Hybrids 147–226 were planted in Xinzhou (Shanxi) in 2014 and Hohhot (Inner Mongolia) in 2015;

Test 4: Hybrids 227–304 were planted in Hohhot (Inner Mongolia) in 2014 and Urumqi (Xinjiang) in 2015.

All field experiments were conducted using a randomized complete block design. Each plot consisted of two rows with a length of 5 m, with three replications arranged per environment. The planting density was 67 500 plants ha⁻¹). Each hybrid was evaluated in only two of the four environments, which might reduce the precision of G × E estimates.

5.2.2 Validation population

The validation population comprised 40 hybrid combinations generated by crossing 20 exotic U.S. inbred lines (as female parents) with two testers (Chang 7-2 and Zheng 58). In 2023, these hybrids were evaluated at three sites: Urumqi (Xinjiang), Yinchuan (Ningxia), and Baotou (Inner Mongolia). Field trials were conducted using a randomized complete block design with the following specifications: a row length of 4 m, two-row plots, two replications, a row spacing of 0.6 m, and a plant spacing of 0.25 m.

5.3 Determination indicators and methods

Eight agronomic traits were assessed: ear length (EL), ear diameter (ED), kernel row number (KRN), kernel number per row (KNR), hundred-grain weight (HGW), seed yield rate (SY), moisture content (MC), and grain yield (GY). The measurement procedures of each trait were as follows:

Ear length (cm): Ten ears were randomly sampled from each plot, and the length from the ear base to the tip was measured.

Ear diameter (cm): Ten ears were randomly sampled from each plot, and the diameter at the midpoint of each ear was measured.

Kernel row number (rows): Ten ears were randomly sampled from each plot, and the number of kernel rows per ear was counted.

Kernel number per row (kernels): Ten ears were randomly sampled from each plot, and kernels in one intact row per ear were counted.

Hundred-grain weight (g): One hundred kernels were weighed twice, with a measurement difference no greater than 0.2 g.

Seed yield rate (%): SY was calculated as the ratio of plot grain yield to dry ear weight from the same plot.

Moisture content (%): Grain moisture content at harvest was determined using a moisture meter.

Grain yield (kg/ha): After air-drying and threshing, the plot grain weight was recorded and then standardized to 14% moisture content before conversion to kg/ha.

5.4 Statistical data analysis

5.4.1 Phenotypic data analysis

Phenotypic data were analyzed in SAS using the PROC MIXED and PROC GLM procedures. First, single-site analysis of variance (ANOVA) was performed for each trait within each environment. Then, a combined ANOVA across environments was conducted with adjustments. In the analysis, year, environment, and block were specified as random effects, whereas variety was treated as a fixed effect.

The formula for calculating broad-sense heritability (H²) is as follows:

(1)H^2={\sigma }_g^2/\left({\sigma }_g^2+\frac{{\sigma }_{ge}^2}{n}+\frac{{\sigma }_e^2}{nr}\right)

where {\sigma }_g^2 = genetic variance; {\sigma }_{ge}^2 = genotype × environment interaction variance; {\sigma }_e^2 = error variance; n = number of environments; r = number of replications.

To minimize the interference of non-genetic factors (e.g., location and year) on phenotypic observations across environments—particularly because the training and validation populations were evaluated at different sites—we estimated BLUPs for multi-environment trials using the lme4 package in R. In this BLUP analysis, all factors were modeled as random effects to obtain phenotypic estimates that better reflect the underlying genetic performance of each genotype. The model was specified as:

(2)Y_{ijk}=u+g_i+e_j+{ge}_{ij}+b_k+s_{ijk}

In the model, u denotes the overall mean; g_i represents the genotypic effect of the i-th hybrid combination; e_j is the effect of the j-th environment; {ge}_{ij} is the genotype × environment interaction effect; b_k denotes the block effect of the k-th replication within the j-th environment; and s_{ijk} is the residual error associated with the j-th environment and k-th replication. Correlation analysis and significance testing of hybrid BLUP values were conducted in R using the PerformanceAnalytics package.

5.4.2 Genotyping and quality control

Genotyping of 172 U.S. inbred lines and two testers was performed using a maize 56K breeding chip. Genotypic data were processed through the following quality-control and imputation pipeline. First, loci with a heterozygosity rate greater than 0.10 among the 172 inbred lines were excluded, and residual heterozygous calls at the remaining loci were recoded as missing. Second, PLINK v1.9 was used to retain SNPs with a minor allele frequency (MAF) greater than 0.05 and a missing data rate below 0.10. Third, the missing genotypes were imputed using Beagle. Finally, hybrid genotypes were inferred by combining the parental genotypes of each cross. After filtering, 28285 high-quality SNP markers were retained for genomic prediction analysis of the hybrid combinations.

5.4.3 Prediction models

In genomic selection, the GBLUP model is the most commonly used GP model in plant breeding, and its linear mixed model is as follows:

(3)Y=1_n\mu +Zu+ϵ

where Y represents the BLUP values of each trait. The design matrix for fixed effects is X=1_n\mu, where 1_n denotes an n-dimensional vector with all elements equal to 1, and \mu is the population mean; Z is the incidence matrix for random effects, and u is the vector of random effects, which follows the distribution \text{u}\sim {\text{N(0,Gσ}}_{\text{u}}^2). ϵ is the vector of residual effects, following the distribution \text{N}\left(0,I{\sigma }_{\epsilon }^2\right),where I is the identity matrix.

Multiple distinct sampling gradients were established to accurately evaluate the effects of training population size and SNP marker density on the prediction accuracy of the GBLUP model. For training population size, 50, 76, 152, 228, 253, 266, and 273 families were randomly selected as training sets under predefined training-to-validation ratios (1:5, 1:3, 1:1, 3:1, 5:1, 7:1, and 9:1). Each sampling gradient was repeated for 50 iterations to improve robustness and reduce sampling bias. For SNP marker density, 5600, 2800, 1400, 700, 350, 175, and 88 markers were randomly sampled genome-wide to construct seven marker-density panels, and each density panel was likewise evaluated across 50 repeated iterations.

Given that the phenotypic performance of hybrid combinations is jointly governed by additive and non-additive genetic effects, phenotypic prediction via estimating the general combining ability (GCA) of female and male parents (denoted as u_1 and u_2, respectively), the specific combining ability (SCA) of hybrids, and their corresponding variance components ({\sigma }_{}^2{u}_1, {\sigma }_{}^2{u}_2, {\sigma }_{}^2{u}_s) is particularly informative. This framework can be expressed using the diallel-model formulation:

(4)y=X\beta +Z_1{u}_1+Z_2{u}_2+Z_s{u}_s+\epsilon

The mixed model equations for this model are:

(5)\left[\begin{array}{cccc}{X}^{{}^{\prime }}{R}^{-1}X& X^{{}^{\prime }}{R}^{-1}{Z}_1& X^{{}^{\prime }}{R}^{-1}{Z}_2& X^{{}^{\prime }}{R}^{-1}{Z}_3\\ Z_1^{{}^{\prime }}{R}^{-1}X& Z_1{R}^{-1}{Z}_1+G_1^{-1}& Z_1^{{}^{\prime }}{R}^{-1}{Z}_2& Z_1^{{}^{\prime }}{R}^{-1}{Z}_3\\ Z_2^{{}^{\prime }}{R}^{-1}X& Z_2^{{}^{\prime }}{R}^{-1}{Z}_1& Z_2^{{}^{\prime }}{R}^{-1}{Z}_2+G_2^{-1}& Z_2^{{}^{\prime }}{R}^{-1}{Z}_3\\ Z_3^{{}^{\prime }}{R}^{-1}X& Z_3^{{}^{\prime }}{R}^{-1}{Z}_1& Z_3^{{}^{\prime }}{R}^{-1}{Z}_2& Z_3^{{}^{\prime }}{R}^{-1}{Z}_3+G_3^{-1}\end{array}\right]\left[\begin{array}{c}{X}^{{}^{\prime }}{R}^{-1}y\\ Z_1^{{}^{\prime }}{R}^{-1}y\\ Z_2^{{}^{\prime }}{R}^{-1}y\\ Z_3^{{}^{\prime }}{R}^{-1}y\end{array}\right]=\left[\begin{array}{c}\beta \\ u_1\\ u_2\\ u_S\end{array}\right]

where \beta is a vector of fixed effects; u_1, u_2, and u_s are the BLUP values of female GCA, male GCA, and SCA effects, respectively; X and Z_s are the incidence matrices for fixed and random effects, respectively. R is the residual variance–covariance matrix (Iσ+²_e); G⁻¹₁, G⁻¹₂, and G⁻¹₃ represent the inverses of the variance–covariance matrices for the corresponding random effects. Model fitting considered both additive (A) and non-additive genetic components. Specifically, genomic relationship matrices constructed for u_1 and u_2 were treated as additive effects, whereas the relationship matrix specified for u_s was designed to capture non-additive variations, including dominance and epistatic effects. Prediction performance was assessed using a five-fold cross-validation with 50 repetitions. Genomic prediction accuracy was quantified as the mean Pearson correlation coefficient between observed phenotypic values and genomic estimated breeding values in the validation sets across the 50 repetitions. All models were implemented in R using the sommer package.

To evaluate model performance under practical breeding conditions, the training population comprised 304 hybrids generated from 152 introduced accessions crossed with two testers, while an independent validation population consisted of 40 hybrids generated from another set of 20 introduced accessions crossed with the same testers. Using the training population, three models—GBLUP, GBLUP + GCA, and GBLUP + GCA + SCA—were fitted to predict the phenotypic performance of the 40 hybrids in the validation population, and the resulting predictions were subsequently validated against observed field data.

5.4.4 Evaluation of prediction accuracy specificity across different environments

Genomic prediction was performed using the multi-environment GBLUP model (Burgueño et al., 2012). The model was specified as:

(6)yij=\mu +Ej+ui+qij+eij

where yij is the phenotypic value of the i-th genotype in the j-th environment; Ej is the fixed environmental effect; ui is the random additive genetic effect which follows u ~ N (0, G_σu²); qij is the random G × E effect with q ~ N (0, (IJ \otimes G)_σge²); and eij is the residual term with e ~ N (0, I_σe²). The genomic relationship matrix G was calculated as G = MM^T/p, where M is the centered and standardized SNP matrix and p is the number of markers.

To evaluate the environmental regulation on the prediction accuracy of the GBLUP model, independent prediction validations were conducted across four environments: Urumqi, Yangling, Xinzhou, and Hohhot. Within each environment, all hybrid combinations were used as the total sample; 80% of the hybrids were randomly selected as the training set and the remaining 20% as the validation set. The GBLUP model was used to predict the phenotypic values for the validation set. Random sampling was repeated 20 times, and the mean Pearson correlation coefficient across the 20 repetitions was defined as the prediction accuracy for each environment, with the standard deviation calculated to assess stability.

5.4.5 Cross-validation schemes for prediction accuracy

To further explore the effect of genetic relatedness between training and validation populations on prediction accuracy, three complementary prediction schemes were designed based on the GBLUP model. For each scheme, five-fold cross-validation was performed with 50 repetitions, and prediction accuracy was measured as the Pearson correlation coefficient between predicted and observed values.

CV0: Prediction within a subgroup. Based on the population structure analysis (Fig. 1-D), the 172 exotic inbred lines were divided into two subgroups: SS (102 lines) and NSS (70 lines). Prediction was conducted within each subgroup separately, with 20% of the hybrids randomly selected as the validation set and the remaining 80% as the training set. The process was repeated 50 times.

CV1 (parents present in training, only tester differs): 76 inbred lines (50%) were randomly selected. Among them, 38 were crossed with Chang 7-2, and the other 38 with Zheng 58, yielding 76 hybrids as the validation set. The training set consisted of 152 hybrids produced by crossing the remaining 76 inbred lines with both testers.

CV2 (parents completely absent from training): 38 inbred lines were randomly selected. Each of these 38 lines was crossed with both testers (i.e., each line produced two hybrids: one with Chang 7-2 and one with Zheng 58), resulting in 76 hybrids as the validation set. The training set comprised 228 hybrids from the remaining 114 inbred lines crossed with both testers.

For the tester-specific prediction schemes (CV3 and CV4), 25% of the inbred lines (38 lines) were randomly selected. In CV3, the validation set comprised hybrids derived from crossing these 38 lines with Chang 7-2, while the training set comprised hybrids from the remaining 75% (114 lines) crossed with the same tester. CV4 followed the same scheme, except that Zheng 58 served as the tester instead of Chang 7-2.

References

[1] Bernardeli A , Guilhen J H S , Oliveira I C M . et al. Genomic selection of maize test-cross hybrids leveraged by marker sampling and genetic effects. The Plant Genome, 2025, 18(2): e70030

[2] Bernardo R , Yu J M . Prospects for genome wide selection for quantitative traits in maize. Crop Science, 2007, 47(3): 1082–1090

[3] Burgueño J , Campos G de los , Weigel K A . et al. Genomic prediction of breeding values when modeling genotype × environment interaction using pedigree and dense molecular markers. Crop Science, 2012, 52: 707–719

[4] Cooper J S , Rice B R , Shenstone E M . et al. Genome-wide analysis and prediction of resistance to Goss’s wilt in maize. The Plant Genome, 2019, 12(2): 1–10

[5] Cuevas J , Crossa J , Montesinos-López O A . et al. Bayesian genomic prediction with genotype × environment interaction kernel models for multi-environment trials. G3: Genes, Genomes, Genetics, 2017, 7(1): 41–53

[6] Dang D , Guan Y , Zheng H . et al. Genome-wide association study and genomic prediction on plant architecture traits in sweet corn and waxy corn. Plants, 2023, 12(2): 303

[7] Dong Y , Zhang Z , Shi Y . et al. Genome-wide association study for maize hybrid performance in a typical breeder population. International Journal of Molecular Sciences, 2024, 25(2): 1190

[8] Guo T T , Li H H , Yan J B . et al. Performance prediction of F1 hybrids between recombinant inbred lines derived from two elite maize inbred lines. Theoretical and Applied Genetics, 2013, 126(1): 189–201

[9] Hayes B J , Bowman P J , Chamberlain A J . et al. Invited review: Genomic selection in dairy cattle: progress and challenges. Journal of Dairy Science, 2009, 92(2): 433–443

[10] Li G L , Dong Y , Zhao Y S . et al. Genome-wide prediction in a hybrid maize population adapted to Northwest China. The Crop Journal, 2020a, 8(5): 830–842

[11] Li H M, Hu R F, Zhang S H. 2005. Genetic contribution of alien germplasm to maize production in China. Scientia Agricultura Sinica, (11): 46-54. (in Chinese).

[12] Li R L, Qiu L, Niu Z L, et al. 2021. Maize germplasm resources and improvement in China. Modern Rural Science and Technology, (1): 114-116. (in Chinese).

[13] Li Y Y , Tian H Z , Zhu L J . et al. Contemporary heterosis analysis of corn kernel weight hybridization. Seed, 2020b, 39(4): 22–28

[14] Liu L , Du Y F , Huo D A . et al. Genetic architecture of maize kernel row number and whole genome prediction. Theoretical and Applied Genetics, 2015, 128(11): 2243–2254

[15] Liu X , Wang H , Wang H . Factors affecting genomic selection revealed by empirical evidence in maize. The Crop Journal, 2018, 6(4): 341–352

[16] Lorenzana R E , Bernardo R . Accuracy of genotypic value predictions for marker-based selection in biparental plant populations. Theoretical and Applied Genetics, 2009, 120(1): 151–161

[17] Luo P , Wang H W , Ni Z Y . et al. Genomic prediction of yield performance among single-cross maize hybrids using a partial diallel cross design. The Crop Journal, 2023, 11(6): 1884–1892

[18] Ma J , Cao Y Y , Wang Y Z . Genomic prediction analysis for maize hybrid performance. Corn Science, 2023, 31(5): 34–41

[19] Melchinger A E , Technow F , Schrag T A . et al. Genomic prediction in hybrid breeding: I. Optimizing the training set design. Theoretical and Applied Genetics, 2023, 136(8): 176

[20] Meuwissen T H , Hayes B J , Goddard M E . Prediction of total genetic value using genome-wide dense marker maps. Genetics, 2001, 157(4): 1819–1829

[21] Norman A , Taylor J , Edwards J . et al. Optimising genomic selection in wheat: Effect of marker density, population size and population structure on prediction accuracy. G3: Genes, Genomes, Genetics, 2018, 8(9): 2889–2899

[22] Pian M , Gao X , Gao X . et al. Research status and thinking of maize germplasm resources in China. Xinjiang Agricultural Reclamation Science and Technology, 2021, 44(4): 68–69

[23] Rogers A R , Bian Y , Krakowsky M . et al. Genomic prediction for the germplasm enhancement of maize project. The Plant Genome, 2022, 15(4): e20267

[24] Schaeffer L R . Strategy for applying genome-wide selection in dairy cattle. Journal of Animal Breeding and Genetics, 2006, 123(4): 218–223

[25] Technow F , Schrag T A , Schipprack W . et al. Genome properties and prospects of genomic prediction of hybrid performance in a breeding program of maize. Genetics, 2014, 197(4): 1343–1355

[26] Wang P , Ma X , Jin X . et al. Fine-tuning quantitative trait loci identified in immortalized F₂ population are essential for genomic prediction of hybrid performance in maize. Agriculture, 2024, 14(3): 340

[27] Wang X , Li L , Yang Z . et al. Predicting rice hybrid performance using univariate and multivariate GBLUP models based on North Carolina mating design II. Heredity (Edinb), 2017, 118(3): 302–310

[28] Yu G , Li F , Wang X , Zhang Y . et al. Enhancing across-population genomic prediction for maize hybrids. Plants (Basel), 2024, 13(21): 3105

[29] Zeng Z Y. 2022. Analysis and suggestions on the current situation of maize production in China. Grain Oil and Feed Technology, (3): 4-8. (in Chinese).

[30] Zhang A , Guan Y , Zhang X . et al. Research progress in genomic selection breeding of maize. Acta Agriculturae Shanghai, 2023, 39(5): 13–18

[31] Zhang A , Pérez-Rodríguez P , Vicente S F . et al. Genomic prediction of the performance of hybrids and the combining abilities for line by tester trials in maize. The Crop Journal, 2022, 10(1): 109–116

[32] Zhang A , Wang H , Beyene Y . et al. Effect of trait heritability, training population size and marker density on genomic prediction accuracy estimation in 22 bi-parental tropical maize populations. Front Plant Sci., 2017, 8: 1916

[33] Zhang X , Pérez-Rodríguez P , Semagn K . et al. Genomic prediction in biparental tropical maize populations in water-stressed and well-watered environments using low-density and GBS SNPs. Heredity, 2015, 114(3): 291–299

[34] Zhang Z , Wang X , Zhang Y . et al. SPDC-HG: An accelerator of genomic hybrid breeding in maize. Plant Biotechnol J., 2025, 23(5): 1847–1861

[35] Zhao X W , Cao Y H , Shao L T . et al. Integration of genome-wide association and genomic prediction for dissecting seed protein and amino acid in foxtail millet. Field Crops Research, 2024, 310: 109344

Rights & permissions

Comparison of three genomic prediction models for testcross populations of U.S. inbred lines