Robustly enhancing crop genomic prediction accuracy through ensemble learning and iterative optimization

Abstract

With climate change and global population growth, accelerating the breeding of superior crop varieties is essential for food security. Genomic prediction, which uses genome-wide genetic markers to predict crop traits, plays an important role in intelligent crop breeding. However, existing methods often lack stable and accurate performance across crops and traits. Here, we propose GEG2P, a genetic algorithm-based ensemble learning method for genotype-to-phenotype prediction, integrates 20 base learners, dynamically selects their combinations through an iterative optimization strategy, and optimizes their weights using the genetic algorithm. Compared with the best-performing single base learners, GEG2P improves prediction accuracy by 4.02% on average across maize, wheat, rice, chickpea, and soybean. We use SHAP to quantify the contribution of SNPs to phenotype prediction and find that SNPs with large effects captured by different base learners are functionally complementary. This study provides a robust and accurate genomic prediction method for crop breeding.

Existing genomic prediction methods often lack stability and accuracy across crops and traits. Here, the authors report a genetic algorithm-based ensemble learning method for genotype-to-phenotype prediction (GEG2P) by integrating 20 base learners and show its application in improving trait prediction accuracy in multiple crops.

Introduction

Faced with the dual challenges of climate change and global population growth, breeding high-yield and high-quality crop varieties has become a research priority of great scientific importance and practical relevance^1,2. Genomic prediction (GP) uses genotype data to predict crop phenotypes by constructing a mapping model between whole-genome markers and phenotype values. Genomic prediction enables early screening of superior agronomic traits, which helps accelerate crop breeding processes and improve breeding efficiency^3,4.

The existing genomic prediction methods mainly include statistical learning, machine learning, and deep learning methods. Statistical methods typically model the relationships between genotypes and phenotype data by setting different prior assumptions, and representative methods include rrBLUP⁵ and the Bayesian series of methods⁶. However, these methods primarily rely on linear assumptions, making it difficult to capture the nonlinear features in genotype data⁷. Subsequently, researchers overcame these limitations by modeling complex nonlinear relationships using machine learning algorithms. For example, CropGBM applies LightGBM, a gradient boosting framework, to effectively enhance phenotype prediction accuracy⁸. However, machine learning methods often rely on feature selection, which can lead to a significant decrease in model performance when the sample size is small or the noise level is high⁹. In recent years, deep learning methods have attracted increasing attention due to their ability to automatically extract features. Deep learning-based models commonly employ convolutional neural networks (CNNs) to extract genotype features^10,11. To address the limitation of CNNs in primarily focusing on local patterns, multi-head attention has been introduced to enhance global modeling capability^12,13. Meanwhile, researchers have attempted to use multi-omics data for phenotype prediction¹⁴. In addition, growing attention has been paid to the associations among different phenotypes, motivating the exploration of transfer learning strategies to further improve prediction performance¹⁵. However, deep learning methods typically require large-scale labeled data for training¹⁶, while acquiring high-quality data in breeding practice is often constrained by high costs and technical challenges. In addition, existing methods often rely on a single type of modeling approach, with their model structures and hyperparameters closely tied to the training data, resulting in insufficient generalization for phenotype prediction across species. Although these methods achieve high prediction accuracy for specific species and phenotypes, they often fail to maintain their performance when applied to other species and phenotypes with different genetic backgrounds. Therefore, improving the generalization and stability of genomic prediction methods has become an urgent and important problem to be addressed.

By integrating the prediction results of multiple base learners to overcome the limitations of single models, ensemble learning has been widely applied in fields including computer vision¹⁷, electrical engineering¹⁸, and healthcare¹⁹. In recent years, ensemble learning has also been gradually applied in genomic prediction. For instance, Kick et al. ²⁰ integrated eight base learners for genomic prediction, effectively overcoming the limitations of a single base learner. Wu et al. ²¹ proposed a more flexible integration method based on a hierarchical strategy, and Zhang et al. ²² integrated seven common GP methods and achieved superior genomic prediction performance compared with a single model. Although ensemble learning has shown potential in genomic prediction, existing methods still have certain limitations. First, the types of candidate base learners are relatively limited, which fails to fully capture the complementarity among them. Second, existing methods only focus on improving prediction accuracy while lacking a systematic analysis of the selection and ensemble strategies for base learners. Finally, existing methods mainly focus on analyzing the correlations between prediction results and population genetic background, making it difficult to explain the biological basis of integrating different base learners to improve prediction performance. These limitations restrict the application of existing methods in breeding practice.

In this work, we propose a genomic prediction method (GEG2P) based on ensemble learning and an iterative optimization strategy, aiming to improve the prediction accuracy and stability of different crops and phenotypes. GEG2P integrates 20 representative genomic prediction methods, including statistical learning, machine learning, and deep learning methods, thereby enhancing the ability to extract features and model complex genotype-phenotype relationships effectively. To preserve the diversity and complementarity of base learners, GEG2P uses an optimal base learner selection strategy based on the genetic algorithm and iterative optimization to identify optimal base learners and explore globally optimized weight combinations. Comprehensive experiments on 36 traits from five crop species show that GEG2P outperforms single base learners and six state-of-the-art genomic prediction methods, demonstrating robust generalization ability and stability across species and traits. Furthermore, we use SHAP (SHapley Additive exPlanations) and a series of analytical strategies, including comparison with previous studies, functional enrichment analysis, genetic variance decomposition, and statistical analyses, to investigate the biological basis of the improvement in prediction accuracy and demonstrate the complementarity of SNP features identified by different base learners.

Results

Architecture of GEG2P

GEG2P integrates various base learners to extract genotype features and employs an iterative optimization strategy to identify the optimal combination of base learners. GEG2P adopts the genetic algorithm to optimize the weights of base learners, thereby enhancing the prediction accuracy across different species and phenotypes. To enhance the effectiveness of feature extraction, GEG2P integrates 20 representative base learners from statistical learning, machine learning, and deep learning. Among them, statistical methods (rrBLUP, BayesA, BayesB, BayesC, BL, BRR, LASSO, RR, SPLS, and BRNN) are capable of effectively handling linear relationships and additive genetic effects among SNPs^5,7,23,24. Machine learning methods (XGBoost, Random Forest (RF), SVR, KNN, and MLP) can model nonlinear relationships and can capture SNP-SNP interactions and non-additive effects that influence complex traits^25–29. Deep learning methods (DLGWAS, DeepGS, LCNN, gMLP, and DNNGP) extract high-dimensional features automatically through neural networks and capture complex nonlinear relationships among SNPs^{10,11,14,30–32}. Benefiting from the complementary modeling capabilities of different base learners, GEG2P can extract both linear relationships and complex nonlinear patterns among SNP loci. Therefore, GEG2P can reduce prediction bias caused by the limitations of theoretical assumptions in single base learners, thereby improving genomic prediction accuracy steadily.

The process of GEG2P includes four stages: data processing, base learner training, iteration and weight optimization, and phenotype prediction (Fig. 1A). In the stage of data processing, genotype data were encoded using the 0/1/2 scheme to ensure a unified input format for all base learners. In the stage of base learner training, we trained all candidate base learners using the same training set. During the iteration and weight optimization stage, we adopted a three-step iterative optimization strategy (Fig. 1B) to gradually construct the GEG2P model. In the first step, we broke the category boundaries among base learners to enhance feature extraction capability and constructed the initial ensemble model GEG2P(v1). In the second step, four intermediate ensemble models, including GEG2P(DL), GEG2P(ML), GEG2P(SS), and GEG2P(v1) were added to construct GEG2P(v2), which enhances the diversity of base learners. Among them, GEG2P(DL), GEG2P(ML), and GEG2P(SS) were obtained from deep learning, machine learning, and statistical methods, respectively, while GEG2P(v1) was retained as the integrated model from the previous iteration. In the third step, we gradually removed base learners with lower prediction accuracy in GEG2P(v2) and dynamically explored to obtain the optimal combination of base learners. In this stage, we used the genetic algorithm to optimize the weights of each base learner, producing the globally optimal combination of weights. Finally, we constructed the final prediction model GEG2P(v3) by integrating the selected base learners with weights optimized through the three-step iterative optimization strategy.

Fig. 1. Framework of GEG2P.

A Based on encoded genotype data, GEG2P first trains and integrates twenty base learners. Subsequently, a three-step iterative optimization strategy is applied to dynamically explore the optimal combination of base learners, and the genetic algorithm is employed to optimize their weights to obtain the final model. B The three-step iterative optimization strategy of GEG2P. In the first step, the category boundaries of base learners are removed by integrating all twenty base learners to obtain GEG2P(v1). In the second step, four intermediate ensemble models, including GEG2P(DL), GEG2P(ML), GEG2P(SS), and GEG2P(v1), are treated as base learners and further integrated to construct GEG2P(v2). In the third step, base learners in GEG2P(v2) are iteratively removed according to their prediction accuracy. This process continues until prediction accuracy is no longer improved, resulting in the final optimized model GEG2P(v3).

Comparison of three types of ensemble models and base learners

To evaluate whether integrating multiple base learners can improve phenotype prediction accuracy, we used the integration strategy of GEG2P to integrate base learners from deep learning, machine learning, and statistical methods for experimental comparison. We denote the ensemble genomic prediction methods that integrate deep learning, machine learning, and statistical methods as GEG2P(DL), GEG2P(ML), and GEG2P(SS), respectively. We conducted experiments using three trait categories from the maize dataset³³, including flowering time-related, plant architecture-related, and yield-related traits. Flowering time-related traits include Days to Tassel (DTT), Days to Anther (DTA), Days to Silk (DTS), Anther-Tassel Interval (ATI), Silk-Anther Interval (SAI), and Silk-Tassel Interval (STI). Plant architecture-related traits include Plant Height (PH), Ear Height (EH), Leaf Number Above Ear (LNAE), Leaf Number Below Ear (LNBE), Tassel Branch Number (TBN), Tassel Length (TL), Ear Leaf Length (ELL), and Ear Leaf Width (ELW). Yield-related traits include Ear Length (EL), Length of Barren Tip (LBT), Ear Diameter (ED), Ear Row Number (ERN), Kernel Number per Row (KNPR), Kernel Number per Ear (KNPE), Ear Weight (EW), Cob Weight (CW), and Kernel Weight per Ear (KWPE). The weights of each base learner in GEG2P(ML), GEG2P(DL), and GEG2P(SS) are illustrated in Fig. 2A and Supplementary Data 1. The prediction accuracy of twenty base learners and the ensemble models GEG2P(DL), GEG2P(ML), and GEG2P(SS) is shown in Fig. 2B–D and Supplementary Data 2.

Fig. 2. Prediction accuracy of base learners and three ensemble models for flowering-time, plant architecture, and yield-related traits in maize.

A Weights of base learners in GEG2P(DL), GEG2P(ML), and GEG2P(SS). Dot size represents the weight assigned to each base learner, and larger dots indicate greater weights. B–D Pearson correlation coefficient (PCC) of phenotype prediction results of flowering time, plant architecture, and yield-related traits in maize using different base learners and three kinds of ensemble models. Bars and error bars indicate average PCCs and standard errors, respectively (n = 10). Bar colors denote deep-learning base learners (orange), machine-learning base learners (pink), statistical base learners (blue), and GEG2P (grey). Source data are provided as a Source Data file.

The experimental results show that the prediction accuracy of three ensemble models, GEG2P(DL), GEG2P(ML), and GEG2P(SS), is significantly higher than that of their corresponding base learners (Fig. 2, Supplementary Data 2). Compared with the best-performing single base learner, the average PCC of the three ensemble models increased by 3.17%, 1.93%, and 1.77%, respectively. In addition, GEG2P exhibits stable performance advantages in phenotype prediction of flowering time, plant architecture, and yield-related traits. For yield-related traits, the average PCC of GEG2P(DL), GEG2P(ML), and GEG2P(SS) improved by 3.72%, 2.60%, and 2.06% compared with that of the best-performing base learners, DLGWAS, SVR, and rrBLUP, respectively. For plant architecture-related traits, the average PCC of GEG2P(DL), GEG2P(ML), and GEG2P(SS) were 0.6740, 0.7015, and 0.6926, which were 3.07%, 1.45%, and 1.15% higher than that of the optimal base learners, DLGWAS, SVR, and BayesB, respectively (Fig. 2C). For flowering-related traits, the average PCC of GEG2P(DL), GEG2P(ML), and GEG2P(SS) were higher by 2.61%, 1.74%, and 1.90% than that of the optimal base learners, respectively (Fig. 2D). Therefore, the ensemble strategy implemented in GEG2P achieves higher prediction accuracy than single base learners by integrating deep learning, machine learning, and statistical genomic prediction methods. In addition, we further evaluated the performance of GEG2P when the dataset was partitioned according to population structure. The results showed that prediction accuracy was positively correlated with the genetic correlation between the subpopulation and the reference population (Supplementary Note 1 and Supplementary Data 3).

Comparison of GEG2P based on a three-step iterative optimization strategy

As described above, the prediction accuracy of GEG2P(ML), GEG2P(DL), and GEG2P(SS) is higher than that of single-base learners. We further constructed GEG2P(v1), GEG2P(v2), and GEG2P(v3) based on the three-step iterative optimization strategy shown in Fig. 1 and evaluated their phenotype prediction performance in maize. The comparison of prediction accuracy among GEG2P(v1), GEG2P(v2), GEG2P(v3), GEG2P(ML), GEG2P(DL), GEG2P(SS), and the best-performing base learner SVR is shown in Fig. 3 and Supplementary Data 4.

Fig. 3. The comparison of prediction accuracy among GEG2P(v1), GEG2P(v2), GEG2P(v3), GEG2P(ML), and SVR in maize.

GEG2P(v1), GEG2P(v2), and GEG2P(v3) represent three versions of GEG2P constructed through the three-step iterative optimization strategy; GEG2P(ML) and SVR represent the ensemble model of machine learning and the base learner with the highest prediction accuracy, respectively. A Flowering time-related traits. B Plant architecture-related traits. C Yield-related traits. Bars and error bars indicate average Pearson correlation coefficients (PCCs) and standard errors, respectively (n = 10). Bar colors denote SVR (light red), GEG2P(ML) (grey), GEG2P(v1) (light green), GEG2P(v2) (light teal), and GEG2P(v3) (green). Source data are provided as a Source Data file.

Compared with the SVR method that achieved the highest accuracy in three phenotype categories, the average PCC of GEG2P(v1) increased by 3.00%. Compared with GEG2P(DL), GEG2P(ML), and GEG2P(SS), the average PCC of GEG2P(v1) increased by 6.02%, 1.05%, and 2.98%, respectively. For flowering-related traits, the average PCC of GEG2P(v1) was higher than that of SVR, GEG2P(DL), GEG2P(ML), and GEG2P(SS), with an average improvement of 3.12% (Fig. 3A and Supplementary Data 4). For plant architecture-related traits, the average PCC of GEG2P(v1) was improved by 2.54% on average (Fig. 3B and Supplementary Data 4). For yield-related traits, the average PCC of GEG2P(v1) was improved by 4.15% on average (Fig. 3C and Supplementary Data 4).

To further enhance the diversity of feature extraction, we integrated twenty base learners with GEG2P(DL), GEG2P(ML), GEG2P(SS) and GEG2P(v1) to obtain GEG2P(v2). Experimental results demonstrate that GEG2P(v2) achieves higher prediction accuracy compared with GEG2P(v1). For flowering-related traits, GEG2P(v2) achieved an average PCC of 0.6715, which is 0.16% and 3.29% higher than those of GEG2P(v1) and SVR, respectively (Fig. 3A). For plant architecture-related and yield-related traits, the average PCC of GEG2P(v2) increased by 0.13% and 0.31% compared with GEG2P(v1), and by 2.42% and 4.00% compared with SVR, respectively (Fig. 3B, 3C).

Although GEG2P(v2) improved phenotype prediction accuracy, experimental results showed that the prediction accuracy of some base learners remained relatively low. For example, the average PCC of GEG2P(v2) across all phenotypes is 50.11% higher than that of the worst-performing base learner DNNGP, indicating that underperforming base learners may negatively affect overall prediction accuracy. During the process of model integration, phenotype prediction accuracy was further improved by sequentially removing base learners with the lowest prediction accuracy. Specifically, we gradually removed the base learner with the lowest genomic prediction accuracy from GEG2P(v2) and constructed GEG2P(v3) until the phenotype prediction accuracy stabilized. The experimental results showed that GEG2P(v3) had the highest prediction accuracy for all traits (Fig. 3). Overall, GEG2P(v3) achieved an average PCC of 0.6560, representing a 0.10% improvement over GEG2P(v2) and a 15.15% average improvement over all single base learners. For flowering-related traits, GEG2P(v3) achieved an average PCC of 0.6726, representing improvements of 0.16% over GEG2P(v2), and an average improvement of 16.14% over all single base learners (Fig. 3A). For plant architecture-related traits, the average PCC of GEG2P(v3) was 0.7086, which was 0.06% higher than that of GEG2P(v2), and on average 12.41% higher than the average PCC of each single base learner (Fig. 3B). For yield-related traits, the average PCC of GEG2P(v3) was 0.11% higher than those of GEG2P(v2), and on average 17.67% higher than the average PCC of each single base learner (Fig. 3C). We further analyzed the prediction performance of GEG2P(v1) and GEG2P(v3) across different numbers of optimization rounds in genetic algorithm. The results showed that both models exhibited stable convergence as the number of optimization rounds increased (Supplementary Fig. 1). Overall, RMSE showed a decreasing trend, whereas PCC showed an increasing trend. Compared with GEG2P(v1), GEG2P(v3) achieved higher PCC values and lower RMSE values for EW, PH, and DTA in maize. These results indicate that the three-step iterative optimization strategy can further improve model performance, even when the single-step model has already converged. This finding further confirms the effectiveness of the proposed three-step iterative optimization strategy. Therefore, the three-step iterative optimization strategy was demonstrated to be effective, leading to consistently improved genomic prediction accuracy of GEG2P across multiple maize traits.

Exploring the phenotype prediction potential of GEG2P across different species

We further evaluated the genomic prediction accuracy of GEG2P across different species, including wheat, rice, soybean, and chickpea. The wheat dataset includes flowering time-related traits (Maturity) and yield-related traits (Grain_Yield and Grain_Size_TKW). The rice dataset involves flowering time-related traits (BLUP_Heading_date), plant architecture-related traits (BLUP_Height), and yield-related traits (BLUP_Yield_per_plant). The chickpea dataset involves flowering time-related traits (Days_to_0.5_flowering), plant architecture-related traits (Plant_height), and yield-related traits (Yield). The soybean dataset involves flowering time-related traits (BBD_BLUP), plant architecture-related traits (PLH_BLUP), and yield-related traits (SL_BLUP and ST_BLUP). The experimental results are shown in Fig. 4 and Supplementary Fig. 2, and Supplementary Data 5.

Fig. 4. The comparison of prediction accuracy among GEG2P and twenty base learners across different species and traits.

A Flowering time-related traits in wheat. B Yield-related traits in wheat. C Flowering time-related traits in rice. D Yield-related traits in rice. E Flowering time-related traits in chickpea. F Yield-related traits in chickpea. G Flowering time-related traits in soybean. H Yield-related traits in soybean. Bars and error bars indicate average Pearson correlation coefficients (PCCs) and standard errors, respectively (n = 10). Bar colors denote deep-learning base learners (orange), machine-learning base learners (pink), statistical base learners (blue), and GEG2P(v3) (grey). Source data are provided as a Source Data file.

In wheat, the mean PCC of GEG2P(v3) was on average 14.77% higher than that of all single base learners. For flowering time-related traits (Fig. 4A) and yield-related traits (Fig. 4B), the average PCC of GEG2P(v3) was on average 17.13% and 13.49% higher than that of the single base learners, respectively. In rice, the average PCC of GEG2P(v3) was on average 7.40% higher than that of single-base learners. Across the three trait categories, the average PCC of GEG2P(v3) for flowering time-related traits (Fig. 4C), plant architecture-related traits (Supplementary Fig. 2, Supplementary Data 5), and yield-related traits (Fig. 4D) was on average 3.78%, 4.46%, and 24.72% higher than those of the single base learners, respectively. In chickpea, the average PCC of GEG2P(v3) was on average 8.05% higher than that of the single base learners. For flowering time-related traits (Fig. 4E), plant architecture-related traits (Supplementary Fig. 2), and yield-related traits (Fig. 4F), the average PCC of GEG2P(v3) was on average 9.24%, 6.39%, and 9.01% higher than those of the single base learners, respectively. In soybean, the average PCC of GEG2P(v3) was on average 8.60% higher than that of the single base learners. For flowering time-related traits (Fig. 4G), plant architecture-related traits (Supplementary Fig. 2), and yield-related traits (Fig. 4H), the average PCC of GEG2P(v3) was on average 4.40%, 8.92%, and 11.54% higher than those of the single base learners, respectively. In summary, GEG2P achieved the highest prediction accuracy in phenotype prediction across wheat, rice, chickpea, and soybean, which demonstrates its strong generalization ability and stability across multiple species.

Comparison of GEG2P with six state-of-the-art (SOTA) methods

To further validate the phenotype prediction performance of GEG2P, we compared it with six state-of-the-art genomic prediction methods (SoyDNGP, Cropformer, WheatGP, EGGPT, RKHS, and Multi-kernel GBLUP) in maize, rice, wheat, chickpea, and soybean. To ensure a fair comparison, we used Optuna³⁴ to optimize the hyperparameters of these six methods. The adjustment range of key parameters for all methods can be seen in Supplementary Data 6. Furthermore, EGGPT supports both SNP-based and PCA-based input modes. In the SNP-based mode, SNP selection is based on GWAS, which results in the exclusion of a large number of SNPs from model training. To avoid potential errors caused by the limited number of SNPs, we used the PCA-based input mode for the experimental evaluation of EGGPT. In this mode, EGGPT integrates five base learners, including CNN, SVR, MLP, Random Forest, and LightGBM. The comparison of prediction accuracy between GEG2P and the six state-of-the-art methods in maize, rice, chickpea, and soybean is shown in Fig. 5 and Supplementary Data 7. The results for wheat are presented in Supplementary Fig. 3 and Supplementary Data 7.

Fig. 5. The comparison of prediction accuracy between GEG2P and six state-of-the-art (SOTA) methods in maize, rice, chickpea, and soybean.

A Maize, (B) Rice, (C) Chickpea, (D) Soybean. Bars and error bars indicate average Pearson correlation coefficients (PCCs) and standard errors, respectively (n = 10). Bar colors denote SoyDNGP (red), Cropformer (orange), WheatGP (green), EGGPT (blue), RKHS (pink), Multi-kernel GBLUP (purple), and GEG2P(v3) (grey). Source data are provided as a Source Data file.

In maize, the average prediction accuracy of GEG2P is 111.26%, 11.03%, 77.25%, 3.04%, 5.94%, and 5.52% higher than that of SoyDNGP, CropFormer, WheatGP, EGGPT, RKHS, and Multi-kernel GBLUP, respectively (Fig. 5A). For flowering time-, plant architecture-, and yield-related traits, the average PCC of GEG2P is at least 1.01%, 3.76%, and 2.31% higher than that of the six comparison methods, respectively. In wheat, the average prediction accuracy of GEG2P improved by 17.26%, 11.43%, 11.46%, 16.91%, 5.33%, and 8.30% compared with the six methods, respectively (Supplementary Fig. 3). Specifically, GEG2P improved the PCC of flowering time-related traits by at least 9.84% (Supplementary Fig. 3A) and yield-related traits by at least 2.84% (Supplementary Fig. 3B). In rice, the prediction accuracy of GEG2P is also higher than that of the six state-of-the-art methods, with the average PCC improved by 14.84%, 9.30%, 11.82%, 1.89%, 3.48%, and 4.40%, respectively (Fig. 5B). From the perspective of trait categories, GEG2P improved the prediction accuracy of flowering time-related traits by at least 1.26%, plant architecture-related traits by at least 0.84%, and yield-related traits by at least 4.46%, respectively. In chickpea, the average PCC of GEG2P increased by 10.67%, 14.83%, 15.61%, 4.91%, 4.30%, and 3.76% compared with the six methods, respectively (Fig. 5C). Specifically, GEG2P showed consistent performance gains, with average PCC improvements of at least 4.61%, 3.45%, and 3.23% for flowering time-related, plant architecture-related, and yield-related traits, respectively. In soybean, GEG2P also achieved the highest prediction accuracy, with the average PCC improved by 18.89%, 6.38%, 3.07%, 3.34%, 6.15%, and 3.82% compared with the six methods, respectively (Fig. 5D). From the perspective of trait categories, GEG2P improved the prediction accuracy of flowering time-related traits by at least 2.65%, plant architecture-related traits by at least 3.52%, and yield-related traits by at least 6.40%, respectively. Furthermore, we conducted statistical comparisons of prediction accuracy between GEG2P and six SOTA methods across all the traits of five species using the Wilcoxon signed-rank test³⁵. The results indicated that GEG2P achieved significantly higher 10-fold cross-validated PCC than SOTA methods for most traits (Supplementary Fig. 4A–E). In addition, R², MAE, and RMSE were also evaluated. The results showed that GEG2P achieved better average performance than six methods across all evaluated metrics (Supplementary Data 8–10). Moreover, correlations between narrow-sense heritability (Supplementary Fig. 5) and all evaluated prediction metrics of GEG2P were assessed. PCC and R² across all 36 phenotypes showed significant correlations with narrow-sense heritability (P values = 2.87 × 10⁻⁷ and 2.13 × 10⁻⁶), with correlation coefficients of 0.738 and 0.699, respectively (Supplementary Fig. 6A, B). In contrast, RMSE and MAE showed no significant correlations with narrow-sense heritability (Supplementary Fig. 6C, D). Overall, these findings indicate that GEG2P can be applied to phenotype prediction across different species and traits, demonstrating stable and significant performance advantages.

Interpretability analysis of robust improvement in prediction accuracy of GEG2P

Using DTA, PH, and EW of maize as examples, we analyzed the weights assigned to different base learners integrated in GEG2P(v3). For DTA, the top five base learners ranked by weight were gMLP, SVR, SPLS, XGBoost, and BayesA, denoted as DTA-Weight-Top-5 (Fig. 6A). The top five base learners ranked by prediction accuracy were BayesB, RR, BayesA, rrBLUP, and BRR, denoted as DTA-PCC-Top-5 (Supplementary Fig. 7). The base learners in DTA-Weight-Top-5 differed from those in DTA-PCC-Top-5. We further calculated the average correlations among the predicted phenotype values of DTA-Weight-Top-5 and DTA-PCC-Top-5, respectively, and the results are shown in Fig. 6B and Supplementary Data 11–13. The average correlation of the predicted phenotype values of DTA-PCC-Top-5 was 0.9892, which was significantly higher than that of DTA-Weight-Top-5 (0.8251). The results indicate that GEG2P pays more attention to the independence of prediction results among base learners in the process of weight allocation, rather than merely determining the weights of base learners based on prediction accuracy. During the genetic algorithm optimization, the weight ranking of DTA-Weight-Top-5 gradually increased with the number of evolutionary rounds and eventually stabilized around the 40th round (Supplementary Fig. 8). In terms of base learner diversity, DTA-Weight-Top-5 includes the methods from all three categories of deep learning, machine learning, and statistical methods (Supplementary Fig. 9 and Supplementary Data 14). Therefore, GEG2P has strong capabilities for both linear and nonlinear feature extraction. For PH and EW in maize, PH-Weight-Top-5 included SVR, XGBoost, KNN, BayesA, and DeepGS (Supplementary Fig. 10A), whereas EW-Weight-Top-5 included SVR, XGBoost, gMLP, DeepGS, and LASSO (Supplementary Fig. 11A). Similar to the results of DTA, the average correlations among the predicted values of PH-Weight-Top-5 and EW-Weight-Top-5 were 0.8191 and 0.7865, respectively, which were 16.59% and 18.88% lower than those of PH-PCC-Top-5 and EW-PCC-Top-5 (0.9821 and 0.9696), as shown in Supplementary Fig. 10B and Supplementary Fig. 11B. During the iterative process of the genetic algorithm, the weights of PH-Weight-Top-5 and EW-Weight-Top-5 gradually increased and remained at relatively high levels around the 40th round (Supplementary Fig. 8). Meanwhile, PH-Weight-Top-5 and EW-Weight-Top-5 covered two or more categories of deep learning, machine learning, and statistical methods (Supplementary Fig. 9 and Supplementary Data 14). These results indicate that GEG2P tends to assign higher weights to base learners with greater independence in their prediction results. Therefore, GEG2P is capable of integrating a wide range of base learners with diverse feature extraction, which helps reduce information redundancy caused by multiple highly correlated base learners.

Fig. 6. Analysis of functional differences and complementarity of DTA-Weight-Top-5.

AWeight proportions of all base learners during 40 iterative optimization rounds of GEG2P. For each box, middle horizontal lines indicate medians; the upper and lower boundaries indicate the interquartile range (IQR, 25th–75th percentiles); whiskers extend to 1.5 × IQR from the box boundaries; and points represent outliers. Different letters above the boxes indicate significant differences among groups as determined by one-way ANOVA followed by Tukey’s multiple-comparisons test based on 40 iterative optimization rounds (n = 40; P value < 0.05). Box plot colors: orange, gMLP; green, SVR; purple, SPLS; yellow, XGBoost; blue, BayesA; grey, all remaining base learners. B Average correlations of the predicted phenotype values among the top five base learners ranked by weight in GEG2P (Weight-Top-5) and those of the top five base learners ranked by prediction accuracy (PCC-Top-5). Bars and error bars indicate average Pearson correlation coefficients (PCCs) and standard errors, respectively (n = 10). P values are from two-sided t-test. C Colocalization results of the Top10% SNPs of DTA-Weight-Top-5 with flowering time-related sQTLs. D The intersection of genes mapped by the Top10% SNPs of the five base learners in DTA-Weight-Top-5. E GO enrichment analysis results of the union of all genes mapped by the Top10% SNPs of the five base learners in DTA-Weight-Top-5. Point size indicates the number of enriched genes. Point color indicates the enrichment significance. P values are from Fisher’s exact test implemented on the DAVID website. F The chromosomal locations of the cloned genes identified in (D). Genes mapped exclusively by the Top10% SNPs of gMLP, SVR, SPLS, XGBoost, and BayesA are indicated in rose, yellow, green, blue, and purple, respectively. G The narrow-sense heritability of successively accumulating the Top10% SNPs from the base learners in DTA-Weight-Top-5. The x-axis represents the cumulative number of base learners. Bar plot colors: blue, union of Top10% SNPs from DTA-Weight-Top-5; orange, equal-number random SNPs. H Potential epistasis network of the Top10% SNPs of base learners in DTA-Weight-Top-5, with rose, yellow, green, blue, and purple nodes representing the specific Top10% SNPs of gMLP, SVR, SPLS, XGBoost, and BayesA, respectively. Black nodes represent the Top10% SNPs shared by two or more base learners. I Potential epistasis network of SNPs that significantly interact with chr5.s_7256657 of the Top10% SNPs of four base learners (SVR, SPLS, XGBoost, BayesA). Yellow, green, blue, and purple nodes represent the specific Top10% SNPs that significantly interact with chr5.s_7256657 of SVR, SPLS, XGBoost, and BayesA, respectively. Black nodes represent the Top10% SNPs shared by two or more base learners that significantly interact with chr5.s_7256657. Red nodes represent chr5.s_7256657. P values for SNP interactions are from two-way ANOVA. Significant SNP interactions are selected at P value < 0.001. Source data are provided as a Source Data file.

We further analyzed the preferences for integrating different base learners in predicting the phenotypes of wheat, rice, chickpea, and soybean using GEG2P. The average correlations of predicted phenotype values of Weight-Top-5 for wheat, rice, chickpea, and soybean were significantly lower than those from PCC-Top-5, as shown in Supplementary Fig. 12. From the perspective of the optimization process of genetic algorithm, the weights of Weight-Top-5 in wheat, rice, chickpea, and soybean increased with the number of optimization rounds and eventually stabilized at their maximum values (Supplementary Fig. 13–16). Similarly, the Weight-Top-5 used for predicting the phenotypes of wheat, rice, chickpea, and soybean included two or more categories of methods (Supplementary Fig. 9 and Supplementary Data 14). In addition, the Weight-Top-5 of wheat, rice, chickpea, and soybean showed a high degree of independence from each other. These results indicate that the Weight-Top-5 gradually achieved higher weights and eventually stabilized during the optimization process of the genetic algorithm, while maintaining category diversity of genomic prediction methods.

To further explore the biological mechanisms underlying the improved prediction accuracy of GEG2P through integrating multiple base learners, we used SHAP (SHapley Additive exPlanations)³⁶ to quantify the contribution of each SNP to phenotype prediction (Supplementary Data 15). To mitigate the impact of scale differences in SHAP values across different models on comparative analysis, this study primarily analyzed the relative ranking of SHAP values of SNPs for each base learner. The importance of SNPs was assessed based on the absolute values of their SHAP scores, and the top 10% ranked SNPs (denoted as Top10% SNPs) were considered as potential phenotype-associated loci. Correspondingly, the Top10% SNPs of DTA-Weight-Top-5 (gMLP, SVR, SPLS, XGBoost, BayesA) were co-located with 682, 405, 645, 479, and 651 loci, respectively, within the reported QTL intervals (sQTLs) associated with single-variant-based GWAS (sGWAS)³³. However, only eight of these co-localized SNPs were shared by all DTA-Weight-Top-5 base learners (Fig. 6C and Supplementary Data 16). In addition, the Top10% SNPs of DTA-Weight-Top-5 mapped to 2311, 2461, 2359, 2460, and 2406 genes, and only 68 genes were shared for all DTA-Weight-Top-5 base learners (Fig. 6D). These results suggest that different base learners capture distinct biologically relevant features associated with the phenotype. Moreover, Gene Ontology (GO) enrichment analysis revealed that genes mapped by the union of the Top10% SNPs of DTA-Weight-Top-5 were significantly enriched in multiple biological processes related to reproduction, including regulation of flower development (GO:0009909, P value = 0.015), negative regulation of long-day photoperiodism, flowering (GO:0048579, P value = 0.045), and establishment or maintenance of cell polarity (GO:0007163, P value = 0.035) (Fig. 6E). However, these terms were not significantly enriched in the genes of the Top10% SNPs identified by any individual base learner (Supplementary Data 17), indicating that integrating multiple base learners enables GEG2P to identify a broader set of phenotype-associated functional genes. Furthermore, the Top10% SNPs identified by DTA-Weight-Top-5 were mapped to several cloned maize flowering time-related genes. For example, chr10.s_94433094 (ranked 658 by SHAP) identified by XGBoost is located within ZmCCT10 (Zm00001d024909). Previous studies have reported that ZmCCT10 regulates the proliferation of archesporial and tapetum cells and plays a key role in early anther development³⁷. Meanwhile, the genes identified by different base learners exhibited variations, reflecting the complementarity of different base learners in mining functionally relevant genes (Fig. 6F and Supplementary Data 18).

According to the descending order of the weights of base learners, we integrated the Top10% SNPs from distinct base learners and estimated the narrow-sense heritability of the union of the Top10% SNPs across different numbers of base learners. The results indicated that the genetic effect explained by the union of Top10% SNPs progressively rose as the number of base learners increased, and this trend was higher than that of the random 10% SNPs (Fig. 6G and Supplementary Data 19). Therefore, these results suggest that GEG2P effectively captured loci highly correlated with phenotype during the integration of multiple base learners. Furthermore, two-way analysis of variance (ANOVA) was performed to evaluate the interaction effects among the Top10% SNPs identified by different base learners. The results indicated that some SNPs exhibited potential epistatic relationships (interaction P value < 0.001), and each base learner identified distinct SNP pairs (Supplementary Fig. 17). Based on the interaction relationships among the Top10% SNPs in DTA-Weight-Top-5, we further constructed a potential epistatic network (Fig. 6H and Supplementary Fig. 18A-D). The interaction networks derived from different base learners were relatively independent, while loci shared by multiple base learners established connections among these networks. These results revealed a potential mechanism underlying feature complementarity in the ensemble. ZMM15 (Zm00001d013259) is a key gene involved in regulating the transition from the vegetative to the reproductive stage of maize³⁸. In addition, we identified a SNP (chr5.s_7256657) within ZMM15 whose absolute SHAP values consistently ranked in the top 10% of the four base learners (SVR, SPLS, XGBoost, and BayesA). In the union set of the Top10% SNPs of these four base learners, chr5.s_7256657 exhibited significant interactions with 1,077 SNPs (P value < 0.001) (Fig. 6I). Moreover, the GO enrichment analysis results showed that the genes mapped by these interactive SNPs were significantly enriched in the biological process of response to gamma radiation (GO:0010332, P value = 0.032) (Supplementary Data 20). This process is associated with light responses and closely related to the transition from vegetative to reproductive growth in plants. In addition, integrating RNA-seq data from 391 accessions of the same population³³ revealed that the expression value of Zm00001d013683, mapped by chr5.s_17285732 among the 1,077 interacting SNPs, was significantly correlated with ZMM15 expression (P value = 3.8 × 10⁻⁸). And earlier flowering was significantly associated with increased expression of Zm00001d013683 (P value = 1.5 × 10⁻⁴) (Supplementary Fig. 19A). These results provide evidence supporting potential interactions among the Top10% SNPs identified by different base learners from the perspective of gene expression and phenotype association. Overall, integrating multiple base learners enables GEG2P to identify more functionally relevant features.

For PH and EW, 4,421 and 979 SNPs from the Top10% SNPs of PH-Weight-Top-5 (SVR, XGBoost, KNN, BayesA, DeepGS) and EW-Weight-Top-5 (SVR, XGBoost, gMLP, DeepGS, LASSO), respectively, were co-located with sQTLs related to maize plant architecture and yield³³. However, only one and three co-localized SNPs were shared by all five base learners, respectively (Supplementary Fig. 10C, Supplementary Fig. 11C, and Supplementary Data 16). In addition, the union of the Top10% SNPs of PH-Weight-Top-5 and EW-Weight-Top-5 mapped to 7747 and 7494 specific genes, respectively. However, only 44 and 56 genes, respectively, were shared by all five base learners (Supplementary Fig. 10D and Supplementary Fig. 11D), indicating that the biologically relevant features captured by different base learners are distinct. GO enrichment analysis results showed that the genes mapped by the union of the Top10% SNPs of PH-Weight-Top-5 were significantly enriched in multiple biological processes related to cell division, including sister chromatid cohesion (GO:0007062, P value = 0.008), purine ribonucleoside salvage (GO:0006166, P value = 0.013), negative regulation of G1/S transition of mitotic cell cycle (GO:2000134, P value = 0.029), regulation of cell shape (GO:0008360, P value = 0.034), and cell division (GO:0051301, P value = 0.036) (Supplementary Fig. 10E), as well as the DNA replication factor C complex (GO:0005663, P value = 0.007) in the cellular component category (Supplementary Data 21). Similarly, the genes mapped by the union of the Top10% SNPs of EW-Weight-Top-5 were significantly enriched in multiple biological processes related to starch and lipid metabolism, including starch biosynthetic process (GO:0019252, P value = 0.024), lipid X metabolic process (GO:2001289, P value = 0.026), and lipid A biosynthetic process (GO:0009245, P value = 0.048) (Supplementary Fig. 11E), as well as the cellular component amyloplast (GO:0009501, P value = 0.003) (Supplementary Data 21), and the molecular function starch binding (GO:2001070, P value = 0.003) (Supplementary Data 21). However, these functions were not significantly enriched in the genes mapped by the Top10% SNPs of any single base learner (Supplementary Data 22 and 23). These findings indicate that integrating multiple base learners enables GEG2P to identify a greater number of functionally relevant genes associated with the phenotype. Furthermore, the Top10% SNPs of PH-Weight-Top-5 and EW-Weight-Top-5 were mapped to several previously cloned genes associated with plant architecture and yield in maize. For example, multiple SNPs in Top10% of PH-Weight-Top-5 are located within Br2 (Zm00001d031871), including chr1.s_204750415, chr1.s_204751737, and chr1.s_204752205. Br2 regulates the polar transport of auxin and thereby affects plant height in maize³⁹. chr6.s_94192268 identified by both SVR and LASSO in EW-Weight-Top-5 is located within KNR6 (Zm00001d036602). Previous studies have reported that KNR6 regulates floret number per ear and kernel row number in maize, and overexpressing KNR6 can significantly increase yield⁴⁰. Meanwhile, genes mapped by distinct base learners also differed, similarly reflecting the complementarity among base learners (Supplementary Figs. 10F, 11F, and Supplementary Data 18).

Similar to the results of DTA, the genetic effect captured by the union of Top10% SNPs identified by PH-Weight-Top-5 and EW-Weight-Top-5 increased as the number of base learners increased. Moreover, the increase was greater than that of the random 10% SNPs (Supplementary Figs. 10G, 11G and Supplementary Data 19). These results indicate that GEG2P can effectively capture loci highly associated with the phenotype through the integration of multiple base learners. In the potential Top10% SNP epistatic networks in PH-Weight-Top-5 and EW-Weight-Top-5, shared SNPs also established connections among the interaction networks derived from different base learners (Supplementary Figs. 10H, 11H, 20–23). BRD1 (Zm00001d033180) is a key gene involved in regulating maize plant height. Previous study have shown that BRD1 mutants in maize exhibit severe dwarfism⁴¹. Furthermore, we identified a SNP (chr1.s_253166238) within BRD1 whose SHAP values consistently ranked in the top 10% of three base learners (XGBoost, BayesA, and DeepGS). In the union set of Top10% SNPs of the three base learners, chr1.s_253166238 exhibited significant interactions with 401 SNPs (P value < 0.001) (Supplementary Fig. 10I). GO enrichment analysis results showed that the genes mapped by these interactive SNPs were significantly enriched in the molecular function of DNA endonuclease activity (GO:0004520, P value = 0.029) and myosin binding (GO:0017022, P value = 0.046) (Supplementary Data 20). These functions influence cell cycle progression and the establishment of cell polarity, both of which are related to the formation of maize plant height. In addition, the expression value of Zm00001d032283, mapped by chr1.s_220370448 among the 401 interacting SNPs, was significantly correlated with BRD1 expression (P value = 3.4 × 10⁻⁸). Moreover, the dwarf phenotype was significantly influenced by the expression value of BRD1 (P value = 0.017) (Supplementary Fig. 19B). These results reflect potential interactions among genes mapped by the Top10% SNPs. Similarly, ZmACO2 (Zm00001d020686) is a key gene involved in regulating ear length and grain yield in maize⁴². We identified a SNP (chr7.s_128315768) within ZmACO2 whose absolute SHAP values consistently ranked in the top 10% of three base learners (SVR, gMLP, and DeepGS). In the union set of Top10% SNPs of the three base learners, chr7.s_128315768 exhibited significant interactions with 268 SNPs (P value < 0.001) (Supplementary Fig. 11I). KEGG pathway analysis results revealed that the genes mapped by these interactive SNPs were significantly enriched in alanine, aspartate, and glutamate metabolism pathway (zma00250, P value = 0.037) (Supplementary Data 24). This pathway is involved in amino acid metabolism and may also participate in the regulation of seed development and endosperm formation. Furthermore, the expression value of Zm00001d012822, mapped by chr5.s_922298 among the 268 interacting SNPs, was significantly correlated with ZmACO2 expression (P value = 1.9 × 10⁻⁸). In addition, the expression value of ZmACO2 showed a significant effect on ear weight (P value = 2.7 × 10⁻⁴) (Supplementary Fig. 19C). These results further provide evidence for potential interactions among the Top10% SNPs identified by different base learners.

Discussion

In this study, GEG2P achieved stable improvements in genomic prediction accuracy by adopting a three-step iterative optimization strategy. By integrating deep learning, machine learning, and statistical methods, GEG2P(v1) combines the feature extraction capabilities of diverse base learners and improves genomic prediction accuracy. In the first step of the iterative optimization, the boundaries among method categories can be overcome. The second step of the iterative optimization makes full use of the advantages of existing ensemble models. By using ensemble models as candidate base learners, GEG2P(v2) further increases the diversity of base learners and achieves higher prediction accuracy. The third step of iterative optimization is to optimize the dynamic combination of base learners. By progressively eliminating base learners with lower genomic prediction accuracy, GEG2P(v3) effectively selects combinations of base learners with superior genomic prediction performance, thereby achieving the highest prediction accuracy across all traits. Overall, GEG2P exhibits two key characteristics in the process of integrating base learners. On the one hand, GEG2P tends to assign higher weights to base learners whose prediction results are more independent, which helps reduce information redundancy among base learners. On the other hand, GEG2P tends to include base learners from different categories, which enables the extraction of a wide range of linear and nonlinear features from genotype data.

The need to integrate multiple base learners is further supported by the limited predictive stability of individual genomic prediction methods. Quantitative traits are often determined by the combined effects of multiple factors, and differences in the genetic bases of traits lead to varying contributions of genetic loci to the phenotype variation (Supplementary Fig. 5). Therefore, the predictive performance of single base learners is often unstable, making it difficult to achieve high prediction accuracy across all traits. Taking the phenotypes of maize as an example, there were significant differences among the base learners that achieved the highest prediction accuracy across all the phenotypes (Supplementary Data 25). For the six flowering-time-related traits, SVR was the base learner with the highest accuracy in predicting DTS, ATI, SAI, and STI, while BayesB was the base learner with the highest accuracy in predicting DTA and DTT. For the eight plant architecture-related traits, SVR showed the highest accuracy in predicting ELW, LNAE, PH, TBN, and TL; BayesB achieved the highest accuracy in predicting ELL and LNBE; and BayesC achieved the highest accuracy in predicting EH. For the nine yield-related traits, SVR was the base learner with the highest accuracy in predicting EL, ERN, KNPR, KWPE, LBT, EW, and ED, while BayesC and RR were the base learners with the highest accuracy in predicting CW and KNPE, respectively. Therefore, there are significant differences in the prediction accuracy of single base learners across different phenotypes within the same species, indicating limited generalization ability.

Meanwhile, it is difficult for a single base learner to achieve the highest prediction accuracy across multiple crops, and its generalization ability in predicting phenotypes of different species is limited. Different base learners exhibit high prediction accuracy only for some traits in specific species, including wheat, rice, chickpea, and soybean (Supplementary Data 25). For example, BayesA and RR achieve high prediction accuracy for some traits of maize, while LASSO and rrBLUP achieve the highest prediction accuracy for several traits of soybean and chickpea, respectively. The Random Forest model achieves relatively high prediction accuracy only for some traits of wheat and chickpea. In summary, existing single base learners often fail to achieve high accuracy of multiple species and traits. GEG2P extracts genotype features by integrating various types of base learners and uses the genetic algorithm together with the iterative optimization strategy to identify the optimal combination of methods. GEG2P achieves consistently higher phenotype prediction accuracy across multiple traits and species, which demonstrates strong generalization ability.

We further assessed how the number and composition of base learners affected prediction performance. The number of base learners has a significant impact on the prediction accuracy of integrated models. The accuracies of GEG2P(ML), GEG2P(DL), and GEG2P(SS) that integrate multiple base learners of the same category of GP algorithms are all superior to those of single base learners. This result is consistent with conclusions from the previously reported studies. For example, the model proposed by Ma et al. ¹⁰, which combines DeepGS with rrBLUP, and the model proposed by Zhang et al. ²² both achieve higher prediction accuracy than single base learners. However, the experimental results indicate that a larger number of base learners does not lead to better performance. During the process of iterative optimization, GEG2P(v3) gradually removes base learners with lower PCC. Taking the maize DTA, PH, and EW phenotypes as examples, most base learners achieve high prediction accuracy although the predictions of a few base learners deviate substantially from the observed values (Supplementary Fig. 24A, C, E). These base learners are assigned lower weights or excluded from the final model (Supplementary Fig. 24B, D, F), thereby reducing their influence on the overall predictions and improving the performance of GEG2P. Thus, achieving the highest genomic prediction performance is not necessarily dependent on a continuous increase in the number of base learners but may require a reasonable balance between the quantity and quality of base learners.

Integrating diverse base learners is crucial for enhancing genomic prediction performance. By integrating heterogeneous base learners, GEG2P(v1) outperforms GEG2P(ML), GEG2P(DL), and GEG2P(SS) that are limited to a single type of base learner. In addition, the top five weighted base learners usually cover three types of machine learning, deep learning, and statistical methods in most species and traits. Similarly, Kick et al.²⁰ reported that the type of base learners can affect the accuracy of genomic prediction. This result indicates that different types of base learners often have different theoretical assumptions and modeling mechanisms, which can extract both linear and nonlinear features embedded in the genotype data from multiple perspectives. Therefore, integrating diverse base learners is beneficial for extracting richer features, which contributes to consistent improvements in phenotype prediction accuracy.

In this study, we first integrate base learners with complementary feature extraction capabilities, enabling the model to transcend their category boundaries. We then treat the three ensemble models constructed from deep learning, machine learning, and statistical learning methods as base learners and further integrate them into GEG2P. Finally, we gradually remove base learners with lower prediction accuracy until the performance of GEG2P stabilizes. The genetic algorithm-based optimization was repeated three times with different random seeds to evaluate the prediction accuracy of GEG2P(v3). The results confirmed that the performance of GEG2P(v3) remained stable across multiple iterations (Supplementary Data 26). We also analyzed the number and types of base learners removed in different species and traits (Supplementary Data 27). We found that at least one base learner from each method category was removed in some cases. These findings further confirm that a single genomic prediction method is unlikely to achieve consistently stable predictive performance in multiple species and traits. Through the three-step iterative optimization strategy, GEG2P retains the base learners that contribute most to genomic prediction accuracy and achieves superior prediction performance.

Currently, researchers are enhancing the accuracy of genomic prediction through multiple strategies. First, some studies enhance nonlinear feature extraction by optimizing the model architecture. For example, DeepGS¹⁰ and DNNGP¹⁴ enhance the ability of feature extraction by employing deep CNNs and Batch Normalization. DLGWAS¹¹ adopts a dual-branch CNN architecture, demonstrating superior predictive performance in multiple datasets. In addition, DeepCCR¹³ improves the modeling of long-range dependencies by combining CNNs with LSTM. Second, some research works optimize the encoding mode of genotype data. SoyDNGP⁴³ employs a 3D input layer and a multi-channel structure to enhance the information acquisition capability of prediction models. Cropformer¹² adopts a 0-9 numerical encoding scheme to fully preserve the form of genotype variation, which aids in capturing complex genotype–phenotype relationships. Third, some studies have employed different model training strategies. For example, TrG2P¹⁵ first trains the model on traits with lower prediction difficulty and then applies transfer learning to enhance the prediction accuracy of the target trait. However, the mechanisms underlying these improvements in prediction accuracy remain unclear. In particular, the interpretability of prediction results represents a major challenge in current genomic selection (GS) research, especially in the context of crop breeding.

To this end, explainable artificial intelligence tools have been widely applied in genomic prediction studies. Among them, SHapley Additive exPlanations (SHAP) has demonstrated strong capability in feature interpretation across numerous studies. For example, Wang et al. ⁴⁴ used SHAP to identify key genes regulating flowering time in Arabidopsis thaliana, successfully revealing differential expression patterns among accessions with distinct flowering times. Wang et al. ¹² combined Cropformer with SHAP to interpret potential quantitative trait loci. He et al. ⁴⁵ applied SHAP to identify key loci with stable regulatory effects on phenotypes across multiple environments. Sun et al. ⁴⁶ further integrated SHAP with GWAS, addressing limitations of GWAS in capturing nonlinear genetic effects. Collectively, these studies highlight the strong capability of SHAP in feature interpretability.

Traditional genomics studies generally assume that a limited number of major-effect genes play dominant roles in determining phenotypic variation. Guided by this concept, current bioinformatics studies often identify phenotype-associated functional genes based on a small set of key genetic features. For example, Gamba et al.⁴⁷. identified key genes from 100 SNPs showing the most significant associations with flowering time in Arabidopsis based on GWAS. Wang et al. ⁴⁴ applied SHAP to select the top 20 genes contributing to genomic prediction and achieved clustering of flowering time among different accessions based on their expression patterns. In addition, Sun et al. ⁴⁶ analyzed the chromosomal distribution of the top 100 SNPs ranked by combined SHAP and GWAS contributions, revealing differences in the genetic architecture among upland cotton phenotypes.

Following the analytical framework of previous studies, we also used SHAP to quantify the contribution of individual SNPs to phenotypic prediction. To evaluate the contribution of SNPs to model predictions in high-dimensional genotype data, we used appropriate SHAP value calculation methods based on the structure of the base learner^12,44,48,49. For the deep learning-based base learners, we used GradientExplainer to calculate SHAP values of SNPs. For the machine learning-based base learners, we used KernelExplainer and TreeExplainer to calculate SHAP values. Specifically, KernelExplainer was used for non-tree-based models, whereas TreeExplainer was used for tree-based models. For the statistical base learners, we used the iml package to calculate the SHAP values of SNPs.

Based on the computed SHAP values of SNPs, we further analyzed the relationships between high-effect SNPs and the phenotype. The results revealed that high-effect SNPs were enriched in genes functionally associated with the phenotype. These results indicate that GEG2P effectively captures complex relationships between genotype and phenotype. Furthermore, we compared the SNPs identified by different base learners. The results revealed that different base learners captured distinct genetic features, consistent with previous findings⁵⁰, reflecting their capacity to model biological mechanisms from diverse perspectives. Nevertheless, each base learner generally achieved high phenotype prediction accuracy despite the differences in the loci they identified. Similarly, genetic variance decomposition analysis results (see the “Methods” section) further demonstrated that Top10% SNPs identified by different base learners consistently exhibited substantial genetic effects. For maize DTA, the additive and epistatic genetic effects of Top10% SNPs in DTA-Weight-Top-5 explained a mean of 70.12% and 6.32% of the phenotypic variance, respectively (Supplementary Fig. 25A). Similarly, the genetic effects of Top10% SNPs in PH-Weight-Top-5 and EW-Weight-Top-5 explained a mean of 75.77% and 76.42% of the phenotypic variance, respectively (Supplementary Fig. 25B, 25C). These results indicate that Top10% SNPs consistently explained the majority of the phenotypic variation despite variation in the genetic features captured by different base learners. Moreover, the variance decomposition model based on the union of Weight-Top-5 SNPs exhibited lower residual variance in most scenarios of maize DTA, PH, and EW (Supplementary Fig. 25A–C). These results indicate that integrating Top10% SNPs from multiple base learners explains a greater proportion of phenotypic variance, reflecting the complementarity of the genetic features captured by different base learners.

Furthermore, previous studies have shown that even the aggregation of all significant loci identified in GWAS explains only a minor proportion of phenotypic variance⁵¹, suggesting that much of the missing heritability likely arises from numerous small-effect variants that remain undetected due to the limitation of sample size^52–55. Through the integration of multiple base learners, GEG2P can utilize the differential genetic features captured by each base learner to identify a greater number of small-effect variants, thereby improving prediction accuracy. Therefore, utilizing artificial intelligence algorithms for genomic prediction is a crucial approach for elucidating the genetic basis of complex traits in the future.

In addition, the omnigenic model^56,57 offers a perspective for deciphering the genetic architecture of complex traits. That is to say, most phenotypic variation is jointly regulated by core and peripheral genes. Core genes exert a direct effect on the phenotype. In contrast, peripheral genes, which are broadly distributed across the genome, influence the phenotype indirectly by modulating core gene activity and may even play a more substantial role. Moreover, the Top10% SNPs identified by different base learners in GEG2P are widely distributed across the genome, consistent with the conclusion of the omnigenic model. In future work, we will investigate the mechanisms underlying the improved predictive performance of GEG2P from the perspective of the omnigenic model.

We further investigated the weight distribution of base learners across multiple species. The maize traits included DTA, PH, and EW. The rice traits included Heading_date, Height, and Yield_per_plant. The soybean traits included BBD, PLH, SL, and ST. The chickpea traits included Days_to_0.5_flowering, Plant_height, and Yield. And the wheat traits included Maturity, Grain_Yield, and Grain_Size_TKW. As shown in Fig. 7A–C, no single base learner consistently ranked among the top five for plant architecture- and flowering time-related traits across all species, whereas XGBoost consistently appeared among the top five methods for yield-related traits. It reflects the advantage of XGBoost in capturing genotype features associated with yield-related traits, supported by its gradient boosting framework, regularization mechanisms, and feature importance-based filtering. In other words, XGBoost can effectively extract the complex nonlinear relationships between high-dimensional genotype features and yield-related traits, which attains high weights in yield prediction tasks of multiple species.

Fig. 7. Stability analysis of XGBoost in predicting yield traits across multiple species.

A–C Overlap of Weight-Top-5 base learners across five species for three trait categories (flowering time, plant architecture, and yield). D–H For the predictions of maize EW, rice Yield_per_plant, soybean SL and ST, and chickpea Yield using XGBoost, genes mapped by the Top10% SNPs were significantly enriched in GO terms associated with transport, defense responses, and ATP metabolism. Bar plot colors indicate biological processes (blue) and molecular functions (orange). The x-axis indicates the number of enriched genes. P values are from Fisher’s exact test implemented on the DAVID website. Only GO terms with P values < 0.05 are shown. Source data are provided as a Source Data file.

Similarly, SHAP was applied to estimate the contribution of each SNP in XGBoost for predicting maize EW, rice Yield_per_plant, soybean SL and ST, and chickpea Yield. And GO enrichment analysis was subsequently conducted for genes mapped by the Top10% SNPs. However, wheat yield traits were excluded because the physical positions of SNPs are unavailable in the wheat genotype data. The results showed that these genes were significantly enriched in transport-related biological processes and molecular functions associated with ATP metabolism across four species (Fig. 7D–H, and Supplementary Data 28). Molecule transport is recognized as a critical process underlying crop yield, and ATP metabolism provides the essential energy required to sustain such transport. Additionally, genes mapped by the Top10% SNPs in maize, soybean, and chickpea were significantly enriched in defense-related biological processes (Fig. 7D, 7F–H, and Supplementary Data 28), suggesting a potential indirect contribution to crop yield through enhanced tolerance to biotic and abiotic stresses. Overall, these results suggest that XGBoost consistently identifies functional loci associated with yield-related traits of diverse species, which may account for its consistently high weighting in yield prediction of multiple species.

Although XGBoost exhibited relatively stable performance in predicting yield-related traits across species, further integration of additional base learners could still improve prediction accuracy. A comparison of 10-fold cross-validated PCCs of XGBoost, GEG2P(ML), and GEG2P(v3) for yield-related traits prediction across species showed that GEG2P(ML) and GEG2P(v3) achieved significantly higher prediction accuracy than XGBoost (Supplementary Fig. 26A-G). These results indicate that the integration of multiple base learners provides critical complementary features for the model, further underscoring the necessity of the ensemble strategy.

In addition to predictive performance, computational resource consumption is also an important consideration for genomic prediction algorithms (Supplementary Data 29). The ensemble learning strategy increases the computational cost of GEG2P, resulting in longer runtime and higher computational resource requirements than those of a single method. This observation is consistent with the inherent characteristics of ensemble learning. Previous studies have shown that ensemble learning generally leads to higher computational cost, whether in ensembles of deep learning models⁵⁸ or in prediction tasks that combine multiple machine learning and deep learning models⁵⁹. Furthermore, the computational resource consumption of GEG2P is mainly concentrated in the feature extraction stage of the base learners. Once the base learners are trained, they can be directly used in subsequent ensemble and optimization processes. Therefore, GEG2P achieves a reasonable balance between computational resource consumption and predictive performance from a practical application perspective.

Increased computational cost is generally acceptable when it results in improved predictive performance in genomic selection, where prediction accuracy is the primary objective. To meet the computational efficiency requirements in practical applications, we implemented and evaluated a parallelized version of GEG2P. Experimental results show that the parallelized implementation reduces the overall runtime of GEG2P by approximately 50%, substantially alleviating the overhead introduced by integrating multiple base learners. These results indicate that GEG2P has good scalability for large-scale breeding scenarios, maintaining high prediction accuracy while ensuring computational efficiency.

Several directions may further extend the practical utility and generalizability of GEG2P. Currently, several online genomic prediction platforms have been developed, including CropGS-Hub⁶⁰, the Smart Breeding Platform⁶¹, BreedingAIDB⁶², and AutoGP⁶³. These platforms deploy multiple genomic prediction algorithms and provide substantial convenience for breeding researchers. In the future, we plan to develop an online genomic prediction platform for GEG2P, enabling researchers to flexibly and efficiently invoke GEG2P and obtain phenotype prediction results in real time. In addition, we will further explore the transferability and generalization ability of GEG2P in phenotype prediction across both plants and animals. By adaptively integrating the optimal combinations of base learners, GEG2P has the potential to play an important role in the domains of crop breeding and livestock improvement. With the continuous accumulation of multi-omics data of transcriptomics, metabolomics, and phenomics, integrating these multi-modal data into GEG2P will become critical for further improving its genomic prediction accuracy⁶⁴. In the future, we aim to leverage multi-omics data to continuously enhance the prediction accuracy of GEG2P and thereby facilitate the rapid improvement of crop varieties.

Methods

Dataset

The maize dataset was derived from the Complete-diallel plus Unbalanced Breeding-derived Inter-Cross (CUBIC) population³³. This population comprises 1,404 lines derived from a combination of complete-diallel crosses and unbalanced breeding. Paired-end sequencing with 125-bp read length was performed on five-week-old seedling leaf tissues from all lines using the Illumina HiSeq 2500 platform, with an average sequencing depth of 1×. The raw sequencing data were quality-controlled using Trimmomatic (Version 0.33) and aligned to the reference genome with BWA (Version 0.7.12). SNP calling was performed using GATK (Version 3.5)⁶⁵ and SAMtools (Version 0.1.19), resulting in over 14 million SNPs. Those with a minor allele frequency (MAF) < 0.05 were subsequently removed, obtaining a total of 7,736,104 SNPs. After matching with the Maize 45 K SNP array data, 42,938 high-quality V4 version SNPs were retained for experimental analyses. In this study, we performed experiments using 23 traits in maize, including 6 flowering time-related traits, 8 plant architecture-related traits, and 9 yield-related traits. The flowering time-related traits include Days to tassel (DTT), Days to anther (DTA), Days to silk (DTS), Anther-tassel interval (ATI), Silk-anther interval (SAI), and Silk-tassel interval (STI). The plant architecture-related traits include Plant height (PH), Ear height (EH), Leaf number above ear (LNAE), Leaf number below ear (LNBE), Tassel branch number (TBN), Tassel length (TL), Ear leaf length (ELL), and Ear leaf width (ELW). The yield-related traits include Ear length (EL), Length of barren tip (LBT), Ear diameter (ED), Ear row number (ERN), Kernel number per row (KNPR), Kernel number per ear (KNPE), Ear weight (EW), Cob weight (CW), and Kernel weight per ear (KWPE).

The rice dataset comprises 1495 elite hybrid rice varieties obtained from the China National Rice Research Institute (Hangzhou, China). 1247 hybrids represent the major cultivated varieties from the 1990s to 2000s, while the remaining 248 hybrids were undergoing national hybrid variety application tests⁶⁶. Paired-end sequencing with 96-bp read length was performed on all lines using the Illumina HiSeq 2000 platform, with an average sequencing depth of 2×. Sequencing reads of all hybrid lines were aligned to the rice IRGSP 1.0 reference genome⁶⁷ using Smalt (Version 0.5.7, http://www.sanger.ac.uk/resources/software/smalt/). The alignment results were then processed with the Ssaha Pileup package (Version 0.8) for SNP calling, yielding a total of 1,651,507 SNPs. Then, a subset of 50,176 SNPs was randomly selected using PLINK (Version 1.90) for experimental analyses. In this study, we performed experiments using three rice traits, including BLUP_Heading_date for flowering time, BLUP_Height for plant architecture, and BLUP_Yield_per_plant for yield.

The wheat dataset was derived from an association panel of 10,375 bread wheat lines, sourced from preliminary and advanced yield testing programs of Australian Grain Technologies Pty Ltd (AGT)⁶⁸. All lines were genotyped using a customized Axiom™ Affymetrix array⁶⁹, resulting in 18,101 SNPs. After removing SNPs with MAF below 0.01, a total of 17,181 SNPs were retained. In this study, three traits (Maturity, Grain_Yield, and Grain_Size_TKW) of wheat were used for the experiments.

The soybean dataset was derived from a panel of 2898 elite soybean accessions, including 103 wild soybeans, 1048 landraces, and 1747 cultivated varieties⁷⁰. Paired-end sequencing with 150-bp read length was performed on all accessions using the Illumina HiSeq 2500 platform, achieving an average sequencing depth of 13×. Sequencing reads from all accessions were aligned to the soybean reference genome Gmax_ZH13⁷¹ using BWA (Version 0.7.12-r1039). SNP calling was then conducted with GATK (Version 3.7-0-gcfedb67)⁶⁵, resulting in a total of 31,870,983 SNPs. Then, a subset of 50,176 SNPs was randomly selected using PLINK (Version 1.90) for experimental analyses. In this study, four soybean phenotypes were used for experimental analyses, including BBD_BLUP (beginning bloom date) related to flowering time, PLH_BLUP (plant height) related to plant architecture, and SL_BLUP (seed length) as well as ST_BLUP (seed thickness) related to yield⁷². BBD_BLUP, PLH_BLUP, SL_BLUP, and ST_BLUP involve 1470, 1469, 1424, and 1424 accessions, respectively.

The chickpea dataset was derived from 2,921 global germplasm collections⁷³. Paired-end sequencing was performed on all accessions using the Illumina HiSeq 2500 platform, achieving an average sequencing depth of 12×. Sequencing reads were aligned to the CDC Frontier reference genome⁷⁴ using BWA-MEM (Version 0.7.15)⁷⁵. SNP calling was then conducted with GATK (Version 3.7)⁶⁵. Then, a subset of 50,176 SNPs was randomly selected using PLINK (Version 1.90) for experimental analyses. In this study, we performed experiments using three chickpea traits, including Days_to_0.5_flowering for flowering time, Plant_height for plant architecture, and Yield for yield.

Overview of GEG2P

GEG2P is a genomic prediction method based on ensemble learning and an iterative optimization strategy. GEG2P uses an iterative optimization strategy to select the optimal combination of base learners and combines the genetic algorithm to optimize the weight allocation of each base learner. Finally, it performs weighted ensemble on the phenotype prediction results of the selected base learners to obtain the prediction results based on the optimized weights and screening results. GEG2P consists of four stages: data processing, base learner training, iteration and weight optimization, and phenotype prediction. GEG2P integrates 20 different base learners to enhance the diversity and complementarity of the extracted features, including 5 machine learning methods, 5 deep learning methods, and 10 statistical methods. During the stage of iteration and weight optimization, GEG2P breaks through the category boundaries of the base learners through a three-step iterative optimization strategy. This method fully utilizes the advantages of the existing ensemble models, gradually removes base learners with lower prediction accuracy, and combines the genetic algorithm to dynamically determine the optimal combination of base learners and the weights of each base learner. The main advantage of GEG2P lies in its ability to widely integrate heterogeneous base learners for prediction. It reduces the prediction bias of a single base learner through the strategy of ensemble learning, thereby improving the stability and generalization ability of phenotype prediction. The calculation method for GEG2P prediction results is shown in Eq. 1.

$$y_{\mathrm{ensemble}}={\sum }_{i=1}^N{w}_i^{*}{y}_i$$ 1

In Eq. 1, y_ensemble denotes the prediction result, and N is the number of base learners obtained through the iterative optimization strategy. y_i represents the prediction result of the i-th base learner, and w_i^* represents the weight of the i-th base learner optimized through the genetic algorithm.

Base learners in GEG2P

GEG2P integrates 20 base learners, including statistical methods, machine learning methods, and deep learning methods. Among them, statistical methods include BayesA, BayesB, BayesC, BL, BRR, rrBLUP, LASSO, SPLS, RR, and BRNN. Machine learning methods include KNN, Random Forest, XGBoost, SVR, and MLP. Deep learning methods include gMLP, DLGWAS, DNNGP, DeepGS, and LCNN.

BayesA is a Bayesian regression model, and it assumes that the marker effect obeys the t distribution. BayesA can better capture the long-tail distribution characteristics of gene effects and has a better prediction effect in small samples and large-scale marker data. In this study, we implemented BayesA through BGLR in the R package⁷.

BayesB is also a Bayesian regression model. BayesB assumes that the marker effect obeys a mixed distribution, allowing some marker effects to be zero. BayesB is suitable for the scenario with sparse marker distribution. In this study, BayesB is implemented by BGLR in R package⁷.

BayesC is also a Bayesian regression model. BayesC assumes that all markers share the same variance, thus providing more stable effect estimation. In the field of genomic prediction, BayesC is suitable for the case where the distribution of marker effects is relatively uniform and only some markers play a major role in the traits. In this study, BayesC is implemented by BGLR in R package⁷.

LASSO is a regression method used for variable selection and regularization. LASSO is often used in genomic prediction to select the most predictive features from a large number of gene markers, improving the explanatory power of the model. This study uses R’s glmnet package to implement LASSO²⁴.

BL (Bayesian LASSO) is a Bayesian version of LASSO regression. BL can effectively identify key SNPs by combining variable selection and regularization, and inhibit the influence of unrelated SNPs on the model. BL is usually suitable for the analysis of high-dimensional genomic data. In this study, BL is implemented by BGLR in R package²³.

BRR (Bayesian Ridge Regression) is a Bayesian ridge regression method that addresses the multicollinearity problem in genomic data by providing a regularized probability framework. In the field of genomic prediction, BRR is widely used to process large-scale SNP data, which can ensure the stability and generalization ability of the model. In this study, BRR is implemented by BGLR in R package²³.

rrBLUP (Ridge Regression Best Linear Unbiased Prediction) combines ridge regression and best linear unbiased prediction (BLUP). At present, rrBLUP has been widely used in genomic prediction research in animal and plant breeding. This study implements rrBLUP through the rrBLUP package in R package⁵.

SPLS (Sparse Partial Least Squares) is a variant of Partial Least Squares Regression (PLS). SPLS is suitable for modeling high-dimensional genomic data by introducing sparsity for variable selection. It can effectively reduce the dimensionality of data while preserving important genetic signals. This study implements SPLS through spls in R package⁷⁶.

RR (Ridge Regression) is used in genomic prediction to handle multicollinearity relationships among gene markers. RR stabilizes effect estimation by adding L2 penalty term, thereby improving prediction accuracy. This study implements RR through glmnet in R package²⁴.

BRNN (Bayesian Regularized Neural Network) combines neural networks and Bayesian regularization to model complex nonlinear relationships between genotype and phenotype data. In the field of genomic prediction, BRNN can effectively prevent overfitting and improve generalization ability. This study implements BRNN through brnn in R package⁷⁷.

KNN (K-nearest neighbor algorithm)²⁵ is a simple instance-based learning algorithm, which is suitable for classification and regression tasks. It is often used for genotype-phenotype association (GPA) and genomic selection (GS) by finding the nearest neighbor for prediction. KNN can handle high-dimensional genomic data, especially in the case of fewer samples but more features. This study implements KNN through Python ‘s scikit-learn library.

Random Forest²⁶ is an ensemble learning method that improves the accuracy and stability of the model by combining multiple decision trees. Random Forest can effectively deal with the nonlinear effects of genotype data and can identify key genetic markers for feature importance analysis. This study implements random forests through Python’s scikit-learn library.

XGBoost²⁷ is an optimized gradient boosting decision tree (GBDT) algorithm, which is famous for its high efficiency and superior performance. XGBoost can model complex genotype-phenotype relationships, and it is superior to many traditional methods in computational efficiency and prediction performance. XGBoost is especially suitable for the processing of large-scale genomic data. This study implements XGBoost through Python’s xgboost package.

SVR (Support Vector Regression)²⁸ is the regression version of support vector machine (SVM). It uses kernel functions to deal with nonlinear relationships, and it is suitable for the regression task of processing high-dimensional genomic data. SVR can be used to model the complex nonlinear relationships of genotype data, especially in the case of a small number of samples but a large number of variables. This study implements SVR through Python’s scikit-learn library.

MLP (Multilayer Perceptron)²⁹ is a classical feedforward neural network. It transmits data through neurons in the input layer, hidden layer, and output layer, and the output of each layer is nonlinearly transformed by the activation function. Multilayer perceptrons are suitable for classification and regression tasks, such as disease prediction and gene-phenotype association analysis. This study implements MLP through Python’s scikit-learn library.

gMLP is a variant of multi-layer perceptron (MLP). It enhances the representation ability of the model by introducing a gating mechanism, so as to effectively capture complex patterns of features. gMLP can model the nonlinear relationships in the genotype and phenotype data, thereby improving the accuracy of phenotype prediction³¹.

DLGWAS is a genome-wide association study (GWAS) method based on deep learning. It can automatically extract features from large-scale genomic data and identify genetic variations associated with traits. Compared with traditional statistical methods, DLGWAS has stronger nonlinear modeling ability. Therefore, DLGWAS can more accurately detect the impact of complex genetic variations on phenotypes, thereby improving the reliability of phenotype prediction¹¹.

DeepGS is a deep learning model used for genome selection (GS), which can efficiently learn the mapping relationships between genotype data and target traits. Compared with traditional linear methods, DeepGS uses deep neural networks (DNN) to automatically extract nonlinear patterns in high-dimensional genomic data, thus having stronger generalization abilit¹⁰.

LCNN (Lightweight Convolutional Neural Network) is an optimized CNN structure. Its goal is to reduce the computational cost and maintain a high ability of feature extraction. LCNN can efficiently process high-dimensional genomic data and automatically extract important features related to traits³⁰.

DNNGP is a genomic prediction method based on a deep neural network (DNN). It can integrate multi-omics data and improve prediction accuracy by extracting deep features. DNNGP uses deep learning models to capture complex patterns in genomic data, and it has good phenotype prediction accuracy¹⁴.

Genetic algorithm in GEG2P

Genetic Algorithm (GA) is a global optimization method based on natural selection and genetic mechanism⁷⁸. It searches for the global optimal solution by simulating the process of biological evolution. In GA, an individual represents a candidate solution, and a population consists of multiple candidate solutions. GEG2P uses GA to determine the optimal weights of the base learners. Specifically, GEG2P takes the weight set of the base learners as a candidate solution, and takes multiple sets of weights as a candidate solution set. GA is used to optimize the candidate solution set to determine the optimal weight of each base learner. The GA in GEG2P mainly includes initialization of the candidate solution set, RMSE-based evaluation, selection, and evolutionary operations. The candidate solution set in GEG2P is shown in Eq. 2.

$$S=\left\{s_1,s_2,\dots ,s_n\right\}$$ 2

In Eq. 2, s_i represents the i-th candidate solution, namely a set of weights assigned to the base learners. n represents the number of candidate solutions, which was set to 50 in GEG2P (Supplementary Data 30). The weights in each candidate solution s_i were initialized according to Eq. 3.

$$s_i=\left\{w_1,w_2,\dots ,w_m\right\}$$ 3

In Eq. 3, irepresents the candidate solution index, and m represents the total number of selected base learners. w_m represents the weight of the m-th base learner, w∈{w | 0≤w ≤ 1,∑w = 1}.

In GEG2P, RMSE-based evaluation was used to evaluate the quality of different candidate solutions, where each candidate solution represented a set of base learner weights. After integrating various base learners based on the weights in a candidate solution, we use the Root Mean Square Error (RMSE) between the predicted phenotype values by GEG2P and the true phenotype values as the evaluation metric, as shown in Eq. 4. A lower RMSE indicates that the weight set represented by the candidate solution is more effective.

$$\mathrm{RMSE}\left(s\right)=\sqrt{{\frac{1}{M}∥\mathbf{y}-{\sum }_{k=1}^K{w}_k{\mathbf{r}}_k∥}_2^2}$$ 4

In Eq. 4, s denotes a candidate solution, namely a set of base learner weights. M denotes the number of samples in the training set, and K denotes the number of base learners. w_k denotes the weight of the k-th base learner in candidate solution s. r_k denotes the vector of predicted phenotype values generated by the k-th base learner for the training set, and y denotes the vector of true phenotype values in the training set. RMSE measures the prediction error after integrating the base learners according to the weights in candidate solution s. A lower RMSE indicates that the predicted phenotype values are closer to the true phenotype values, suggesting that the weight combination represented by the candidate solution is more effective.

To simulate the natural selection mechanism in biological evolution, this study used the tournament selection strategy to select candidate solutions with lower RMSE from the candidate solution set for the subsequent evolution. Specifically, GEG2P randomly selected k candidate solutions from the candidate solution set to form a tournament group and then selected the candidate solution with the lowest RMSE in the group as a parent solution. This process was repeated until the predetermined number of parent solutions was obtained. The selected candidate solutions were then used in the subsequent crossover and mutation operations to generate a new candidate solution set. The selection operation is defined in Eq. 5.

$${\mathrm{Parent}}_i=\begin{array}{c}\hfill \mathrm{argmin\; RMSE}\left(s\right)\hfill \\ \hfill s\in T_i\hfill \end{array},T_i\subset S,∣T_i∣=k$$ 5

In Eq. 5, S represents the candidate solution set, and T_i denotes the tournament group formed during the i-th selection. k denotes the number of candidate solutions in the tournament group, s represents the candidate solution in T_i, RMSE(s) represents the prediction error of candidate solution s, and Parent_i represents the parent candidate solution selected for the i-th tournament.

In order to effectively explore the solution space and maintain the diversity of the candidate solution set, this study adopts a combination strategy of mixed crossover and polynomial mutation. In the mixed crossover operation, the corresponding base learner weights in the parent candidate solutions are averaged in a weighted manner to generate offspring candidate solutions. The mixed crossover operation is shown in Eq. 6.

$$w_k^C=\alpha \cdot w_{1k}+\left(1-\alpha \right)\cdot w_{2k},\alpha \in \left[0,1\right]$$ 6

In Eq. 6, w_1k and w_2k represent the weights of the k-th base learner in the two parent candidate solutions, respectively. w_k^c represents the weight of the k-th base learner of the offspring candidate solution, and α represents the crossover coefficient. We set α to 0.7 in GEG2P (Supplementary Data 30).

In the polynomial mutation operation, this study perturbed the weights assigned to the base learners in the offspring candidate solution within a specified range. For the weight w_k^c of the k-th base learner in the offspring candidate solutions, the mutation operation is shown in Eq. 7.

$$w_k^M=w_k^C+\mathrm{\Delta }{w}_k$$ 7

In Eq. 7, $\mathrm{\Delta }{w}_k$ is the variance, as shown in Eq. 8.

$$\mathrm{\Delta }{w}_k=\eta \cdot \left(w_k^{\max }-w_k^{\min }\right)\cdot \left(\frac{2\cdot \mathrm{rand}-1}{{\mathrm{\mid rand\mid }}^{\eta }}\right)$$ 8

In Eq. 8, $w_k^{\max }$ represents the upper bound of weight w_k, and w_k^min represents the lower bound of weight w_k. ηrepresents the intensity of variation. rand is a random number with values ranging from 0 to 1. Equation 8 shows that the perturbation of the weights of base learners in offspring individuals is influenced by the weight, mutation intensity, and random number. To preserve the relative stability of base learner weights in offspring candidate solutions, this study applied a mutation probability to determine whether these weights are perturbed. In GEG2P, the mutation probability is set to 0.2 (Supplementary Data 30).

GEG2P explores the global optimal solution of different base learner weights through a multi-generational evolutionary strategy. In each generation of the candidate solution set, candidate solutions underwent the operations of selection, crossover, mutation, and their performance was evaluated according to RMSE until the maximum number of generations was reached. In GEG2P, the evolution rounds are set to 40 (Supplementary Data 30). During the iteration process, GEG2P gradually optimized the weight distribution, ultimately obtaining the weight combination with the lowest RMSE and the optimal phenotype prediction model.

Iterative optimization strategy

This study uses an iterative optimization strategy to break the boundary of the GEG2P method category, integrates the classification-integrated GEG2P methods again, and gradually eliminates the base learner with low accuracy to further improve the accuracy of phenotype prediction. The pseudocode for the three-step iterative optimization strategy can be seen in Supplementary Note 2.

First, this study integrates machine learning, deep learning and statistical methods to construct GEG2P(DL), GEG2P(ML) and GEG2P(SS). The experimental results show that the phenotype prediction accuracy of the three ensemble models is better than that of the single base learner, which verifies the effectiveness of the ensemble strategy. Considering the differences in feature extraction capabilities of different categories of methods, we integrated 20 genomic prediction methods to obtain GEG2P(v1). GEG2P(v1) can break through the category boundaries of GEG2P methods and directly combine models with different categories and complementary capabilities of feature extraction, thereby effectively improving the accuracy of phenotype prediction.

GEG2P(DL), GEG2P(ML), GEG2P(SS), and GEG2P(v1) are the models that integrate multiple base learners based on different strategies, and they have a wider range of feature extraction capabilities. These four models are treated as base learners and further integrated with 20 base learners to obtain GEG2P(v2). Therefore, GEG2P(v2) has stronger feature extraction capabilities than GEG2P(v1), which integrates 20 kinds of single methods, further improving the accuracy of phenotype prediction.

In addition, some base learners exhibit low genomic prediction accuracy, which may have a negative impact on overall performance. Therefore, we use an iterative strategy of gradual elimination to further improve the model performance. In each iteration, the worst-performing base learner is removed, and the prediction accuracy of the resulting ensemble models is evaluated. When the accuracy of phenotype prediction no longer increases, the iteration process ends and GEG2P(v3). Through the iterative optimization strategy mentioned above, GEG2P(v3) can maximize the retention of base learners that have made practical contributions to improve prediction performance, thereby achieving high phenotype prediction accuracy.

Comparative genomic prediction methods

We conducted experimental analysis between GEG2P and six mainstream genomic prediction methods. Among them, SoyDNGP⁴³ processes genotype data through a multi-channel encoding method and then adaptively fuses multi-channel features to improve the feature extraction ability of the model. Cropformer¹² used a 0-9 coding scheme to process genotype data. This method combines CNN and multi-head self-attention mechanism to achieve local and global feature extraction, effectively capturing the complex mapping relationships between genotype and phenotype. WheatGP⁷⁹ integrates multi-scale genotype features by combining CNN and LSTM. EGGPT²¹ is an ensemble learning method that achieves flexible integration of multiple base learners through a five-layer, highly decoupled framework. RKHS (Reproducing Kernel Hilbert Space) models the complex nonlinear relationship between genotype and phenotype by mapping genotype data to a feature space defined by kernel functions. By utilizing nonlinear kernel functions such as Gaussian kernels, RKHS can effectively capture nonlinear features in genotype data⁸⁰. Multi-kernel GBLUP⁸¹ divides genotype data into multiple kernel matrices based on the traditional GBLUP framework, which are constructed from different subsets of markers. By simultaneously modeling multiple genomic relationship matrices, this method can more flexibly characterize the characteristics of different genetic regions.

Narrow-sense heritability calculation

Narrow-sense heritability is an important metric that quantifies the proportion of phenotypic variation attributable to genetic factors⁸². In this study, VCFtools (Version 0.1.16)⁸³ was used to extract the genotypes of the Top10% SNPs identified by each base learner. Subsequently, a genetic relationship matrix (GRM) was constructed for these Top10% SNPs using PLINK (Version 1.90), employing the --make-grm-bin option. The GRM was subsequently fitted to a mixed linear model (MLM) using GCTA (Version 1.94.1)⁸⁴, and narrow-sense heritability of the Top10% SNPs was estimated via restricted maximum likelihood (REML). For the control, an equal number of SNPs were randomly sampled from the whole genome, with each control set repeated 50 times for the analysis.

Heritability was estimated using the mixed linear model, as shown in Eq. 9.

$$\mathbf{y}=\mathbf{X}\mathit{\beta }+\mathbf{g}+\mathit{\epsilon }$$ 9

In Eq. 9, y is an n × 1 phenotype vector, and n denotes the sample size. X denotes the fixed effect matrix (the fixed effect for all individuals was set to 1 in this study), and β denotes the fixed effect vector. g is an n × 1 vector of the total genetic effects of the individuals. g ~ N (0, $\mathbf{A}{\sigma }_g^2$), A denotes the genetic relationship matrix among individuals, and ${\sigma }_g^2$ represents the genetic variance. Ɛ denotes the residual effects. Then, the covariance matrix of the phenotype vector y is shown in Eq. 10.

$$\mathbf{V}=\mathbf{A}{\sigma }_g^2+\mathbf{I}{\sigma }_{\epsilon }^2$$ 10

In Eq. 10, I is an n × n matrix, and n denotes the sample size. ${\sigma }_{\epsilon }^2$ denotes the residual variance. Subsequently, the narrow-sense heritability of the phenotype can be estimated using Eq. 11.

$$h^2=\frac{{\sigma }_g^2}{{\sigma }_g^2+{\sigma }_{\epsilon }^2}$$ 11

Evaluation of potential epistatic interaction effects among SNPs

This study employed a two-way ANOVA to evaluate the potential interaction effects among SNPs. Initially, the genotype VCF files were converted to a numerical format using the “--recodeA” parameter in PLINK (Version 1.90). Subsequently, a linear regression model was constructed for each pair of SNPs using the base function lm() in R (Version 4.3.3), as shown in Eq. 12.

$$\mathbf{y}~{\mathbf{SNP}}_{\mathbf{1}}+{\mathbf{SNP}}_{\mathbf{2}}+{\mathbf{SNP}}_{\mathbf{1}}\times {\mathbf{SNP}}_{\mathbf{2}}$$ 12

In Eq. 12, y is an n × 1 vector of phenotypes, n denotes the sample size. SNP₁ and SNP₂ denote the genotype data of two SNPs, both being n × 1 vectors. SNP₁×SNP₂ is used to evaluate the epistatic interaction effect between SNP₁ and SNP₂. If the interaction term in the linear regression model makes a significant contribution to phenotype variation (P value < 0.05), the interaction between SNP₁ and SNP₂ is considered to exhibit a significant epistatic effect.

Genetic variance decomposition

In this study, the BGLR (Version 1.1.4)²³ R package was used to perform genetic variance decomposition for both Top10% SNPs of individual base learners and the union of Top10% SNPs of Weight-Top-5. Since the maize dataset consists entirely of inbred lines, only additive (G_a) and epistatic (G_e) effects were modeled in the variance decomposition. The mixed linear model is shown in Eq. 13.

$$\mathbf{y}=\mu +{\mathbf{G}}_{\mathbf{a}}+{\mathbf{G}}_{\mathbf{e}}+\mathit{\epsilon }$$ 13

In Eq. 13, y is a vector of phenotypes assumed to follow a normal distribution. μ is the overall mean. G_a ~ N(0, ${\mathbf{GRM}}_{\mathbf{a}}{\sigma }_a^2$), G_e ~ N(0, ${\mathbf{GRM}}_{\mathbf{e}}{\sigma }_e^2$) are vectors of additive and additive epistatic genotypic effects, respectively. Ɛ ~ N(0, ${\mathbf{I}}_{\mathit{\epsilon }}{\sigma }_{\epsilon }^2$) denotes the model residual. I_Ɛ denotes the corresponding identity matrix. G_a, G_e and Ɛ are assumed to be mutually independent random effects following multivariate normal distributions. GRM_a and GRM_e are the covariance matrices for the additive and additive epistatic effects, which are defined in Eqs. 14 and 15, respectively.

$${\mathbf{GRM}}_{\mathbf{a}}=\frac{\mathbf{X}{\mathbf{X}}^{\mathbf{T}}}{2{\sum }_{k=1}^p{p}_k\left(1-p_k\right)}$$ 14

$${\mathbf{GRM}}_{\mathbf{e}}={\mathbf{GRM}}_{\mathbf{a}}\mathit{\odot }{\mathbf{GRM}}_{\mathbf{a}}$$ 15

In Eq. 14, X = (x_ij – 2p_j), where x_ij represents the genotype coding of the i^th genotype at the j^th SNP marker, and p_j is the reference allele frequency at the j^th SNP marker. X^T is the transpose matrix of X. Accordingly, the covariance matrices for additive epistatic effects in Eq. 15 were approximated using the Hadamard product of GRM_a.

Following the analytical framework of Gogna et al.⁸⁵, additive (${\sigma }_a^2$), additive epistatic (${\sigma }_e^2$), and residual (${\sigma }_{\epsilon }^2$) variances were estimated based on the Bayesian regression framework implemented in BGLR package. The proportions of additive, additive epistatic, and residual variance were estimated using Eqs. 16, 17, and 18.

$${\mathrm{PVE}}_{\mathrm{a}}=\frac{{\sigma }_a^2}{{\sigma }_a^2+{\sigma }_e^2+{\sigma }_{\epsilon }^2}$$ 16

$${\mathrm{PVE}}_{\mathrm{e}}=\frac{{\sigma }_e^2}{{\sigma }_a^2+{\sigma }_e^2+{\sigma }_{\epsilon }^2}$$ 17

$${\mathrm{PVE}}_{\mathrm{\epsilon }}=\frac{{\sigma }_{\epsilon }^2}{{\sigma }_a^2+{\sigma }_e^2+{\sigma }_{\epsilon }^2}$$ 18

Visualization tools and functional enrichment analysis

The physical positions of genes mapped by Top10% SNPs of each base learner on the chromosomes were visualized using the MG2C online tool (http://mg2c.iask.in/mg2c_v2.1/ index_cn.html)⁸⁶. Potential epistasis networks were constructed in Gephi (https://gephi.org/)⁸⁷ based on the significant SNP-SNP interactions among the Top10% SNPs of each base learner. GO enrichment analysis and KEGG pathway analysis were conducted using the Functional Annotation Tool on the DAVID website (https://davidbioinformatics.nih.gov/)⁸⁸.

Model training and evaluation metrics

We used 10-fold cross-validation to evaluate model performance, and each experimental dataset was divided into 90% training samples and 10% test samples. Bayesian optimization was employed for hyperparameter tuning. The prediction accuracy of each model was evaluated by calculating the average Pearson’s correlation coefficient (PCC) and mean squared error (MSE) across the 10 folds, while the standard error (SE) across folds was used to assess the stability of the prediction model. During optimization of base learner weights using the genetic algorithm, the sample partitioning strategy from the training phase is strictly followed to avoid data leakage. To evaluate the overall performance of the genomic prediction methods, we calculated their average PCC across multiple traits, as shown in Eq. 19.

$${\mathrm{PCC}}_{\mathrm{avg}}=\frac{1}{N}{\sum }_{i=1}^N{\mathrm{PCC}}_i$$ 19

In Eq. 19, i denotes the trait index, PCCᵢ represents the prediction accuracy of the genomic prediction method for trait i, and N is the total number of traits. In addition, we used Eq. 20 to quantify the improvement in prediction accuracy of GEG2P compared with other genomic prediction methods.

$$I_{\mathrm{GEG}2\mathrm{P},M}=\frac{{\mathrm{PCC}}_{\mathrm{GEG}2\mathrm{P}}-{\mathrm{PCC}}_M}{{\mathrm{PCC}}_M}\times 100\%$$ 20

In Eq. 20, PCC_GEG2P represents the average PCC of GEG2P across multiple traits, and PCC_M denotes the average PCC of genomic prediction method M across multiple traits.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

Conceptualization, J.L., Y.X., and W.Y.; Methodology, Z.Y., L.W., L.Z., X.L., Q.W., F.W., and G.W.; Writing-Original Draft, Z.Y., L.W., L.Z., and X.L.; Writing-Review & Editing, Z.Y., L.W., and L.Z.; Funding Acquisition, J.L.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

Funding

This work has been supported by the National Natural Science Foundation of China [32572406], Major Program (JD) of Hubei Province (2025BEA003), the National Key Research and Development Program of China [2022YFD1201504], Major Project of Hubei Hongshan Laboratory (2022HSZD031), Guizhou Provincial Basic Research Program (Natural Science) [MS[2025]096)] and [MS[2026]814)].

Data availability

Genotypic data of maize accessions are deposited in the NCBI Bioproject database under accession PRJNA597703³³ and phenotypic data are available at CropGS-Hub⁶⁰_. The genotypic and phenotypic data of wheat are available at Figshare [https://figshare.com/s/287c2c7f1623008487a5]⁶⁸. Genotypic data of rice accessions are deposited in the European Nucleotide Archive under accession ERP005527 and phenotypic data are reported in by Huang et al. [10.1038/ncomms7258]⁶⁶. Genotypic data of soybean accessions are deposited in the Genome Variation Map under accession GVM000063⁷⁰ and phenotypic data are available at SoyOmics⁷². The genotypic and phenotypic data of chickpea are deposited in CicerSeq [https://cegresources.icrisat.org/cicerseq]⁷³. The dataset containing significant interaction pairs (P value < 0.05) of the Top10% SNPs identified by Weight-Top-5 in maize generated in this study has been deposited in Zenodo [10.5281/zenodo.21018418]⁸⁹. Source data are provided with this paper.

Code availability

Scripts used in this study are available at GitHub [https://github.com/Deep-Breeding/GEG2P]⁸⁹. We also provide a Docker image to enable users to run our code more easily. The Docker image is publicly available on Docker Hub [https://hub.docker.com/r/coder02lq/geg2p].

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-75788-x.