EGGPT：an extensible and growing genomic prediction technology

EGGPT：an extensible and growing genomic prediction technology | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article EGGPT：an extensible and growing genomic prediction technology Jianhui Wu, Yuze Wang, Rui Yu, Linsiwan Long, Jiwen Zhao, Meng Yuan, and 8 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4581596/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Genomic selection (GS) is an effective way to aid breeders in enhancing the precision and efficiency of plant and animal breeding through the use of genomic prediction (GP) methods. However, most of GP methods based on a single algorithm are poor robustness and lags behind the development of algorithms in the field of artificial intelligence (AI). To address these limitations, we present an extensible and growing genomic prediction technology (EGGPT). EGGPT is designed on engineering principles, that abstracts the GP process into a five-layer structure including data collection, processing, encoding, base and meta model construction. Using the ensemble learning, EGGPT overcomes the poor robustness. And the highly decoupled modular architecture enables rapid integration with new methods to achieve the best performance for all datasets. These datasets involve 84 various traits across 7 plant and 1 animal species, suggesting that EGGPT could emerge as a new paradigm in GP. Biological sciences/Computational biology and bioinformatics/Computational models Biological sciences/Computational biology and bioinformatics/Machine learning Genomic prediction method extensible and growing ensemble learning machine and deep learning artificial intelligence Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction Food security faces two primary challenges: a growing global population and a worsening global environment. The world population is expected to reach 9.5 billion people by 2050, and must address environmental issues such as the reduction in cultivation area and increasing number of extreme weather events, as well as a greater threat from pests and diseases 1–4 . Although traditional breeding methods are effective, they require a long breeding cycle in addressing these challenges. Consequently, it is necessary to develop new methods to speed up the breeding process. GS is one such method 5, 6 . GS is a method to select candidate individuals by using prediction models based on genetic markers. This approach can drastically reduce the time needed to develop new cultivars compared to traditional phenotype-based selection 7 . GS is widely adopted and recognized as a valuable tool for accelerating genetic gain in plant and animal breeding programs 8–12 . The effectiveness of GS in accelerating the breeding process is dependent on many factors, including the size and structure of the training population, coverage of genetic markers across the genome, heritability of the traits, and the GP method 13, 14 . GP methods, as a key factor in the effectiveness of GS, have rapidly developed over the past two decades. The trends in development have primarily shifted from traditional statistical algorithms to machine learning and deep learning algorithms. Initially dominated by statistical algorithms such as BLUP, Bayes, and LASSO in the 2000s, the focus shifted to machine learning and deep learning algorithms like gradient boosting machine (GBM), random forest (RF), support vector machine (SVM), multi-layer perceptron (MLP), and convolutional neural network (CNN) in the 2010s 15–26 . This trend can be observed across numerous disciplines 27, 28 . Although AI algorithms such as SVM, RF, ANN, and CNN have been applied to GS, their adoption lags behind the development of algorithms in the field of AI. For instance, CNN, introduced in 1998, was not adopted in GS for two decades, around 2018 26, 29 . Furthermore, the transformer algorithm has been available since 2017 and has not been widely adopted in GS to date 30 . Therefore, rapid utilization of advanced and effective algorithms is an important way to enhance the effectiveness of GS. Moreover, current GP models, which primarily rely on a single algorithm, have inherent limitations; for example, they often achieve peak performance only in a subset genotypes within a species and for certain traits, and therefore cannot perform consistently and optimally across species and traits 23, 24, 26, 31, 32 . This lack of universality highlights the need for a universal and robust GP model. In this study, we developed EGGPT, an innovative genomic prediction technology designed for extension capacity, future growth, and universal application across species. Built on engineering principles, EGGPT is characterized by its modular and decoupled design; it has a five-layer architecture with each layer and the components within each layer being independent. Based on its highly decoupled modular architecture, EGGPT overcomes the limitations of traditional genomic prediction models relying on a single algorithmic. Instead, EGGPT employs a stacking method to ensemble learning that combines multiple algorithms, thus enhancing overall accuracy. The design allows EGGPT to integrate a diversity of algorithms from numerous fields. Presently, EGGPT has extended many methods such as principal component analysis (PCA), p values for SNP, SVM, RF, MLP, CNN, long short-term memory networks (LSTM), and transformer. This transformer not only outperforms most existing models relying on a single algorithm but also significantly enhances the overall performance of EGGPT. By extending these methods, EGGPT, an extensible and growing genomic prediction technology, consistently achieved optimal performance across datasets for 84 traits across eight species. 2. Results 2.1 Overview of EGGPT EGGPT is based on a highly decoupled modular architecture, which is preliminarily divided into five layers: data collection layer, data processing layer, data encoding layer, base model construction layer, and meta model construction layer. As components in each layer are extended, EGGPT's capabilities correspondingly increase (Fig. 1 ). The data collection layer collects essential information for genomic prediction, including the phenotypic and genomic data. This layer not only supports genomic data, such as single nucleotide polymorphisms (SNP), but also supports multi-omics data, such as gene expression (GE). The data processing layer processes the collected phenotypic and genomic data. The first step is divided into a training set, a validation set, and a test set. Following, the divided data is processed with the selected components. Currently, the components of this layer include PCA and p value; PCA is utilized for global dimensionality reduction of the genomic data; p value is utilized for the filtering of SNPs associated with phenotypes. It is important to emphasize that PCA and p value components are applied to the training set. The validation and test sets are processed using the information derived from the training set. The data encoding layer captures a wide range of effects through multi-dimensional encoding and transforms the data into a format that aligns with the requirements of the base model. This layer currently includes one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) encoding components. After dimensional encoding, adaptive encoding is applied to ensure that the data conforms to the input format required by the base model. The base model construction layer develops a diversity of base learners to be used in a stacking ensemble. Currently, this layer includes many models, such as SVM, RF, MLP, and CNN, which are widely used in GP; moreover, it also includes the LSTM based on Recurrent Neural Networks (RNN) and the transformer, both of which are not commonly used in GP. Note that in EGGPT, the current CNN architecture is the same as for DNNGP 31 . The meta model construction layer builds the meta learner, which is a critical component of the stacking methods. Currently, this layer includes a meta model component and a model pruning component based on the greedy algorithm. The model pruning component is the foundation for enabling growth in accuracy. It obtains a more optimal group of base learners by discarding those that negatively affect accuracy. This process not only helps in optimizing the ensemble for better performance but also ensures that the final model does not become unnecessarily complex. 2.2 Assessment Criteria Accuracy metric. In the main body of this study, the accuracy metric is the root mean absolute error (RMSE). A lower RMSE indicates better model performance. In the supplementary materials, pearson correlation coefficient ( r ), coefficient of determination ( R 2 ), and mean absolute percentage error (MAPE) is also employed as an additional metric of accuracy. 10-fold cross-validation. In this study, the assessment of accuracy employs a 10-fold cross-validation. Each dataset was randomly split into ten equally sized folds. Each fold would be the validation set and the remaining nine folds were grouped into the training set. The final accuracy for the dataset is the mean of the accuracies obtained from each validation set. Hyperparameter. In both machine learning and deep learning, the setting of model hyperparameters significantly impacts the model performance on a dataset. An appropriate hyperparameter configuration can enable the model to achieve better performance on the specific dataset currently in use. For all results presented in this study, except for the hyperparameter adjustments specially mentioned, our EGGPT used the same hyperparameter configuration across all datasets. The same hyperparameter configuration further demonstrates universal applicability of EGGPT across diverse species and traits, and indicates that achievement the best performance in each trait is attributed to its architecture, rather than to specific hyperparameter tuning for each trait. Early stopping. Early stopping is a regularization technique used to stop the training of a deep learning model if the performance on a validation set does not improve during a specified number of training iterations. In this study, all deep learning models employed the same early stopping mechanism to ensure consistency. 2.3 Impact of extending components in each layer Impact of extending components in the data collection layer. To demonstrate the extension capacity and growth potential of EGGPT in the data collection layer, we conducted 3 iterations of EGGPT on the Wheat406 dataset, labeled EGGPT1.1 (E1.1) through E1.3 (Fig. 2 a). The results show that the RMSE is lower when the data processing layer is extended with additional component (Fig. 2 b, Supplementary Table 1). E1.3, which is based on E1.1, extended the data collection layer component used in E1.2 (GE). The RMSE of E1.3 across all traits in Wheat406 marked an average reduction of 4% when compared to the lowest previous iteration specific to each trait. Impact of extending components in the data processing layer. To demonstrate the extension capacity and growth potential of EGGPT in the data processing layer, we conducted 3 iterations on the datasets encompassing 8 species and 84 traits, labeled E2.1 through E2.3 (Fig. 2 c). For each iteration, we held all layers constant, except for the data processing layer, to ensure that any observed difference in performance was attributable to this layer. The results showed that the RMSE falls when the data processing layer is extended with additional component (Fig. 2 d). The results were consistent across all remaining traits (Supplementary Table 2). E2.3, which is based on E2.1, extended the data processing layer component used in E2.2. The RMSE of E2.3 across all traits marked an average 3.4% reduction compared to the lowest single-component iteration specific to each trait. The greatest RMSE reduction was observed in GWD (grain width) of rice, which obtained a 13.2% relative reduction. By contrast, the smallest reduction was observed in FT (flowering time) of rapeseed, with a 0% relative reduction. Compared to single data processing component iterations, E2.3 demonstrated superior performance across all traits, with an average RMSE reduction of 4.3% compared to E2.1, and 7.3% compared to E2.2. Impact of extending components in the data encoding layer. To demonstrate the extension capacity and growth potential of EGGPT in the data encoding layer, we conducted 5 iterations on datasets encompassing 8 species and 84 traits, labeled E3.1 through E3.5 (Fig. 2 e). For each iteration, we held all layers constant, except for the data encoding layer, to ensure that any observed difference in performance was attributable to this layer. The results showed that the RMSE falls when the data encoding layer is extended with additional components (Fig. 2 f). The results were consistent across all remaining traits (Supplementary Table 3). E3.3, which is based on E3.1, extended the data encoding layer component used in E3.2. The RMSE of E3.3 across all traits marked an average reduction of 1.1% when compared to the lowest previous iteration specific to each trait. E3.5, which was based on E3.3, extended the data encoding layer component used in E3.4. The RMSE of E3.5 across all traits marked an average reduction of 0.4% when compared to the lowest previous iteration specific to each trait. E3.5, which utilized three types of components simultaneously in the data encoding layer, achieved an average reduction of 1.4% across all traits, compared to the lowest single-component iteration specific to each trait. The greatest RMSE reduction was a 8% relative reduction in GWD (grain width) in rice. By contrast, the smallest reduction was in the MSPD (panicle diameter of the main stem) of millet, with only 0% relative reduction. Compared to single data encoding component iterations, E3.5 demonstrated superior performance across all traits, with an average RMSE reduction of 2.1% compared to E3.1, 2.7% compared to E3.2, and 3.1% compared to E3.4. Impact of extending components in the base model construction layer. To demonstrate the extension capacity and growth potential of EGGPT in the base model construction layer, we conducted 9 iterations on datasets encompassing 8 species and 84 traits, labeled E4.1 through E4.9 (Fig. 3 a). For each iteration, we held all layers constant, except for the base model construction layer, to ensure that any observed difference in performance was attributed to this layer. The RMSE declined when the base model construction layer was extended with additional components (Fig. 3 b). The results were consistent across all the remaining traits (Supplementary Table 4). E4.3, which was based on E4.1, extended the base model construction layer component used in E4.2. The RMSE of E4.3 across all traits marked an average reduction of 1% when compared to the lowest previous iteration specific to each trait. E4.5, which was based on E4.3, extended the base model construction layer component used in E4.4. The RMSE of E4.5 across all traits marked an average reduction of 1.1% when compared to the lowest previous iteration specific to each trait. E4.7, which was based on E4.5, extended the base model construction layer component used in E4.6. The RMSE of E4.7 across all traits marked an average reduction of 0.3% when compared to the lowest previous iteration specific to each trait. E4.9, which is based on E4.7, extended the base model construction layer component used in E4.8. The RMSE of E4.9 across all traits marked an average reduction of 0.5% when compared to the lowest previous iteration specific to each trait. E4.9 utilizing 5 types of components simultaneously in the base model construction layer achieved an average reduction of 2.2% across all traits, compared to the lowest single-component iteration specific to each trait. The greatest RMSE reduction was observed in GSLC (glucosinolate content) of rapeseed, with a 6.5% relative reduction. By contrast, the smallest reduction was observed in SS (seed setting rate) of rice, with a 0.1% relative reduction. Compared to single base model iterations, E4.9 demonstrated superior performance across all traits, with an average RMSE reduction of 4% compared to E4.1, 6.4% compared to E4.2, 3.2% compared to E4.4, 14.6% compared to E4.6, and 7.5% compared to E4.8. Impact of extending components in the meta model construction layer. To demonstrate the extension capacity and growth potential of EGGPT in the meta model construction layer, we conducted 10 iterations on the datasets encompassing 8 species and 84 traits, labeled E5.1 through E5.10 (Fig. 3 c). For each iteration, we held all layers constant, except for the base model construction layer and the meta model construction layer, to ensure that any observed difference in performance was attributed to these layers. The RMSE exhibited non-negative reduction when the meta model construction layer was extended with model pruning component (Fig. 3 d). The results were consistent across all traits in the remaining datasets (Supplementary Table 5). E5.1 to E5.5 were not extended with the model pruning component, resulting in respective average RMSE changes across all traits of -4.5%, -0.3%, -1.6%, and − 0.8%. Conversely, E5.6 to E5.10 were extended with the model pruning component, leading to respective average RMSE changes across all traits of -5.5%, -2.4%, -0.4%, and − 0.7%. Notably, the RMSE of E5.10 across all traits marked an average reduction of 1.8% when compared to E5.5. The greatest RMSE reduction was observed for C18_1 in rapeseed, with a 7.2% relative reduction. By contrast, the smallest reduction was observed in GWD (grain width) in rice with a 0% relative reduction. 2.4 Impact of extending components in multiple layers To demonstrate the extension capacity and growth potential of EGGPT, we conducted single iterations on the datasets labeled E6.1 (Fig. 3 e). E6.1, extended with multiple components, achieved the lowest RMSE (Fig. 3 f). The results were consistent across all traits in the remaining datasets (Supplementary Table 6). Compared to iterations with a single-layer extension component, E6.1 demonstrated superior performance across all traits, with an average RMSE reduction of 4.7% compared to E2.3, 6.8% compared to E3.5, and 5% compared to E4.9. 2.5 Impact of extending transformer Here, we developed a model based on the encoder component of the transformer. It contains 10 transformer layers, each containing one multi-head attention block with two heads, two layer-normalization blocks and one MLP block. The MLP block contained one input layer, one output layer, one hidden layer and two dropout layers, with the number of units in the hidden layer being six times the number of units in the input layer. To evaluate the ability of this model, we conducted 6 iterations on the datasets, labeled E7.1 through E7.6 (Fig. 4 a). E7.1 (MLP) achieved optimal performance for 13 traits, E7.2 (SVR) for 5, E7.3 (RF) for 49, E7.4 (CNN) for 1, E7.5 (LSTM) for 3, and E7.6 (transformer) for 13 traits (Supplementary Table 7). Specifically, the DNNGP model demonstrated superior performance on the Maize1404 dataset 31 . We then adjusted the CNN model hyperparameters to match the settings used by DNNGP for four traits in the Maize1404 dataset. In comparing the performance of the base models on the four traits, the RF model was the top performer. However, except for the RF, the transformer still maintained an advantage over the other base models in certain traits, such as KNPE and KWPE (Fig. 4 b). After extending transformer to EGGPT, we conducted a single iteration on the 8 species, 84 traits datasets, labeled E8.1 (Fig. 4 c). This iteration demonstrated a 0.849% reduction in average RMSE across all traits compared to E6.1. To further assess the importance of each base model in EGGPT, we conducted five iterations, labeled E8.2 through E8.6 (Fig. 4 c). Compared to E8.1, average RMSE increases across all datasets were + 0.898% for E6.1 (with transformer removed), + 0.817% for E8.2 (with MLP removed), + 0.547% for E8.3 (with SVR removed), + 0.128% for E8.4 (with RF removed), + 0.645% for E8.5 (with CNN removed), and + 0.207% for E8.6 (with LSTM removed) (Fig. 4 d, Supplementary Table 8). Based on these findings, the importance of ranking of the base models was as follows: transformer, MLP, CNN, SVR, LSTM, and RF. 2.6 Impact of population size Population size influences the performance of machine learning and deep learning models; therefore, it was an essential consideration in comprehensive evaluation of EGGPT performance 13 . We used the seven traits in Rice1495 to assess the impact of population size on EGGPT. Initially, we used a 10-fold cross-validation to split the Rice1495 dataset. In the training phase, we started with a training set of 150 samples, progressively increasing the sizes to 300, 600, and finally, 1,345. For all seven traits in the Rice1495 dataset, there was an improvement in prediction accuracy with increased sample size (Fig. 4 e, Supplementary Table 9). When comparing the 150-sample size with the 1,345-sample size, the greatest RMSE reduction was in GW, which underwent a 27.8% relative reduction. By contrast, the smallest reduction was observed in FLW, with a 7.6% relative reduction. 3. Discussion GP research currently faces two challenges: 1) slow uptake of advanced and effective algorithms from various fields to enhance GS efficiency, and 2) limited cross-species and cross-trait applicability of GS methods based on a single algorithm. EGGPT addresses the first challenge with a design based on engineering principles that ensures extensibility. It overcomes the second challenge by utilizing stacking methods to integrate diverse base models, enhancing cross-species and cross-trait applicability. In addition, it uses a model pruning algorithm component, which ensures non-negative improvements in model accuracy when extending with new components. In "Results", we presented the impact of extending EGGPT in each layer and its performance across all datasets. This not only proved its power and growth potential but also its universality. Furthermore, we introduced a transformer architecture. By integrating this transformer, EGGPT achieves further performance improvement. Note that some component combinations are not supported in the current version of EGGPT, such as GE-p value, PCA-2D encoding, PCA-3D encoding, PCA-transformer, and PCA-LSTM. For machine learning and deep learning models, the architectural design and hyperparameter configurations have a pronounced effect on accuracy in analysing specific datasets 33, 34 . In EGGPT, each individual model uses an identical set of hyperparameter configurations and model architecture across all datasets, demonstrating that its superior predictive accuracy can be attributed to its comprehensive architectural design. However, in practical applications, fine-tuning the hyperparameters can further enhance accuracy for specific datasets. For example, for the SRDS (stripe rust disease severity) in wheat, the RMSE reduction of 3.1% in using appropriate hyperparameter configurations (Supplementary Table 10). Moreover, EGGPT also can incorporate other high-performing GP models, such as DeepGS and SoyDNGP. DeepGS builds on 1DCNN with a sampling layer, and an architecture that generates superior results in some datasets 26 . For such datasets, we can substitute the CNN in the base model construction layer with the DeepGS architecture to match or exceed DeepGS's accuracy. Similarly, SoyDNGP employs a deep and narrow CNN structure and incorporates a coordinate attention (CA) mechanism after the first and final convolutional layers 32 . We can also substitute CNN with SoyDNGP's structure to match or exceed SoyDNGP's accuracy. EGGPT has many potential developmental directions. Firstly, EGGPT allows for extension capacity and growth potential in each layer. Addition of components to each layer is the primary development, such as diverse omics data and base models. Secondly, the model pruning algorithm is crucial for EGGPT. Currently, it is based on the greedy algorithm and often finds local optima 35 . Therefore, developing the model pruning algorithm to find near-optimal parsing results is one of the future development directions. Thirdly, EGGPT has the potential to obtain cross-environment prediction capabilities by incorporation of growth models. For example, a recent study showed that temperature during a window of 9 to 50 days after germination is a key environmental factor affecting the flowering time in rice. The application of a joint genomic regression analysis (JGRA) that integrates environmental indices with genomic predictions enables high-precision forecasting of flowering time across different environments 36 . Accordingly, for the growth model mentioned above, we can integrate the key environmental factor as a specific component to add the cross-environment prediction capabilities of EGGPT. Therefore, with the incorporation of growth models to get cross-environment prediction capabilities is one of the future developmental directions. An online prediction service to assist breeders is also one of the future development directions. This platform not only needs to offer easy access for breeders, but also needs to reduce response times, which depend primarily on the inference time of EGGPT. Like all deep learning-based methods, the runtime of EGGPT is principally divided into training time and inference time. Typically, the training time is borne by the developers, who are responsible for providing a service for users. Users are primarily concerned with inference time, which in the context of EGGPT, refers to the time taken to make predictions. In EGGPT, inference time is influenced by the size of the genomic data as well as the overall complexity of the model. Based on the scale of EGGPT in this study, the maximum inference time across all datasets stands at 109.8 milliseconds per individual. Although the current inference time of the EGGPT is acceptable, we need to continue the optimization. Nevertheless, we believe that EGGPT will see continuous refinement and development, evolving from the egg to the eagle. 4. Methods 4.1 Datasets used in data collection layer Nine datasets were collected, encompassing data for 8 species and 84 traits were used in the study. The first dataset, Rice1495, consisted of 1,495 hybrid rice cultivars genotyped at 1,654,030 SNP loci; 38 traits were evaluated in two environments 37 . Only 12 traits from the Hangzhou location were utilized to evaluate the EGGPT performance. The traits included yield per plant, panicle number, grain number per panicle, seed setting rate, grain weight, heading date, height, flag leaf length, flag leaf width, panicle length, grain length, and grain width. The second dataset, Maize1404, comprised 1,404 inbred maize lines genotyped at 11,825,030 SNP loci; 23 traits were evaluated 38 . All trait data were used in assessing the performance of EGGPT. These traits included days to tasseling, days to anthesis; days to silking, interval between anthesis and tasseling, interval between silking and tasseling, interval between silking and anthesis, plant height; ear height, ear leaf length, ear leaf width, leaf number above ear, leaf number below ear, tassel branch number, tassel length; ear weight, ear diameter, ear length, ear row number, kernel number per row, kernel number per ear, kernel weight per ear, cob weight; and length of barren tip. The third dataset, Millet827, included 827 accessions genotyped at 161,562 SNP loci; 12 traits were evaluated and all were included in the study 39 . The traits included top second leaf length; top second leaf width, main stem height, main stem width, panicle diameter of the main stem, fringe neck length, panicle length of the main stem, per plant grain weight, main stem panicle weight, hundred kernel weight, spikelet number of the main stem, and grain number per spike. The fourth dataset, Cotton1245, encompassed 1,245 inbred lines genotyped at 1,122,352 SNP loci; 4 traits were evaluated to assess the performance of EGGPT 40 . The traits included fiber micronaire, fiber length, fiber strength, and fiber elongation rate. The fifth dataset, Rapeseed991, included 991 inbred line genotyped at 4,286,896 SNP loci; 8 traits were evaluated and were used in the present study 41 . The traits included flowering time, glucosinolate content, protein content, oil content, and C16:0, C18:1, C18:2, C18:3 levels. The sixth dataset, Soybean2795, encompassed 2795 inbred line genotyped at 31,580,805 SNP loci and 111 traits were evaluated across multiple environments 42 . Data for 13 traits tested at Beijing in 2013 were included in this work. The traits were beginning of blooming date, FA16 content, FA18 content, total FA content, 100-seed weight, leaf length, leaf width, pod maturity date, plant height, protein content, seed length, seed thickness, and valid branch number. The seventh dataset, Wheat406, included 406 inbred lines genotyped at 605,352 SNP loci; 5 traits were evaluated to assess the performance of EGGPT 43 . The traits included total root length, root surface, root volume, root diameter and roof fresh weight. The eighth dataset, Pigeon556, encompassed 556 individuals genotyped at 160,434 SNP loci. All 6 traits evaluated were included in assessing the performance of EGGPT 44 . The traits included body weight, chest width, shin length, keel length, body length, and pectoral thickness. The ninth dataset, Wheat1458, included 1458 inbred lines genotyped at 180,000 SNP loci; 1 trait were evaluated to assess the performance of EGGPT. The trait is stripe rust disease severity. The first six datasets were downloaded from the CropGS-Hub 45 . Since the primary focus was on the extensible, growth potential, and universality of EGGPT, datasets containing more than 180,000 SNPs were uniformly subsampled to 180,000 SNPs using PLINK 46 . 4.2 Methods used in the data processing layer In the data processing layer, we applied two dimensional reduction (DR) methods, p value calculation and PCA to improve the accuracy of GP. P value was utilized as a featured selection method to identify SNPs associated with phenotypes 47 . This method allowed us to focus on a subset rather than an entire genomic dataset, thus effectively reducing the complexity of the features and capturing the genetic variation most likely to be effective for GP. To decrease runtime, we utilized a python package from https://github.com/STRIDES-Codes/GPU-GWAS that utilizes the parallel processing power of GPUs. This method significantly reduced the processing time. We used the top 1% of SNPs by p value as selected items. PCA was utilized as a global DR method to transform the full set of SNPs into a new coordinate system 48 . This method reduces the dimensionality of the data by transforming the original correlated variables into a smaller number of uncorrelated variables that still capture most of the variation in the original data. Unlike p value, which selects a subset of SNPs, PCA reduces dimensionality by creating new variables that are linear combinations of the original SNPs. We used PCA to extract the top 95% of feature variance. The combined use of p value for feature selection and PCA for global dimensionality reduction provides a comprehensive strategy to DR. 4.3 Methods used in the data encoding layer In the data processing layer we employed two encoding methods: dimensional encoding and adaptive encoding. dimensional encoding involves transforming the data to one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) representations. For example, in the case of the SNP-p value calculation component combination, SNPs indicate three types of genetic variation: homozygous reference (0/0), heterozygous variant (0/1), and homozygous alternative variant (1/1). The one-dimensional encoding component uses a one-dimensional feature vector to represent these variations: \(\left[0\right]\) encodes a homozygous reference, \(\left[1\right]\) encodes a heterozygous variant, and \(\left[2\right]\) encodes a homozygous variant. The two-dimensional encoding component uses a two-dimensional feature vector: [1, 0] encodes a homozygous reference, [0.5, 0.5] encodes a heterozygous variant, and [0, 1] encodes a homozygous alternative variant. Similarly, the three-dimensional encoding component uses a three-dimensional feature vector: [1, 0, 0] encodes a homozygous reference, [0, 1, 0] encodes a heterozygous variant, and [0, 0, 1] encodes a homozygous variant. For another example, in the case of the SNP-PCA component combination, the one-dimensional encoding component uses a one-dimensional feature vector [ 1 ] multiplied by each element of the PCA results. Adaptive encoding further transforms the data into formats suitable for input requirements for base models. For base models such as SVR, RF, MLP, and 1DCNN, the data can be simply flattened to meet the input feature requirements. However, for LSTM and transformer, the flattened data need to be divided into subsets, where the number of SNPs and the encoding dimensions dictate the segmentation logic. In most datasets used in this study, SNP counts were 180,000 and filtered to the top 1% of P values. The remaining 1,800 SNPs were the input features for the base models. After dimensional encoding and flattening, these SNPs were represented in dimensions of 1,800, 3,600, and 5,400. The 1,800-dimensional data were divided into 30 subsets, each with 60 dimensions. Similarly, the 3,600-dimensional data were divided into 30 subsets of 120 dimensions, and the 5,400-dimensional data were divided into 30 subsets with 180 dimensions. These formats like 30x60, 30x120, and 30x180 meet the input feature requirements of LSTM and transformer. The adaptive encoding ensured that the dimensionally reduced data was compatible with the diverse structures of our ensemble of base models. 4.4 Methods used in the base model construction layer In the base model construction layer, we used six models from the fields of machine learning and deep learning. These models include SVR, RF, MLP, CNN, LSTM, and transformer. Each algorithm is based on unique foundational logic and principles, and suited to different types of data and problems. We used these six models simultaneously to support diverse species and traits. SVR is a regression algorithm derived from the support vector machine 49 . The goal of SVR is to find a function that deviates no more than ε from the actual target values for the entire training dataset, while maintaining the function's flatness. SVR applies the principle of minimizing an error within a specific margin. The ε-insensitive loss function is pivotal in this model, allowing some errors to be tolerated within the ε-tube around the true data points. For a given training dataset \(\left({\text{x}}_{\text{i}}\right.,\left.{\text{y}}_{\text{i}}\right), \text{i}=1,\cdots ,\text{n}\) ,where \({\text{x}}_{\text{i}}\) is the input vector and \({\text{y}}_{\text{i}}\) the corresponding target value, SVR solves the following optimization problem: $$\underset{\text{w},\text{b},{\xi },{{\xi }}^{\ast }}{\text{min}}\frac{1}{2}{‖\text{w}‖}^{2}+\text{C}\sum _{\text{i}=1}^{\text{n}}({{\xi }}_{\text{i}}+{{\xi }}_{\text{j}}^{\ast })$$ subject to: $${\text{y}}_{\text{i}}-\left(⟨\text{w},\left.{\text{x}}_{\text{i}}⟩+\text{b}\right)\le {\epsilon }+{{\xi }}_{\text{i} },\right.$$ $$\left(⟨\text{w},\right.\left.{\text{x}}_{\text{i}}⟩+\text{b}\right)-{\text{y}}_{\text{i}}\le {\epsilon }+{{\xi }}_{\text{j}}^{\ast } ,$$ $${{\xi }}_{\text{i} },{{\xi }}_{\text{j}}^{\ast }\ge 0, \text{i}=1,\cdots ,\text{n}.$$ where variables \(\text{w}\) and \(\text{b}\) denote the coefficients of the hyperplane, \({{\xi }}_{\text{i} }\) and \({{\xi }}_{\text{j}}^{\ast }\) are slack variables representing the distance of points outside the ε-tube, and \(\text{C}\) is a regularization parameter. RF is an ensemble learning method used for classification and regression tasks 50 . It to operates by constructing multiple decision trees during the training phase. The specific process is as follows: Bootstrapping: for a training set of size N, sample N with replacement to create a bootstrapped dataset for each tree. Feature randomness: at each node in the tree, select m features from the total M (where m < < M) to find the best split. Tree growing: grow each tree to the largest extent possible without pruning to maximize diversity among the trees. Aggregation: for classification, use voting to combine tree predictions. For regression, calculate the average of the tree predictions. The SVR and RF methods were implemented in Python version 3.9.16 using the ''Scikit-learn'' (2019) module 51 . MLP, a class of feedforward artificial neural network (ANN), consists of at least three layers: an input layer, one or more hidden layers, and an output layer 52 . Each artificial neuron is connected with weighted edges to the neurons in the next layer, and applies an activation function to the weighted inputs. The specific process is as follows: 1. Initialization: set initial random weights and biases for all neurons in the network. 2. Forward propagation: for each input, propagate the data forward through the network by calculating the weighted sum of inputs and applying the activation function to compute the output of each neuron. The weighted sum calculation is: $${z}_{j}^{\left(l\right)}=\sum _{i}{w}_{ji}^{\left(l\right)}{a}_{i}^{\left(l-1\right)}+{b}_{j}^{\left(l\right)}$$ where \({z}_{j}^{\left(l\right)}\) is the weighted sum for the \({j}^{tℎ}\) neuron in the \({l}^{tℎ}\) layer, \({w}_{ji}^{\left(l\right)}\) is the weight connecting the \({i}^{tℎ}\) neuron in the \({\left(l-1\right)}^{tℎ}\) layer to the \({j}^{tℎ}\) neuron, \({a}_{i}^{\left(l-1\right)}\) is the activation of the \({i}^{tℎ}\) neuron in the \({\left(l-1\right)}^{tℎ}\) layer, and \({b}_{j}^{\left(l\right)}\) is the bias of the \({j}^{tℎ}\) neuron. In the MLP model used in this study, we adopted a Gaussian error linear unit (GELU) as the activation function. GELU can be described as $$\text{G}\text{E}\text{L}\text{U}\left(\text{x}\right)=\text{x}\cdot {\Phi }\left(\text{x}\right)$$ where \(\text{x}\) is the input to the function, and \({\Phi }\left(\text{x}\right)\) represents the cumulative distribution function of the standard normal distribution, expressed as: $${\Phi }\left(\text{x}\right)=\frac{1}{2}\left[1+\text{e}\text{r}\text{f}\left(\frac{\text{x}}{\sqrt{2}}\right)\right]$$ Here, \(\text{e}\text{r}\text{f}\) denotes the error function. The use of GELU allows the network to benefit from the properties of both ReLU and probabilistic non-linearities introduced by the Gaussian distribution, enhancing the model's capability to generalize from the training data. 3. Backpropagation: compute the error at the output and propagate it back through the network to update the weights and biases, thereby reducing the error. In the MLP model, we adopt Mean Squared Error (MSE) as the loss function. MSE can be described as: $$\text{M}\text{S}\text{E}=\frac{1}{\text{N}}\sum _{\text{i}=1}^{\text{N}}{\left({\text{y}}_{\text{i}}-{\widehat{\text{y}}}_{\text{i}}\right)}^{2}$$ where \({\text{y}}_{\text{i}}\) is the observed value, and \({\widehat{\text{y}}}_{\text{i}}\) is predicted value. The weight updates rule can be described as: $${w}_{ji}^{\left(l\right)}={w}_{ji}^{\left(l\right)}-\eta \frac{\partial E}{\partial {w}_{ji}^{\left(l\right)}}$$ where \(\eta\) is the learning rate and \(\frac{\partial E}{\partial {w}_{ji}^{\left(l\right)}}\) is the partial derivative of the error with respect to the weight. 4. Repeat: repeat steps 2 and 3 for a specific number of epochs or until the network reaches a satisfactory level of performance. CNN, a class of deep neural networks, automatically and adaptively learns spatial hierarchies of features from input data 29 . The output of a convolutional layer can be defined as an integral transformation and is represented as follows: $$\text{s}\left(\text{t}\right)=\left(\text{f}\times \text{k}\right)\left(\text{t}\right)=\sum _{\text{x}}\text{k}\left(\text{t}-\text{x}\right)\text{f}\left(\text{x}\right)$$ where k represents the kernel, and convolution is the transformation of f to s(t). LSTM, a class of Recurrent Neural Networks (RNN), can learn long-term dependencies 53 . LSTM are designed to remember information for long periods, making them well-suited for sequential data. An LSTM unit is composed of a cell, which retains its state across time steps, and three types of gates - the input gate, the forget gate, and the output gate - that regulate the flow of information into the cell, within the cell, and out of the cell, respectively. Let \({x}_{t}\) be the input at time step \(t\) , \({ℎ}_{t-1}\) be the hidden state from the previous time step, and \({C}_{t-1}\) be the cell state from the previous time step. The LSTM update equations are as follows: 1. Forget gate: $${f}_{t}=\sigma \left({W}_{f}\cdot \left[{ℎ}_{t-1},{x}_{t}\right]+{b}_{f}\right)$$ 2. Input gate: $${i}_{t}=\sigma \left({W}_{i}\cdot \left[{ℎ}_{t-1},{x}_{t}\right]+{b}_{i}\right)$$ $$\stackrel{\sim}{{C}_{t}}=tanℎ\left({W}_{c}\cdot \left[{ℎ}_{t-1},{x}_{t}\right]+{b}_{C}\right)$$ 3. Cell state update: $${C}_{t}={f}_{t}\ast {C}_{t-1}+{i}_{t}\ast \stackrel{\sim}{{C}_{t}}$$ 4. Output gate: $${o}_{t}=\sigma {W}_{o}\cdot \left[{ℎ}_{t-1},{x}_{t}\right]+{b}_{o}$$ $${ℎ}_{t}={o}_{t}\ast tanℎ\left({C}_{t}\right)$$ In these equations, \(W\) and \(b\) represent the weights and biases associated with their respective gates, \(\sigma\) denotes the sigmoid function, $$\sigma \left(x\right)=\frac{1}{1+{e}^{-x}}$$ and \(tanℎ\) represents the hyperbolic tangent function. $$tanℎ\left(x\right)=\frac{{e}^{2x}-1}{{e}^{2x}+1}$$ The operations \(+\) and \(\cdot\) denote element-wise addition and matrix multiplication, respectively, and \(\ast\) is element-wise multiplication. Transformer, a deep learning model introduced in 2017, differs from the recurrent layers used in previous models, such as LSTM and GRU, and instead relies entirely on an attention mechanism to draw global dependencies 30 . The Transformer model is composed of an encoder and decoder, each consisting of a stack of identical layers. Each layer has a multi-head self-attention mechanism and a fully connected feed-forward network. In this study, we only used the encoder component. The key components of the transformer are as follows: 1. Attention: $$\text{A}\text{t}\text{t}\text{e}\text{n}\text{t}\text{i}\text{o}\text{n} \left(\text{Q},\text{K},\text{V}\right)=\text{s}\text{o}\text{f}\text{t}\text{m}\text{a}\text{x}\left(\frac{\text{Q}{\text{K}}^{\text{T}}}{\sqrt{{\text{d}}_{\text{k}}}}\right)\text{V}$$ where \(\text{Q}\) is the query matrix, \(\text{K}\) is the key matrix, \(\text{V}\) is the value matrix, and \({\text{d}}_{\text{k}}\) is the dimension of the key vectors. 2. Multi-Head attention: $$\text{M}\text{u}\text{l}\text{t}\text{i}\text{H}\text{e}\text{a}\text{d} \left(\text{Q},\text{K},\text{V}\right)=\text{C}\text{o}\text{n}\text{c}\text{a}\text{t}\left({\text{h}\text{e}\text{a}\text{d}}_{\text{i}},\cdots ,{\text{h}\text{e}\text{a}\text{d}}_{\text{n}}\right){\text{W}}^{\text{O}}$$ where \({\text{h}\text{e}\text{a}\text{d}}_{\text{i}}=\text{A}\text{t}\text{t}\text{e}\text{n}\text{t}\text{i}\text{o}\text{n} \left(\text{Q}{\text{W}}_{\text{i}}^{\text{Q}},\text{K}{\text{W}}_{\text{i}}^{\text{K}},\text{V}{\text{W}}_{\text{i}}^{\text{V}}\right)\) and \({\text{W}}^{\text{O}}\) , \({\text{W}}_{\text{i}}^{\text{Q}}\) , \({\text{W}}_{\text{i}}^{\text{K}}\) , \({\text{W}}_{\text{i}}^{\text{V}}\) ) are parameter matrices. 3. Positional encoding: $$\text{P}{\text{E}}_{\left(\text{p}\text{o}\text{s},2\text{i}\right)}=\text{sin}\left(\frac{\text{p}\text{o}\text{s}}{10000\frac{2\text{i}}{{\text{d}}_{\text{m}\text{o}\text{d}\text{e}\text{l}}}}\right)$$ $$\text{P}{\text{E}}_{\left(\text{p}\text{o}\text{s},2\text{i}+1\right)}=\text{cos}\left(\frac{\text{p}\text{o}\text{s}}{10000\frac{2\text{i}}{{\text{d}}_{\text{m}\text{o}\text{d}\text{e}\text{l}}}}\right)$$ where \(\text{p}\text{o}\text{s}\) is the position of the token in the sequence, \(\text{i}\) is the dimension, \({\text{d}}_{\text{m}\text{o}\text{d}\text{e}\text{l}}\) is the model dimensionality. 4.5 Methods used in the meta model construction layer Stacking is an ensemble learning method that uses the predictive capabilities of several base learners and then uses a meta learner to ensemble their predictions 54 . The goal of stacking is to improve the predictive performance beyond the level that any single base learner can achieve. The underlying premise of stacking is to consider the predictions of various base learners as input features for the meta learner. Through this approach, the meta learner can capture the strengths and weaknesses of each base model, thereby providing a superior final prediction. Typically, the base learners are diverse to ensure a rich set of predictions for the meta-learner to consider. The specific process is as follows: Training base learners: a set of base learners is trained on the complete training dataset. Generating base predictions: each base learner is used to predict based on a test set or through cross-validation, producing a new set of features for each instance in the dataset. Building the meta feature set: the predictions from each base learner are combined to build a new feature set, where each element corresponds to the prediction of the base learner for the instance. Training the meta learner: a meta learner is trained on the meta feature set. The model pruning algorithm aims to find a more effective ensemble model. In this study, model pruning is based on the overall results of a 10-fold cross-validation, rather than having a specific model combination for each fold. This approach allows us to identify an ensemble model that has the best generalization capability across the entire dataset. The specific process is as follows: 1. Model extension: add a base model to the base learner sets. 2. Selective pruning: after each addition, evaluate the model and initiate a pruning cycle: 1) iteratively remove individual model components. 2) after each removal, assess the model's overall performance on each validation set of the 10 folds. 3) identify the removal that produces the highest non-negative gain compared to the pre-pruning performance. 4) implement this removal and use the resulting base learner set as the starting point for the next round of pruning. 5) terminate pruning when there is no non-negative gain in performance. 3. Repeat: repeat steps 1 and 2, grow and prune the model until no new base model can be added.- Declarations Funding This work was supported by the National Key R&D Program of China (2022YFE0116200 and 2021YFD1200600), National Natural Science Foundation of China (Grant No. 31961143019, 32272088), Key R&D Program of Qinghai Province (2022-NK-125). Author Contributions Y.W. designed the experiments, analyzed the data and wrote the manuscript. D.H. and J.W. conceived and supervised the project and revised the manuscript. R.Y. performed most of the genotype data analysis and revised the manuscript. L.L. collected the public genotype and phenotype data and revised the manuscript. J.Z., M.Y., C.Z., T.C., and H.D. participated in data analysis and revised the manuscript. C.L., W.Z., Z.K. and Q.Z., contributed to the field trials and revised the manuscript. All authors read and approved the final manuscript. Acknowledgements We take this opportunity to pay deep memory of Prof. Changfa Wang for his contributions in the previous work. The authors would like to thank all members of the plant immunity research team in the State Key Laboratory of Crop Stress Resistance and High-Efficiency Production, Northwest A&F University for helpful comments; Drs. Li Li and Shouyang Liu for their helpful suggestions and discussions; Prof. R.A. McIntosh for language editing and proofreading of the draft manuscript. Competing interests The authors declare no competing interests. Data availability Complete data sets can be found within the main text, supplementary materials and referenced studies, as well as in public databases. Code availability The source code of EGGPT is available at https://github.com/wangyzzzz/EGGPT-V1.0 . The results in this study support reproducibility. The hyperparameters and computing environment used for obtaining these results are available in the supplementary information. 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Result of E7.1 to E7.6 Supplemental Table 8. Result of E6.1, E8.1 to E8.6 Supplemental Table 9.Impact of population size Supplemental Table 10.Execution device and hyperparameters documentation Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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University","correspondingAuthor":false,"prefix":"","firstName":"zhensheng","middleName":"","lastName":"kang","suffix":""},{"id":318934018,"identity":"eab3627f-18fe-416d-8f6d-13bdc48f1160","order_by":12,"name":"Qingdong Zeng","email":"","orcid":"https://orcid.org/0000-0002-7856-2340","institution":"State Key Laboratory of Crop Stress Biology for Arid Areas, Northwest A\u0026F University","correspondingAuthor":false,"prefix":"","firstName":"Qingdong","middleName":"","lastName":"Zeng","suffix":""},{"id":318934022,"identity":"6b32172a-5bea-4ec5-b1ac-fc3853145c75","order_by":13,"name":"Dejun Han","email":"","orcid":"","institution":"Northwest A\u0026F University","correspondingAuthor":false,"prefix":"","firstName":"Dejun","middleName":"","lastName":"Han","suffix":""}],"badges":[],"createdAt":"2024-06-14 11:01:31","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4581596/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4581596/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":60433441,"identity":"64d90203-dba9-4e48-b973-61a673d7987f","added_by":"auto","created_at":"2024-07-16 17:00:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":63211,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe EGGPT structure.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"Fig1.png","url":"https://assets-eu.researchsquare.com/files/rs-4581596/v1/ef90835cd57e967cec7f3659.png"},{"id":60434307,"identity":"9a6d21c0-62cd-4fda-93b9-ae3b4cda9548","added_by":"auto","created_at":"2024-07-16 17:08:00","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":149831,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eImpact of extending components in the data collection layer, the data processing layer, and the data encoding layer. a\u003c/strong\u003e Components used in E1.1 to E1.3. \u003cstrong\u003eb\u003c/strong\u003eRMSE of E1.1 to E1.3 on root diameter, roof fresh weight, root surface, and total root length in wheat. A lower RMSE indicates better model performance. The bar with an orange border simultaneously used all the components for the previously displayed bars without orange borders. \u003cstrong\u003ec\u003c/strong\u003e Components used in E2.1 to E2.3. \u003cstrong\u003ed\u003c/strong\u003e RMSE of E2.1 to E2.3 on C18 fatty acid content in soybean, fiber strength in cotton, grain width in rice and leaf number below ear in maize. \u003cstrong\u003ee\u003c/strong\u003e Components used in E3.1 to E3.5. \u003cstrong\u003ef\u003c/strong\u003e RMSE of E3.1 to E3.5 on grain weight in rice, C18:1 fatty acid in rapeseed, and days of interval between anthesis and tasseling of maize.\u003c/p\u003e","description":"","filename":"Fig2.png","url":"https://assets-eu.researchsquare.com/files/rs-4581596/v1/219ca2ee784bd862d742da98.png"},{"id":60434308,"identity":"94acd780-aabd-42fe-90d6-81289d28e7bf","added_by":"auto","created_at":"2024-07-16 17:08:00","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":170907,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eImpact of extending components in the base model construction layer, the meta model construction layer, and multiple layers. a \u003c/strong\u003eComponents used in E4.1 to E4.9. \u003cstrong\u003eb\u003c/strong\u003eRMSE of E4.1 to E4.9 on the glucosinolate content in rapeseed and the 100-seed weight of soybean. \u003cstrong\u003ec\u003c/strong\u003e Components used in E5.1 to E5.10. \u003cstrong\u003ed\u003c/strong\u003e RMSE of E5.1 to E5.10 on the panicle length of the main stem in millet and the tassel length of maize. \u003cstrong\u003ee\u003c/strong\u003e Components used in E2.3, E3.5, E4.9, and E6.1. \u003cstrong\u003ef\u003c/strong\u003eRMSE of E2.3, E3.5, E4.9, and E6.1 on the grain length in rice, the seed length in soybean, the tassel branch number in maize, and the main stem width of millet.\u003c/p\u003e","description":"","filename":"Fig3.png","url":"https://assets-eu.researchsquare.com/files/rs-4581596/v1/824843c0abdb4fdd6c5f6d06.png"},{"id":60433446,"identity":"bf36b46c-a489-4079-8d5b-98d46c95a3ad","added_by":"auto","created_at":"2024-07-16 17:00:01","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":125771,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eImpact of six base models and population size to EGGPT. a\u003c/strong\u003e Components used in E7.1 to E7.6. \u003cstrong\u003eb\u003c/strong\u003eRMSE of E7.1 to E7.6 on days to anthesis, plant height, kernel number per ear, and kernel weight per ear in maize. \u003cstrong\u003ec\u003c/strong\u003e Components used in E6.1 and E8.1 to E8.6. \u003cstrong\u003ed\u003c/strong\u003e average RMSE changes of E6.1 and E8.2 to E8.6 relative to E8.1 on 84 traits. \u003cstrong\u003ee\u003c/strong\u003e RMSE for four different training set sizes in flag leaf length and height of rice.\u003c/p\u003e","description":"","filename":"Fig4.png","url":"https://assets-eu.researchsquare.com/files/rs-4581596/v1/1a5dafb0a119f089d66cbf25.png"},{"id":60435591,"identity":"2b4b15cd-0772-4bd0-b202-d9ef302b4d9b","added_by":"auto","created_at":"2024-07-16 17:24:04","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1238000,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4581596/v1/1e7a4141-1ac7-4d92-9ac3-b39b149abd8b.pdf"},{"id":60433445,"identity":"c697b05b-351b-4fc1-9c4b-896684b88814","added_by":"auto","created_at":"2024-07-16 17:00:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":8618265,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSupplementary information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental Table 1. \u003c/strong\u003eResult of E1.1 to E1.3\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental Table 2.\u003c/strong\u003eResult of E2.1 to E2.3\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental Table 3. \u003c/strong\u003eResult of E3.1 to E3.5\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental Table 4.\u003c/strong\u003eResult of E4.1 to E4.9\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental Table 5. \u003c/strong\u003eResult of E5.1 to E5.10\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental Table 6.\u003c/strong\u003eResult of E2.3, E3.5, E4.9, and E6.1\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental Table 7. \u003c/strong\u003eResult of E7.1 to E7.6\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental Table 8. \u003c/strong\u003eResult of E6.1, E8.1 to E8.6\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental Table 9.\u003c/strong\u003eImpact of population size\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplemental Table 10.\u003c/strong\u003eExecution device and hyperparameters documentation\u003c/p\u003e","description":"","filename":"EGGPTST.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4581596/v1/7b6e1e3b63097018d7303d07.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"EGGPT：an extensible and growing genomic prediction technology","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eFood security faces two primary challenges: a growing global population and a worsening global environment. The world population is expected to reach 9.5\u0026nbsp;billion people by 2050, and must address environmental issues such as the reduction in cultivation area and increasing number of extreme weather events, as well as a greater threat from pests and diseases\u003csup\u003e1\u0026ndash;4\u003c/sup\u003e. Although traditional breeding methods are effective, they require a long breeding cycle in addressing these challenges. Consequently, it is necessary to develop new methods to speed up the breeding process. GS is one such method\u003csup\u003e5, 6\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eGS is a method to select candidate individuals by using prediction models based on genetic markers. This approach can drastically reduce the time needed to develop new cultivars compared to traditional phenotype-based selection\u003csup\u003e7\u003c/sup\u003e. GS is widely adopted and recognized as a valuable tool for accelerating genetic gain in plant and animal breeding programs\u003csup\u003e8\u0026ndash;12\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe effectiveness of GS in accelerating the breeding process is dependent on many factors, including the size and structure of the training population, coverage of genetic markers across the genome, heritability of the traits, and the GP method\u003csup\u003e13, 14\u003c/sup\u003e. GP methods, as a key factor in the effectiveness of GS, have rapidly developed over the past two decades. The trends in development have primarily shifted from traditional statistical algorithms to machine learning and deep learning algorithms. Initially dominated by statistical algorithms such as BLUP, Bayes, and LASSO in the 2000s, the focus shifted to machine learning and deep learning algorithms like gradient boosting machine (GBM), random forest (RF), support vector machine (SVM), multi-layer perceptron (MLP), and convolutional neural network (CNN) in the 2010s\u003csup\u003e15\u0026ndash;26\u003c/sup\u003e. This trend can be observed across numerous disciplines\u003csup\u003e27, 28\u003c/sup\u003e. Although AI algorithms such as SVM, RF, ANN, and CNN have been applied to GS, their adoption lags behind the development of algorithms in the field of AI. For instance, CNN, introduced in 1998, was not adopted in GS for two decades, around 2018\u003csup\u003e26, 29\u003c/sup\u003e. Furthermore, the transformer algorithm has been available since 2017 and has not been widely adopted in GS to date\u003csup\u003e30\u003c/sup\u003e. Therefore, rapid utilization of advanced and effective algorithms is an important way to enhance the effectiveness of GS. Moreover, current GP models, which primarily rely on a single algorithm, have inherent limitations; for example, they often achieve peak performance only in a subset genotypes within a species and for certain traits, and therefore cannot perform consistently and optimally across species and traits\u003csup\u003e23, 24, 26, 31, 32\u003c/sup\u003e. This lack of universality highlights the need for a universal and robust GP model.\u003c/p\u003e \u003cp\u003eIn this study, we developed EGGPT, an innovative genomic prediction technology designed for extension capacity, future growth, and universal application across species. Built on engineering principles, EGGPT is characterized by its modular and decoupled design; it has a five-layer architecture with each layer and the components within each layer being independent. Based on its highly decoupled modular architecture, EGGPT overcomes the limitations of traditional genomic prediction models relying on a single algorithmic. Instead, EGGPT employs a stacking method to ensemble learning that combines multiple algorithms, thus enhancing overall accuracy. The design allows EGGPT to integrate a diversity of algorithms from numerous fields. Presently, EGGPT has extended many methods such as principal component analysis (PCA), \u003cem\u003ep\u003c/em\u003e values for SNP, SVM, RF, MLP, CNN, long short-term memory networks (LSTM), and transformer. This transformer not only outperforms most existing models relying on a single algorithm but also significantly enhances the overall performance of EGGPT. By extending these methods, EGGPT, an extensible and growing genomic prediction technology, consistently achieved optimal performance across datasets for 84 traits across eight species.\u003c/p\u003e"},{"header":"2. Results","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Overview of EGGPT\u003c/h2\u003e \u003cp\u003eEGGPT is based on a highly decoupled modular architecture, which is preliminarily divided into five layers: data collection layer, data processing layer, data encoding layer, base model construction layer, and meta model construction layer. As components in each layer are extended, EGGPT's capabilities correspondingly increase (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe data collection layer collects essential information for genomic prediction, including the phenotypic and genomic data. This layer not only supports genomic data, such as single nucleotide polymorphisms (SNP), but also supports multi-omics data, such as gene expression (GE).\u003c/p\u003e \u003cp\u003eThe data processing layer processes the collected phenotypic and genomic data. The first step is divided into a training set, a validation set, and a test set. Following, the divided data is processed with the selected components. Currently, the components of this layer include PCA and \u003cem\u003ep\u003c/em\u003e value; PCA is utilized for global dimensionality reduction of the genomic data; \u003cem\u003ep\u003c/em\u003e value is utilized for the filtering of SNPs associated with phenotypes. It is important to emphasize that PCA and \u003cem\u003ep\u003c/em\u003e value components are applied to the training set. The validation and test sets are processed using the information derived from the training set.\u003c/p\u003e \u003cp\u003eThe data encoding layer captures a wide range of effects through multi-dimensional encoding and transforms the data into a format that aligns with the requirements of the base model. This layer currently includes one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) encoding components. After dimensional encoding, adaptive encoding is applied to ensure that the data conforms to the input format required by the base model.\u003c/p\u003e \u003cp\u003eThe base model construction layer develops a diversity of base learners to be used in a stacking ensemble. Currently, this layer includes many models, such as SVM, RF, MLP, and CNN, which are widely used in GP; moreover, it also includes the LSTM based on Recurrent Neural Networks (RNN) and the transformer, both of which are not commonly used in GP. Note that in EGGPT, the current CNN architecture is the same as for DNNGP\u003csup\u003e31\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe meta model construction layer builds the meta learner, which is a critical component of the stacking methods. Currently, this layer includes a meta model component and a model pruning component based on the greedy algorithm. The model pruning component is the foundation for enabling growth in accuracy. It obtains a more optimal group of base learners by discarding those that negatively affect accuracy. This process not only helps in optimizing the ensemble for better performance but also ensures that the final model does not become unnecessarily complex.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Assessment Criteria\u003c/h2\u003e \u003cp\u003e \u003cb\u003eAccuracy metric.\u003c/b\u003e In the main body of this study, the accuracy metric is the root mean absolute error (RMSE). A lower RMSE indicates better model performance. In the supplementary materials, pearson correlation coefficient (\u003cem\u003er\u003c/em\u003e), coefficient of determination (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e), and mean absolute percentage error (MAPE) is also employed as an additional metric of accuracy.\u003c/p\u003e \u003cp\u003e \u003cb\u003e10-fold cross-validation.\u003c/b\u003e In this study, the assessment of accuracy employs a 10-fold cross-validation. Each dataset was randomly split into ten equally sized folds. Each fold would be the validation set and the remaining nine folds were grouped into the training set. The final accuracy for the dataset is the mean of the accuracies obtained from each validation set.\u003c/p\u003e \u003cp\u003e \u003cb\u003eHyperparameter.\u003c/b\u003e In both machine learning and deep learning, the setting of model hyperparameters significantly impacts the model performance on a dataset. An appropriate hyperparameter configuration can enable the model to achieve better performance on the specific dataset currently in use. For all results presented in this study, except for the hyperparameter adjustments specially mentioned, our EGGPT used the same hyperparameter configuration across all datasets. The same hyperparameter configuration further demonstrates universal applicability of EGGPT across diverse species and traits, and indicates that achievement the best performance in each trait is attributed to its architecture, rather than to specific hyperparameter tuning for each trait.\u003c/p\u003e \u003cp\u003e \u003cb\u003eEarly stopping.\u003c/b\u003e Early stopping is a regularization technique used to stop the training of a deep learning model if the performance on a validation set does not improve during a specified number of training iterations. In this study, all deep learning models employed the same early stopping mechanism to ensure consistency.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Impact of extending components in each layer\u003c/h2\u003e \u003cp\u003e \u003cb\u003eImpact of extending components in the data collection layer.\u003c/b\u003e To demonstrate the extension capacity and growth potential of EGGPT in the data collection layer, we conducted 3 iterations of EGGPT on the Wheat406 dataset, labeled EGGPT1.1 (E1.1) through E1.3 (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). The results show that the RMSE is lower when the data processing layer is extended with additional component (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb, Supplementary Table\u0026nbsp;1). E1.3, which is based on E1.1, extended the data collection layer component used in E1.2 (GE). The RMSE of E1.3 across all traits in Wheat406 marked an average reduction of 4% when compared to the lowest previous iteration specific to each trait.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eImpact of extending components in the data processing layer.\u003c/b\u003e To demonstrate the extension capacity and growth potential of EGGPT in the data processing layer, we conducted 3 iterations on the datasets encompassing 8 species and 84 traits, labeled E2.1 through E2.3 (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec). For each iteration, we held all layers constant, except for the data processing layer, to ensure that any observed difference in performance was attributable to this layer. The results showed that the RMSE falls when the data processing layer is extended with additional component (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed). The results were consistent across all remaining traits (Supplementary Table\u0026nbsp;2). E2.3, which is based on E2.1, extended the data processing layer component used in E2.2. The RMSE of E2.3 across all traits marked an average 3.4% reduction compared to the lowest single-component iteration specific to each trait. The greatest RMSE reduction was observed in GWD (grain width) of rice, which obtained a 13.2% relative reduction. By contrast, the smallest reduction was observed in FT (flowering time) of rapeseed, with a 0% relative reduction. Compared to single data processing component iterations, E2.3 demonstrated superior performance across all traits, with an average RMSE reduction of 4.3% compared to E2.1, and 7.3% compared to E2.2.\u003c/p\u003e \u003cp\u003e \u003cb\u003eImpact of extending components in the data encoding layer.\u003c/b\u003e To demonstrate the extension capacity and growth potential of EGGPT in the data encoding layer, we conducted 5 iterations on datasets encompassing 8 species and 84 traits, labeled E3.1 through E3.5 (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee). For each iteration, we held all layers constant, except for the data encoding layer, to ensure that any observed difference in performance was attributable to this layer. The results showed that the RMSE falls when the data encoding layer is extended with additional components (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ef). The results were consistent across all remaining traits (Supplementary Table\u0026nbsp;3). E3.3, which is based on E3.1, extended the data encoding layer component used in E3.2. The RMSE of E3.3 across all traits marked an average reduction of 1.1% when compared to the lowest previous iteration specific to each trait. E3.5, which was based on E3.3, extended the data encoding layer component used in E3.4. The RMSE of E3.5 across all traits marked an average reduction of 0.4% when compared to the lowest previous iteration specific to each trait. E3.5, which utilized three types of components simultaneously in the data encoding layer, achieved an average reduction of 1.4% across all traits, compared to the lowest single-component iteration specific to each trait. The greatest RMSE reduction was a 8% relative reduction in GWD (grain width) in rice. By contrast, the smallest reduction was in the MSPD (panicle diameter of the main stem) of millet, with only 0% relative reduction. Compared to single data encoding component iterations, E3.5 demonstrated superior performance across all traits, with an average RMSE reduction of 2.1% compared to E3.1, 2.7% compared to E3.2, and 3.1% compared to E3.4.\u003c/p\u003e \u003cp\u003e \u003cb\u003eImpact of extending components in the base model construction layer.\u003c/b\u003e To demonstrate the extension capacity and growth potential of EGGPT in the base model construction layer, we conducted 9 iterations on datasets encompassing 8 species and 84 traits, labeled E4.1 through E4.9 (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). For each iteration, we held all layers constant, except for the base model construction layer, to ensure that any observed difference in performance was attributed to this layer. The RMSE declined when the base model construction layer was extended with additional components (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). The results were consistent across all the remaining traits (Supplementary Table\u0026nbsp;4). E4.3, which was based on E4.1, extended the base model construction layer component used in E4.2. The RMSE of E4.3 across all traits marked an average reduction of 1% when compared to the lowest previous iteration specific to each trait. E4.5, which was based on E4.3, extended the base model construction layer component used in E4.4. The RMSE of E4.5 across all traits marked an average reduction of 1.1% when compared to the lowest previous iteration specific to each trait. E4.7, which was based on E4.5, extended the base model construction layer component used in E4.6. The RMSE of E4.7 across all traits marked an average reduction of 0.3% when compared to the lowest previous iteration specific to each trait. E4.9, which is based on E4.7, extended the base model construction layer component used in E4.8. The RMSE of E4.9 across all traits marked an average reduction of 0.5% when compared to the lowest previous iteration specific to each trait. E4.9 utilizing 5 types of components simultaneously in the base model construction layer achieved an average reduction of 2.2% across all traits, compared to the lowest single-component iteration specific to each trait. The greatest RMSE reduction was observed in GSLC (glucosinolate content) of rapeseed, with a 6.5% relative reduction. By contrast, the smallest reduction was observed in SS (seed setting rate) of rice, with a 0.1% relative reduction. Compared to single base model iterations, E4.9 demonstrated superior performance across all traits, with an average RMSE reduction of 4% compared to E4.1, 6.4% compared to E4.2, 3.2% compared to E4.4, 14.6% compared to E4.6, and 7.5% compared to E4.8.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eImpact of extending components in the meta model construction layer.\u003c/b\u003e To demonstrate the extension capacity and growth potential of EGGPT in the meta model construction layer, we conducted 10 iterations on the datasets encompassing 8 species and 84 traits, labeled E5.1 through E5.10 (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec). For each iteration, we held all layers constant, except for the base model construction layer and the meta model construction layer, to ensure that any observed difference in performance was attributed to these layers. The RMSE exhibited non-negative reduction when the meta model construction layer was extended with model pruning component (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed). The results were consistent across all traits in the remaining datasets (Supplementary Table\u0026nbsp;5). E5.1 to E5.5 were not extended with the model pruning component, resulting in respective average RMSE changes across all traits of -4.5%, -0.3%, -1.6%, and \u0026minus;\u0026thinsp;0.8%. Conversely, E5.6 to E5.10 were extended with the model pruning component, leading to respective average RMSE changes across all traits of -5.5%, -2.4%, -0.4%, and \u0026minus;\u0026thinsp;0.7%. Notably, the RMSE of E5.10 across all traits marked an average reduction of 1.8% when compared to E5.5. The greatest RMSE reduction was observed for C18_1 in rapeseed, with a 7.2% relative reduction. By contrast, the smallest reduction was observed in GWD (grain width) in rice with a 0% relative reduction.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Impact of extending components in multiple layers\u003c/h2\u003e \u003cp\u003eTo demonstrate the extension capacity and growth potential of EGGPT, we conducted single iterations on the datasets labeled E6.1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee). E6.1, extended with multiple components, achieved the lowest RMSE (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef). The results were consistent across all traits in the remaining datasets (Supplementary Table\u0026nbsp;6). Compared to iterations with a single-layer extension component, E6.1 demonstrated superior performance across all traits, with an average RMSE reduction of 4.7% compared to E2.3, 6.8% compared to E3.5, and 5% compared to E4.9.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Impact of extending transformer\u003c/h2\u003e \u003cp\u003eHere, we developed a model based on the encoder component of the transformer. It contains 10 transformer layers, each containing one multi-head attention block with two heads, two layer-normalization blocks and one MLP block. The MLP block contained one input layer, one output layer, one hidden layer and two dropout layers, with the number of units in the hidden layer being six times the number of units in the input layer.\u003c/p\u003e \u003cp\u003eTo evaluate the ability of this model, we conducted 6 iterations on the datasets, labeled E7.1 through E7.6 (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). E7.1 (MLP) achieved optimal performance for 13 traits, E7.2 (SVR) for 5, E7.3 (RF) for 49, E7.4 (CNN) for 1, E7.5 (LSTM) for 3, and E7.6 (transformer) for 13 traits (Supplementary Table\u0026nbsp;7). Specifically, the DNNGP model demonstrated superior performance on the Maize1404 dataset\u003csup\u003e31\u003c/sup\u003e. We then adjusted the CNN model hyperparameters to match the settings used by DNNGP for four traits in the Maize1404 dataset. In comparing the performance of the base models on the four traits, the RF model was the top performer. However, except for the RF, the transformer still maintained an advantage over the other base models in certain traits, such as KNPE and KWPE (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAfter extending transformer to EGGPT, we conducted a single iteration on the 8 species, 84 traits datasets, labeled E8.1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). This iteration demonstrated a 0.849% reduction in average RMSE across all traits compared to E6.1. To further assess the importance of each base model in EGGPT, we conducted five iterations, labeled E8.2 through E8.6 (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). Compared to E8.1, average RMSE increases across all datasets were +\u0026thinsp;0.898% for E6.1 (with transformer removed), +\u0026thinsp;0.817% for E8.2 (with MLP removed), +\u0026thinsp;0.547% for E8.3 (with SVR removed), +\u0026thinsp;0.128% for E8.4 (with RF removed), +\u0026thinsp;0.645% for E8.5 (with CNN removed), and +\u0026thinsp;0.207% for E8.6 (with LSTM removed) (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed, Supplementary Table\u0026nbsp;8). Based on these findings, the importance of ranking of the base models was as follows: transformer, MLP, CNN, SVR, LSTM, and RF.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.6 Impact of population size\u003c/h2\u003e \u003cp\u003ePopulation size influences the performance of machine learning and deep learning models; therefore, it was an essential consideration in comprehensive evaluation of EGGPT performance\u003csup\u003e13\u003c/sup\u003e. We used the seven traits in Rice1495 to assess the impact of population size on EGGPT. Initially, we used a 10-fold cross-validation to split the Rice1495 dataset. In the training phase, we started with a training set of 150 samples, progressively increasing the sizes to 300, 600, and finally, 1,345. For all seven traits in the Rice1495 dataset, there was an improvement in prediction accuracy with increased sample size (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee, Supplementary Table\u0026nbsp;9). When comparing the 150-sample size with the 1,345-sample size, the greatest RMSE reduction was in GW, which underwent a 27.8% relative reduction. By contrast, the smallest reduction was observed in FLW, with a 7.6% relative reduction.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Discussion","content":"\u003cp\u003eGP research currently faces two challenges: 1) slow uptake of advanced and effective algorithms from various fields to enhance GS efficiency, and 2) limited cross-species and cross-trait applicability of GS methods based on a single algorithm.\u003c/p\u003e \u003cp\u003eEGGPT addresses the first challenge with a design based on engineering principles that ensures extensibility. It overcomes the second challenge by utilizing stacking methods to integrate diverse base models, enhancing cross-species and cross-trait applicability. In addition, it uses a model pruning algorithm component, which ensures non-negative improvements in model accuracy when extending with new components. In \"Results\", we presented the impact of extending EGGPT in each layer and its performance across all datasets. This not only proved its power and growth potential but also its universality. Furthermore, we introduced a transformer architecture. By integrating this transformer, EGGPT achieves further performance improvement. Note that some component combinations are not supported in the current version of EGGPT, such as GE-p value, PCA-2D encoding, PCA-3D encoding, PCA-transformer, and PCA-LSTM.\u003c/p\u003e \u003cp\u003eFor machine learning and deep learning models, the architectural design and hyperparameter configurations have a pronounced effect on accuracy in analysing specific datasets\u003csup\u003e33, 34\u003c/sup\u003e. In EGGPT, each individual model uses an identical set of hyperparameter configurations and model architecture across all datasets, demonstrating that its superior predictive accuracy can be attributed to its comprehensive architectural design. However, in practical applications, fine-tuning the hyperparameters can further enhance accuracy for specific datasets. For example, for the SRDS (stripe rust disease severity) in wheat, the RMSE reduction of 3.1% in using appropriate hyperparameter configurations (Supplementary Table\u0026nbsp;10). Moreover, EGGPT also can incorporate other high-performing GP models, such as DeepGS and SoyDNGP. DeepGS builds on 1DCNN with a sampling layer, and an architecture that generates superior results in some datasets\u003csup\u003e26\u003c/sup\u003e. For such datasets, we can substitute the CNN in the base model construction layer with the DeepGS architecture to match or exceed DeepGS's accuracy. Similarly, SoyDNGP employs a deep and narrow CNN structure and incorporates a coordinate attention (CA) mechanism after the first and final convolutional layers\u003csup\u003e32\u003c/sup\u003e. We can also substitute CNN with SoyDNGP's structure to match or exceed SoyDNGP's accuracy.\u003c/p\u003e \u003cp\u003eEGGPT has many potential developmental directions. Firstly, EGGPT allows for extension capacity and growth potential in each layer. Addition of components to each layer is the primary development, such as diverse omics data and base models. Secondly, the model pruning algorithm is crucial for EGGPT. Currently, it is based on the greedy algorithm and often finds local optima\u003csup\u003e35\u003c/sup\u003e. Therefore, developing the model pruning algorithm to find near-optimal parsing results is one of the future development directions. Thirdly, EGGPT has the potential to obtain cross-environment prediction capabilities by incorporation of growth models. For example, a recent study showed that temperature during a window of 9 to 50 days after germination is a key environmental factor affecting the flowering time in rice. The application of a joint genomic regression analysis (JGRA) that integrates environmental indices with genomic predictions enables high-precision forecasting of flowering time across different environments\u003csup\u003e36\u003c/sup\u003e. Accordingly, for the growth model mentioned above, we can integrate the key environmental factor as a specific component to add the cross-environment prediction capabilities of EGGPT. Therefore, with the incorporation of growth models to get cross-environment prediction capabilities is one of the future developmental directions.\u003c/p\u003e \u003cp\u003eAn online prediction service to assist breeders is also one of the future development directions. This platform not only needs to offer easy access for breeders, but also needs to reduce response times, which depend primarily on the inference time of EGGPT. Like all deep learning-based methods, the runtime of EGGPT is principally divided into training time and inference time. Typically, the training time is borne by the developers, who are responsible for providing a service for users. Users are primarily concerned with inference time, which in the context of EGGPT, refers to the time taken to make predictions. In EGGPT, inference time is influenced by the size of the genomic data as well as the overall complexity of the model. Based on the scale of EGGPT in this study, the maximum inference time across all datasets stands at 109.8 milliseconds per individual. Although the current inference time of the EGGPT is acceptable, we need to continue the optimization. Nevertheless, we believe that EGGPT will see continuous refinement and development, evolving from the egg to the eagle.\u003c/p\u003e"},{"header":"4. Methods","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n\u003ch2\u003e4.1 Datasets used in data collection layer\u003c/h2\u003e\n\u003cp\u003eNine datasets were collected, encompassing data for 8 species and 84 traits were used in the study.\u003c/p\u003e\n\u003cp\u003eThe first dataset, Rice1495, consisted of 1,495 hybrid rice cultivars genotyped at 1,654,030 SNP loci; 38 traits were evaluated in two environments\u003csup\u003e37\u003c/sup\u003e. Only 12 traits from the Hangzhou location were utilized to evaluate the EGGPT performance. The traits included yield per plant, panicle number, grain number per panicle, seed setting rate, grain weight, heading date, height, flag leaf length, flag leaf width, panicle length, grain length, and grain width.\u003c/p\u003e\n\u003cp\u003eThe second dataset, Maize1404, comprised 1,404 inbred maize lines genotyped at 11,825,030 SNP loci; 23 traits were evaluated\u003csup\u003e38\u003c/sup\u003e. All trait data were used in assessing the performance of EGGPT. These traits included days to tasseling, days to anthesis; days to silking, interval between anthesis and tasseling, interval between silking and tasseling, interval between silking and anthesis, plant height; ear height, ear leaf length, ear leaf width, leaf number above ear, leaf number below ear, tassel branch number, tassel length; ear weight, ear diameter, ear length, ear row number, kernel number per row, kernel number per ear, kernel weight per ear, cob weight; and length of barren tip.\u003c/p\u003e\n\u003cp\u003eThe third dataset, Millet827, included 827 accessions genotyped at 161,562 SNP loci; 12 traits were evaluated and all were included in the study\u003csup\u003e39\u003c/sup\u003e. The traits included top second leaf length; top second leaf width, main stem height, main stem width, panicle diameter of the main stem, fringe neck length, panicle length of the main stem, per plant grain weight, main stem panicle weight, hundred kernel weight, spikelet number of the main stem, and grain number per spike.\u003c/p\u003e\n\u003cp\u003eThe fourth dataset, Cotton1245, encompassed 1,245 inbred lines genotyped at 1,122,352 SNP loci; 4 traits were evaluated to assess the performance of EGGPT\u003csup\u003e40\u003c/sup\u003e. The traits included fiber micronaire, fiber length, fiber strength, and fiber elongation rate.\u003c/p\u003e\n\u003cp\u003eThe fifth dataset, Rapeseed991, included 991 inbred line genotyped at 4,286,896 SNP loci; 8 traits were evaluated and were used in the present study\u003csup\u003e41\u003c/sup\u003e. The traits included flowering time, glucosinolate content, protein content, oil content, and C16:0, C18:1, C18:2, C18:3 levels.\u003c/p\u003e\n\u003cp\u003eThe sixth dataset, Soybean2795, encompassed 2795 inbred line genotyped at 31,580,805 SNP loci and 111 traits were evaluated across multiple environments\u003csup\u003e42\u003c/sup\u003e. Data for 13 traits tested at Beijing in 2013 were included in this work. The traits were beginning of blooming date, FA16 content, FA18 content, total FA content, 100-seed weight, leaf length, leaf width, pod maturity date, plant height, protein content, seed length, seed thickness, and valid branch number.\u003c/p\u003e\n\u003cp\u003eThe seventh dataset, Wheat406, included 406 inbred lines genotyped at 605,352 SNP loci; 5 traits were evaluated to assess the performance of EGGPT\u003csup\u003e43\u003c/sup\u003e. The traits included total root length, root surface, root volume, root diameter and roof fresh weight.\u003c/p\u003e\n\u003cp\u003eThe eighth dataset, Pigeon556, encompassed 556 individuals genotyped at 160,434 SNP loci. All 6 traits evaluated were included in assessing the performance of EGGPT\u003csup\u003e44\u003c/sup\u003e. The traits included body weight, chest width, shin length, keel length, body length, and pectoral thickness.\u003c/p\u003e\n\u003cp\u003eThe ninth dataset, Wheat1458, included 1458 inbred lines genotyped at 180,000 SNP loci; 1 trait were evaluated to assess the performance of EGGPT. The trait is stripe rust disease severity.\u003c/p\u003e\n\u003cp\u003eThe first six datasets were downloaded from the CropGS-Hub\u003csup\u003e45\u003c/sup\u003e. Since the primary focus was on the extensible, growth potential, and universality of EGGPT, datasets containing more than 180,000 SNPs were uniformly subsampled to 180,000 SNPs using PLINK\u003csup\u003e46\u003c/sup\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n\u003ch2\u003e4.2 Methods used in the data processing layer\u003c/h2\u003e\n\u003cp\u003eIn the data processing layer, we applied two dimensional reduction (DR) methods, p value calculation and PCA to improve the accuracy of GP.\u003c/p\u003e\n\u003cp\u003eP value was utilized as a featured selection method to identify SNPs associated with phenotypes\u003csup\u003e47\u003c/sup\u003e. This method allowed us to focus on a subset rather than an entire genomic dataset, thus effectively reducing the complexity of the features and capturing the genetic variation most likely to be effective for GP. To decrease runtime, we utilized a python package from \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/STRIDES-Codes/GPU-GWAS\u003c/span\u003e\u003c/span\u003e that utilizes the parallel processing power of GPUs. This method significantly reduced the processing time. We used the top 1% of SNPs by p value as selected items.\u003c/p\u003e\n\u003cp\u003ePCA was utilized as a global DR method to transform the full set of SNPs into a new coordinate system\u003csup\u003e48\u003c/sup\u003e. This method reduces the dimensionality of the data by transforming the original correlated variables into a smaller number of uncorrelated variables that still capture most of the variation in the original data. Unlike p value, which selects a subset of SNPs, PCA reduces dimensionality by creating new variables that are linear combinations of the original SNPs. We used PCA to extract the top 95% of feature variance.\u003c/p\u003e\n\u003cp\u003eThe combined use of p value for feature selection and PCA for global dimensionality reduction provides a comprehensive strategy to DR.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n\u003ch2\u003e4.3 Methods used in the data encoding layer\u003c/h2\u003e\n\u003cp\u003eIn the data processing layer we employed two encoding methods: dimensional encoding and adaptive encoding. dimensional encoding involves transforming the data to one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) representations. For example, in the case of the SNP-p value calculation component combination, SNPs indicate three types of genetic variation: homozygous reference (0/0), heterozygous variant (0/1), and homozygous alternative variant (1/1). The one-dimensional encoding component uses a one-dimensional feature vector to represent these variations:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left[0\\right]\\)\u003c/span\u003e\u003c/span\u003e encodes a homozygous reference, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left[1\\right]\\)\u003c/span\u003e\u003c/span\u003e encodes a heterozygous variant, and\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left[2\\right]\\)\u003c/span\u003e\u003c/span\u003e encodes a homozygous variant. The two-dimensional encoding component uses a two-dimensional feature vector: [1, 0] encodes a homozygous reference, [0.5, 0.5] encodes a heterozygous variant, and [0, 1] encodes a homozygous alternative variant. Similarly, the three-dimensional encoding component uses a three-dimensional feature vector: [1, 0, 0] encodes a homozygous reference, [0, 1, 0] encodes a heterozygous variant, and [0, 0, 1] encodes a homozygous variant. For another example, in the case of the SNP-PCA component combination, the one-dimensional encoding component uses a one-dimensional feature vector [\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e] multiplied by each element of the PCA results. Adaptive encoding further transforms the data into formats suitable for input requirements for base models. For base models such as SVR, RF, MLP, and 1DCNN, the data can be simply flattened to meet the input feature requirements. However, for LSTM and transformer, the flattened data need to be divided into subsets, where the number of SNPs and the encoding dimensions dictate the segmentation logic. In most datasets used in this study, SNP counts were 180,000 and filtered to the top 1% of P values. The remaining 1,800 SNPs were the input features for the base models. After dimensional encoding and flattening, these SNPs were represented in dimensions of 1,800, 3,600, and 5,400. The 1,800-dimensional data were divided into 30 subsets, each with 60 dimensions. Similarly, the 3,600-dimensional data were divided into 30 subsets of 120 dimensions, and the 5,400-dimensional data were divided into 30 subsets with 180 dimensions. These formats like 30x60, 30x120, and 30x180 meet the input feature requirements of LSTM and transformer. The adaptive encoding ensured that the dimensionally reduced data was compatible with the diverse structures of our ensemble of base models.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n\u003ch2\u003e4.4 Methods used in the base model construction layer\u003c/h2\u003e\n\u003cp\u003eIn the base model construction layer, we used six models from the fields of machine learning and deep learning. These models include SVR, RF, MLP, CNN, LSTM, and transformer. Each algorithm is based on unique foundational logic and principles, and suited to different types of data and problems. We used these six models simultaneously to support diverse species and traits.\u003c/p\u003e\n\u003cp\u003eSVR is a regression algorithm derived from the support vector machine\u003csup\u003e49\u003c/sup\u003e. The goal of SVR is to find a function that deviates no more than \u0026epsilon; from the actual target values for the entire training dataset, while maintaining the function's flatness. SVR applies the principle of minimizing an error within a specific margin. The \u0026epsilon;-insensitive loss function is pivotal in this model, allowing some errors to be tolerated within the \u0026epsilon;-tube around the true data points. For a given training dataset\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left({\\text{x}}_{\\text{i}}\\right.,\\left.{\\text{y}}_{\\text{i}}\\right), \\text{i}=1,\\cdots ,\\text{n}\\)\u003c/span\u003e\u003c/span\u003e,where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{x}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e is the input vector and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{y}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e the corresponding target value, SVR solves the following optimization problem:\u003c/p\u003e\n\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equa\" class=\"mathdisplay\"\u003e$$\\underset{\\text{w},\\text{b},{\\xi },{{\\xi }}^{\\ast }}{\\text{min}}\\frac{1}{2}{‖\\text{w}‖}^{2}+\\text{C}\\sum _{\\text{i}=1}^{\\text{n}}({{\\xi }}_{\\text{i}}+{{\\xi }}_{\\text{j}}^{\\ast })$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003esubject to:\u003c/p\u003e\n\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equb\" class=\"mathdisplay\"\u003e$${\\text{y}}_{\\text{i}}-\\left(⟨\\text{w},\\left.{\\text{x}}_{\\text{i}}⟩+\\text{b}\\right)\\le {\\epsilon }+{{\\xi }}_{\\text{i} },\\right.$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equc\" class=\"mathdisplay\"\u003e$$\\left(⟨\\text{w},\\right.\\left.{\\text{x}}_{\\text{i}}⟩+\\text{b}\\right)-{\\text{y}}_{\\text{i}}\\le {\\epsilon }+{{\\xi }}_{\\text{j}}^{\\ast } ,$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equd\" class=\"mathdisplay\"\u003e$${{\\xi }}_{\\text{i} },{{\\xi }}_{\\text{j}}^{\\ast }\\ge 0, \\text{i}=1,\\cdots ,\\text{n}.$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere variables \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{w}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{b}\\)\u003c/span\u003e\u003c/span\u003e denote the coefficients of the hyperplane, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\xi }}_{\\text{i} }\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\xi }}_{\\text{j}}^{\\ast }\\)\u003c/span\u003e\u003c/span\u003e are slack variables representing the distance of points outside the \u0026epsilon;-tube, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{C}\\)\u003c/span\u003e\u003c/span\u003e is a regularization parameter.\u003c/p\u003e\n\u003cp\u003eRF is an ensemble learning method used for classification and regression tasks\u003csup\u003e50\u003c/sup\u003e. It to operates by constructing multiple decision trees during the training phase. The specific process is as follows:\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003e\n\u003cp\u003eBootstrapping: for a training set of size N, sample N with replacement to create a bootstrapped dataset for each tree.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eFeature randomness: at each node in the tree, select m features from the total M (where m\u0026thinsp;\u0026lt;\u0026thinsp;\u0026lt;\u0026thinsp;M) to find the best split.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eTree growing: grow each tree to the largest extent possible without pruning to maximize diversity among the trees.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eAggregation: for classification, use voting to combine tree predictions. For regression, calculate the average of the tree predictions.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eThe SVR and RF methods were implemented in Python version 3.9.16 using the ''Scikit-learn'' (2019) module\u003csup\u003e51\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eMLP, a class of feedforward artificial neural network (ANN), consists of at least three layers: an input layer, one or more hidden layers, and an output layer\u003csup\u003e52\u003c/sup\u003e. Each artificial neuron is connected with weighted edges to the neurons in the next layer, and applies an activation function to the weighted inputs. The specific process is as follows:\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003e1. Initialization: set initial random weights and biases for all neurons in the network.\u003c/p\u003e\n\u003cp\u003e2. Forward propagation: for each input, propagate the data forward through the network by calculating the weighted sum of inputs and applying the activation function to compute the output of each neuron. The weighted sum calculation is:\u003c/p\u003e\n\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Eque\" class=\"mathdisplay\"\u003e$${z}_{j}^{\\left(l\\right)}=\\sum _{i}{w}_{ji}^{\\left(l\\right)}{a}_{i}^{\\left(l-1\\right)}+{b}_{j}^{\\left(l\\right)}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({z}_{j}^{\\left(l\\right)}\\)\u003c/span\u003e\u003c/span\u003e is the weighted sum for the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({j}^{tℎ}\\)\u003c/span\u003e\u003c/span\u003e neuron in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({l}^{tℎ}\\)\u003c/span\u003e\u003c/span\u003e layer, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{ji}^{\\left(l\\right)}\\)\u003c/span\u003e\u003c/span\u003e is the weight connecting the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({i}^{tℎ}\\)\u003c/span\u003e\u003c/span\u003e neuron in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\left(l-1\\right)}^{tℎ}\\)\u003c/span\u003e\u003c/span\u003e layer to the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({j}^{tℎ}\\)\u003c/span\u003e\u003c/span\u003e neuron, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({a}_{i}^{\\left(l-1\\right)}\\)\u003c/span\u003e\u003c/span\u003e is the activation of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({i}^{tℎ}\\)\u003c/span\u003e\u003c/span\u003e neuron in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\left(l-1\\right)}^{tℎ}\\)\u003c/span\u003e\u003c/span\u003e layer, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({b}_{j}^{\\left(l\\right)}\\)\u003c/span\u003e\u003c/span\u003e is the bias of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({j}^{tℎ}\\)\u003c/span\u003e\u003c/span\u003e neuron.\u003c/p\u003e\n\u003cp\u003eIn the MLP model used in this study, we adopted a Gaussian error linear unit (GELU) as the activation function. GELU can be described as\u003c/p\u003e\n\u003cdiv id=\"Equf\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equf\" class=\"mathdisplay\"\u003e$$\\text{G}\\text{E}\\text{L}\\text{U}\\left(\\text{x}\\right)=\\text{x}\\cdot {\\Phi }\\left(\\text{x}\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{x}\\)\u003c/span\u003e\u003c/span\u003e is the input to the function, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Phi }\\left(\\text{x}\\right)\\)\u003c/span\u003e\u003c/span\u003e represents the cumulative distribution function of the standard normal distribution, expressed as:\u003c/p\u003e\n\u003cdiv id=\"Equg\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equg\" class=\"mathdisplay\"\u003e$${\\Phi }\\left(\\text{x}\\right)=\\frac{1}{2}\\left[1+\\text{e}\\text{r}\\text{f}\\left(\\frac{\\text{x}}{\\sqrt{2}}\\right)\\right]$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eHere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{e}\\text{r}\\text{f}\\)\u003c/span\u003e\u003c/span\u003e denotes the error function. The use of GELU allows the network to benefit from the properties of both ReLU and probabilistic non-linearities introduced by the Gaussian distribution, enhancing the model's capability to generalize from the training data.\u003c/p\u003e\n\u003cp\u003e3. Backpropagation: compute the error at the output and propagate it back through the network to update the weights and biases, thereby reducing the error.\u003c/p\u003e\n\u003cp\u003eIn the MLP model, we adopt Mean Squared Error (MSE) as the loss function. MSE can be described as:\u003c/p\u003e\n\u003cdiv id=\"Equh\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equh\" class=\"mathdisplay\"\u003e$$\\text{M}\\text{S}\\text{E}=\\frac{1}{\\text{N}}\\sum _{\\text{i}=1}^{\\text{N}}{\\left({\\text{y}}_{\\text{i}}-{\\widehat{\\text{y}}}_{\\text{i}}\\right)}^{2}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{y}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e is the observed value, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\widehat{\\text{y}}}_{\\text{i}}\\)\u003c/span\u003e\u003c/span\u003e is predicted value. The weight updates rule can be described as:\u003c/p\u003e\n\u003cdiv id=\"Equi\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equi\" class=\"mathdisplay\"\u003e$${w}_{ji}^{\\left(l\\right)}={w}_{ji}^{\\left(l\\right)}-\\eta \\frac{\\partial E}{\\partial {w}_{ji}^{\\left(l\\right)}}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\eta\\)\u003c/span\u003e\u003c/span\u003e is the learning rate and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{\\partial E}{\\partial {w}_{ji}^{\\left(l\\right)}}\\)\u003c/span\u003e\u003c/span\u003e is the partial derivative of the error with respect to the weight.\u003c/p\u003e\n\u003cp\u003e4. Repeat: repeat steps 2 and 3 for a specific number of epochs or until the network reaches a satisfactory level of performance.\u003c/p\u003e\n\u003cp\u003eCNN, a class of deep neural networks, automatically and adaptively learns spatial hierarchies of features from input data\u003csup\u003e29\u003c/sup\u003e. The output of a convolutional layer can be defined as an integral transformation and is represented as follows:\u003c/p\u003e\n\u003cdiv id=\"Equj\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equj\" class=\"mathdisplay\"\u003e$$\\text{s}\\left(\\text{t}\\right)=\\left(\\text{f}\\times \\text{k}\\right)\\left(\\text{t}\\right)=\\sum _{\\text{x}}\\text{k}\\left(\\text{t}-\\text{x}\\right)\\text{f}\\left(\\text{x}\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere k represents the kernel, and convolution is the transformation of f to s(t).\u003c/p\u003e\n\u003cp\u003eLSTM, a class of Recurrent Neural Networks (RNN), can learn long-term dependencies\u003csup\u003e53\u003c/sup\u003e. LSTM are designed to remember information for long periods, making them well-suited for sequential data. An LSTM unit is composed of a cell, which retains its state across time steps, and three types of gates - the input gate, the forget gate, and the output gate - that regulate the flow of information into the cell, within the cell, and out of the cell, respectively. Let \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{t}\\)\u003c/span\u003e\u003c/span\u003e be the input at time step \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(t\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ℎ}_{t-1}\\)\u003c/span\u003e\u003c/span\u003e be the hidden state from the previous time step, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({C}_{t-1}\\)\u003c/span\u003e\u003c/span\u003e be the cell state from the previous time step. The LSTM update equations are as follows:\u003c/p\u003e\n\u003cp\u003e1. Forget gate:\u003c/p\u003e\n\u003cdiv id=\"Equk\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equk\" class=\"mathdisplay\"\u003e$${f}_{t}=\\sigma \\left({W}_{f}\\cdot \\left[{ℎ}_{t-1},{x}_{t}\\right]+{b}_{f}\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e2. Input gate:\u003c/p\u003e\n\u003cdiv id=\"Equl\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equl\" class=\"mathdisplay\"\u003e$${i}_{t}=\\sigma \\left({W}_{i}\\cdot \\left[{ℎ}_{t-1},{x}_{t}\\right]+{b}_{i}\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equm\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equm\" class=\"mathdisplay\"\u003e$$\\stackrel{\\sim}{{C}_{t}}=tanℎ\\left({W}_{c}\\cdot \\left[{ℎ}_{t-1},{x}_{t}\\right]+{b}_{C}\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e3. Cell state update:\u003c/p\u003e\n\u003cdiv id=\"Equn\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equn\" class=\"mathdisplay\"\u003e$${C}_{t}={f}_{t}\\ast {C}_{t-1}+{i}_{t}\\ast \\stackrel{\\sim}{{C}_{t}}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003e4. Output gate:\u003c/p\u003e\n\u003cdiv id=\"Equo\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equo\" class=\"mathdisplay\"\u003e$${o}_{t}=\\sigma {W}_{o}\\cdot \\left[{ℎ}_{t-1},{x}_{t}\\right]+{b}_{o}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equp\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equp\" class=\"mathdisplay\"\u003e$${ℎ}_{t}={o}_{t}\\ast tanℎ\\left({C}_{t}\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eIn these equations, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(W\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(b\\)\u003c/span\u003e\u003c/span\u003e represent the weights and biases associated with their respective gates, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sigma\\)\u003c/span\u003e\u003c/span\u003e denotes the sigmoid function,\u003c/p\u003e\n\u003cdiv id=\"Equq\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equq\" class=\"mathdisplay\"\u003e$$\\sigma \\left(x\\right)=\\frac{1}{1+{e}^{-x}}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(tanℎ\\)\u003c/span\u003e\u003c/span\u003e represents the hyperbolic tangent function.\u003c/p\u003e\n\u003cdiv id=\"Equr\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equr\" class=\"mathdisplay\"\u003e$$tanℎ\\left(x\\right)=\\frac{{e}^{2x}-1}{{e}^{2x}+1}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eThe operations \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(+\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\cdot\\)\u003c/span\u003e\u003c/span\u003e denote element-wise addition and matrix multiplication, respectively, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ast\\)\u003c/span\u003e\u003c/span\u003e is element-wise multiplication.\u003c/p\u003e\n\u003cp\u003eTransformer, a deep learning model introduced in 2017, differs from the recurrent layers used in previous models, such as LSTM and GRU, and instead relies entirely on an attention mechanism to draw global dependencies\u003csup\u003e30\u003c/sup\u003e. The Transformer model is composed of an encoder and decoder, each consisting of a stack of identical layers. Each layer has a multi-head self-attention mechanism and a fully connected feed-forward network. In this study, we only used the encoder component. The key components of the transformer are as follows:\u003c/p\u003e\n\u003cp\u003e1. Attention:\u003c/p\u003e\n\u003cdiv id=\"Equs\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equs\" class=\"mathdisplay\"\u003e$$\\text{A}\\text{t}\\text{t}\\text{e}\\text{n}\\text{t}\\text{i}\\text{o}\\text{n} \\left(\\text{Q},\\text{K},\\text{V}\\right)=\\text{s}\\text{o}\\text{f}\\text{t}\\text{m}\\text{a}\\text{x}\\left(\\frac{\\text{Q}{\\text{K}}^{\\text{T}}}{\\sqrt{{\\text{d}}_{\\text{k}}}}\\right)\\text{V}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{Q}\\)\u003c/span\u003e\u003c/span\u003e is the query matrix, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{K}\\)\u003c/span\u003e\u003c/span\u003e is the key matrix, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{V}\\)\u003c/span\u003e\u003c/span\u003e is the value matrix, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{d}}_{\\text{k}}\\)\u003c/span\u003e\u003c/span\u003e is the dimension of the key vectors.\u003c/p\u003e\n\u003cp\u003e2. Multi-Head attention:\u003c/p\u003e\n\u003cdiv id=\"Equt\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equt\" class=\"mathdisplay\"\u003e$$\\text{M}\\text{u}\\text{l}\\text{t}\\text{i}\\text{H}\\text{e}\\text{a}\\text{d} \\left(\\text{Q},\\text{K},\\text{V}\\right)=\\text{C}\\text{o}\\text{n}\\text{c}\\text{a}\\text{t}\\left({\\text{h}\\text{e}\\text{a}\\text{d}}_{\\text{i}},\\cdots ,{\\text{h}\\text{e}\\text{a}\\text{d}}_{\\text{n}}\\right){\\text{W}}^{\\text{O}}$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{h}\\text{e}\\text{a}\\text{d}}_{\\text{i}}=\\text{A}\\text{t}\\text{t}\\text{e}\\text{n}\\text{t}\\text{i}\\text{o}\\text{n} \\left(\\text{Q}{\\text{W}}_{\\text{i}}^{\\text{Q}},\\text{K}{\\text{W}}_{\\text{i}}^{\\text{K}},\\text{V}{\\text{W}}_{\\text{i}}^{\\text{V}}\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{W}}^{\\text{O}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{W}}_{\\text{i}}^{\\text{Q}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{W}}_{\\text{i}}^{\\text{K}}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{W}}_{\\text{i}}^{\\text{V}}\\)\u003c/span\u003e\u003c/span\u003e) are parameter matrices.\u003c/p\u003e\n\u003cp\u003e3. Positional encoding:\u003c/p\u003e\n\u003cdiv id=\"Equu\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equu\" class=\"mathdisplay\"\u003e$$\\text{P}{\\text{E}}_{\\left(\\text{p}\\text{o}\\text{s},2\\text{i}\\right)}=\\text{sin}\\left(\\frac{\\text{p}\\text{o}\\text{s}}{10000\\frac{2\\text{i}}{{\\text{d}}_{\\text{m}\\text{o}\\text{d}\\text{e}\\text{l}}}}\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Equv\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equv\" class=\"mathdisplay\"\u003e$$\\text{P}{\\text{E}}_{\\left(\\text{p}\\text{o}\\text{s},2\\text{i}+1\\right)}=\\text{cos}\\left(\\frac{\\text{p}\\text{o}\\text{s}}{10000\\frac{2\\text{i}}{{\\text{d}}_{\\text{m}\\text{o}\\text{d}\\text{e}\\text{l}}}}\\right)$$\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{p}\\text{o}\\text{s}\\)\u003c/span\u003e\u003c/span\u003e is the position of the token in the sequence, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{i}\\)\u003c/span\u003e\u003c/span\u003e is the dimension, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{d}}_{\\text{m}\\text{o}\\text{d}\\text{e}\\text{l}}\\)\u003c/span\u003e\u003c/span\u003e is the model dimensionality.\u003c/p\u003e\n\u003cp\u003e4.5 Methods used in the meta model construction layer\u003c/p\u003e\n\u003cp\u003eStacking is an ensemble learning method that uses the predictive capabilities of several base learners and then uses a meta learner to ensemble their predictions\u003csup\u003e54\u003c/sup\u003e. The goal of stacking is to improve the predictive performance beyond the level that any single base learner can achieve. The underlying premise of stacking is to consider the predictions of various base learners as input features for the meta learner. Through this approach, the meta learner can capture the strengths and weaknesses of each base model, thereby providing a superior final prediction. Typically, the base learners are diverse to ensure a rich set of predictions for the meta-learner to consider. The specific process is as follows:\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003e\n\u003cp\u003eTraining base learners: a set of base learners is trained on the complete training dataset.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eGenerating base predictions: each base learner is used to predict based on a test set or through cross-validation, producing a new set of features for each instance in the dataset.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eBuilding the meta feature set: the predictions from each base learner are combined to build a new feature set, where each element corresponds to the prediction of the base learner for the instance.\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eTraining the meta learner: a meta learner is trained on the meta feature set.\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eThe model pruning algorithm aims to find a more effective ensemble model. In this study, model pruning is based on the overall results of a 10-fold cross-validation, rather than having a specific model combination for each fold. This approach allows us to identify an ensemble model that has the best generalization capability across the entire dataset. The specific process is as follows:\u003c/p\u003e\n\u003cp\u003e1. Model extension: add a base model to the base learner sets.\u003c/p\u003e\n\u003cp\u003e2. Selective pruning: after each addition, evaluate the model and initiate a pruning cycle:\u003c/p\u003e\n\u003cp\u003e1) iteratively remove individual model components.\u003c/p\u003e\n\u003cp\u003e2) after each removal, assess the model's overall performance on each validation set of the 10 folds.\u003c/p\u003e\n\u003cp\u003e3) identify the removal that produces the highest non-negative gain compared to the pre-pruning performance.\u003c/p\u003e\n\u003cp\u003e4) implement this removal and use the resulting base learner set as the starting point for the next round of pruning.\u003c/p\u003e\n\u003cp\u003e5) terminate pruning when there is no non-negative gain in performance.\u003c/p\u003e\n\u003cp\u003e3. Repeat: repeat steps 1 and 2, grow and prune the model until no new base model can be added.-\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by the National Key R\u0026amp;D Program of China (2022YFE0116200 and 2021YFD1200600), National Natural Science Foundation of China (Grant No. 31961143019, 32272088), Key R\u0026amp;D Program of Qinghai Province (2022-NK-125).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eY.W. designed the experiments,\u0026nbsp;analyzed the data\u0026nbsp;and\u0026nbsp;wrote\u0026nbsp;the manuscript. D.H. and J.W.\u0026nbsp;conceived and supervised the project\u0026nbsp;and\u0026nbsp;revised\u0026nbsp;the manuscript. R.Y. performed most of the genotype data analysis and revised the manuscript. L.L. collected the public genotype and phenotype data and\u0026nbsp;revised the manuscript. J.Z., M.Y., C.Z., T.C., and H.D. participated in data analysis and revised the manuscript. C.L., W.Z., Z.K. and Q.Z., contributed to the field trials and revised the manuscript.\u0026nbsp;All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe take this opportunity to pay deep memory of Prof. Changfa Wang for his contributions in the previous work. The authors would like to thank all members of the plant immunity research team in the State Key Laboratory of Crop Stress Resistance and High-Efficiency Production, Northwest A\u0026amp;F University for helpful comments; Drs. Li Li and Shouyang Liu for their helpful suggestions and discussions; Prof. R.A. McIntosh for language editing and proofreading of the draft manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eComplete data sets can be found within the main text, supplementary materials and referenced studies, as well as in public databases.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe source code of EGGPT is available at\u0026nbsp;\u003ca href=\"https://github.com/wangyzzzz/EGGPT-V1.0\"\u003ehttps://github.com/wangyzzzz/EGGPT-V1.0\u003c/a\u003e. The results in this study support reproducibility. The hyperparameters and computing environment used for obtaining these results are available in the supplementary information.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eHe, T. \u0026amp; Li, C. Harness the power of genomic selection and the potential of germplasm in crop breeding for global food security in the era with rapid climate change. The Crop Journal 8, 688\u0026ndash;700 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDeutsch, C.A. et al. Increase in crop losses to insect pests in a warming climate. Science 361, 916\u0026ndash;919 (2018).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePfleiderer, P., Schleussner, C.-F., Kornhuber, K. \u0026amp; Coumou, D. Summer weather becomes more persistent in a 2\u0026deg;C world. Nature Climate Change 9, 666\u0026ndash;671 (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSavary, S. et al. 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Nature Machine Intelligence 2, 500\u0026ndash;508 (2020).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Genomic prediction method, extensible and growing, ensemble learning, machine and deep learning, artificial intelligence","lastPublishedDoi":"10.21203/rs.3.rs-4581596/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4581596/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eGenomic selection (GS) is an effective way to aid breeders in enhancing the precision and efficiency of plant and animal breeding through the use of genomic prediction (GP) methods. However, most of GP methods based on a single algorithm are poor robustness and lags behind the development of algorithms in the field of artificial intelligence (AI). To address these limitations, we present an extensible and growing genomic prediction technology (EGGPT). EGGPT is designed on engineering principles, that abstracts the GP process into a five-layer structure including data collection, processing, encoding, base and meta model construction. Using the ensemble learning, EGGPT overcomes the poor robustness. And the highly decoupled modular architecture enables rapid integration with new methods to achieve the best performance for all datasets. These datasets involve 84 various traits across 7 plant and 1 animal species, suggesting that EGGPT could emerge as a new paradigm in GP.\u003c/p\u003e","manuscriptTitle":"EGGPT：an extensible and growing genomic prediction technology","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-16 16:59:55","doi":"10.21203/rs.3.rs-4581596/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"65240e88-f7a7-4ca8-aee2-ea87fe75322d","owner":[],"postedDate":"July 16th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":33725337,"name":"Biological sciences/Computational biology and bioinformatics/Computational models"},{"id":33725338,"name":"Biological sciences/Computational biology and bioinformatics/Machine learning"}],"tags":[],"updatedAt":"2024-07-16T16:59:57+00:00","versionOfRecord":[],"versionCreatedAt":"2024-07-16 16:59:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4581596","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4581596","identity":"rs-4581596","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}