Maize Genomics and Genetics 2025, Vol.16, No.6, 304-315 http://cropscipublisher.com/index.php/mgg 306 2.3 Historical development and limitations of single-environment models The initial maize genome prediction models were all rather "simple"-targeting a single environment, a single trait, and most of them only analyzed additive genetic effects (Rice and Lipka, 2021). These models do open up new ideas for breeders and the prediction accuracy is relatively moderate. However, the problem is that they hardly take into account environmental differences or the connections among multiple traits (Fritsche-Neto et al., 2021). The result is that once the region is changed or abnormal climate is encountered, the performance of the model is greatly discounted. As research deepened, people gradually realized that breeding was not carried out in a vacuum. The multi-environment and multi-trait model was thus proposed to be closer to the actual breeding conditions. They can simultaneously simulate genotype × environment interaction (G×E), and also utilize the correlations between traits to enhance prediction accuracy. However, although such models are smarter, they also consume more computing power and have a huge amount of computation. Further optimization is still needed in practical applications (De Oliveira et al., 2020). 3 Multi-Environment Genomic Prediction (MEGP) Models 3.1 Definition and key components of MEGP models Evaluating the performance of corn hybrids in different environments has never been an easy task. Climate, soil and management methods-each one could cause trouble. The emergence of multi-environment genomic prediction (MEGP) models can be regarded as providing a more systematic solution to this difficult problem. Its principle is not complicated. It can be understood as a method of "mixing genomic information and multi-environmental test data together for calculation", used to predict in advance the possible performance of hybrids under different conditions. The basic components of the model are actually not complicated: first, genomic marker data (commonly used ones include SNPS); second, phenotypic data obtained from multi-environment experiments; third, explicitly modeled genotype-environment (G×E) interactions; and third, statistical or machine learning algorithms that can comprehensively utilize genetic and environmental covariations. This type of model typically views genotype and environment as random effects, and introduces kernel functions (such as GBLUP or Gaussian kernels) when necessary. Sometimes, deep learning is even employed to capture nonlinear relationships that are difficult to reveal through traditional statistics (Costa-Neto et al., 2020). 3.2 Comparison between single-environment and multi-environment approaches If the single-environment model is more like "fixed-point observation", then the multi-environment model is closer to "panoramic monitoring". The former only predicts the performance of hybrids in specific environments and does not take into account the interaction between genotypes and the environment (G×E), thus it is easy to "fail to see the whole picture". The MEGP model is different. It incorporates data from various locations and under different conditions and explicitly models the G×E interaction, making the prediction more stable and accurate. Many studies have actually mentioned similar results: Whether it is key traits such as grain yield or moisture content, the predictive performance of the MEGP model is generally significantly higher than that of the single-environment model, approximately improving by 10% to 20% (Barreto et al., 2024). What's more interesting is that in those new environments without measured data, it can still provide relatively reliable predictions, while single-environment models are often not very effective. Of course, this does not mean that the environmental model alone is of no value. It can still be useful when there are too few data samples or the calculation conditions are limited, at least providing a general direction for subsequent analysis. 3.3 Model types: G×E interaction, reaction norm, and factor analytic models Not all multi-environment models follow the same approach. Take the G×E interaction model as an example. It
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