MeNet: A mixed-effect deep neural network for multi-environment genomic prediction of agronomic traits

Accurate genomic prediction of agronomic traits is critical for modern breeding and agriculture. Deep learning has great potential to enhance prediction by modelling nonlinearity, yet its applications remain limited by inconsistent performance across diverse agronomic traits and environments, and a lack of biological interpretability. Here, we propose a mixed-effect deep neural network (MeNet), a novel framework that unifies the statistical rigor of the mixed-effect model with the nonlinear modelling power of neural networks to advance genomic prediction. It employs dual embeddings to model phenotype-specific genetic relatedness as random effects, and cumulative nonlinear impact of genomic variants as fixed effects. Their contributions are dynamically adjusted through adaptive learning of the genetic complexity of the trait. Tests on 3 datasets of three crops, including 12 rice traits under 3 environments, wheat grain yield under 4 environments, and 3 maize traits, MeNet achieved superior performance in 34 of 36 evaluations, outperforming 11 state-of-the-art models, including conventional statistical models and deep learning approaches. Notably, it exceeded the theoretical upper bound of additive heritability for key traits, demonstrating its capacity to capture epistatic and gene-by-environment interactions. MeNet enables direct exploitation of genomic variants without dimensionality reduction and scales robustly with marker quantity. It allows cross-environment prediction using only 10% field samples for training, achieving on average 57.07% of gain over baseline models. MeNet's robustness and generalizability underscore the potential for foundation models to streamline multi-site and multi-year prediction with minimal field data in breeding of climate-resilient crops.