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 modeling nonlinearity, but 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 modeling power of neural networks to advance genomic prediction. It employs dual embeddings to model phenotype-specific genetic relatedness as random effects and the cumulative nonlinear effect of genomic variants as fixed effects. Their contributions are dynamically adjusted through adaptive learning of the genetic complexity of the trait. When tested on three datasets from three crops, including 12 rice traits under three environments, wheat grain yield under four environments, and three 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 performs cross-environment prediction using only 10% of field samples for training, achieving, on average, a 57.07% 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 for the breeding of climate-resilient crops.