Megavariate methods capture complex genotype-by-environment interactions.

Genomic prediction models that capture genotype-by-environment (GxE) interaction are useful for predicting site-specific performance by leveraging information among related individuals and correlated environments, but implementing such models is computationally challenging. This study describes the algorithm of these scalable approaches, including 2 models with latent representations of GxE interactions, namely MegaLMM and MegaSEM, and an efficient multivariate mixed-model solver, namely Pseudo-expectation Gauss-Seidel (PEGS), fitting different covariance structures [unstructured, extended factor analytic (XFA), Heteroskedastic compound symmetry (HCS)]. Accuracy and runtime are benchmarked on simulated scenarios with varying numbers of genotypes and environments. MegaLMM and PEGS-based XFA and HCS models provided the highest accuracy under sparse testing with 100 testing environments. PEGS-based unstructured model was orders of magnitude faster than restricted maximum likelihood (REML) based multivariate genomic best linear unbiased predictions (GBLUP) while providing the same accuracy. MegaSEM provided the lowest runtime, fitting a model with 200 traits and 20,000 individuals in ∼5 min, and a model with 2,000 traits and 2,000 individuals in less than 3 min. With the genomes-to-fields data, the most accurate predictions were attained with the univariate model fitted across environments and by averaging environment-level genomic estimated breeding values (GEBVs) from models with HCS and XFA covariance structures.