Additional file 1 Supplemntary Methods. Expanded description of the prior distributions and derivation of the MCMC algorithm used in MegaLMM [72–76]. Figure S1. Prediction accuracies for each target gene expression trait relative to MegaLMM. Figure S2. Prediction accuracies for each target gene expression trait as a function of dataset size. Figure S3. Accuracy of covariance estimates in simulated data. Figure S4. Sensitivity of MegaLMM to changes in K. Figure S5. Performance of single-trait and multi-trait genomic prediction for wheat yield across 20 experiments. Figure S6. Relationship between genetic correlation and benefit of MvLMM across Genomes2Fields site-years. Table S1. Default hyperparameters for user-customizable prior distributions.