Fig. 2

MegaLMM scales efficiently for very high-dimensional traits. Four competing methods were used to fit multi-trait genomic prediction models to predict genetic values for a single focal gene expression trait using complete data from t additional traits. Data are from an Arabidopsis thaliana gene expression data with 20,843 genes and 665 lines. A Average estimated genomic prediction accuracy across 20 focal traits using t additional secondary traits for each of the four prediction methods (rrBLUP is a univariate prediction method and was only run for the focal trait). Genomic prediction accuracy was estimated by cross-validation as \(\rho _{g} = \text {cor}_{g}(\hat {\mathbf {u}},\mathbf {y})\sqrt {h^{2}(\hat {\mathbf {u}})}\) to account for non-genetic correlations between the secondary traits and focal traits since all were measured in the same sample. Smoothed curves are estimated by stats::lowess. The number of latent factors used for MegaLMM (K) is listed in red at the top of the figure. B Computational times required to find a solution for each MvLMM. For the MCMC methods MCMCglmm and MegaLMM, times were estimated as the time required to collect an effective sample size of at least 1000 for >90% of the elements in the genetic covariance matrix U. Computational times for MCMCglmm and MTG2 above 64 traits were linearly extrapolated (on log scale) based on the slope between 32 and 64 traits. Black lines show the slope of exponential scaling functions with the specified exponents for reference