All panels contain five model classes: linear regression on other phenotypes (‘P', yellow), linear regression with additive effects determined by forward selection (‘QTLs', purple), prediction based on the realized genetic relatedness (‘BLUP', green), the best LMM with additive and interaction effects (‘LMM', blue) and the best LMM with additive and interaction effects together with other phenotypes (‘LMM+P', red). All prediction accuracies denote coefficient of determination *R*^{2}, and are determined by fourfold cross-validation. (**a**) Models using a single source of information predict less accurately than a combined one. Predicted (*y* axis) and observed (*x* axis) growth in NaCl for every measured hybrid strain (dots) for each model class, with coefficient of determination (*R*^{2}) of the predictions labelled. Perfect predictions would lie on the grey dashed line *y*=*x*. (**b**) Linear mixed models with information from other phenotypes give very accurate predictions. Predictive performance (*R*^{2}, *x* axis) for different models (*y* axis) for each of the measured phenotypes (nine boxes). Bars indicate the range of *R*^{2} over the four cross-validation folds. The dashed lines show narrow-sense heritability *h*^{2} (black, left) and repeatability *H*^{2} (black, right) estimates for the mean phenotype, and the dotted line (red) shows repeatability of a single measurement *H*_{1}^{2}. (**c**) Prediction can be more accurate than one measurement. Prediction accuracy of mean phenotype (*R*^{2}, *y* axis) compared with different types of heritability estimates (*x* axis) for the four model classes: narrow-sense heritability of average phenotype (*h*^{2}, top panel), repeatability of average phenotype (*H*^{2}, middle panel) and repeatability of a single measurement (*H*_{1}^{2}, bottom panel). Grey dashed lines denote the identity *y*=*x*.