Prediction accuracy of direct and indirect approaches, and their relationships with prediction ability of calibration models.

Milk infrared spectra are routinely used for phenotyping traits of interest through links developed between the traits and spectra. Predicted individual traits are then used in genetic analyses for estimated breeding value (EBV) or for phenotypic predictions using a single-trait mixed model; this approach is referred to as indirect prediction (IP). An alternative approach [direct prediction (DP)] is a direct genetic analysis of (a reduced dimension of) the spectra using a multitrait model to predict multivariate EBV of the spectral components and, ultimately, also to predict the univariate EBV or phenotype for the traits of interest. We simulated 3 traits under different genetic (low: 0.10 to high: 0.90) and residual (zero to high: ±0.90) correlation scenarios between the 3 traits and assumed the first trait is a linear combination of the other 2 traits. The aim was to compare the IP and DP approaches for predictions of EBV and phenotypes under the different correlation scenarios. We also evaluated relationships between performances of the 2 approaches and the accuracy of calibration equations. Moreover, the effect of using different regression coefficients estimated from simulated phenotypes (β), true breeding values (β), and residuals (β) on performance of the 2 approaches were evaluated. The simulated data contained 2,100 parents (100 sires and 2,000 cows) and 8,000 offspring (4 offspring per cow). Of the 8,000 observations, 2,000 were randomly selected and used to develop links between the first and the other 2 traits using partial least square (PLS) regression analysis. The different PLS regression coefficients, such as β, β, and β, were used in subsequent predictions following the IP and DP approaches. We used BLUP analyses for the remaining 6,000 observations using the true (co)variance components that had been used for the simulation. Accuracy of prediction (of EBV and phenotype) was calculated as a correlation between predicted and true values from the simulations. The results showed that accuracies of EBV prediction were higher in the DP than in the IP approach. The reverse was true for accuracy of phenotypic prediction when using β but not when using β and β, where accuracy of phenotypic prediction in the DP was slightly higher than in the IP approach. Within the DP approach, accuracies of EBV when using β were higher than when using β only at the low genetic correlation scenario. However, we found no differences in EBV prediction accuracy between the β and β in the IP approach. Accuracy of the calibration models increased with an increase in genetic and residual correlations between the traits. Performance of both approaches increased with an increase in accuracy of the calibration models. In conclusion, the DP approach is a good strategy for EBV prediction but not for phenotypic prediction, where the classical PLS regression-based equations or the IP approach provided better results.