A comparison of five methods to predict genomic breeding values of dairy bulls from genome-wide SNP markers

Abstract

Background: Genomic selection (GS) uses molecular breeding values (MBV) derived from dense markers across the entire genome for selection of young animals. The accuracy of MBV prediction is important for a successful application of GS. Recently, several methods have been proposed to estimate MBV. Initial simulation studies have shown that these methods can accurately predict MBV. In this study we compared the accuracies and possible bias of five different regression methods in an empirical application in dairy cattle.

Methods: Genotypes of 7,372 SNP and highly accurate EBV of 1,945 dairy bulls were used to predict MBV for protein percentage (PPT) and a profit index (Australian Selection Index, ASI). Marker effects were estimated by least squares regression (FR-LS), Bayesian regression (Bayes-R), random regression best linear unbiased prediction (RR-BLUP), partial least squares regression (PLSR) and nonparametric support vector regression (SVR) in a training set of 1,239 bulls. Accuracy and bias of MBV prediction were calculated from cross-validation of the training set and tested against a test team of 706 young bulls.

Results: For both traits, FR-LS using a subset of SNP was significantly less accurate than all other methods which used all SNP. Accuracies obtained by Bayes-R, RR-BLUP, PLSR and SVR were very similar for ASI (0.39-0.45) and for PPT (0.55-0.61). Overall, SVR gave the highest accuracy.All methods resulted in biased MBV predictions for ASI, for PPT only RR-BLUP and SVR predictions were unbiased. A significant decrease in accuracy of prediction of ASI was seen in young test cohorts of bulls compared to the accuracy derived from cross-validation of the training set. This reduction was not apparent for PPT. Combining MBV predictions with pedigree based predictions gave 1.05 - 1.34 times higher accuracies compared to predictions based on pedigree alone. Some methods have largely different computational requirements, with PLSR and RR-BLUP requiring the least computing time.

Conclusions: The four methods which use information from all SNP namely RR-BLUP, Bayes-R, PLSR and SVR generate similar accuracies of MBV prediction for genomic selection, and their use in the selection of immediate future generations in dairy cattle will be comparable. The use of FR-LS in genomic selection is not recommended.

Figure 1

Distribution of EBVs for Australian Selection Index (ASI, a) and protein percentage (PPT, b), distribution of reliabilities of EBVs (c), and number of bulls within year of birth (d).

Figure 2

Partial least squares regression model optimization for Australian Selection Index using cross-validation. Shown is the mean prediction error (MSEP) in the training (MSEP_training) data set, the average MSEP in the 5-fold cross-validation samples (MSEP_CV), the proportion of EBV (Var_EBV) and SNP variance (Var_SNP) explained in the training data for models with an increasing number of latent components; the optimal prediction model includes the first 5 latent components, identified by the smallest MSEP_CV.

Figure 3

Fit of models relating EBVs and predicted MBVs in the training data and in young bulls. To avoid cluttering predictions are plotted for a single fold of the cross-validation (CV) of the training data set and young bull cohort 1998; ASI: Australian Selection Index; PPT: protein percentage; FR-LS: fixed regression-least squares; RR-BLUP: random regression-BLUP; Bayes-R: Bayesian regression; SVR: support vector regression; PLSR: partial least squares regression.

Figure 4

Distribution of 7,372 SNP effects along the genome estimated by four methods. The right most 772 SNPs are unassigned to chromosomes; ASI: Australian Selection Index; PPT: protein percentage; FR-LS: fixed regression-least squares; RR-BLUP: random regression-BLUP; Bayes-R: Bayesian regression.