Reducing dimensionality for prediction of genome-wide breeding values.

Partial least square regression (PLSR) and principal component regression (PCR) are methods designed for situations where the number of predictors is larger than the number of records. The aim was to compare the accuracy of genome-wide breeding values (EBV) produced using PLSR and PCR with a Bayesian method, 'BayesB'. Marker densities of 1, 2, 4 and 8 Ne markers/Morgan were evaluated when the effective population size (Ne) was 100. The correlation between true breeding value and estimated breeding value increased with density from 0.611 to 0.681 and 0.604 to 0.658 using PLSR and PCR respectively, with an overall advantage to PLSR of 0.016 (s.e = 0.008). Both methods gave a lower accuracy compared to the 'BayesB', for which accuracy increased from 0.690 to 0.860. PLSR and PCR appeared less responsive to increased marker density with the advantage of 'BayesB' increasing by 17% from a marker density of 1 to 8Ne/M. PCR and PLSR showed greater bias than 'BayesB' in predicting breeding values at all densities. Although, the PLSR and PCR were computationally faster and simpler, these advantages do not outweigh the reduction in accuracy, and there is a benefit in obtaining relevant prior information from the distribution of gene effects.

A fast algorithm for BayesB type of prediction of genome-wide estimates of genetic value.

Genomic selection uses genome-wide dense SNP marker genotyping for the prediction of genetic values, and consists of two steps: (1) estimation of SNP effects, and (2) prediction of genetic value based on SNP genotypes and estimates of their effects. For the former step, BayesB type of estimators have been proposed, which assume a priori that many markers have no effects, and some have an effect coming from a gamma or exponential distribution, i.e. a fat-tailed distribution. Whilst such estimators have been developed using Monte Carlo Markov chain (MCMC), here we derive a much faster non-MCMC based estimator by analytically performing the required integrations. The accuracy of the genome-wide breeding value estimates was 0.011 (s.e. 0.005) lower than that of the MCMC based BayesB predictor, which may be because the integrations were performed one-by-one instead of for all SNPs simultaneously. The bias of the new method was opposite to that of the MCMC based BayesB, in that the new method underestimates the breeding values of the best selection candidates, whereas MCMC-BayesB overestimated their breeding values. The new method was computationally several orders of magnitude faster than MCMC based BayesB, which will mainly be advantageous in computer simulations of entire breeding schemes, in cross-validation testing, and practical schemes with frequent re-estimation of breeding values.

Persistence of accuracy of genome-wide breeding values over generations when including a polygenic effect.

BACKGROUND: When estimating marker effects in genomic selection, estimates of marker effects may simply act as a proxy for pedigree, i.e. their effect may partially be attributed to their association with superior parents and not be linked to any causative QTL. Hence, these markers mainly explain polygenic effects rather than QTL effects. However, if a polygenic effect is included in a Bayesian model, it is expected that the estimated effect of these markers will be more persistent over generations without having to re-estimate the marker effects every generation and will result in increased accuracy and reduced bias. METHODS: Genomic selection using the Bayesian method, 'BayesB' was evaluated for different marker densities when a polygenic effect is included (GWpEBV) and not included (GWEBV) in the model. Linkage disequilibrium and a mutation drift balance were obtained by simulating a population with a Ne of 100 over 1,000 generations. RESULTS: Accuracy of selection was slightly higher for the model including a polygenic effect than for the model not including a polygenic effect whatever the marker density. The accuracy decreased in later generations, and this reduction was stronger for lower marker densities. However, no significant difference in accuracy was observed between the two models. The linear regression of TBV on GWEBV and GWpEBV was used as a measure of bias. The regression coefficient was more stable over generations when a polygenic effect was included in the model, and was always between 0.98 and 1.00 for the highest marker density. The regression coefficient decreased more quickly with decreasing marker density. CONCLUSIONS: Including a polygenic effect had no impact on the selection accuracy, but showed reduced bias, which is especially important when estimates of genome-wide markers are used to estimate breeding values over more than one generation.