Genomic prediction of breeding values using previously estimated SNP variances.

Genomic prediction requires estimation of variances of effects of single nucleotide polymorphisms (SNPs), which is computationally demanding, and uses these variances for prediction. We have developed models with separate estimation of SNP variances, which can be applied infrequently, and genomic prediction, which can be applied routinely. SNP variances were estimated with Bayes Stochastic Search Variable Selection (BSSVS) and BayesC. Genome-enhanced breeding values (GEBV) were estimated with RR-BLUP (ridge regression best linear unbiased prediction), using either variances obtained from BSSVS (BLUP-SSVS) or BayesC (BLUP-C), or assuming equal variances for each SNP. Datasets used to estimate SNP variances comprised (1) all animals, (2) 50% random animals (RAN50), (3) 50% best animals (TOP50), or (4) 50% worst animals (BOT50). Traits analysed were protein yield, udder depth, somatic cell score, interval between first and last insemination, direct longevity, and longevity including information from predictors. BLUP-SSVS and BLUP-C yielded similar GEBV as the equivalent Bayesian models that simultaneously estimated SNP variances. Reliabilities of these GEBV were consistently higher than from RR-BLUP, although only significantly for direct longevity. Across scenarios that used data subsets to estimate GEBV, observed reliabilities were generally higher for TOP50 than for RAN50, and much higher than for BOT50. Reliabilities of TOP50 were higher because the training data contained more ancestors of selection candidates. Using estimated SNP variances based on random or non-random subsets of the data, while using all data to estimate GEBV, did not affect reliabilities of the BLUP models. A convergence criterion of 10(-8) instead of 10(-10) for BLUP models yielded similar GEBV, while the required number of iterations decreased by 71 to 90%. Including a separate polygenic effect consistently improved reliabilities of the GEBV, but also substantially increased the required number of iterations to reach convergence with RR-BLUP. SNP variances converged faster for BayesC than for BSSVS. Combining Bayesian variable selection models to re-estimate SNP variances and BLUP models that use those SNP variances, yields GEBV that are similar to those from full Bayesian models. Moreover, these combined models yield predictions with higher reliability and less bias than the commonly used RR-BLUP model.

Calus MP ，Schrooten C ，Veerkamp RF 《-》

Variable selection models for genomic selection using whole-genome sequence data and singular value decomposition.

Non-linear Bayesian genomic prediction models such as BayesA/B/C/R involve iteration and mostly Markov chain Monte Carlo (MCMC) algorithms, which are computationally expensive, especially when whole-genome sequence (WGS) data are analyzed. Singular value decomposition (SVD) of the genotype matrix can facilitate genomic prediction in large datasets, and can be used to estimate marker effects and their prediction error variances (PEV) in a computationally efficient manner. Here, we developed, implemented, and evaluated a direct, non-iterative method for the estimation of marker effects for the BayesC genomic prediction model. The BayesC model assumes a priori that markers have normally distributed effects with probability [Formula: see text] and no effect with probability (1 - [Formula: see text]). Marker effects and their PEV are estimated by using SVD and the posterior probability of the marker having a non-zero effect is calculated. These posterior probabilities are used to obtain marker-specific effect variances, which are subsequently used to approximate BayesC estimates of marker effects in a linear model. A computer simulation study was conducted to compare alternative genomic prediction methods, where a single reference generation was used to estimate marker effects, which were subsequently used for 10 generations of forward prediction, for which accuracies were evaluated. SVD-based posterior probabilities of markers having non-zero effects were generally lower than MCMC-based posterior probabilities, but for some regions the opposite occurred, resulting in clear signals for QTL-rich regions. The accuracies of breeding values estimated using SVD- and MCMC-based BayesC analyses were similar across the 10 generations of forward prediction. For an intermediate number of generations (2 to 5) of forward prediction, accuracies obtained with the BayesC model tended to be slightly higher than accuracies obtained using the best linear unbiased prediction of SNP effects (SNP-BLUP model). When reducing marker density from WGS data to 30 K, SNP-BLUP tended to yield the highest accuracies, at least in the short term. Based on SVD of the genotype matrix, we developed a direct method for the calculation of BayesC estimates of marker effects. Although SVD- and MCMC-based marker effects differed slightly, their prediction accuracies were similar. Assuming that the SVD of the marker genotype matrix is already performed for other reasons (e.g. for SNP-BLUP), computation times for the BayesC predictions were comparable to those of SNP-BLUP.

Meuwissen THE ，Indahl UG ，Ødegård J 《-》

Comparison of genomic predictions using genomic relationship matrices built with different weighting factors to account for locus-specific variances.

Various models have been used for genomic prediction. Bayesian variable selection models often predict more accurate genomic breeding values than genomic BLUP (GBLUP), but GBLUP is generally preferred for routine genomic evaluations because of low computational demand. The objective of this study was to achieve the benefits of both models using results from Bayesian models and genome-wide association studies as weights on single nucleotide polymorphism (SNP) markers when constructing the genomic matrix (G-matrix) for genomic prediction. The data comprised 5,221 progeny-tested bulls from the Nordic Holstein population. The animals were genotyped using the Illumina Bovine SNP50 BeadChip (Illumina Inc., San Diego, CA). Weighting factors in this investigation were the posterior SNP variance, the square of the posterior SNP effect, and the corresponding minus base-10 logarithm of the marker association P-value [-log10(P)] of a t-test obtained from the analysis using a Bayesian mixture model with 4 normal distributions, the square of the estimated SNP effect, and the corresponding -log10(P) of a t-test obtained from the analysis using a classical genome-wide association study model (linear regression model). The weights were derived from the analysis based on data sets that were 0, 1, 3, or 5 yr before performing genomic prediction. In building a G-matrix, the weights were assigned either to each marker (single-marker weighting) or to each group of approximately 5 to 150 markers (group-marker weighting). The analysis was carried out for milk yield, fat yield, protein yield, fertility, and mastitis. Deregressed proofs (DRP) were used as response variables to predict genomic estimated breeding values (GEBV). Averaging over the 5 traits, the Bayesian model led to 2.0% higher reliability of GEBV than the GBLUP model with an original unweighted G-matrix. The superiority of using a GBLUP with weighted G-matrix over GBLUP with an original unweighted G-matrix was the largest when using a weighting factor of posterior variance, resulting in 1.7 percentage points higher reliability. The second best weighting factors were -log10 (P-value) of a t-test corresponding to the square of the posterior SNP effect from the Bayesian model and -log10 (P-value) of a t-test corresponding to the square of the estimated SNP effect from the linear regression model, followed by the square of estimated SNP effect and the square of the posterior SNP effect. In addition, group-marker weighting performed better than single-marker weighting in terms of reducing bias of GEBV, and also slightly increased prediction reliability. The differences between weighting factors and scenarios were larger in prediction bias than in prediction accuracy. Finally, weights derived from a data set having a lag up to 3 yr did not reduce reliability of GEBV. The results indicate that posterior SNP variance estimated from a Bayesian mixture model is a good alternative weighting factor, and common weights on group markers with a size of 30 markers is a good strategy when using markers of the 50,000-marker (50K) chip. In a population with gradually increasing reference data, the weights can be updated once every 3 yr.

Su G ，Christensen OF ，Janss L ，Lund MS ... -  《-》

Modeling heterogeneous (co)variances from adjacent-SNP groups improves genomic prediction for milk protein composition traits.

Accurate genomic prediction requires a large reference population, which is problematic for traits that are expensive to measure. Traits related to milk protein composition are not routinely recorded due to costly procedures and are considered to be controlled by a few quantitative trait loci of large effect. The amount of variation explained may vary between regions leading to heterogeneous (co)variance patterns across the genome. Genomic prediction models that can efficiently take such heterogeneity of (co)variances into account can result in improved prediction reliability. In this study, we developed and implemented novel univariate and bivariate Bayesian prediction models, based on estimates of heterogeneous (co)variances for genome segments (BayesAS). Available data consisted of milk protein composition traits measured on cows and de-regressed proofs of total protein yield derived for bulls. Single-nucleotide polymorphisms (SNPs), from 50K SNP arrays, were grouped into non-overlapping genome segments. A segment was defined as one SNP, or a group of 50, 100, or 200 adjacent SNPs, or one chromosome, or the whole genome. Traditional univariate and bivariate genomic best linear unbiased prediction (GBLUP) models were also run for comparison. Reliabilities were calculated through a resampling strategy and using deterministic formula. BayesAS models improved prediction reliability for most of the traits compared to GBLUP models and this gain depended on segment size and genetic architecture of the traits. The gain in prediction reliability was especially marked for the protein composition traits β-CN, κ-CN and β-LG, for which prediction reliabilities were improved by 49 percentage points on average using the MT-BayesAS model with a 100-SNP segment size compared to the bivariate GBLUP. Prediction reliabilities were highest with the BayesAS model that uses a 100-SNP segment size. The bivariate versions of our BayesAS models resulted in extra gains of up to 6% in prediction reliability compared to the univariate versions. Substantial improvement in prediction reliability was possible for most of the traits related to milk protein composition using our novel BayesAS models. Grouping adjacent SNPs into segments provided enhanced information to estimate parameters and allowing the segments to have different (co)variances helped disentangle heterogeneous (co)variances across the genome.

Gebreyesus G ，Lund MS ，Buitenhuis B ，Bovenhuis H ，Poulsen NA ，Janss LG ... -  《-》

Genomic selection models double the accuracy of predicted breeding values for bacterial cold water disease resistance compared to a traditional pedigree-based model in rainbow trout aquaculture.

Previously, we have shown that bacterial cold water disease (BCWD) resistance in rainbow trout can be improved using traditional family-based selection, but progress has been limited to exploiting only between-family genetic variation. Genomic selection (GS) is a new alternative that enables exploitation of within-family genetic variation. We compared three GS models [single-step genomic best linear unbiased prediction (ssGBLUP), weighted ssGBLUP (wssGBLUP), and BayesB] to predict genomic-enabled breeding values (GEBV) for BCWD resistance in a commercial rainbow trout population, and compared the accuracy of GEBV to traditional estimates of breeding values (EBV) from a pedigree-based BLUP (P-BLUP) model. We also assessed the impact of sampling design on the accuracy of GEBV predictions. For these comparisons, we used BCWD survival phenotypes recorded on 7893 fish from 102 families, of which 1473 fish from 50 families had genotypes [57 K single nucleotide polymorphism (SNP) array]. Naïve siblings of the training fish (n = 930 testing fish) were genotyped to predict their GEBV and mated to produce 138 progeny testing families. In the following generation, 9968 progeny were phenotyped to empirically assess the accuracy of GEBV predictions made on their non-phenotyped parents. The accuracy of GEBV from all tested GS models were substantially higher than the P-BLUP model EBV. The highest increase in accuracy relative to the P-BLUP model was achieved with BayesB (97.2 to 108.8%), followed by wssGBLUP at iteration 2 (94.4 to 97.1%) and 3 (88.9 to 91.2%) and ssGBLUP (83.3 to 85.3%). Reducing the training sample size to n = ~1000 had no negative impact on the accuracy (0.67 to 0.72), but with n = ~500 the accuracy dropped to 0.53 to 0.61 if the training and testing fish were full-sibs, and even substantially lower, to 0.22 to 0.25, when they were not full-sibs. Using progeny performance data, we showed that the accuracy of genomic predictions is substantially higher than estimates obtained from the traditional pedigree-based BLUP model for BCWD resistance. Overall, we found that using a much smaller training sample size compared to similar studies in livestock, GS can substantially improve the selection accuracy and genetic gains for this trait in a commercial rainbow trout breeding population.

Vallejo RL ，Leeds TD ，Gao G ，Parsons JE ，Martin KE ，Evenhuis JP ，Fragomeni BO ，Wiens GD ，Palti Y ... -  《-》