The success of genomic selection depends on the potential to predict genome-assisted breeding values (GEBVs) with high accuracy over several generations without additional phenotyping after estimating marker effects. Results from both simulations and practical applications have to be evaluated for this potential, which requires linkage disequilibrium (LD) between markers and QTL. This study shows that markers can capture genetic relationships among genotyped animals, thereby affecting accuracies of GEBVs. Strategies to validate the accuracy of GEBVs due to LD are given. Simulations were used to show that accuracies of GEBVs obtained by fixed regression-least squares (FR-LS), random regression-best linear unbiased prediction (RR-BLUP), and Bayes-B are nonzero even without LD. When LD was present, accuracies decrease rapidly in generations after estimation due to the decay of genetic relationships. However, there is a persistent accuracy due to LD, which can be estimated by modeling the decay of genetic relationships and the decay of LD. The impact of genetic relationships was greatest for RR-BLUP. The accuracy of GEBVs can result entirely from genetic relationships captured by markers, and to validate the potential of genomic selection, several generations have to be analyzed to estimate the accuracy due to LD. The method of choice was Bayes-B; FR-LS should be investigated further, whereas RR-BLUP cannot be recommended. D UE to advances in molecular genetics, genomewide dense marker data are becoming available for livestock species. These can be used to estimate genome-assisted breeding values (GEBVs) as proposed by Meuwissen et al. (2001). First, marker effects are estimated with a training data set containing individuals with marker genotypes and trait phenotypes. Then, GEBVs of any genotyped individual in the population can be calculated using the estimated marker effects. The greatest advantage of this approach is the potential to predict GEBVs with high accuracy over several generations without repeated phenotyping, which results in lower costs and shorter generation intervals. This approach requires linkage disequilibrium (LD) between marker loci and quantitative trait loci (QTL), otherwise the accuracy is expected to decline fast in the generations following the estimation of marker effects. In simulation studies, Meuwissen et al. (2001) and Solberg et al. (2006) predicted the true breeding values of offspring of individuals in the training data to validate the potential advantage of GEBVs. In practical applications, cross-validation with individuals from the same population is used, and either breeding values estimated from trait phenotypes and pedigree data or progeny means corrected for environmental effects and EBVs of mates are used to validate the potential advantage of GEBVs. Thus, both in simulation and in practical applications, individuals in the validation group are related to individuals in the training data. However, markers used in the statistical models to estimate marker effects can...

BackgroundTwo Bayesian methods, BayesCπ and BayesDπ, were developed for genomic prediction to address the drawback of BayesA and BayesB regarding the impact of prior hyperparameters and treat the prior probability π that a SNP has zero effect as unknown. The methods were compared in terms of inference of the number of QTL and accuracy of genomic estimated breeding values (GEBVs), using simulated scenarios and real data from North American Holstein bulls.ResultsEstimates of π from BayesCπ, in contrast to BayesDπ, were sensitive to the number of simulated QTL and training data size, and provide information about genetic architecture. Milk yield and fat yield have QTL with larger effects than protein yield and somatic cell score. The drawback of BayesA and BayesB did not impair the accuracy of GEBVs. Accuracies of alternative Bayesian methods were similar. BayesA was a good choice for GEBV with the real data. Computing time was shorter for BayesCπ than for BayesDπ, and longest for our implementation of BayesA.ConclusionsCollectively, accounting for computing effort, uncertainty as to the number of QTL (which affects the GEBV accuracy of alternative methods), and fundamental interest in the number of QTL underlying quantitative traits, we believe that BayesCπ has merit for routine applications.

BackgroundThe impact of additive-genetic relationships captured by single nucleotide polymorphisms (SNPs) on the accuracy of genomic breeding values (GEBVs) has been demonstrated, but recent studies on data obtained from Holstein populations have ignored this fact. However, this impact and the accuracy of GEBVs due to linkage disequilibrium (LD), which is fairly persistent over generations, must be known to implement future breeding programs.Materials and methodsThe data set used to investigate these questions consisted of 3,863 German Holstein bulls genotyped for 54,001 SNPs, their pedigree and daughter yield deviations for milk yield, fat yield, protein yield and somatic cell score. A cross-validation methodology was applied, where the maximum additive-genetic relationship (amax) between bulls in training and validation was controlled. GEBVs were estimated by a Bayesian model averaging approach (BayesB) and an animal model using the genomic relationship matrix (G-BLUP). The accuracy of GEBVs due to LD was estimated by a regression approach using accuracy of GEBVs and accuracy of pedigree-based BLUP-EBVs.ResultsAccuracy of GEBVs obtained by both BayesB and G-BLUP decreased with decreasing amax for all traits analyzed. The decay of accuracy tended to be larger for G-BLUP and with smaller training size. Differences between BayesB and G-BLUP became evident for the accuracy due to LD, where BayesB clearly outperformed G-BLUP with increasing training size.ConclusionsGEBV accuracy of current selection candidates varies due to different additive-genetic relationships relative to the training data. Accuracy of future candidates can be lower than reported in previous studies because information from close relatives will not be available when selection on GEBVs is applied. A Bayesian model averaging approach exploits LD information considerably better than G-BLUP and thus is the most promising method. Cross-validations should account for family structure in the data to allow for long-lasting genomic based breeding plans in animal and plant breeding.

Genomic best linear unbiased prediction (BLUP) is a statistical method that uses relationships between individuals calculated from single-nucleotide polymorphisms (SNPs) to capture relationships at quantitative trait loci (QTL). We show that genomic BLUP exploits not only linkage disequilibrium (LD) and additive-genetic relationships, but also cosegregation to capture relationships at QTL. Simulations were used to study the contributions of those types of information to accuracy of genomic estimated breeding values (GEBVs), their persistence over generations without retraining, and their effect on the correlation of GEBVs within families. We show that accuracy of GEBVs based on additive-genetic relationships can decline with increasing training data size and speculate that modeling polygenic effects via pedigree relationships jointly with genomic breeding values using Bayesian methods may prevent that decline. Cosegregation information from half sibs contributes little to accuracy of GEBVs in current dairy cattle breeding schemes but from full sibs it contributes considerably to accuracy within family in corn breeding. Cosegregation information also declines with increasing training data size, and its persistence over generations is lower than that of LD, suggesting the need to model LD and cosegregation explicitly. The correlation between GEBVs within families depends largely on additive-genetic relationship information, which is determined by the effective number of SNPs and training data size. As genomic BLUP cannot capture short-range LD information well, we recommend Bayesian methods with t-distributed priors. To understand better how genomic relationships capture relationships at QTL, we propose to apply concepts of pedigree analyses that define founders in a recent past generation. Based on these concepts, we show that coefficients of the genomic relationship matrix do not explain genetic covariances between individuals at QTL unless either there is linkage disequilibrium (LD) between QTL and SNPs measured in founders or selection candidates are related by pedigree to the training individuals. The latter results in cosegregation of alleles at QTL and SNPs that are