Dorian J. Garrick

BACKGROUND: Two 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. RESULTS: Estimates 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. CONCLUSIONS: Collectively, 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.

Genomic prediction of breeding values involves a so-called training analysis that predicts the influence of small genomic regions by regression of observed information on marker genotypes for a given population of individuals. Available observations may take the form of individual phenotypes, repeated observations, records on close family members such as progeny, estimated breeding values (EBV) or their deregressed counterparts from genetic evaluations. The literature indicates that researchers are inconsistent in their approach to using EBV or deregressed data, and as to using the appropriate methods for weighting some data sources to account for heterogeneous variance. A logical approach to using information for genomic prediction is introduced, which demonstrates the appropriate weights for analyzing observations with heterogeneous variance and explains the need for and the manner in which EBV should have parent average effects removed, be deregressed and weighted. An appropriate deregression for genomic regression analyses is EBV/r2 where EBV excludes parent information and r2 is the reliability of that EBV. The appropriate weights for deregressed breeding values are neither the reliability nor the prediction error variance, two alternatives that have been used in published studies, but the ratio (1 - h2)/[(c + (1 - r2)/r2)h2] where c > 0 is the fraction of genetic variance not explained by markers. Phenotypic information on some individuals and deregressed data on others can be combined in genomic analyses using appropriate weighting.

Genomic selection can increase genetic gain per generation through early selection. Genomic selection is expected to be particularly valuable for traits that are costly to phenotype and expressed late in the life cycle of long-lived species. Alternative approaches to genomic selection prediction models may perform differently for traits with distinct genetic properties. Here the performance of four different original methods of genomic selection that differ with respect to assumptions regarding distribution of marker effects, including (i) ridge regression-best linear unbiased prediction (RR-BLUP), (ii) Bayes A, (iii) Bayes Cπ, and (iv) Bayesian LASSO are presented. In addition, a modified RR-BLUP (RR-BLUP B) that utilizes a selected subset of markers was evaluated. The accuracy of these methods was compared across 17 traits with distinct heritabilities and genetic architectures, including growth, development, and disease-resistance properties, measured in a Pinus taeda (loblolly pine) training population of 951 individuals genotyped with 4853 SNPs. The predictive ability of the methods was evaluated using a 10-fold, cross-validation approach, and differed only marginally for most method/trait combinations. Interestingly, for fusiform rust disease-resistance traits, Bayes Cπ, Bayes A, and RR-BLUB B had higher predictive ability than RR-BLUP and Bayesian LASSO. Fusiform rust is controlled by few genes of large effect. A limitation of RR-BLUP is the assumption of equal contribution of all markers to the observed variation. However, RR-BLUP B performed equally well as the Bayesian approaches.The genotypic and phenotypic data used in this study are publically available for comparative analysis of genomic selection prediction models.

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.