title: Genomic breeding value prediction using three Bayesian methods and application to reduced density marker panels.
abstract: BACKGROUND
  Bayesian approaches for predicting genomic breeding values (GEBV) have been proposed that allow for different variances for individual markers resulting in a shrinkage procedure that uses prior information to coerce negligible effects towards zero. These approaches have generally assumed application to high-density genotype data on all individuals, which may not be the case in practice. In this study, three approaches were compared for their predictive power in computing GEBV when training at high SNP marker density and predicting at high or low densities: the well- known Bayes-A, a generalization of Bayes-A where scale and degrees of freedom are estimated from the data (Student-t) and a Bayesian implementation of the Lasso method. Twelve scenarios were evaluated for predicting GEBV using low-density marker subsets, including selection of SNP based on genome spacing or size of additive effect and the inclusion of unknown genotype information in the form of genotype probabilities from pedigree and genotyped ancestors.
  
  
  RESULTS
  The GEBV accuracy (calculated as correlation between GEBV and traditional breeding values) was highest for Lasso, followed by Student-t and then Bayes-A. When comparing GEBV to true breeding values, Student-t was most accurate, though differences were small. In general the shrinkage applied by the Lasso approach was less conservative than Bayes-A or Student-t, indicating that Lasso may be more sensitive to QTL with small effects. In the reduced-density marker subsets the ranking of the methods was generally consistent. Overall, low-density, evenly-spaced SNPs did a poor job of predicting GEBV, but SNPs selected based on additive effect size yielded accuracies similar to those at high density, even when coverage was low. The inclusion of genotype probabilities to the evenly-spaced subsets showed promising increases in accuracy and may be more useful in cases where many QTL of small effect are expected.
  
  
  CONCLUSIONS
  In this dataset the Student-t approach slightly outperformed the other methods when predicting GEBV at both high and low density, but the Lasso method may have particular advantages in situations where many small QTL are expected. When markers were selected at low density based on genome spacing, the inclusion of genotype probabilities increased GEBV accuracy which would allow a single low- density marker panel to be used across traits.
authors.affiliation: Genus plc., 100 Bluegrass Commons Blvd., Suite 2200, Hendersonville, TN, 37075, USA.
authors.forename: Matthew A
authors.initials: MA
authors.lastname: Cleveland
authors.affiliation: Genus plc., 100 Bluegrass Commons Blvd., Suite 2200, Hendersonville, TN, 37075, USA.
authors.forename: Selma
authors.initials: S
authors.lastname: Forni
authors.affiliation: Genus plc., 100 Bluegrass Commons Blvd., Suite 2200, Hendersonville, TN, 37075, USA.
authors.forename: Nader
authors.initials: N
authors.lastname: Deeb
authors.affiliation: North Carolina State University, Department of Animal Science, Raleigh, NC, 27695-7627, USA.
authors.forename: Christian
authors.initials: C
authors.lastname: Maltecca