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

The recent detection of thousands to millions of SNP markers and the dramatic improvements in high-throughput, cost effective genotyping technology have made it possible to apply marker assisted selection at a genome wide scale, which is termed genomic selection [1]. These authors suggested three methods for the estimation of genetic value from dense SNP marker data, namely GS-BLUP, BayesA, and BayesB. GS-BLUP applies the BLUP approach to the estimation of the effects of the marker alleles, which assumes a normal prior distribution for the marker effects, where the variance of the prior distribution was assumed equal for all the markers. Since an equal variance for each of the marker effects seems unrealistic, the BayesA method extended the GS-BLUP method by estimating the variance of every marker separately, and an inverse chi-square prior was used for the estimation of these variances. In the BayesB method it was assumed that many of the markers will actually have no effect, and the prior distribution of the variances was a mixture of a distribution with zero variance and an inverse chi-squared distribution. In a simulation study where the genetic model included a finite number of loci with exponentially distributed effects, BayesB provided more accurate prediction of genetic value than BayesA, which in turn was more accurate than GS-BLUP.Although BayesB has the potential for the development of more faithful genetic models, and so seems the method of choice for estimating genome wide breeding values (GW-EBV), its calculation requires the use of computer intensive MCMC techniques. For practical applications and for computer simulations of genomic selection breeding schemes, where many selection rounds and replications are required, it would be advantageous if a much faster algorithm for the calculation of BayesB GW-EBV would be available. Thus, our aim here is to present a fast non-MCMC based algorithm for the calculation of BayesB type estimates of GW-EBV. By usin