Kernel methods and haplotypes used in selection of sparse DNA markers for protein yield in dairy cattle

Recently, genome wide DNA markers have been used in breeding value estimation of livestock species. The computational technique is known as genomic selection. Typically, a large number of marker effects are estimated from a small number of animals, which presents an under-determined problem. In this paper, we propose sparse marker selection methods using haplotypes for both breeding value estimation and QTL mapping. By applying a two-stage regression strategy, markers are selected in the first stage, then in the second stage the selected markers are fitted in a range of models including linear, kernel and semi-parametric models. The estimation accuracy of breeding values is measured by the correlation coefficient, as well as the regression coefficient, between the true breeding values and the estimated breeding values by the models. We show that the estimation accuracy by using sparse markers, as low as 5000 or 500 dimensions, is comparable to that obtained from genome wide markers of about 230,000 dimensions of DNA haplotypes. The selected sparse markers can also be used for QTL mapping. In this paper we use protein yield to demonstrate the methods, and show that loci of large effects confirm published QTL.