Predicting breeding values of spring barley accessions by using the singular value decomposition of genetic similarities

As pedigree information among parental lines is often incomplete, selection response can be enhanced if a matrix containing genetic similarities is used in the mixed model equations (MME) to predict breeding values. However, a low number of molecular markers may cause this matrix to be singular. This study was conducted to determine if breeding values are still accurate when a singular value decomposition of genetic similarities was performed setting negative singular values to zero. Two-year data for four traits of 152 spring barley accessions, which were analyzed by 23 SSR markers, were used in the prediction of breeding values. In general, similar values of Akaike Information Criteria and of overall standard error of difference and a Spearman rank correlation coefficient between breeding values ranging from 0.92 to 0.99 were obtained independent of whether the prediction was based on a singular value decomposition of genetic similarities or not. In conclusion, the singular value decomposition of genetic similarities appears to be a suitable method in the case of singular matrices.