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Open Access Highly Accessed Methodology article

A Bayesian method and its variational approximation for prediction of genomic breeding values in multiple traits

Takeshi Hayashi1* and Hiroyoshi Iwata2

Author Affiliations

1 Agroinformatics Division, National Agriculture and Food Research Organization, Agricultural Research Center, Kannondai, Tsukuba, Ibaraki, 305-8666, Japan

2 Department of Agricultural and Environmental Biology, Graduate School of Agricultural and Life Sciences, The University of Tokyo, 1-1-1 Yayoi, Bunkyo, Tokyo, 113-8657, Japan

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BMC Bioinformatics 2013, 14:34  doi:10.1186/1471-2105-14-34

Published: 31 January 2013



Genomic selection is an effective tool for animal and plant breeding, allowing effective individual selection without phenotypic records through the prediction of genomic breeding value (GBV). To date, genomic selection has focused on a single trait. However, actual breeding often targets multiple correlated traits, and, therefore, joint analysis taking into consideration the correlation between traits, which might result in more accurate GBV prediction than analyzing each trait separately, is suitable for multi-trait genomic selection. This would require an extension of the prediction model for single-trait GBV to multi-trait case. As the computational burden of multi-trait analysis is even higher than that of single-trait analysis, an effective computational method for constructing a multi-trait prediction model is also needed.


We described a Bayesian regression model incorporating variable selection for jointly predicting GBVs of multiple traits and devised both an MCMC iteration and variational approximation for Bayesian estimation of parameters in this multi-trait model. The proposed Bayesian procedures with MCMC iteration and variational approximation were referred to as MCBayes and varBayes, respectively. Using simulated datasets of SNP genotypes and phenotypes for three traits with high and low heritabilities, we compared the accuracy in predicting GBVs between multi-trait and single-trait analyses as well as between MCBayes and varBayes. The results showed that, compared to single-trait analysis, multi-trait analysis enabled much more accurate GBV prediction for low-heritability traits correlated with high-heritability traits, by utilizing the correlation structure between traits, while the prediction accuracy for uncorrelated low-heritability traits was comparable or less with multi-trait analysis in comparison with single-trait analysis depending on the setting for prior probability that a SNP has zero effect. Although the prediction accuracy with varBayes was generally lower than with MCBayes, the loss in accuracy was slight. The computational time was greatly reduced with varBayes.


In genomic selection for multiple correlated traits, multi-trait analysis was more beneficial than single-trait analysis and varBayes was much advantageous over MCBayes in computational time, which would outweigh the loss of prediction accuracy caused by the approximation procedure, and is thus considered a practical method of choice.

Genomic selection; Multiple traits; Bayesian regression; MCMC iteration; Variational approximation