Effect of the prior distribution of SNP effects on the estimation of total breeding value

Five main methods, commonly applied in genomic selection, were used to estimate the GEBV on the 15th QTLMAS workshop dataset: GBLUP, LASSO, Bayes A and two Bayes B type of methods (BBn and BBt). GBLUP is a mixed model approach where GEBV are obtained using a relationship matrix calculated from the SNP genotypes. The remaining methods are regression-based approaches where the SNP effects are first estimated and, then GEBV are calculated given the individuals' genotypes.

The differences between the regression-based methods are in their prior distributions for the SNP effects. The prior distribution for LASSO is a Laplace distribution, for Bayes A is a scaled Student-t distribution, and the Bayes B type methods have a Spike and Slab prior where only a proportion (π) of SNP has an effect, following a given distribution. In this study, two different distributions were considered for the Bayes B type methods: (i) normal and (ii) scaled Student-t. They are referred here as the BBn and BBt methods, respectively. These prior distributions are defined by one or more parameters controlling their scale/rate (λ), shape (df) or proportion of SNP with effect (π). LASSO requires one (λ); two for Bayes A (λ, df) and Bayes Bn (λ, π); and three for Bayes Bt (λ, df, π). In this study, all parameters were estimated from the data. An extra scenario for Bayes A and BBt was included where df was not estimated but fixed to 4 (suffixed _4df). The implementation of GBLUP was done using ASREML, the heritability was also estimated from the data. All other methods were implemented using a MCMC approach.

All Bayes A and B methods showed accuracy (correlation between True and Estimated BV) as high as 0.94 except for BA_4df (r = 0.91). Compared to the traditional BLUP using pedigree information, these methods improved the accuracy between 50 and 55%. GBLUP and LASSO were less accurate (0.81 and 0.85 respectively) and the improvements were 34 and 40% compared to BLUP.

Results of all methods were consistent and the accuracies for GEBV ranged between 0.81 and 0.94. When all parameters were estimated the results were similar for the Bayes A and Bayes B methods. Results showed that Bayes A was more sensitive to the changes in the shape parameter, and the parameter changes led to change in the accuracy of GEBV. However BBt was more robust to the change in this parameter. This may be explained by the fact that BBt estimates one extra parameter and it can buffer against a non-proper shape parameter.