On the use of GBLUP and its extension for GWAS with additive and epistatic effects

Genomic best linear unbiased prediction (GBLUP) is the most widely used model for genome-wide predictions. Interestingly, it is also possible to perform genome-wide association studies (GWAS) based on GBLUP. Although the estimated marker effects in GBLUP are shrunken and the conventional test based on such effects has low power, it was observed that a modified test statistic can be produced and the result of test was identical to a standard GWAS model. Later, a mathematical proof was given for the special case that there is no fixed covariate in GBLUP. Since then, the new approach has been called "GWAS by GBLUP". Nevertheless, covariates such as environmental and subpopulation effects are very common in GBLUP. Thus, it is necessary to confirm the equivalence in the general case. Recently, the concept was generalized to GWAS for epistatic effects and the new approach was termed rapid epistatic mixed-model association analysis (REMMA) because it greatly improved the computational efficiency. However, the relationship between REMMA and the standard GWAS model has not been investigated. In this study, we first provided a general mathematical proof of the equivalence between "GWAS by GBLUP" and the standard GWAS model for additive effects. Then, we compared REMMA with the standard GWAS model for epistatic effects by a theoretical investigation and by empirical data analyses. We hypothesized that the similarity of the two models is influenced by the relative contribution of additive and epistatic effects to the phenotypic variance, which was verified by empirical and simulation studies.