Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments

Abstract

We compared the predictive ability of various prediction models for a maize dataset derived from 910 doubled haploid lines from European landraces (Kemater Landmais Gelb and Petkuser Ferdinand Rot), which were tested in six locations in Germany and Spain. The compared models were Genomic Best Linear Unbiased Prediction (GBLUP) as an additive model, Epistatic Random Regression BLUP (ERRBLUP) accounting for all pairwise SNP interactions, and selective Epistatic Random Regression BLUP (sERRBLUP) accounting for a selected subset of pairwise SNP interactions. These models have been compared in both univariate and bivariate statistical settings within and across environments. Our results indicate that modeling all pairwise SNP interactions into the univariate/bivariate model (ERRBLUP) is not superior in predictive ability to the respective additive model (GBLUP). However, incorporating only a selected subset of interactions with the highest effect variances in univariate/bivariate sERRBLUP can increase predictive ability significantly compared to the univariate/bivariate GBLUP. Overall, bivariate models consistently outperform univariate models in predictive ability. Over all studied traits, locations, and landraces, the increase in prediction accuracy from univariate GBLUP to univariate sERRBLUP ranged from 5.9 to 112.4 percent, with an average increase of 47 percent. For bivariate models, the change ranged from −0.3 to +27.9 percent comparing the bivariate sERRBLUP to the bivariate GBLUP. The average increase across traits and locations was 11 percent. This considerable increase in predictive ability achieved by sERRBLUP may be of interest for “sparse testing” approaches in which only a subset of the lines/hybrids of interest is observed at each location.Key MessageThe prediction accuracy of genomic prediction of phenotypes can be increased by only including top ranked pairwise SNP interactions into the prediction models.

Bivariate genomic prediction of phenotypes by selecting epistatic interactions across years

“…We used the bivariate statistical framework as the basis of the genomic prediction models. In this regard, GBLUP, ERRBLUP and sERRBLUP as three different methods described in Vojgani et al (2020) were used for genomic prediction of phenotypes which differ in dispersion matrices representing their covariance structure of the genetic effects. GBLUP as an additive model is based on a genomic relationship matrix calculated according to VanRaden (2008).…”

“…In addition, inclusion of epistasis, defined as the interaction between loci (Falconer and Mackay 1996; Lynch and Walsh 1998), into the genomic prediction model results in more accurate phenotype prediction (Hu et al 2011; Wang et al 2012; Mackay 2014; Martini et al 2016; Vojgani et al 2019b) due to the considerable contribution of epistasis in genetic variation of quantitative traits (Mackay 2014). In this context, several statistical models have been proposed.…”

“…In this approach, the full epistasis model was reduced to a model with a subset of the largest epistatic interaction effects, resulting in an increase in predictive ability (Martini et al 2016), through borrowing information across environments. Vojgani et al (2019b) showed that the prediction accuracy can be increased even further by selecting the interactions with the highest absolute effect sizes / variances in the epistasis model. Resulting higher computational needs were offset by the development of a highly efficient software package (Vojgani et al 2019a) to perform computations in a bit-wise manner (Schlather 2020).…”

“…Resulting higher computational needs were offset by the development of a highly efficient software package (Vojgani et al 2019a) to perform computations in a bit-wise manner (Schlather 2020). Thus, enabling to conduct such predictions with data sets of practically relevant size across environments in the same year, both with respect to sample size and number of markers (Vojgani et al 2019b).…”

“…The aim of this study is to assess the bivariate genomic prediction models which incorporate pairwise SNP interactions with the target of borrowing information across years to maximize the predictive ability. Since the accuracy of genomic prediction of phenotypes was shown to be increased by both borrowing information across environments and years (Covarrubias-Pazaran et al 2018; Schrag et al 2019b) and inclusion of epistasis into the prediction model (Martini et al 2016; Vojgani et al 2020), we combine these two approaches to make the best use of the available information. We further aim to assess the optimum proportion of SNP interactions to be kept in the model in the variable selection step across years.…”