Modeling Epistasis in Genomic Selection

Abstract

Modeling epistasis in genomic selection is impeded by a high computational load. The extended genomic best linear unbiased prediction (EG-BLUP) with an epistatic relationship matrix and the reproducing kernel Hilbert space regression (RKHS) are two attractive approaches that reduce the computational load. In this study, we proved the equivalence of EG-BLUP and genomic selection approaches, explicitly modeling epistatic effects. Moreover, we have shown why the RKHS model based on a Gaussian kernel captures epistatic effects among markers. Using experimental data sets in wheat and maize, we compared different genomic selection approaches and concluded that prediction accuracy can be improved by modeling epistasis for selfing species but may not for outcrossing species.KEYWORDS epistasis; genomic selection; genomic best linear unbiased prediction (G-BLUP); extended G-BLUP (EG-BLUP); reproducing kernel Hilbert space regression (RKHS); GenPred; shared data resource E PISTASIS has long been recognized as an important component in dissecting genetic pathways and understanding the evolution of complex genetic systems (Phillips 2008). It is hence a biologically influential component contributing to the genetic architecture of quantitative traits (Mackay 2014). The influence of epistasis on genome-wide QTL mapping ranges from limited (e.g., Buckler et al. 2009;Tian et al. 2011) to high (e.g., Carlborg et al. 2006;Würschum et al. 2011;Huang et al. 2014). These discrepancies can be explained by the complexities of the examined traits, which are controlled by many loci exhibiting small effects entailing a low QTL detection power. In addition, the estimation of QTL main and interaction effects is very likely biased (Beavis 1994), which makes it challenging to reliably elucidate the role of epistasis through genome-wide QTL mapping studies.Genomic selection has been suggested as an alternative to tackle complex traits that are regulated by many genes, each exhibiting a small effect (Meuwissen et al. 2001). Genomic selection approaches based on additive and dominance effects have been successfully applied to predict complex traits in human (Yang et al. 2010), animal (Hayes et al. 2009, and plant populations (Jannink et al. 2010;Zhao et al. 2015). Moreover, several genomic selection approaches have been developed to model both main and epistatic effects (Xu 2007;Cai et al. 2011;Wittenburg et al. 2011;Wang et al. 2012). While in some studies prediction accuracies increased (Hu et al. 2011), in others modeling epistasis adversely affected prediction accuracies (Lorenzana and Bernardo 2009).Despite these first attempts, epistasis is often ignored in genomic selection approaches using parametric models mainly because of the high associated computational load, especially if a large number of markers are available. An attractive solution to reduce the computational load is to extend genomic best linear unbiased prediction (G-BLUP) models (VanRaden 2008) by adding marker-based epistatic relationship matrices [extended genomic...

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