Estimating Additive and Non-Additive Genetic Variances and Predicting Genetic Merits Using Genome-Wide Dense Single Nucleotide Polymorphism Markers

Abstract

Non-additive genetic variation is usually ignored when genome-wide markers are used to study the genetic architecture and genomic prediction of complex traits in human, wild life, model organisms or farm animals. However, non-additive genetic effects may have an important contribution to total genetic variation of complex traits. This study presented a genomic BLUP model including additive and non-additive genetic effects, in which additive and non-additive genetic relation matrices were constructed from information of genome-wide dense single nucleotide polymorphism (SNP) markers. In addition, this study for the first time proposed a method to construct dominance relationship matrix using SNP markers and demonstrated it in detail. The proposed model was implemented to investigate the amounts of additive genetic, dominance and epistatic variations, and assessed the accuracy and unbiasedness of genomic predictions for daily gain in pigs. In the analysis of daily gain, four linear models were used: 1) a simple additive genetic model (MA), 2) a model including both additive and additive by additive epistatic genetic effects (MAE), 3) a model including both additive and dominance genetic effects (MAD), and 4) a full model including all three genetic components (MAED). Estimates of narrow-sense heritability were 0.397, 0.373, 0.379 and 0.357 for models MA, MAE, MAD and MAED, respectively. Estimated dominance variance and additive by additive epistatic variance accounted for 5.6% and 9.5% of the total phenotypic variance, respectively. Based on model MAED, the estimate of broad-sense heritability was 0.506. Reliabilities of genomic predicted breeding values for the animals without performance records were 28.5%, 28.8%, 29.2% and 29.5% for models MA, MAE, MAD and MAED, respectively. In addition, models including non-additive genetic effects improved unbiasedness of genomic predictions.

Modeling Epistasis in Genomic Selection

“…This extended G-BLUP model was recently used by Su et al (2012) and Muñoz et al (2014). When the number of markers is large, we proved that EG-BLUP is equivalent to the model EG-BLUP* with explicit epistatic effects of markers (see the Appendix),…”

“…Dating back to Henderson (1985), EG-BLUP enables the estimation of epistatic components of the genotypic values without explicitly assessing individually epistatic effects. Applied to predicting daily gain in pigs and the total height of pine trees, EG-BLUP outperformed G-BLUP (Su et al 2012;Muñoz et al 2014). The equivalence between G-BLUP and genomic selection approaches, with explicit relevance for modeling marker main effects, has been demonstrated (Habier et al 2007).…”

Marker-based estimates reveal significant non-additive effects in clonally propagated cassava (Manihot esculenta): implications for the prediction of total genetic value and the selection of varieties

“…Aside from cassava, breeding of other noninbred, clonally propagated species also identifies and makes use of nonadditive effects, including in potato (Killick 1977), Eucalyptus (Costa et al 2004), and loblolly pine (Muñoz et al 2014). More recently, marker-based and GRM-based models have identified significant nonadditive effects in pigs (Su et al 2012;Nishio and Satoh 2014), mice (Vitezica et al 2013), beef cattle (Bolormaa et al 2015), dairy cows (Morota et al 2014), maize (Dudley and Johnson 2009), soy (Hu et al 2011), loblolly pine (Muñoz et al 2014), and apple (Kumar et al 2015). Results from the present study suggest that accounting for nonadditive effects in the variety development pipeline should increase the value of hybrids released by cassava breeding programs.…”

“…The G matrix was calculated using the A.mat function in the rrBLUP package (Endelman 2011). We constructed a matrix to capture dominance relationships using the formulation originally proposed by Su et al (2012). The dominance relationship matrix, which we will call D Ã (see below), is…”

“…Although our focus in the present study is not on the prediction of breeding value, the matrix D has been shown by Zhu et al (2015) to have the advantage of being uncorrelated (under Hardy-Weinberg equilibrium) with the matrix G. For this reason, we tested the D and D Ã matrices and provide comparison of their results. Except where explicitly comparing matrices, we use D to indicate the dominance matrix D Ã as in Su et al (2012).…”