Academic journal article Genetics

Orthogonal Estimates of Variances for Additive, Dominance, and Epistatic Effects in Populations

Academic journal article Genetics

Orthogonal Estimates of Variances for Additive, Dominance, and Epistatic Effects in Populations

Article excerpt

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DOMINANCE and epistasis may play an important role in the genetic determinism of complex traits of interest, such as human health or economic traits in livestock and crops. The existence of interactions within and across loci is supported by classic quantitative genetic studies, QTL mapping, and the wide application of crossbreeding as a breeding strategy. Nowadays, genomics provides tools to understand the effects of the genes and their interactions and to offer new directions for genetic improvement (Mäki-Tanila and Hill 2014). In quantitative genetics, the partition of the variance in statistical components due to additivity, dominance, and epistasis does not reflect the biological (or functional) effect of the genes but it is most useful for prediction, selection, and evolution (Huang and Mackay 2016).

In livestock populations, one of the main reasons why dominance or higher-order interaction terms have not been considered in genetic evaluations is that pedigree relationships are not informative enough. However, genomic selection methods are beginning to demonstrate their potential to include nonadditive effects in evaluation models. Inclusion of dominant or/and epistatic effects in genomic evaluation has been proposed by several authors (Toro and Varona 2010; Su et al. 2012; Vitezica et al. 2013; Nishio and Satoh 2014; Jiang and Reif 2015). Most epistatic models only consider additive-by-additive epistatic interactions (e.g., Su et al 2012; Jiang and Reif 2015), although dominant-by-dominant and dominant-by-additive interactions may play a major role in heterosis and also in inbreeding and outbreeding depression (Lynch and Walsh 1998, p.223). Moreover, to date these models assume Hardy-Weinberg equilibrium (HWE) (e.g., Vitezica et al. 2013). New statistical approaches to genomic selection that account for dominance and epistasis in a general context (i.e., in populations not in HWE, like crosses or inbred populations) are needed both in animal and plant breeding and for QTL association studies.

Genomic evaluation models can fit marker or haplotypic additive genetic effects either explicitly, estimating the effect of each marker (Meuwissen et al. 2001), or implicitly through the so-called "genomic" relationship matrix (VanRaden 2008; Goddard 2009; Yang et al. 2010), which uses an equivalent model from which the marker effects can be inferred by backsolving. Dominance and higher-order interaction terms can also be modeled using the "genomic" relationship approach. Several approaches exist (Su et al. 2012; Muñoz et al. 2014; Jiang and Reif 2015) but none has addressed the issue of orthogonality of the model, additive and dominant components, and all possible interactions.

For plant and animal breeders and evolutionary geneticists, a meaningful partition of the variance is such that estimates can be interpreted in the classical terms, as variances of breeding values, dominant deviations, epistatic deviations, and so on (Hill et al. 2008). A nonorthogonal partition may lead to the erroneous conclusion that assortative mating and inclusion of dominance and/or epistasis can yield higher genetic gains as opposed to the consideration of additivity and random mating. For instance, Muñoz et al. (2014) concluded that dominance accounted for 39% of the total genetic variance when they used a nonorthogonal partition, vs. 24% when they used the orthogonal partition in Vitezica et al. (2013).

In this study, we develop a general procedure to estimate genomic relationship matrices for interaction terms of any order, expanding the natural and orthogonal interactions (NOIA) approach (Álvarez-Castro and Carlborg 2007) to the scope of the covariances between individuals. We present how to compute epistatic relationships from genotypes. Our results generalize the results of Cockerham (1954) to genomic models (something that had not been proven so far) and to any population, either in HWE or not. …

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