Abstract
We established a genomic model of quantitative trait with genomic additive and dominance relationships that parallels the traditional quantitative genetics model, which partitions a genotypic value as breeding value plus dominance deviation and calculates additive and dominance relationships using pedigree information. Based on this genomic model, two sets of computationally complementary but mathematically identical mixed model methods were developed for genomic best linear unbiased prediction (GBLUP) and genomic restricted maximum likelihood estimation (GREML) of additive and dominance effects using SNP markers. These two sets are referred to as the CE and QM sets, where the CE set was designed for large numbers of markers and the QM set was designed for large numbers of individuals. GBLUP and associated accuracy formulations for individuals in training and validation data sets were derived for breeding values, dominance deviations and genotypic values. Simulation study showed that GREML and GBLUP generally were able to capture small additive and dominance effects that each accounted for 0.00005–0.0003 of the phenotypic variance and GREML was able to differentiate true additive and dominance heritability levels. GBLUP of the total genetic value as the summation of additive and dominance effects had higher prediction accuracy than either additive or dominance GBLUP, causal variants had the highest accuracy of GREML and GBLUP, and predicted accuracies were in agreement with observed accuracies. Genomic additive and dominance relationship matrices using SNP markers were consistent with theoretical expectations. The GREML and GBLUP methods can be an effective tool for assessing the type and magnitude of genetic effects affecting a phenotype and for predicting the total genetic value at the whole genome level.
Highlights
Genomic prediction using genome-wide single nucleotide polymorphism (SNP) markers has been shown to be a powerful tool to capture small genetic effects dispersed over the genome for predicting an individual’s genetic potential of a phenotype [1,2,3,4,5]
This method uses a standardization of the 0–1–2 additive coding and the subtraction step of this standardization leads to additive effects that are breeding values under the traditional quantitative genetics model assuming Hardy-Weinberg equilibrium [2,6,7]
The genetic model of SNP markers is an expansion of the additive model used in genomic evaluations [2,4,5] by adding a dominance component to the additive model
Summary
Genomic prediction using genome-wide single nucleotide polymorphism (SNP) markers has been shown to be a powerful tool to capture small genetic effects dispersed over the genome for predicting an individual’s genetic potential of a phenotype [1,2,3,4,5]. Two SNP models for genomic prediction of additive effects were described: a traditional quantitative genetics model and a model with (21)-0–1 SNP coding [2]. The traditional quantitative genetics model is attractive because it is equivalent to a conventional animal model with the relationship matrix calculated from the SNP genotypes [5] and it directly predicts genomic breeding values [2,4,5]. Method and computing tool are available for estimating genomic heritability using genome-wide SNP markers [6]. This method uses a standardization of the 0–1–2 additive coding and the subtraction step of this standardization leads to additive effects that are breeding values under the traditional quantitative genetics model assuming Hardy-Weinberg equilibrium [2,6,7]. The mixed model implementation of this method is ideal for a large number of markers but is not ideal for a large number of individuals because the size of the matrix that needs to be inverted increases as the number of individuals increases
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