Abstract
The traditional quantitative genetics model was used as the unifying approach to derive six existing and new definitions of genomic additive and dominance relationships. The theoretical differences of these definitions were in the assumptions of equal SNP effects (equivalent to across-SNP standardization), equal SNP variances (equivalent to within-SNP standardization), and expected or sample SNP additive and dominance variances. The six definitions of genomic additive and dominance relationships on average were consistent with the pedigree relationships, but had individual genomic specificity and large variations not observed from pedigree relationships. These large variations may allow finding least related genomes even within the same family for minimizing genomic relatedness among breeding individuals. The six definitions of genomic relationships generally had similar numerical results in genomic best linear unbiased predictions of additive effects (GBLUP) and similar genomic REML (GREML) estimates of additive heritability. Predicted SNP dominance effects and GREML estimates of dominance heritability were similar within definitions assuming equal SNP effects or within definitions assuming equal SNP variance, but had differences between these two groups of definitions. We proposed a new measure of genomic inbreeding coefficient based on parental genomic co-ancestry coefficient and genomic additive correlation as a genomic approach for predicting offspring inbreeding level. This genomic inbreeding coefficient had the highest correlation with pedigree inbreeding coefficient among the four methods evaluated for calculating genomic inbreeding coefficient in a Holstein sample and a swine sample.
Highlights
Genomic relationship among individuals is a measure of genomic relatedness or similarity among individuals and allows genomic prediction and variance component estimation to use theoretical results and computational strategies of best linear unbiased prediction (BLUP)
In contrast to pedigree relationships, genomic relationships are realized relationships calculated from genome-wide single nucleotide polymorphism (SNP) markers resulting from generations of drift, recombination, mutation and selection that are not considered by pedigree relationships, and estimates of genomic relationships for different individuals generally had their own genomic specificity unobservable from the pedigree estimates on average genomic and pedigree relationships were consistent [6]
We show that quantitative genetics theory can be the unifying theory for deriving existing and new genomic additive and dominance relationships and for studying the theoretical differences among various definitions of genomic relationships
Summary
Genomic relationship among individuals is a measure of genomic relatedness or similarity among individuals and allows genomic prediction and variance component estimation to use theoretical results and computational strategies of best linear unbiased prediction (BLUP). VanRaden derived the first genomic additive relationship formula based on the standardization of the 2-1-0 (or 0-1-2) coding of SNP genotypes [2] This formula divides the WaWa0 matrix by the total expected heterozygosity of all SNP markers, where Wa is the model matrix for SNP additive effects with each SNP coding being the deviation of the 2-1-0 coding from its mean. This approach leads to the prediction of genomic breeding values [2, 3]. In contrast to pedigree relationships, genomic relationships are realized relationships calculated from genome-wide SNP markers resulting from generations of drift, recombination, mutation and selection that are not considered by pedigree relationships, and estimates of genomic relationships for different individuals generally had their own genomic specificity unobservable from the pedigree estimates on average genomic and pedigree relationships were consistent [6]
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