Y. Masuda1*, A. Legarra2, H.L. Bradford3, P.M. VanRaden4, and I. Misztal1
1Department of Animal and Dairy Science, University of Georgia, Athens, GA 30602, USA
2UMR GenPhySE, INRA Toulouse, BP52626, 31326, Castanet Tolosan, France
3Department of Animal and Poultry Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
4United States Department of Agriculture, Agricultural Research Service, Animal Genomics and Improvement Laboratory, Beltsville, Maryland, 20705-2350, USA
*Corresponding author
Background: Single-step genomic best linear unbiased prediction (ssGBLUP) is a method for genomic prediction that integrates matrices for pedigree relationships (A) and genomic relationships (G) as the inverse of a unified matrix (H-1) into a linear mixed model. In practice, pedigree information is often incomplete and unknown-parent groups (UPGs) are assigned to missing parents to account for genetic progress from the base population. Because integration of UPGs into ssGBLUP have usually been described ad hoc, this study derives several H-1 with UPGs under different assumptions.
Results: The inverse of A was computed using a rapid method with missing parents assumed to be either non-inbred or inbred. The G should be aligned (“tuned”) to the additive relationship matrix for genotyped individuals (A22) to share the same base populations based on mean genetic level and genetic variance. Each H-1 was derived from the joint density assuming different prior density of breeding values for genotyped and non-genotyped individuals. When all H was known a priori, H-1 with UPGs was the same as available from QP-transformation of H-1 (i.e. a combination of H-1 without UPGs and a marginal matrix with a function of G-1 and A22-1. This result implied that G and A must share the same information, including the relationships for missing parents. When A was known a priori and an aligned G was integrated to the joint density, G-1 was excluded from the marginal matrix. This result suggested that genomic bases for genotyped individuals can be aligned to non-genotyped individuals, whereas the genetic bases for individuals with missing pedigree must be separately adjusted with UPGs.
Conclusions: A QP-transformation of the whole H-1 may work in genomic prediction if only a portion of G is aligned with A22. When G is aligned, the marginal matrix for UPGs should contain only A22-1, because the genomic base is already adjusted using alignment. This choice is reasonable for H-1 with UPGs in ssGBLUP, because the group effects are applied only to pedigree relationships.