Journal
JOURNAL OF DAIRY SCIENCE
Volume 92, Issue 9, Pages 4656-4663Publisher
AMER DAIRY SCIENCE ASSOC-ADSA
DOI: 10.3168/jds.2009-2061
Keywords
genetic evaluation; genomic selection; relationship matrix; mixed model
Funding
- Maison de Relations Internationales (INRA)
- Holstein Association of America
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Dense molecular markers are being used in genetic evaluation for parts of the population. This requires a two-step procedure where pseudo-data (for instance, daughter yield deviations) are computed from full records and pedigree data and later used for genomic evaluation. This results in bias and loss of information. One way to incorporate the genomic information into a full genetic evaluation is by modifying the numerator relationship matrix. A naive proposal is to substitute the relationships of genotyped animals with the genomic relationship matrix. However, this results in incoherencies because the genomic relationship matrix includes information on relationships among ancestors and descendants. In other words, using the pedigree-derived covariance between genotyped and ungenotyped individuals, with the pretense that genomic information does not exist, leads to inconsistencies. It is proposed to condition the genetic value of ungenotyped animals on the genetic value of genotyped animals via the selection index (e. g., pedigree information), and then use the genomic relationship matrix for the latter. This results in a joint distribution of genotyped and ungenotyped genetic values, with a pedigree-genomic relationship matrix H. In this matrix, genomic information is transmitted to the covariances among all ungenotyped individuals. The matrix is (semi) positive definite by construction, which is not the case for the naive approach. Numerical examples and alternative expressions are discussed. Matrix H is suitable for iteration on data algorithms that multiply a vector times a matrix, such as preconditioned conjugated gradients.
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