02476naa a2200241 a 450000100080000000500110000800800410001902200140006002400310007410000160010524500980012126000090021950000770022852017180030565000260202365300230204965300220207265300160209465300240211070000160213470000160215077300680216610128372019-10-09       2009    bl uuuu     u00u1 u    #d  a0022-03027 a10.3168/jds.2009-20612DOI1 aLEGARRA, A.  aA relationship matrix including full pedigree and genomic information.h[electronic resource]  c2009  aArticle history:  Received January 26, 2009. // Accepted April 28, 2009.  aABSTRACT. 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-de- rived 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.  © American Dairy Science Association, 2009.  aEVALUACIÓN GENÉTICA  aGENETIC EVALUATION  aGENOMIC SELECTION  aMIXED MODEL  aRELATIONSHIP MATRIX1 aAGUILAR, I.1 aMISZTAL, I.  tJournal of Dairy Science, 2009, 92 (9): 4656-4663. OPEN ACCESS.