This issue, however, can be reduced by accounting for population structure using the relationship matrix or distance matrix among the lines [ 28].
The fundamental reason for this failure is that mixed model predictions of merit using the relationship matrix and applied to young animals can, with sufficient historical data, reliably predict the parent average (PA) effects, but are unable to predict the Mendelian sampling effects without having phenotypic observations on the individual or its descendants [ 6].
Given the ontologies T1, T2,…, T k, we can first integrate T1 and T2 into T1,2 and then build the closeness matrix between T1,2 and T3 using the relationship matrices between T1 and T2 and between T1 and T3.
For estimating narrow sense heritability, the additive kinship matrix described in the rrBLUP package was used as the relationship matrix, and, for estimating broad sense heritability, the non-additive Gaussian kernel was used.
A genomic kingship matrix, generated by calculating the average identity-by-state between individuals in the pedigree (ibs in GenABEL), was used as the relationship matrix for FASTA and GRAMMAS.
Calculate an update for by using the relationship: (3)., is a matrix with elements formed from the allocated weightings such that if and for the diagonal elements.
(3) Calculate an update for by using the relationship: (3) where, is a matrix with elements formed from the allocated weightings such that if and for the diagonal elements.
Practical considerations of computing additive and dominance relationships using the genomic relationship matrix are discussed.
Adding genetic effects through the use of the relationship matrix would have the same influence as increasing the number of events per horse: increasing the number of comparisons between horses.
Genomic BLUP (G-BLUP) EBVs of both training and validation bulls were obtained by mixed-model equations using the genomic relationship matrix, whereas pedigree-based BLUP (P-BLUP) EBVs were obtained by using the numerator relationship matrix [ 24, 25].
Once the complete SNP matrix was established (supporting information, File S1), the missing data were imputed using the realized relationship matrix method multivariate normal expectation maximization (MVN-EM) described by Poland et al. (2012b) with the R environment (R Development Core Team 2008) package rrBLUP (Endelman 2011).
