Pre-selection approaches or some models with Mendelian sampling terms

Mendelian Sampling model

Abstract

Two equivalent models based on orthogonal random effects were presented. The first model was based on the LDL transformation of the relationship matrix of animals with observations, the second model was based on the LDL transformation of the full relationship matrix of all animals in the pedigree.  The latter model yields directly the estimates of Mendelian Sampling terms, which can then be back transformed to breeding values. Models were tested using a small three country MACE protein data. Being analogous to the SNP-BLUP model, the transformed models were fitted using a regression design matrix approach with off-the-shelf breeding value estimation program MiX99.  Both the orthogonal models and the original MACE model gave the same estimates for breeding values. From the new approaches, the full pedigree transformation was computationally more efficient although it required many more iterations to converge than the normal MACE model.  The reason for better efficiency was postulated to the sparsity (low number of non-zeros) in the transformed design matrix.  An approach to account for the reduction in MS-term variance due to genomic preselection was suggested.