Inversion of a part of the numerator relationship matrix using pedigree information

摘要

BackgroundIn recent theoretical developments, the information available (e.g. genotypes) divides the original population into two groups: animals with this information (selected animals) and animals without this information (excluded animals). These developments require inversion of the part of the pedigree-based numerator relationship matrix that describes the genetic covariance between selected animals (>A22). Our main objective was to propose and evaluate methodology that takes advantage of any potential sparsity in the inverse of >A22 in order to reduce the computing time required for its inversion. This potential sparsity is brought out by searching the pedigree for dependencies between the selected animals. Jointly, we expected distant ancestors to provide relationship ties that increase the density of matrix >A22 but that their effect on A22-1 might be minor. This hypothesis was also tested.