Strategies for computation and inversion of the additive relationship matrix among genotyped animals

Large-scale genetic evaluations became only possible with the direct construction of the inverse of the numerator relationship matrix (A). For genomic evaluations, even if computing the inverse of the genomic might not be needed depending on the implementation, computation of a subpart of the numerator relationship matrix (A). the sub-matrix (An). and its subsequent inversion is still required. for genomic evaluations, one can expect that it wilí include two sets of genotyped animals: animals already involved in a previous evaluation and newly genotyped animals. Therefore, strategies that reuse already performed computations could be valuable. Two strategies for computation and inversion of A22 In the first one, currently mostly used strategy, A22 is computed, inverted and used at each evaluation but not stored on disk. In the second one, alternative strategy, only relationships between relationship matrix Also, were compared. newly genotyped animals and all others genotyped animals are computed. Then, the stored inverted Ay of the previous evaluation is updated for newly genotyped animals for the new evaluation. Comparisons between strategies were performed using two criterions: required computing time and memory for both computation and inversion. Tests were conducted using the Walloon pedigree for routine genetic evaluations with different simulated scenarios: (1) number of already genotyped animals and (2) number of newly genotyped animals added in current evaluation. Depending on factors (1) and (2), it may be shown that first strategy was efficient for small number of genotyped animals whereas the second one prevails for greater numbers. As for large-scale genetic evaluations, large-scale genomic evaluation may be greatly facilitated with advanced algorithms allowing the successive construction of the inverse of the sub-matrix (A22) or even the genomic relationship matrix.