Effects of data structures on the solving of animal model equations by preconditioned conjugate gradient iteration

Abstract

To predict breeding values in dairy cattle, preconditioned conjugate gradient (PCG) algorithm has become of interest lately as a means of solving large sets of mixed model equations (MME) . Thereby, the effects of data structure on the solving of MME by PCG algorithms were investigated by using data in a computer simulation. A large number of animals did not cause slow convergence if the data structure (e.g. number of generations and mating ratio) was fixed. The numbers of breeding animals and their progeny affected the structure of the A-inverse matrix, but selection methods did not. An increasing number of iterations seemed to be due to an imbalance of nonzero elements in the A-inverse matrix, which resulted in the imbalance of nonzero elements in the MME. The number of iterations until convergence was roughly constant for two-trait animal model when the heritability of a trait was constant regardless of the heritability of another trait, and it was the smallest when the heritabilities of both traits were about 0.5 to 0.6. Increasing absolute values of genetic and environmental correlations resulted in slow convergence. In particular, genetic correlation affected convergence strongly.