Heterogeneity in convergence behaviour of the single-step SNP-BLUP model across different effects and animal groups

The single-step model is becoming increasingly popular for national genetic evaluations of dairy cattle due to the benefits that it offers such as joint breeding value estimation for genotyped and ungenotyped animals. However, the complexity of the model due to a large number of correlated effects can lead to significant computational challenges, especially in terms of accuracy and efficiency of the preconditioned conjugate gradient method used for the estimation. The aim of this study was to investigate the effect of pedigree depth on the model's overall convergence rate as well as on the convergence of different components of the model, in the context of the single-step single nucleotide polymorphism best linear unbiased prediction (SNP-BLUP) model.

The results demonstrate that the dataset with a truncated pedigree converged twice as fast as the full dataset. Still, both datasets showed very high Pearson correlations between predicted breeding values. In addition, by comparing the top 50 bulls between the two datasets we found a high correlation between their rankings. We also analysed the specific convergence patterns underlying different animal groups and model effects, which revealed heterogeneity in convergence behaviour. Effects of SNPs converged the fastest while those of genetic groups converged the slowest, which reflects the difference in information content available in the dataset for those effects. Pre-selection criteria for the SNP set based on minor allele frequency had no impact on either the rate or pattern of their convergence. Among different groups of individuals, genotyped animals with phenotype data converged the fastest, while non-genotyped animals without own records required the largest number of iterations.

We conclude that pedigree structure markedly impacts the convergence rate of the optimisation which is more efficient for the truncated than for the full dataset.