Is single-step genomic REML with the algorithm for proven and young more computationally efficient when less generations of data are present?

The estimation of variance components is computationally expensive under large-scale genetic evaluations due to several inversions of the coefficient matrix. Variance components are used as parameters for estimating breeding values in mixed model equations (MME). However, resulting breeding values are not Best Linear Unbiased Predictions (BLUP) unless the variance components approach the true parameters. The increasing availability of genomic data requires the development of new methods for improving the efficiency of variance component estimations. Therefore, this study aimed to reduce the costs of single-step genomic REML (ssGREML) with the Algorithm for Proven and Young (APY) for estimating variance components with truncated pedigree and phenotypes using simulated data. In addition, we investigated the influence of truncation on variance components and genetic parameter estimates. Under APY, the size of the core group influences the similarity of breeding values and their reliability compared to the full genomic matrix. In this study, we found that to ensure reliable variance component estimation, it is required to consider a core size that corresponds to the number of largest eigenvalues explaining around 98% of the total variation in G to avoid biased parameters. In terms of costs, the use of APY slightly decreased the time for ordering and symbolic factorization with no impact on estimations.