Software

UD approach and its application in variance component estimation

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Abstract

Variance component estimation (VCE) with REML often needs repeated computation of the inverse of the mixed model equations coefficient matrix, which becomes computationally intensive for genomic models. The objective of this study is to show that with large models, inverses can be avoided by using Monte Carlo sampling (MC), and models with genomic relationship matrices (G) can be efficiently handled when combined with singular value decomposition. Since the rank (r) of the G matrix is less than the number of genotyped individuals (N), inverses require a rank constraint matrix to be added to G before inversion. The presented method, the UD approach, the genomic relationship matrix is decomposed into singular vectors (U) and singular values (D) before the addition of the rank constraint matrix. Using the Woodbury matrix equality, the orthogonality and diagonality of the components of the decomposition allow us to store only the r singular columns and a diagonal vector of the squared singular values, which substantially reduces the computational requirements while maintaining accuracy. We validated our approach using a soybean dataset with approximately 108,000 individuals, retaining approximately 19,800 singular vectors which represented 99.9% of the sum of the eigenvalues of the G matrix. Genic correlation estimates between three production traits showed minimal differences between the UD approach and REML with a full G matrix, with the correlation of breeding values between methods exceeding 0.999 for all trait combinations. In VCE, each round of REML requires an estimation of breeding values. When N is two times r, the REML exploiting UD approach and the REML with G-1 require roughly the same computing time, but when the N grows relative to r, the number of computations in the UD approach grows linearly with N, while normal REML computations increase quadratically. For a 6-trait model analysis, the UD approach reduced computing time from nearly 10 days to under 1.5 days and decreased average disk usage from 121.1 GB to 36.4 GB. The UD approach can save time and cost for large-scale VCE in animal and plant breeding with negligible differences in genic correlations compared to using a full G matrix.

Keywords: 2026

How to Cite:

Hollifield, M., Strandén, I., Heuer, C., Cheng, M., Branston, K., Tseng, M. & Mäntysaari, E., (2026) “UD approach and its application in variance component estimation”, World Congress on Genetics Applied to Livestock Production Digital Archive 2026(1): 2286676. doi: https://doi.org/10.31274/wcgalp.24093

Rights: 1