Solving efficiently large single-step genomic best linear unbiased prediction models

Area of Science:

• Animal Genetics
• Quantitative Genetics
• Bioinformatics

Background:

• Single-step genomic BLUP (ssGBLUP) relies on large matrices for mixed model equations (MME), increasing computational demands with more genotyped animals.
• The computational bottleneck in ssGBLUP is the dense matrix, a difference between genomic (G) and pedigree (A22) relationship matrices.

Purpose of the Study:

• To develop and evaluate computationally efficient methods for inverting relationship matrices in ssGBLUP.
• To reduce the solving time of MME in genomic evaluations for a large number of genotyped animals.

Main Methods:

• Implemented alternative approaches to avoid direct inversion of the A22 matrix, including iteration on pedigree (IOP), matrix iteration in memory (IM), and Cholesky decomposition (CM).
• Utilized the APY (Algorithm for Proven and Young) approach with Cholesky decomposition for inverting the genomic relationship matrix (G).
• Tested methods on a joint genetic evaluation of Nordic Holstein cattle for fertility traits, involving 81,031 genotyped animals.

Main Results:

• The Cholesky decomposition (CM) method for A22 inversion resulted in the fastest computation time per iteration (1.21 min) compared to ssGBLUP (1.19 min), IOP (1.49 min), and IM (1.32 min).
• Using the APY approach with a core of 10,000 animals reduced total computing time by 75% while yielding genomic estimated breeding values (GEBVs) comparable to the standard ssGBLUP.
• The developed methods significantly decreased total computing time by avoiding the inversion of the A22 relationship matrix.

Conclusions:

• The developed methods for inverting relationship matrices in ssGBLUP offer substantial computational savings.
• These advancements are expected to facilitate genomic evaluations for significantly larger populations of genotyped animals.
• Efficient inversion techniques are crucial for the scalability and practical application of ssGBLUP in livestock breeding programs.