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Table 1 Processing time in real time seconds (hours) for various tasks and the additional memory requirement in gigabyte specific to the model when iteratively solving a SS-T-BLUP, SS-H-BLUP and SS-\(\widetilde{\text {H}}\)-BLUP model using a multi-trait Australian Angus BREEDPLAN dataset with 35 traits, 2.6 million animals and 77 million equations

From: More animals than markers: a study into the application of the single step T-BLUP model in large-scale multi-trait Australian Angus beef cattle genetic evaluation

Task

SS-H-BLUP\(_{150}^{1}\)

SS-\(\widetilde{\text {H}}\)-BLUP\(_{150}\)

SS-T-BLUP\(_{150}\)

SS-T-BLUP\(_{400}^{2}\)

\(\mathbf{G }\)

1756

1756

\(\mathbf{A }_{2,2}\)

250

250

\(\mathbf{G }\) \(^{-1}\)

9150

9150

\(\mathbf{A }_{2,2}\) \(^{-1}\)

3500

\(\mathbf{M }^{\dagger }\) and K

3422

4210

\(\mathbf{K }_{\mathbf{u }}\)

352

320

\(\mathbf{M }^{*}\)

629

1170

\(\mathbf{A }_{2,2}^{-1}\) \(\hbox {diag}^{3}\)

262

262

219

Preprocessing total

14,656 (4)

11,418 (3.2)

4,665 (1.3)

5,919 (1.6)

Iteration time per round

7.5

11.2

8.6

12

Total iteration time

19,123 (5.3)

28,716 (7.9)

22,134 (6.1)

30,809 (8.5)

Total evaluation time

33,779 (9.4)

40,134 (11.1)

26,799 (7.4)

36,728 (10.2)

\(\approx\) \(\text {RAM}^{4}\)

180

180

104

216

  1. (1) 150,000 individuals with genotypes. (2) 400,000 individuals with genotypes. (3) Sampling of diagonal elements of \(\mathbf{A }_{2,2}^{-1}\) using 10,000 samples. (4) Approximated model specific memory requirement in addition to the memory requirement common to all models. SS-H-BLUP: \(\mathbf{G }_{\mathbf{w }}\) and \(\mathbf{A }_{2,2}\) were build explicitly and inverted. SS-\(\widetilde{\text {H}}\)-BLUP: \(\mathbf{G }_{\mathbf{w }}\) and \(\mathbf{A }_{2,2}\) were build explicitly. \(\mathbf{G }_{\mathbf{w }}\) was inverted explicitly, \(\mathbf{A }^{2,2}-\mathbf{A }^{2,1}(\mathbf{A }^{1,1})^{-1}\mathbf{A }^{1,2}\) was used whilst solving. SS-T-BLUP: an implicit representation of \(\mathbf{G }_{\mathbf{w }}^{-1}\) and \(\mathbf{A }^{2,2}-\mathbf{A }^{2,1}(\mathbf{A }^{1,1})^{-1}\mathbf{A }^{1,2}\) were used whilst solving