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E-Supplements
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Table S1 Number of purebred and crossbred animals with a phenotype per generation
517
(average for the 5 replicates; SD within brackets).
518
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Table S2 Number of purebred and crossbred animals with a phenotype and a genotype per
520
generation (average for the 5 replicates; SD within brackets).
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Table S3. Relative accuracies (average for the 5 replicates; SD within brackets) of GEBV
523
from alternative core groups for the purebred (PB) and crossbred (CB) performance for
524
genotyped selection candidates.
525
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Table S4. Pearson correlations (average for the 5 replicates; SD within brackets) between
527
GEBV for genotyped selection candidates from alternative core groups1 and GEBV from the
528
direct inversion of G.
529
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Table S5. Regression coefficients (average for the 5 replicates; SD within brackets) of TBV
531
on GEBV from alternative core groups and the direct inversion of G for genotyped selection
532
candidates.
533
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Table S6. Relative mean squares errors (average for the 5 replicates; SD within brackets) of
535
GEBV from alternative core groups for genotyped selection candidates.
536
537
Figures
538 539
540
Figure 2.
541
542
543
Figure 3.
544
545
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Figure 4.
547
548
549
Figure 5.
550
551
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Figure 6.
553
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Figure 1. Schematic representation of the simulation. The crossbreeding program started at
555
generation 200 (generation numbers in bold). The number of males (M) and females (F) per
556
generation and per breed (A, B, and C), or per cross (BC, and A(BC)), are reported within
557
brackets. Blue arrows denote the sires and dams of the next generation; red arrows denote the
558
dams of the next generation; green arrows denote the sires of the next generation.
559
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Figure 2. Projections of genomic relationships for purebred (A, B, and C) and crossbred (BC
561
and A(BC)) genotyped animals into the two first eigenvectors for the first replicate.
562
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Figure 3. Proportions of core animals per generation and breed composition of one replicate
564
for the scenario using 8,000 core animals. Core animals were selected using four different
565
strategies: 1) only from breed A animals (Breed A), 2) from purebred animals of breed A, B
566
and C (PB), 3) from purebred animals of breed A, B and C, and crossbred BC and A(BC)
567
animals (PB + CB), and (4) chosen based on a QR decomposition of the genotype matrix
568
(QR). Darker colours represent higher proportions of core animals per generation and breed
569
composition.
570
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Figure 4. Relative correlations of GEBV from different sizes of core groups with only breed
572
A animals. Relative correlations for the purebred performance (PP) and crossbred
573
performance (CP) traits are defined as the ratio between the accuracies of GEBV from
574
alternative core groups and the corresponding accuracies of GEBV from 𝐆𝑑𝑖𝑟𝑒𝑐𝑡−1 . Vertical
575
columns depict the number of eigenvalues that explained 98% and 99% of the variation in 𝐆∗.
576
Results are averages for the 5 replicates.
577
578
579
Figure 5. Relative correlations of GEBV from alternative core groups for the purebred
580
performance traits. Core groups include randomly selected purebred and crossbred animals
581
(Purebred + Crossbred core), randomly selected purebred animals (Purebred core), and
582
animals selected based on a QR decomposition of the genotype matrix (QR core). Relative
583
correlations are defined as the ratio between the accuracies of GEBV from alternative core
584
groups and the corresponding accuracies of GEBV from 𝐆𝑑𝑖𝑟𝑒𝑐𝑡−1 . Vertical columns depict the
585
number of eigenvalues that explained 98% and 99% of the variation in 𝐆∗. Results are
586
averages for the 5 replicates.
587
588
Figure 6. Relative correlations of GEBV from alternative core groups for the crossbred
589
performance trait. Core groups include randomly selected purebred and crossbred animals
590
(Purebred + Crossbred core), randomly selected purebred animals (Purebred core), and
591
animals selected based on a QR decomposition of the genotype matrix (QR core). Relative
592
correlations are defined as the ratio between the accuracies of GEBV from alternative core
593
groups and the corresponding accuracies of GEBV from 𝐆𝑑𝑖𝑟𝑒𝑐𝑡−1 . Vertical columns depict the
594
number of eigenvalues that explained 98% and 99% of the variation in 𝐆∗. Results are
595
averages for the 5 replicates.
596
597
Tables
598
Table 1. Heritabilities (diagonal) and genetic correlations (off-diagonal) among the five
599
simulated traits.
600
Trait Purebred A Purebred B Purebred C Crossbred BC Crossbred A(BC) Purebred A 0.28
Purebred B 0.46 0.39
Purebred C 0.27 0.80 0.22
Crossbred BC 0.33 0.58 0.30 0.36
Crossbred A(BC) 0.55 0.31 0.26 0.69 0.23
601
Table 2. Accuracies, bias, and mean square errors (MSE) of GEBV from the direct inversion
602
of 𝐆 (average for the 5 replicates; SD within brackets).
603
Selection candidates
Number Purebred performance Crossbred performance Accuracy Bias MSE Accuracy Bias MSE
Breed A 5010
(24)
0.81 (0.02)
1.04 (0.05)
1.11 (0.69)
0.68 (0.04)
0.98 (0.08)
0.68 (0.51)
Breed B 4975
(30)
0.85 (0.01)
1.06 (0.03)
1.16 (0.81)
0.63 (0.02)
0.95 (0.04)
0.90 (0.43)
Breed C 5016
(45)
0.79 (0.04)
1.04 (0.03)
1.42 (0.74)
0.71 (0.04)
1.04 (0.07)
1.35 (1.18) 604
Table 3. Regression coefficients (average for the 5 replicates; SD within brackets) of TBV on
605
GEBV from alternative core groups1 for genotyped selection candidates.
606
Number of core animals
Purebred performance Crossbred performance Breed
A
PB PB+CB QR Breed
A
PB PB+CB QR
Breed A selection candidates
4000 1.04 Breed B selection candidates
4000 1.49 Breed C selection candidates
4000 1.69
1 Core groups include 1) randomly selected breed A animals only (Breed A), 2) randomly selected purebred 607
animals (PB), 3) randomly selected purebred and crossbred animals (PB+CB), and 4) animals selected based on 608
a QR decomposition of the genotype matrix (QR).
609 610
Table 4. Relative mean squares errors1 (average for the 5 replicates; SD within brackets) of
611
GEBV from alternative core groups2 for genotyped selection candidates.
612
Number of core animals
Purebred performance Crossbred performance Breed
A
PB PB+CB QR Breed
A
PB PB+CB QR
Breed A selection candidates
4000 1.09 Breed B selection candidates
4000 1.75 Breed C selection candidates
4000 1.29
1 Results are expressed as the ratio between MSE of GEBV from alternative core groups and MSE of GEBV 613
from the direct inversion of 𝐆.
614
2 Core groups include 1) randomly selected breed A animals only (Breed A), 2) randomly selected purebred 615
animals (PB), 3) randomly selected purebred and crossbred animals (PB+CB), and 4) animals selected based on 616
a QR decomposition of the genotype matrix (QR).
617 618
619
Table 5. Quality of GEBV using APY for the core and non-core selection candidates. 1 620
Selection candidates
Number Purebred performance Crossbred performance Accuracy2 Reg.
coef.
1 Results (average for the 5 replicates; SD within brackets) are shown for the scenario using 8000 core animals 621
randomly selected among purebred and crossbred animals.
622
2 Results for accuracies and mean square errors (MSE) are expressed as the ratio between accuracies (MSE) of 623
GEBV using APY and accuracies (MSE) of GEBV using the direct inversion of 𝐆.
624 625