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Single-step genomic BLUP for
national beef cattle evaluation in US: from initial developments to final implementation
Daniela LourencoS. Tsuruta, B.O. Fragomeni, Y. Masuda, I. Aguilar
A. Legarra, S. Miller, D. Moser, I. Misztal
11th WCGALP 2018
Angus
• Main beef cattle breed in USA• Genomic Selection since 2009
2
Multistep Genomic Evaluation
Kachman, 2008
2,25311,756
38,988
57,550
108,211
2010 2012 2013 2014 2016
Records for Calibration
3
Problems with Multistep
• Rank change for bulls with high accuracy
• Big fluctuations in GEBV for new calibration
-0.4
-0.2
0
0.2
0.4
0.6
0.8
19
72
19
74
19
76
19
78
19
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82
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84
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86
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88
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00
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Marbling
Multistep Traditional
• High genetic correlation between phenotype and MBV
4
• Overfitted models – 2x the number of traits
Single-step genomic BLUP (ssGBLUP)
H−1=A−1+0 0
0 G−𝟏– A22
−1
Aguilar et al., 2010
Phenotypes
ssGBLUP
GEBV
Pedigree SNP
UGA group (2008 – now) 5
Initial tests of ssGBLUP for Angus
82,000
112,000132,000
152,000
184,354
219,849
303,246
335,325
406,033
442,635
Number of Genotyped Animals
07 2014 01 2015 07 2015 10 2015 01 2016 07 2016 02 2017 05 2017 11 2017 01 2018
6
Ability to predict future performance
2017
• 10M animals in pedigree
• 8M BW and WW
• 4.2M PWG
• 335k genotyped animals
• 18.7k born in 2016
2014
• 8M animals in pedigree
• 6M BW and WW
• 3.4M PWG
• 52k genotyped animals
• 18.7k born in 2013
Predictive ability direct = COR(Y_adj, GEBV)
Predictive ability maternal = COR(Y_adj, total_maternal_GEBV)7
Ability to predict future performance
0.29
0.34
0.23
0.39 0.38
0.29
0.47
0.40
0.35
BW WW PWG
Predictive Ability
BLUP ssGBLUP14 ssGBLUP17
Average Gain
Direct
2014 = 25%
2017 = 36%
Maternal
2014 = 8%
2017 = 10%
8
USMARC comparisons of ssGBLUP x multistep
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
BW WW YWT
USMARC Predictive Ability
MS SS
Kuehn et al., 2017
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
BW WW YWT MILK CWT MARB REA FAT
Correlation with MARC EBV for 143 bulls
MS SS
9
Genetic trends for carcass traits
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
19
72
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
20
00
20
02
20
04
20
06
20
08
20
10
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12
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14
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16
Marbling
ssGBLUP Multistep Traditional
-20
-10
0
10
20
30
40
50
19
72
19
74
19
76
19
78
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80
19
82
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84
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86
19
88
19
90
19
92
19
94
19
96
19
98
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00
20
02
20
04
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06
20
08
20
10
20
12
20
14
20
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Carcass Weight
ssGBLUP Multistep Traditional 10
Increasing number of genotyped animals
𝐆APY−1 = Gcc
−1 00 0
+ −Gcc−1GcnI
Mnn−1
−GncGcc−1 I Mnn = gii − gicGcc
−1gci
• APY ssGBLUP
• Borrowed from algorithm to construct A-1
• Core and Non-core
Misztal et al., 2014
• Number of genotyped animals increased 5-fold from 2014 to 2018
• 150,000
• > 2 hours
• > 700Gb RAM
11
APY ssGBLUP in 2014
core
non-core
G-1APY G-1
How to choose core animals?
12
APY ssGBLUP in 2014
0.94
0.97
0.99 0.99 0.99
2k 4k 8k 10k 33k
Co
rrel
atio
n (
GEB
V,G
EBV
_ap
y)
PWG – Core based on accuracy
Lourenco et al., 2015aLourenco et al., 2015b
0.97
0.99 0.99 0.99
5k 10k 15k 20k
Co
rrel
atio
n (
GEB
V,G
EBV
_ap
y)
PWG – Random Core
28 min
Regular inversion = 213 min
16 Gb
230 Gb 13
How to choose the number of core in APY?
• Ne, Me, ESM, Eigen of G
• Limited dimensionality
Pocrnic et al., 2016Misztal, 2016
90 95 98 99
3654
6166
10605
14555
Nu
mb
er o
f Ei
gen
valu
es
% of Variance
AAA – 82k
3654, 0.96
6166, 0.98
10605, 0.9914555, 0.99
0.90
0.92
0.94
0.96
0.98
1.00
0 2000 4000 6000 8000 10000 12000 14000 16000
CO
R (
GEB
V,G
EBV
_AP
Y)
NUMBER OF EIGENVALUES
AAA - 82k
14
Additional features in ssGBLUP
• Commercial products
• e.g. GeneMax for non-registered animals
• Based on SNP effects
• Accurate SNP effects with APY?
15
SNP effects in APY ssGBLUP
𝒂𝐆 = λ𝐃 𝐙′G−1 u
𝒂𝐆𝒄𝒄−𝟏 = λ𝐃 𝐙′G𝐶𝐶−1 𝒖APY
𝒂𝐆𝑨𝑷𝒀−𝟏 = λ𝐃 𝐙′𝐆APY
−1 𝒖APY
a
G−1
𝐆APY−1
𝐆𝑐𝑐−1
𝐙 a
G−1
𝐆APY−1
𝐆𝑐𝑐−1
16
Additional features in ssGBLUP
• Interim evaluations
• Indirect predictions
• Quick evaluations between official runs
• Should be comparable to GEBV
17
Indirect predictions for young animals
W′W + α A−1+ α0 0
0 G−1− A22
−1 u= W′y
GEBV = w1PA + w2YD + w3PC + w4DGV – w5PP
yield
deviationprogeny
contribution
pedigree
prediction
direct
genomic
value
parent
average
GEBVy = w1PA + w4DGV – w5PP
GEBVy ≈ DGV
Lourenco et al., 2015
18
Problem with Indirect predictions
COR(GEBV,DGV) > 0.99
Avg(GEBV) ≈ 100 Avg(DGV) ≈ 0
19
• Base of SSGBLUP: modelled as a mean in genotyped animals
• 𝑝 𝒖𝑔 = 𝑁 𝟏𝜇, 𝐆 Vitezica et al. (2011)
• 𝜇 = (Pedigree base) – (Genomic base)
Lourenco et al., 2015
-20
0
20
40
60
80
100
120
Za Legarra_2017 Double_Fit Average_GEBV
GEBV − uip
Correcting for bias of indirect predictions
E 𝒖 𝒂 = 𝜇 + 𝐙 𝒂
≈
𝐃𝐆𝐕 = GEBV + 𝐙 𝒂
Lourenco et al., 2018 20
Issues in the implementation of ssGBLUP for Angus
1) Omega = 0.7 indicates inflation in GEBV
InbreedingInbreedingNO InbreedingInbreeding
Solution: adding inbreeding for A-1 removed inflation in GEBVOmega = 1.0
21
Issues in the implementation of ssGBLUP for Angus
2) Inclusion of external EBV into growth evaluation
• 10k Red Angus EBV
• External EBV + genomics was not supported
• E = external• I = internal• T = PEV for E
Adapted from Legarra et al., 2007
22
Issues in the implementation of ssGBLUP for Angus
3) Calving ease evaluation was not quite easy
• BW + CE in linear-threshold model
• BLUP = 12 hours
• 152k genotyped animals
• APY ssGBLUP = 4.5 days
ScenarioDescription of parameters
rounds hourscorrelation with
genomic pcg rounds alpha betatraditional 40 - 60 12 -genomic 40 0.9 0.1 488 108 -
1 100 0.9 0.1 81 43 0.9992 100 0.85 0.15 62 32 0.9993 200 0.9 0.1 24 25 0.9994 200 0.85 0.15 19 19 0.99923
Issues in the implementation of ssGBLUP for Angus
4) Accuracy of GEBV
Diag(CZZ+) = PEV
• Large datasets
• Impossible to invert
𝐿𝐻𝑆𝑢𝑢𝑖𝑖 =
1(λ + 𝑑𝑖
𝑟 + 𝑑𝑖𝑝)
• 𝑑𝑖𝑟and 𝑑𝑖
𝑝are approximated
(Misztal and Wiggans, 1988)
• Accuracy = 1 - 𝐿𝐻𝑆-1
24
Issues in the implementation of ssGBLUP for Angus
4) Accuracy of GEBV
Z′Z+ λA−1+ λ0 0
0 G−1−A22−1
𝑑𝑖𝑟 𝑑𝑖
𝑝
𝑑𝑖𝑔
𝐿𝐻𝑆𝑢𝑢𝑖𝑖 =
1(λ + 𝑑𝑖
𝑟 + 𝑑𝑖𝑝+ 𝑑𝑖
𝑔)
= var_ratio *[𝑅𝑒𝑙 + (1 − 𝑔𝑖𝑖) + 𝑧𝑒𝑡𝑎 ∗ 𝑅𝑒𝑙 − 𝑅𝑒𝑙𝑃𝐴]
25
Issues in the implementation of ssGBLUP for Angus
4) Accuracy of GEBV
26
Cor = 0.87Avg_True = 0.55Avg_approx. = 0.50MSE = 0.0035
Implementation of ssGBLUP on 7/7/2017
• Current Angus evaluation with ~ 450k• 19k core• Weekly evaluations• ~ 18 traits (maternal, categorical, external information)
𝒂𝐆𝒄𝒄−𝟏 = λ𝐃 𝐙′G𝐶𝐶−1 𝒖APY• Indirect predictions based on SNP effects
• Minimal changes for proven animals
• Considerable changes for young animals
• More variation among half- and full-sibs 27
Final Remarks• ssGBLUP tests were extensive and took couple of years
• More stable than multistep
• Implementation of ssGBLUP by Angus raised several issues
• All solved
• Successful weekly evaluations for 7 months
• Evaluation with ~450k genotyped animals is possible with APY
• Implementation of ssGBLUP for Angus in 2017 set new standards for beef
cattle evaluation in USA
28
Acknowledgements
29