tuning indirect predictions based on snp effects from...
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Indirect predictions based on SNP effects from ssGBLUP
in large genotyped populations
Daniela Lourenco
A. Legarra, S. Tsuruta, Y. Masuda, T. Lawlor, I. Misztal
ADSA 2018
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Why Indirect predictions (IP)?
• Interim evaluations• Between official runs
• Not all genotyped animals are in the evaluations• Animals with incomplete pedigree increase bias and lower R2
• Commercial products• e.g. GeneMax for non-registered animals
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Indirect predictions in ssGBLUP
X′X X′W
W′X W′W+𝐇−𝟏λ
𝑏 𝑢=
X′y
W′y
H−1=A−1+0 0
0 G−𝟏– A22
−1
𝒂 = λ𝐃 𝐙′G−1 𝒖
GAPY−1
GEBVsSNP effects
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GEBVyoung = w1PA + w2GP – w3PP
GEBVyoung ≈ GP
Lourenco et al., 2015
COR( GEBV𝑦𝑜𝑢𝑛𝑔, 𝐙 a) > 0.99
GEBVyoung ≈ GP = 𝐙 a
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Problems with Indirect predictions
COR( GEBV𝑦𝑜𝑢𝑛𝑔, 𝐙 a) > 0.99
Avg( GEBV) ≈ 100 Avg(𝐙 a) ≈ 0
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Objectives
1) Fine-tune indirect predictions to be compatible with GEBV
2) Investigate whether SNP effects are accurate when APY is used
• Possibly use subset of core animals
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Dataset
• US Holstein 2014 type data
• 8.3M animals in pedigree
• No UPG
• 9.2M Udder Depth (UD)
• h2 = 0.33
• 9.2M Foot Angle (FA)
• h2 = 0.11
• 105k genotyped
• Training: 100k
• Validation: 5k
• Complete
• Phenotypes up to 2010
• Genotypes up to 2010 (105k)
• Reduced
• Phenotypes up to 2010
• NO Genotypes for validation (100k)
• SNP effects and IP from Reduced
• Compare with GEBV from Complete
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Accuracy of SNP effects
𝒂𝐆 = λ𝐃 𝐙′G−1 u
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G-1
𝒂𝐆𝑨𝑷𝒀−𝟏 𝐑 = λ𝐃 𝐙
′𝐆APY_𝑟𝑎𝑛𝑑𝑜𝑚−1 𝒖APY
𝒂𝐆𝑨𝑷𝒀−𝟏 𝐇 = λ𝐃 𝐙
′𝐆APY_ℎ𝑖𝑔ℎ_𝑟𝑒𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦−1 𝒖APY
APY G-1
15k core85k noncore
100k
𝒂𝐆𝒄𝒄−𝟏𝐑 = λ𝐃 𝐙′Gcc_𝑟𝑎𝑛𝑑𝑜𝑚−1 𝒖APY
𝒂𝐆𝒄𝒄−𝟏𝐇 = λ𝐃 𝐙′G𝐶𝐶_ℎ𝑖𝑔ℎ_𝑟𝑒𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑦−1 𝒖APY
G-1 core
15k
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Statistics for SNP effects - 𝐆APY−1
8Udder Depth Foot Angle
G−1
𝐆APY_𝐻𝑖𝑔ℎ−1
𝐆APY_𝑅𝑎𝑛𝑑−1
G−1
𝐆APY_𝐻𝑖𝑔ℎ−1
𝐆APY_𝑅𝑎𝑛𝑑−1
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Statistics for SNP effects - 𝐆CC−1
Udder Depth
c
Foot Angle
c
G−1
G𝐶𝐶_𝐻𝑖𝑔ℎ−1
G𝐶𝐶_𝑅𝑎𝑛𝑑−1
G−1
G𝐶𝐶_𝐻𝑖𝑔ℎ−1
G𝐶𝐶_𝑅𝑎𝑛𝑑−1
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Statistics for 𝐙 a - 𝐆CC−1
10Udder Depth
c
Foot Angle
c
G−1
G𝐶𝐶_𝐻𝑖𝑔ℎ−1
G𝐶𝐶_𝑅𝑎𝑛𝑑−1
G−1
G𝐶𝐶_𝐻𝑖𝑔ℎ−1
G𝐶𝐶_𝑅𝑎𝑛𝑑−1
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Understanding genetic and genomic bases
• Base of BLUP: founders of the pedigree
• Base of GBLUP: genotyped animals
• Base of SSGBLUP: Vitezica et al. (2011) modeled as a mean for genotyped
• 𝑝 𝒖𝑔 = 𝑁 𝟏𝜇, 𝐆
• 𝜇 = (Pedigree base) – (Genomic base)
Fine-tuning indirect predictions from ssGBLUP
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Fine-tuning indirect predictions from ssGBLUP
𝒖𝑖𝑝= 𝜇 + 0.95𝐙 a + 0.05 𝒖𝑝𝑎𝑟𝑒𝑛𝑡𝑠1) Formula in Legarra (2017)
2) Double fitting
a) fit a regression using genotyped animals in the evaluation
GEBV𝑒𝑣𝑎𝑙 = 𝑏0 + 𝑏1𝐙 𝑎
b) apply regression for indirectly predicted animals
𝒖𝑖𝑝= 𝑏0 + 𝑏1𝐙 𝑎
3) Add average GEBV 𝒖𝑖𝑝= 𝐺𝐸𝐵𝑉𝑒𝑣𝑎𝑙 + 𝐙 𝑎
SNP and pedigree fractions
SNP and pedigree fractions
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Bias of indirect predictions
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-1
0
1
2
3
4
5
6
GEBV − uip
Foot AngleUdder Depth
-1
0
1
2
3
4
5
6
GEBV − uip
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0.980.98
0.98 0.980.980.98
0.98 0.98
Za Legarra_2017 Double_Fitting Average_GEBV
Co
rrel
atio
n(G
EBV,
uip
)
FA UD
Correlation between GEBV and indirect predictions
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Fine-tuning indirect predictions in ssGBLUP
E( 𝒖| 𝒂) = 𝜇 + 𝐙𝟏
𝟐 𝒑(𝟏 − 𝒑)𝐈𝟏
𝟐 𝒑(𝟏 − 𝒑)
−𝟏
( 𝒂 − 0)
E( 𝒖| 𝒂) = 𝜇 + 𝐙 𝒂
E( 𝒖| 𝒂) = 𝐺𝐸𝐵𝑉 + 𝐙 𝒂
≈
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Final Remarks
• SNP effects can be calculated based on APY G-1 or core G-1
• Slightly less accurate with core
• Indirect predictions based on core animals are accurate
• Reduction in computing time compared to G-1
• Similar computing time as APY G-1
• Indirect predictions are unbiased after corrections
• Average GEBV, Legarra (2017) or double fitting
• Can be used as interim evaluation16
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Acknowledgements
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