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

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

2

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

3

GEBVyoung = w1PA + w2GP – w3PP

GEBVyoung ≈ GP

Lourenco et al., 2015

COR( GEBV𝑦𝑜𝑢𝑛𝑔, 𝐙 a) > 0.99

GEBVyoung ≈ GP = 𝐙 a

Problems with Indirect predictions

COR( GEBV𝑦𝑜𝑢𝑛𝑔, 𝐙 a) > 0.99

Avg( GEBV) ≈ 100 Avg(𝐙 a) ≈ 0

4

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

5

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

6

Accuracy of SNP effects

𝒂𝐆 = λ𝐃 𝐙′G−1 u

7

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

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

9

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

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

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

11

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

12

Bias of indirect predictions

13

-1

0

1

2

3

4

5

6

GEBV − uip

Foot AngleUdder Depth

-1

0

1

2

3

4

5

6

GEBV − uip

14

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

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

≈

15

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

Acknowledgements

17