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

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Marbling

Multistep Traditional

• High genetic correlation between phenotype and MBV

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• 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

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BW WW YWT

USMARC Predictive Ability

MS SS

Kuehn et al., 2017

0

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BW WW YWT MILK CWT MARB REA FAT

Correlation with MARC EBV for 143 bulls

MS SS

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Genetic trends for carcass traits

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Marbling

ssGBLUP Multistep Traditional

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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

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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?

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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

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Additional features in ssGBLUP

• Interim evaluations

• Indirect predictions

• Quick evaluations between official runs

• Should be comparable to GEBV

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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

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Problem with Indirect predictions

COR(GEBV,DGV) > 0.99

Avg(GEBV) ≈ 100 Avg(DGV) ≈ 0

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• 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

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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

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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

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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

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Acknowledgements

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