gmace implementation

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GMACE Implementation

Pete Sullivan, CDN&

Paul VanRaden*, USDA

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Genomics Timeline

2007 50K SNP chips developed by NLD, USA 2008 Unofficial GEBV provided within country2008 Interbull Genomics Task Force formed2009 Official GEBV in several countries2009 Genomic MACE methods developed2010 Software provided to Interbull Centre2010 Research on actual GEBVs beginning???? GMACE test run and implementation

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EBV Exchange History

1975-1994 Conversion formulas Exporting country j computes EBVj

Importing country i converts EBVi = a + b EBVj

1995-2010 MACE Countries each send EBVj, receive EBVi from Interbull Standard formats, 2n vs. n2 file transfers , less labor Combines information from daughters in all countries Trend validation introduced

2010-???? Genomic MACE Countries send young and old bull GEBVj to Interbull GEBVj combine information using traditional A-1

Validation tests revised, market barriers removed

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Young Bulls

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Genotype Exchanges

Combine genotypes within country groupsNorth AmericaNew Zealand and IrelandEuroGenomicsMany small countries are currently excluded

Combine reference genotypes worldwideBrown Swiss project at InterbullOther breeds less organizedHolstein global exchange could add reliabilityMulti-country genotype evaluation is theoretically better

than Genomic MACE

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Objectives

Compare equations forMACE, GMACE and multi-country genotype

evaluation (mtGEN)Deregression methods, daughter equivalents

Demonstrate using simulated BSW9 countries, 8,073 proven bulls, 120 youngSame data as 2009, but split into 2 groups:

CHE, USA, CAN, NLD, and NZL DEU, ITA, FRA, and SVN

Update on actual GEBV test

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De-regression

MACE: obtain y from EBV (a) and D [D + A-1k] a = D y GMACE: obtain yg from GEBV (g), D, Dg

[D+Dg + A-1k] g = (D+Dg) yg

Dg includes daughter equivalents from genomics and from foreign daughters of genotyped bulls

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Foreign Daughter Equivalents in Dg

Foreign phenotypes included via MACE for foreign genotyped bullsExample: CAN reference bulls on USA scale

Alternative: compute GEBV from only domestic data for InterbullTwice as much work for national centersNot checked as carefully, not recommended

Use only domestic bulls in GMACE? Use multi-country deregression?

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Multi-Country Evaluation

MACE: combine y across countries [D + A-1 T-1] a = D y GMACE: combine yg across countries [D+Dg + A-1 T-1] g = (D+Dg) yg

mtGEBV: Multi-country genotype exchange [D + G-1 T-1] a = D y

T is genetic covariance matrix across countriesG is genomic relationship matrix for bulls

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Multi-Country Evaluation

MACE: combine y across countries [D + A-1 T-1] a = D y GMACE: combine yg across countries [E-1 + A-1 T-1] g = (E-1) yg

mtGEBV: Multi-country genotype exchange [D + G-1 T-1] a = D y

E accounts for residual covariances from data sharing

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Residual Correlationsin GMACE

D and Dg are diagonal matricesResidual variances of de-regressed proofs

E accounts for shared genotypes, MACE EBVResiduals covariances from shared foreign data

Max correlation between genomic

predictions

% common (shared) data

Genomic portion of variance

c jiji EEgrijE

( = %EDC from genomics)

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Example cij for BSW

CHE USA CAN NLD NZL DEU ITA FRA SVN

CHE 1 1 1 1 1 0 0 0 0

USA 1 1 1 1 1 0 0 0 0

CAN 1 1 1 1 1 0 0 0 0

NLD 1 1 1 1 1 0 0 0 0

NZL 1 1 1 1 1 0 0 0 0

DEU 0 0 0 0 0 1 1 1 1

ITA 0 0 0 0 0 1 1 1 1

FRA 0 0 0 0 0 1 1 1 1

SVN 0 0 0 0 0 1 1 1 1

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3 Ways to Compute Dg

Dg1: Compare genomic to traditional RELConvert each to daughter equivalents Subtract D from Dtotal to get Dg1

Dg2: Equate diagonals of matrix inverses [D + Dg2 + A-1k]-1 = [D + G-1k]-1

Solve for Dg2 using math similar to Misztal and Wiggans (1988)

Dg3: Use constant Dg3 for all animalsDg3 = Σ(traditional REL – parent average REL) / rChoose r to make genomic REL = observed

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Compare Dg1, Dg2, Dg3

Dg from North American HolsteinsYoung bull means were 19.4, 19.1, and 22.3Proven bull means were 23.5, 22.9, and 22.3Young bull SD were 1.2, 1.4, and 0Proven bull SD were 11.3, 11.3, and 0

Dg1 and Dg2 were correlated by .81 Formula Dg1 used to test GMACE with

BSW simulation

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Reliabilities for Young BSW Bulls from USA

Ctry PA MACE n_GEBV r_GEBV GMACE mtGENCHE 14 17 65 68 72 73USA 20 18 55 68 72 70CAN 4 15 9 55 61 61NLD 1 14 6 55 62 58NZL 1 0 1 22 28 26DEU 5 11 64 63 69 69ITA 1 12 34 54 63 64FRA 2 15 21 54 66 66SVN 3 11 6 46 56 55

n_GEBV = national GEBV, r_GEBV = regional GEBV

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GMACE Reliability

MACE reliability approximationHarris and Johnson, 1998Within-country progeny absorptions

No residual correlations between countries GMACE reliability approximation

Similar to MACE approximation, exceptMulti-country progeny absorptions

Residual correlations from genomic data sharing

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Sire-Dam or MGS Pedigree?

Software tested with animal model Traditional MACE uses sire-MGS Conversion to AM-MACE planned

Initial study in NLD (van der Linde, 2005)Pilot study at Interbull (Fikse, 2008)All countries supply sire-dam pedigree

Animal model GMACE recommendedOption to include cow GEBVs in the future

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Remaining GMACE Issues

Countries might report inconsistent Dg

Actual Dg should be similar if countries share genotypes and genetic correlations are high

If reported Dg differ too much, GMACE gives sub-optimal (surprisingly poor) results Restrict the variation of Dg among countries?

– Similar to bending correlation matrix T for MACE Refine the GMACE equations? Research is ongoing…

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Formats

GEBVs for proven and young bullsSame formats as 010, 015, 016, 017, 018, 019Genomic daughter equivalents (GEDCs)

Truncated GEBVs for validationSame formats, but 4 years less data

Validation test results (format 731)Squared correlations, regressions, bias

Top Proven Bulls in 2006

2006 Net Merit (adj) 2010 NM$

Dtrs Trad Gen Dtrs Gen

O Man 1,317 653 646 54,573 729

OBrian 94 385 496 877 448

Billion 73 470 461 1,687 249

Jet Stream 108 444 458 7,439 417

Alton 108 484 452 5,142 506

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Top Young Bulls in 2006

2006 NM$ (adj) 2010 Net Merit

Name Trad Gen Dtrs Trad Gen

Freddie 467 762 70 801 824

Awesome 472 731 90 513 637

Garrett 509 688 126 604 589

Fortunato 523 669 97 475 556

Logan 521 646 101 617 642

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Freddie

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Conclusions

GEBVs now official in several countries GMACE software testing by Interbull

Accounts for data shared by country groupsPrograms applied to simulated BSW GEBVsReal HOL GEBVs sent Feb 22 by 9 countries

Genotype vs. GEBV exchange Fuller use of data with genotype exchangeLets smaller populations do genomic selection

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Acknowledgements

Interbull genomics task forceGeorgios BanosMario CalusVincent DucrocqJoão DϋrrHossein Jorjani Esa MäntysaariZengting Liu

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