1 GMACE Implementation Pete Sullivan, CDN & Paul VanRaden*, USDA

2 Genomics Timeline K SNP chips developed by NLD, USA 2008Unofficial GEBV provided within country 2008Interbull Genomics Task Force formed 2009Official GEBV in several countries 2009Genomic MACE methods developed 2010Software provided to Interbull Centre 2010Research on actual GEBVs beginning ????GMACE test run and implementation

3 EBV Exchange History  Conversion formulas  Exporting country j computes EBV j  Importing country i converts EBV i = a + b EBV j  MACE  Countries each send EBV j, receive EBV i from Interbull  Standard formats, 2n vs. n 2 file transfers, less labor  Combines information from daughters in all countries  Trend validation introduced  2010-???? Genomic MACE  Countries send young and old bull GEBV j to Interbull  GEBV j combine information using traditional A -1  Validation tests revised, market barriers removed

4 Young Bulls

5 Genotype Exchanges  Combine genotypes within country groups  North America  New Zealand and Ireland  EuroGenomics  Many small countries are currently excluded  Combine reference genotypes worldwide  Brown Swiss project at Interbull  Other breeds less organized  Holstein global exchange could add reliability  Multi-country genotype evaluation is theoretically better than Genomic MACE

6 Objectives  Compare equations for  MACE, GMACE and multi-country genotype evaluation (mtGEN)  Deregression methods, daughter equivalents  Demonstrate using simulated BSW  9 countries, 8,073 proven bulls, 120 young  Same data as 2009, but split into 2 groups:  CHE, USA, CAN, NLD, and NZL  DEU, ITA, FRA, and SVN  Update on actual GEBV test

7 De-regression  MACE: obtain y from EBV (a) and D  [D + A -1 k] a = D y  GMACE: obtain y g from GEBV (g), D, D g  [D+D g + A -1 k] g = (D+D g ) y g  D g includes daughter equivalents from genomics and from foreign daughters of genotyped bulls

8 Foreign Daughter Equivalents in D g  Foreign phenotypes included via MACE for foreign genotyped bulls  Example: CAN reference bulls on USA scale  Alternative: compute GEBV from only domestic data for Interbull  Twice as much work for national centers  Not checked as carefully, not recommended  Use only domestic bulls in GMACE?  Use multi-country deregression?

9 Multi-Country Evaluation  MACE: combine y across countries  [D + A -1 T -1 ] a = D y  GMACE: combine y g across countries  [D+D g + A -1 T -1 ] g = (D+D g ) y g  mtGEBV: Multi-country genotype exchange  [D + G -1 T -1 ] a = D y  T is genetic covariance matrix across countries  G is genomic relationship matrix for bulls

10 Multi-Country Evaluation  MACE: combine y across countries  [D + A -1 T -1 ] a = D y  GMACE: combine y g across countries  [E -1 + A -1 T -1 ] g = (E -1 ) y g  mtGEBV: Multi-country genotype exchange  [D + G -1 T -1 ] a = D y  E accounts for residual covariances from data sharing

11 Residual Correlations in GMACE  D and D g are diagonal matrices  Residual variances of de-regressed proofs  E accounts for shared genotypes, MACE EBV  Residuals covariances from shared foreign data Max correlation between genomic predictions % common (shared) data Genomic portion of variance ( = %EDC from genomics )

12 Example c ij for BSW CHEUSACANNLDNZLDEUITAFRASVN CHE USA CAN NLD NZL DEU ITA FRA SVN

13 3 Ways to Compute D g  D g1 : Compare genomic to traditional REL  Convert each to daughter equivalents  Subtract D from D total to get D g1  D g2 : Equate diagonals of matrix inverses  [D + D g2 + A -1 k] -1 = [D + G -1 k] -1  Solve for D g2 using math similar to Misztal and Wiggans (1988)  D g3 : Use constant D g3 for all animals  D g3 = Σ(traditional REL – parent average REL) / r  Choose r to make genomic REL = observed

14 Compare D g1, D g2, D g3  D g from North American Holsteins  Young bull means were 19.4, 19.1, and 22.3  Proven bull means were 23.5, 22.9, and 22.3  Young bull SD were 1.2, 1.4, and 0  Proven bull SD were 11.3, 11.3, and 0  D g1 and D g2 were correlated by.81  Formula D g1 used to test GMACE with BSW simulation

15 Reliabilities for Young BSW Bulls from USA CtryPAMACEn_GEBVr_GEBVGMACEmtGEN CHE USA CAN NLD NZL DEU ITA FRA SVN n_GEBV = national GEBV, r_GEBV = regional GEBV

16 GMACE Reliability  MACE reliability approximation  Harris and Johnson, 1998  Within-country progeny absorptions  No residual correlations between countries  GMACE reliability approximation  Similar to MACE approximation, except  Multi-country progeny absorptions  Residual correlations from genomic data sharing

17 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 recommended  Option to include cow GEBVs in the future

18 Remaining GMACE Issues  Countries might report inconsistent D g  Actual D g should be similar if countries share genotypes and genetic correlations are high  If reported D g differ too much, GMACE gives sub-optimal (surprisingly poor) results  Restrict the variation of D g among countries? –Similar to bending correlation matrix T for MACE  Refine the GMACE equations?  Research is ongoing…

19 Formats  GEBVs for proven and young bulls  Same formats as 010, 015, 016, 017, 018, 019  Genomic daughter equivalents (GEDCs)  Truncated GEBVs for validation  Same formats, but 4 years less data  Validation test results (format 731)  Squared correlations, regressions, bias

Top Proven Bulls in Net Merit (adj)2010 NM$ DtrsTradGenDtrsGen O Man1, , OBrian Billion , Jet Stream , Alton ,142506

21 Top Young Bulls in NM$ (adj)2010 Net Merit NameTradGenDtrsTradGen Freddie Awesome Garrett Fortunato Logan

22 Freddie

23 Conclusions  GEBVs now official in several countries  GMACE software testing by Interbull  Accounts for data shared by country groups  Programs applied to simulated BSW GEBVs  Real HOL GEBVs sent Feb 22 by 9 countries  Genotype vs. GEBV exchange  Fuller use of data with genotype exchange  Lets smaller populations do genomic selection

24 Acknowledgements  Interbull genomics task force  Georgios Banos  Mario Calus  Vincent Ducrocq  João Dϋrr  Hossein Jorjani  Esa Mäntysaari  Zengting Liu

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