GMACE Implementation

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

2. Genomics Timeline

3. 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

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-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

8. Foreign Daughter Equivalents in Dg • 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 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 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 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

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

12. Example cij for BSW

13. 3 Ways to Compute Dg • Dg1: Compare genomic to traditional REL • Convert 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 animals • Dg3 = Σ(traditional REL – parent average REL) / r • Choose r to make genomic REL = observed

14. Compare Dg1, Dg2, Dg3 • Dg 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 • Dg1 and Dg2 were correlated by .81 • Formula Dg1 used to test GMACE with BSW simulation

15. Reliabilities for Young BSW Bulls from USA 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 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…

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

20. Top Proven Bulls in 2006

21. Top Young Bulls in 2006

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

25. Thank You!