1. 2007 Paul VanRaden Animal Improvement Programs Lab, Beltsville, MD Paul.VanRaden@ars.usda.gov 2011 Avoiding bias from genomic pre- selection in converting daughter information across countries

2. Interbull Workshop, Verona, Italy, February 2012 (2) Paul VanRaden 2012  Including foreign data in national EBV and GEBV  Including genomic data by 1-step or multi-step methods Iterative method with G instead of G -1 Results from national Jersey data  Exchanging foreign phenotypic data in MACE without bias Topics

3. Interbull Workshop, Verona, Italy, February 2012 (3) Paul VanRaden 2012 Introduction  Paradox: National GEBVs require traditional MACE phenotypes without genomics Genomic pre-selection will bias foreign EBVs but not 1-step GEBVs  Question: How can we continue to exchange foreign phenotype data without bias?

4. Interbull Workshop, Verona, Italy, February 2012 (4) Paul VanRaden 2012  Expected value of Mendelian sampling no longer equal to 0  Key assumption of animal models  References: Patry, Ducrocq 2011 GSE 43:30 Vitezica et al 2011 Genet Res (Camb) pp. 1–10. Bias from Pre-Selection

5. Interbull Workshop, Verona, Italy, February 2012 (5) Paul VanRaden 2012  Bulls born in 2008, progeny tested in 2009, with daughter records in 2012, were pre-selected: 3,434 genotyped vs. 1,096 sampled Now >10 genotyped per 1 marketed  Potential for bias: 178 genotyped progeny 32 sons progeny tested Pre-Selection Bias Now Beginning

6. Interbull Workshop, Verona, Italy, February 2012 (6) Paul VanRaden 2012  1-Step to incorporate genotypes Flexible models, many recent studies Foreign data not yet included  Multi-step GEBV, then insert in AM Same trait (Ducrocq and Liu, 2009) Or correlated trait (Mantysaari and Stranden, 2010; Stoop et al, 2011) Foreign genotyped bulls included National Methods to Reduce Bias

7. Interbull Workshop, Verona, Italy, February 2012 (7) Paul VanRaden 2012  1-step genomic model G and A 22 too big to invert (>150,000) Add extra equations (Legarra et al)  Multi-step insertion of GEBV [Z’R -1 Z + A -1 k] u = Z’R -1 y (without G) Previous studies added genomic information to Z’R -1 Z and Z’R -1 y Instead: insert GEBV into u, iterate Genomic Algorithms Used

8. Interbull Workshop, Verona, Italy, February 2012 (8) Paul VanRaden 2012  Foreign portion of deregressed MACE EBV added as “daughters” Adapted from Bonaiti, Boichard 1995 Subtract domestic portion of MACE Add 1 observation weighted by EDC instead of adding n “daughters” For multitrait, pre-multiply by T -1  Mean included to adjust foreign data to genetic base of solutions Adding Foreign Information

9. Interbull Workshop, Verona, Italy, February 2012 (9) Paul VanRaden 2012  Convert and exchange DYD g National GEBV and DYD g unbiased Can’t deregress GEBV without G Exchange similar to simple GMACE  Other countries need DYD anyway Deregress, reregress EBVs in MACE Countries deregress MACE EBV Avoid bias by exchanging DYD g International Bias Reduction

10. Interbull Workshop, Verona, Italy, February 2012 (10) Paul VanRaden 2012  Traditional DYD = ∑(q w) (YD -.5 EBVmate) / ∑(q w) Adjusts merit of mates, herdmates  Genomic DYD g = ∑(q w) (YD g -.5 GEBVmate) / ∑(q w) Genomic merit of mates, herdmates  YD g = ZR -1 (y – nongenetic effects) / diag(ZR -1 Z) Compare DYD g vs. DYD: Methods

11. Interbull Workshop, Verona, Italy, February 2012 (11) Paul VanRaden 2012  National U.S. Jersey data 4.4 million lactation phenotypes 4.1 million animals in pedigree Multi-trait milk, fat, protein yields 5,364 male, 11,488 female genotypes  Foreign deregressed proofs for 7,072 bulls (foreign dams not yet included)  Deregession: PA IB + (EBV – PA IB )/REL IB Data

12. Interbull Workshop, Verona, Italy, February 2012 (12) Paul VanRaden 2012 Foreign Data: NoYes Genomic Data: None (PA) Insert GEBV 1-Step GEBV No, None1.0.9998.9997.9993 Yes, None1.0.9996.9993 Yes, Insert1.0.9997 Yes, 1-step1.0 Correlation of DYDg with DYD

13. Interbull Workshop, Verona, Italy, February 2012 (13) Paul VanRaden 2012 Foreign Data: NoYes Genomic Data: None (PA) Insert GEBV 1-Step GEBV No, None1.0.997.856.868 Yes, None1.0.853.869 Yes, Insert1.0.966 Yes, 1-step1.0 Corr (GEBV or PA) - Young Bulls

14. Interbull Workshop, Verona, Italy, February 2012 (14) Paul VanRaden 2012  6,743 bulls with no USA daughters  Corr (National EBV, MACE EBV).77 before adding foreign data.995 after adding foreign data  Few foreign bulls in JE reference population, so hard to test gain in REL of young bull GEBV Foreign Data in 1-Step: Results

15. Interbull Workshop, Verona, Italy, February 2012 (15) Paul VanRaden 2012 EvaluationRegression Squared Correlation Parent Average.73.436 Multi-Step GEBV.75.520 1-Step GEBV.85.520 Expected.93 1-Step vs Multi-Step: Results Data cutoff in August 2008

16. Interbull Workshop, Verona, Italy, February 2012 (16) Paul VanRaden 2012  Holstein convergence much slower JE took 11 sec / round including G HO took 1.6 min / round including G JE needed ~1000 rounds HO needed >5000 rounds  All-breed model without genomics Replace software used since 1989 Correlations >.995 with traditional AM Preliminary Larger Analyses

17. Interbull Workshop, Verona, Italy, February 2012 (17) Paul VanRaden 2012  Genotyped but EBVs are deleted 479 HOL bulls born before 1985 and exchanged by USA, CAN, ITA, GBR 64 BSW bulls born before 1980 and evaluated in Intergenomics 100 JER bulls born before 1980  Use in estimating EBV and genetic correlations but not SDs Exchange Old Bulls in MACE

18. Interbull Workshop, Verona, Italy, February 2012 (18) Paul VanRaden 2012 Conclusions  National EBV, MACE will be biased  Exchanging DYD g may be possible  Foreign data can add to 1-step  Equations solved for 3 JE traits, but slow convergence for HO and divergence with more traits  Further work needed on algorithm

19. Interbull Workshop, Verona, Italy, February 2012 (19) Paul VanRaden 2012  Andres Legarra, Ignacy Misztal, Ignacio Aguilar, Vincent Ducrocq, Tom Lawlor, and George Wiggans provided advice on algorithms and shared software  Cow photo (De-Su Oman 6121) by John Erbsen Acknowledgments