1. 2007 2008 Strategies to Incorporate Genomic Prediction Into Population-Wide Genetic Evaluations Nicolas Gengler 1,2 & Paul VanRaden 3 1 Animal Science Unit, Gembloux Agricultural University, Belgium 2 National Fund for Scientific Research (FNRS), Brussels, Belgium 3 USDA Animal Improvement Programs Laboratory, Beltsville, MD Joint ADSA-ASAS Meeting July 7-11, 2008, Indianapolis

2. Issues for Genomic Breeding Values and Population-Wide Genetic Evaluations  How to avoid any confusion in the mind of users?  Do markets accept even more “black-box”?  How to create confidence? All these points could be partially addressed by answering this question: How to feedback genomic information to breeders? Therefore integration of genomic breeding values and population-wide genetic evaluations a necessity!

3. Two Main Goals 1.Include data from other phenotyped relatives into the genotyped animals’ combined EBV, called hereafter “integration” 2.Transfer information from genotyped to non- genotyped animals to allow for them also computation of combined EBV, called hereafter “propagation” Two goals basically needed to achieve tight integration of genomic and phenotypic information

4. Three strategies 1.Selection index to combine sources of information into a single set of breeding values for genotyped animals 2.Predict SNP gene content, then use it, alternatively predict genomic breeding values than integrate these values using 1 3.Integrate genomic breeding values as external information into genetic evaluation using a Bayesian framework

5. Strategy 1: Selection Index  Define three types of EBV (û 1, û 2, û 3 ) as components of information vector (û) by  û 1 = genomic EBV, known for genotyped animals, their data being YD, DYD or DRP  û 2 = non-genomic EBV (PA), known for genotyped animals and based on their data (YD, DYD, DRP)  û 3 = traditional EBV (PA) from national / intl. data  Define combined EBV as û c

6. Strategy 1: Selection Index  Define needed variances and covariance as proportional to reliabilities (R) and genetic variance: 

7. Strategy 1: Selection Index  Predicting û c using standard SI   Average SI coefficients (approximate)   Intuitively eliminates double counting for PA  Very similar to values obtained by multiple regression  Achieves “Integration” (Goal 1)  Solves double-counting of PA for genotyped animals

8. Strategy 2:  Background  SNP data only known for few animals  First idea: propagation of gene content for all animals can be done through out pedigree Conditional expectation of gene contents for SNP for ungenotyped animals given molecular and pedigree data Gengler et al. JDS 2008 91: 1652- 1659  Leads directly to needed covariance structures combining genomic relationship if known with pedigree relationships  However basic idea can be extended easily  Also presented here (Strategy 2b)

9. Strategy 2: Predict SNP Gene Content Unknown SNP gene contents for non- genotyped animals Known SNP gene contents for genotyped animals Average gene content = Allele frequency x 2 Additive relationship matrix among genotyped animals Additive relationship matrix between ungenotyped and genotyped animals Gengler et al. JDS 2008 91: 1652 - 1659 NB: n = non-genotyped, g = genotyped animals

10. Strategy 2: Predict SNP Gene Content  Predicted gene content for SNP can be used to predict individual genomic EBV  Leads directly to needed covariance structures combining genomic relationship if known with pedigree relationships  However method can also extended to predict directly individual genomic EBV  Also much simpler than estimating individual SNP gene contents

11. Strategy 2b: Predict Genomic EBV Unknown genomic breeding values for non-genotyped animals Known genomic breeding values for genotyped animals Average genomic breeding value Additive relationship matrix between unknown and known animals Additive relationship matrix among genotyped animals NB: n = non-genotyped, g = genotyped animals

12. Strategy 2b: Equivalent BLUP Method  Equivalent BLUP model to predict û n  Solving of associated mixed model equations equivalent BLUP prediction of û n NB: n = non-genotyped, g = genotyped animals

13. Strategy 2b: Equivalent BLUP Method  Prediction of associated individual reliabilities for every û n needed  Transfers information from genotyped to non- genotyped animals, achieves “Propagation” (Goal 2)  To allow for non-genotyped animals also computation of combined EBV, use of Method 1 (or other method) needed

14. Remark  Even by combining genomic EBV from Method 2 (including step from Method 1)  Still not direct integration  However Genomic EBV can also be considered external evaluation known a priori for some animals  Theory exists for Bayesian Integration as used in the beef genetic evaluation systems

15. Strategy 3: Mixed Model Equations for Bayesian Integration  Following Legarra et al. (2007)  Very similar to regular Mixed Model Equations, only two changes

16. Strategy 3: Mixed Model Equations for Bayesian Integration Prediction error variance matrix of genomic EBV Modified G matrix (Co)variance matrix of genomic TBV NB: n = non-genotyped, g = genotyped animals

17. Strategy 3: Mixed Model Equations for Bayesian Integration RHS of theoretical BLUP equations for genomic EBV Least square part of LHS of theoretical BLUP equations for genomic EBV NB: n = non-genotyped, g = genotyped animals

18. Strategy 3: Mixed Model Equations for Bayesian Integration  Additional simplifications (assumptions) used :  D = diagonal matrix whose elements proportional to REL and genetic variance  G gg = diagonal matrix whose elements proportional to genetic variance, represent maximum PEV  Experience with Bayesian method  Theory sound  However strong assumptions  Also practical experience fine-tuning needed

19. Discussion  Strategy 1:  Is used since April 2008 in the USA  Achieves “Integration” (Goal 1)  But does not propagate genomic EBV across the pedigree  Strategy 2:  Allows to propagate SNP gene content or even genomic EBV across the pedigree (“Propagation”, Goal 2)  Even if leads to combined genomic – pedigree relationships, their use (inversion) not obvious with many animals  Strategy 3:  Achieves directly both “Integration” (Goal 1) and “Propagation” (Goal 2) because of modified Mixed Model Equations (relatives are also affected, as are other effects in the model)  Potentially a good compromise, also existing standard software can be easily modified

20. Thank you for your attention Presenting author’s e-mail: gengler.n@fsagx.ac.be Acknowledgments: Study supported through FNRS grants F.4552.05 and 2.4507.02, RW-DGA project D31-1168