1. Bayesian integration of external information into the single step approach for genomically enhanced prediction of breeding values J. Vandenplas, I. Misztal, P. Faux, N. Gengler 1

2. Unbiased EBV if genomic, pedigree and phenotypic information considered simultaneously Problem –Only records related to selected animals available –Bias due to genomic pre-selection Single step genomic evaluation (ssGBLUP) – Simultaneous combination of genomic, pedigree and phenotypic information (=internal information) –No integration of external information (e.g. MACE-EBV) Introduction 2

3. Integration of a priori known external information into ssGBLUP –By a Bayesian approach –To avoid multi-step methods –By considering simplifications of computational burden, a correct propagation of external information, and no multiple considerations of contributions due to relationships. Objective 3

4. Methods Bayesian approach (Dempfle, 1977; Legarra et al., 2007) 2 groups of animals 1) animals I = internal animals with only records in  Ia: non genotyped animals Ib: genotyped animals 2) animals E = external animals with records in and possible records in  Ea: non genotyped animals Eb: genotyped animals 4

5. Methods An internal evaluation –All animals Ia, Ib, Ea, Eb –Only – instead of where 5

6. Methods An unknown external ssGBLUP –All animals Ia, Ib, E –Genomic information included in –Only ( precorrected for fixed effects) 6

7. Methods Problem –Unknown external ssGBLUP Available –External genetic evaluation of animals Ea and Eb without animals Ia and Ib without genomic information  7

8. Methods Substitution in the unknown external ssGBLUP – and 8

9. Methods Finally, internal evaluation = ssGBLUP integrating external information 9

10. Methods Approximations and simplifications of computational burden 10  RHS: add a product between a matrix and a vector

11. Methods Approximations and simplifications of computational burden 11  LHS: add a block diagonal matrix

12. Simulation 12