Estimates of Genetic Correlations When Evaluations of Both Parents are Available

1. Estimates of Genetic Correlations When Evaluations of Both Parents are Available

2. Goals • Use parent evaluations directly • Daughter contributions more precise • Sire-MGS model problems reduced • Deregression mixes dam, daughter info • Biased SD due to selection of dams • Unknown parent grouping is arbitrary • Foreign dam updates centralized • Estimate correlations at run time • Reduce dependence on test runs

3. International Evaluation Methods • Conversion formulas • EBVi = aij + bij EBVj • Pairwise estimates, multiple EBVi • Sire-MGS MACE • EBVi = PIi + aijt + bij (EBVj – PIj) • Simultaneous estimates, combined EBVi • Animal Model MACE • EBVi = PAi + bij (EBVj – PAj) • Conversions used for missing sires, dams

4. Interbull Guidelines(Bulletin 28, 2001) “Nowadays, almost all countries have moved from sire model to animal model” “National genetic evaluation centers are recommended to use the following set of priorities: a) An animal model in contrast to a sire model”

5. Reliability of Dam’s EBV(VanRaden, Powell, and Emanuelson, 2000)

6. Reliability of Mendelian Sampling • Begin with animal, sire, dam REL • Separate daughter from parent info • Obtain 3x3 REL matrix using 3x3 A-1 • Misztal and Wiggans, 1988 • VanRaden, 2000, Fikse et al, 2003 • Sullivan, Harris, and Fikse, 1998 • Var (estimated MS) / genetic var • [ 1 -.5 -.5 ] RELa,s,d [ 1 -.5 -.5 ]’

7. Combine Bull EBV • Combine EBV by selection index • EBVi = PAi + Cov(MSi , EMSj) Var-1 (EMSj) (EBVj – PAj) • Generalize if more than 1 country • Cov, Var depend on RELj and Gij • Var-1 (EMSj) replaces deregression • Calculate reliabilities • RELi = RELpai + Cov Var-1 Cov’

8. REML AlgorithmsHarville, 1977, VanRaden, 1986 • Slower EM: • Vij = [ûi’A-1ûj + tr(A-1 Cij)] / n • Faster EM: • Vij = ûi’A-1ûj / [n - tr(A-1 Cij)/vij] • vij is previous estimate of Vij • Boosted EM (can diverge if x too big): • Vij = (ûi’A-1ûj– x) / [n – (tr(A-1 Cij) – x)/vij]

9. Computing Methods • Read data twice / variance iteration • Convert and store parent EBV’s • Combine MS for each bull, age order • Sum MSi MSj and E(MSi MSj) • Divide MS quadratic by expectation • Invert matrices of very small size (countries with data for each bull) • Obtain EBV’s, corr’s in 1 program

10. Computing Time • Convergence • Number of iterations was 2500 • SD and corr’s each change < .000016 • All 8 eigenvalues positive (1 was set to .0000001 from iteration 22 to 62) • Correlations treated random (10 d.f.) • Time per iteration = 36 seconds • Total time per trait = 12 hours

11. Standard Deviations - Protein

12. Official Correlations – Feb 2000

13. AM Correlations (preliminary)

14. Correlation Differences (AM–SM)

15. SM Correlations (Weigel et al 2001)

16. Correlation of MACE Results • EBV had higher correlation across scales if same parameters used • 35,414 bulls on 8 country scales • .987 to .996 with SM, .994 to .999 AM • With new parameter estimates, EBV correlations reduced because intercept estimation not yet ideal • .961 to .992 with AM, new parameters

17. Conclusions • Genetic parameters were estimated using animal model MACE and selection index. • Methods were tested for 8 countries that provided sire and dam evaluations in 2000. • Genetic SD were about 1.12 times larger and most genetic correlations were higher. • EBV’s were not more consistent across scales because of poorer intercept estimates. • Animal model methods might be possible for both national and international evaluations.

18. Thank You to: • The 8 countries that contributed parent genetic evaluations in 2000 • Rex Powell for combining and editing these evaluations • Ulf Emanuelson for computing a corresponding 8-country MACE