N. Gengler 1,2 , G.R. Wiggans *,3 , J.R. Wright 3 , and T. Druet 1,2

1. Simultaneous accounting for heterogeneity of (co)variance components in genetic evaluation of type traits N. Gengler1,2, G.R. Wiggans*,3, J.R. Wright3, and T. Druet1,2 1 Gembloux Agricultural University, Belgium 2 National Fund for Scientific Research, Brussels, Belgium 3 Agricultural Research Service, USDA, Beltsville, MD

2. USDA Type evaluation • Breeds: • Ayrshire • Brown Swiss • Guernsey • Jersey • Milking Shorthorn • Red and White • 15 Linear traits and Final Score • Multi-trait Model • Canonical Transformation • Estimation of missing values

3. Heterogeneity of (co)variance • Variances and (co)variances assumed constant across herds and time • Holstein Association accounts for heterogeneity in final score • Variance tends to decrease with increasing herd average final score • Changes in appraisal program over time can be a cause

4. Methods of HV estimation • Holstein Association estimates phenotypic variance using combination • observed variance • predicted variance from model including • mean final score • registry status • number of appraisals for herd-classification date • Meuwissen proposed simultaneous estimation of variances and breeding values • expected to improve accuracy of both estimates

5. USDA HV adjustment system • Apply Canonical transformation to linear traits • Prepare data for 2 models • score= herd-sire + herd-year-season-parity + parity-time_period-age + parity-time_period-stage • var= mean + parity-group_size + parity-herd_mean_final_score + parity-year-season + herd-year-month

6. Variance model • Herd-year-month effect in variance model random • Regression of variances within parity toward population mean (fixed effects) • Method R estimation of variance ratios within each EBV iteration

7. Computational requirements

8. Iteration • Time increased due to • iteration for variance model • estimation of variance ratios • Convergence sensitive to • quality of the starting values • size of unknown parent groups • Ways of reducing processing time • parallel processing • using a faster computer • limiting iteration for variances

9. Correlations between HV-adjusted official evaluations • February 2001 official evaluations • 2497 Jersey AI bulls born 1980+ • All correlations .989 or higher

10. Change in slope of PTA for Jersey AI bulls

11. Differences between HV-adjusted and official evaluation • Standard deviations & mean absolute values • increased as reliabilities increased to 80% • decreased slightly for reliabilities of > 90% • Mean differences largest for bulls • born from 1985 through 1994 • with lowest mean daughters final scores

12. Mendelian sampling • Mendelian sampling • evaluation minus mean of parent evaluations • Jersey cows born from 1984 through 1998 • regression of SD on birth year

13. Mendelian sampling

14. Interbull trend validation • Trend tests conducted for • Stature • Udder support • Comparison • first parity v. all parities • without recent years v. all data • Trend differences within tolerance

15. HV model implementation plans • Jersey - May 2001 • Other breeds by Feb 2002

16. Conclusions • Simultaneous estimation of BV & Variances possible • Requires substantially more computer time • Improves stability of Mendelian Sampling Variance over time • HV adjusted EBV enable more accurate selection decisions