# Presentation: 378439

## Accounting for Heterogeneous Variances in Multi-trait Evaluation of Jersey Type Traits 

**Accounting for Heterogeneous Variances in Multi-trait Evaluation of Jersey Type Traits**

- N. Gengler*, G. R. Wiggans†, L. L. M. Thornton†, J. R. Wright†, and T. Druet*

- *National Fund for Scientific Research, B-1000 Brussels, Belgium
- †Animal Improvement Programs Laboratory, Agricultural Research Service, USDA, Beltsville, MD 20705-2350

- Correlations between parent average from truncated data with EBV from full data with and without HV adjustment for bulls with more than five daughters

-  Additional computation times required are manageable.
-  Problems with convergence may occur.
-  Starting values for iteration affect outcome.
-  A run without adjustment may be used to create starting values.
-  Evaluations with HV adjustment are correlated with those without adjustment, but differ in expected ways.
-  Bulls with greatest change in evaluation were those born most recently.
-  Records on progeny of these bulls would receive the most adjustment.
-  Lower slopes from the HV analysis also indicate superiority of HV adjusted evaluations.
-  Some reduction in SD of Mendelian sampling is expected if older animals have higher reliability and lower inbreeding.
-  Those factors are unlikely to explain higher slopes found in  evaluations without HV adjustment.
-  Reduction in estimates of genetic trend also indicates that the HV adjustment has affected comparisons across time.
-  The HV adjusted evaluations were adopted as the official evaluations for the Jersey breed in May 2001 and were adopted by all other breeds that have evaluations calculated by USDA for in February 2002.

-  Type evaluations are calculated by multi-trait model.
-  Variance decreases as average final score increases.
-  Variances are heterogeneous for all type traits.
-  A method of adjustment for heterogeneous variance (HV) including prediction of variance from herd mean final score, registry status, and number of appraisals for the herd-classification date has been developed.
-  Pre-adjustment of this type is independent of the model and does not account for genetic or other (co)variances.
-  Requires a priori estimates of adjustment factors that may become outdated.
-  Method for stabilization of heterogeneous (co)variances simultaneously with the computation of the evaluations was developed by Meuwissen et al., 1996.
-  Objectives of this study were to describe this application and assess its impact on prediction of future progeny and variance of Mendelian sampling.

- Abstr. M23

***Data***
-  14 linear type traits: stature, strength, dairy form, foot angle, rear legs (side view), rump angle, rump width, fore udder attachment, rear udder height, rear udder width, udder depth, udder cleft, front teat placement, and teat length.
-  Final score is computed from the linear type scores.
-  Data provided by the American Jersey Cattle Association.
***Model information***
-  Mixed model equation:
-  Includes type records, fixed, random, and residual effects.
-  Additive corrections were applied for age and stage of lactation.
-  Only first and second parities were used.
-  Genetic groups defined based on birth year (_<_ 1966, 1967 and 1968, ... , 1995 and 1996, _>_ 1997).
-  Inbreeding was accounted for.
-  Canonical transformation with missing traits method applied.
-  Integrated HV Adjustment
-  Using proposed HV model (Meuwissen et al., 1996):
-  Herd-year variances regressed toward expectation.
-  Expectation based on:
-  Herd size.
-  Mean final score.
-  Month of classification by parity.
-  6-mo period by year by parity.

- Materials and Methods cont.
***Computational aspects****** ***
-  The publicly available computer program MTJAAM was modified:
-  Relaxation factor used for the second order Jacobi procedure was adjusted according to value of the convergence criterion of the genetic effect.
-  Computed at every iteration.
-  Imposed minimum of 5 heterogeneity rounds to avoid convergence problems.
***Genetic trend****** ***
-  Mean EBV calculated by birth year.
-  Genetic trend calculated by regressing these means on birth year and birth year squared.
-  Slope evaluated for 2000 births, the most recent year with complete data.
-  Data from birth years 1981 through 2001 were included.
***Comparison of evaluations with or without HV adjustment****** ***
-  Four sets of evaluations were calculated. In truncated data set appraisals after 2000 were removed to calculate parent averages of recent animals not including their own data or any of their progeny.
-  Data with HV adjustment, no truncation
-  Data without HV adjustment, no truncation
-  Data with HV adjustment, with truncation
-  Data without HV adjustment, with truncation
-  Correlations calculated between parent average from the truncated sets and EBV from the complete sets.
-  Mean absolute values of differences between and standard deviations (SD) of those differences also were calculated.
-  Absolute values were stratified by reliability and birth year.
-  Mendelian sampling computed as difference between EBV and parent average for animals with known ancestors.
-  Variances for cows born 1981 and later were studied.
-  Mean, SD, and the linear regression of the Mendelian sampling variances on birth year were calculated.

- N. Gengler, Chercheur Qualifié of the National Fund for Scientific Research (Brussels, Belgium) and T. Druet, Chargé de recherches of the National Fund for Scientific Research (Brussels, Belgium), currently at the Institut National de la Recherche Agronomique (Jouy-en-Josas, France), acknowledge the financial support of their organization. Partial funding was also provided by the American Jersey Cattle Association (Reynoldsburg, Ohio).

- Results and Discussion cont.
-  Mendelian sampling SD declined less over time for HV adjusted evaluations for all traits.
-  Slope ranged from 22% for udder depth score to 48% for teat length.
-  Ideally, slope would be stable over time.

- Mean and standard deviation of differences between evaluations with and without HV adjustment by birth year group

- Trend in SD of Mendelian Sampling for cows born 1981-2001

- Introduction

- Materials and Methods

- Results and Discussion

- HV adjustment took approximately 35% longer to complete.
- Correlations for AI bulls with more than five daughters improved by an average of 0.0003 over all traits.
- Correlations did not improve for final score, dairy form, foot angle, rear legs, rear udder width, or teat length.
- Standard deviations of differences were largest for bulls born 1986 through 1990
-  Younger bulls deviate less from the parent average because they have fewer progeny contributions to evaluation calculations.
-  Mean differences were largest for bulls born 1996 through 2000

- Conclusions

- Acknowledgements