# Presentation: 232690

## Estimates of Genetic Correlations When Evaluations of Both Parents are Available

## 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**

## International Evaluation Methods

**Conversion formulas**
**EBV****i**** = a****ij**** + b****ij**** EBV****j**
**Pairwise estimates, multiple EBV****i****  **
**Sire-MGS MACE**
**EBV****i**** = PI****i**** + a****ijt**** + b****ij**** (EBV****j**** – PI****j****)**
**Simultaneous estimates, combined EBV****i**** **
**Animal Model MACE**
**EBV****i**** = PA****i**** + b****ij**** (EBV****j**** – PA****j****)**
**Conversions used for missing sires, dams**

## 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”**

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

| Reliability of Dams from: | Mean | Max |
| --- | --- | --- |
| Belgium | 52 | 84 |
| Canada | 73 | 96 |
| Denmark | 41 | 93 |
| Estonia | 39 | 57 |
| France | 37 | 61 |
| Switzerland (Red) | 35 | 80 |
| The Netherlands | 71 | 96 |
| United States | 77 | 96 |

## 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 ] REL****a,s,d**** [ 1  -.5  -.5 ]’**

## Combine Bull EBV

**Combine EBV by selection index**
**EBV****i**** = PA****i**** + Cov(MS****i ****, EMS****j****) Var****-1 ****(EMS****j****) (EBV****j**** – PA****j****)**
**Generalize if more than 1 country**
**Cov, Var depend on REL****j**** and G****ij**
**Var****-1 ****(EMS****j****) replaces deregression**
**Calculate reliabilities**
**REL****i**** = RELpa****i**** + Cov Var****-1**** Cov’**

## REML AlgorithmsHarville, 1977, VanRaden, 1986

**Slower EM:**
**V****ij**** = [****û****i****’A****-1****û****j**** + tr(A****-1**** C****ij****)] / n**
**Faster EM:**
**V****ij**** = ****û****i****’A****-1****û****j**** / [n - tr(A****-1**** C****ij****)/v****ij****]**
**v****ij**** is previous estimate of V****ij**
**Boosted EM (can diverge if x too big):**
**V****ij**** = (****û****i****’A****-1****û****j****– x) / [n – (tr(A****-1**** C****ij****) – x)/v****ij****]**

## Computing Methods

**Read data twice / variance iteration**
**Convert and store parent EBV’s**
**Combine MS for each bull, age order**
**Sum ****MS****i**** MS****j**** and ****E(MS****i**** MS****j****)**
**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 **

## 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**

## Standard Deviations - Protein

|  | CAN | DNK | FRA | NLD | USA | BEL | EST | CHR |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Sire-MGS SD | 22.6 | 13.4 | 20.0 | 15.0 | 20.6 | 14.8 | 13.8 | 13.5 |
| AM SD | 23.9 | 14.1 | 24.5 | 15.8 | 23.2 | 13.7 | 16.0 | 18.7 |
| Ratio | 1.05 | 1.05 | 1.23 | 1.05 | 1.13 | .93 | 1.16 | 1.39 |

## Official Correlations – Feb 2000

|  | CAN | DNK | FRA | NLD | USA | BEL | EST | CHR |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| CAN | 1.00 | .90 | .92 | .91 | .94 | .91 | .87 | .91 |
| DNK | .90 | 1.00 | .92 | .95 | .93 | .92 | .87 | .90 |
| FRA | .92 | .92 | 1.00 | .94 | .92 | .92 | .86 | .90 |
| NLD | .91 | .95 | .94 | 1.00 | .93 | .96 | .88 | .92 |
| USA | .94 | .93 | .92 | .93 | 1.00 | .92 | .88 | .91 |
| BEL | .91 | .92 | .92 | .96 | .92 | 1.00 | .88 | .92 |
| EST | .87 | .87 | .86 | .88 | .88 | .88 | 1.00 | .88 |
| CHR | .91 | .90 | .90 | .92 | .91 | .92 | .88 | 1.00 |

## AM Correlations (preliminary)

|  | CAN | DNK | FRA | NLD | USA | BEL | EST | CHR |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| CAN | 1.00 | .96 | .90 | .96 | .95 | .94 | .92 | .88 |
| DNK | .96 | 1.00 | .94 | .98 | .93 | .97 | .94 | .91 |
| FRA | .90 | .94 | 1.00 | .94 | .84 | .95 | .94 | .92 |
| NLD | .96 | .98 | .94 | 1.00 | .92 | .98 | .94 | .91 |
| USA | .95 | .93 | .84 | .92 | 1.00 | .90 | .92 | .86 |
| BEL | .94 | .97 | .95 | .98 | .90 | 1.00 | .93 | .92 |
| EST | .92 | .94 | .94 | .94 | .92 | .93 | 1.00 | .91 |
| CHR | .88 | .91 | .92 | .91 | .86 | .92 | .91 | 1.00 |

## Correlation Differences (AM–SM)

|  | CAN | DNK | FRA | NLD | USA | BEL | EST | CHR |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| CAN |  | .06 | –.02 | .05 | .01 | .03 | .05 | –.03 |
| DNK | .06 |  | .02 | .03 | .00 | .05 | .07 | .01 |
| FRA | .02 | .02 |  | .00 | –.08 | .03 | .08 | .02 |
| NLD | .05 | .03 | .00 |  | –.01 | .02 | .06 | –.01 |
| USA | .01 | .00 | –.08 | –.01 |  | –.02 | .04 | –.05 |
| BEL | .03 | .05 | .03 | .02 | –.02 |  | .05 | .00 |
| EST | .05 | .07 | .08 | .06 | .04 | .05 |  | .03 |
| CHR | .03 | .01 | .02 | –.01 | –.05 | .00 | .03 |  |

## SM Correlations (Weigel et al 2001)

|  | BEL | CAN | EST | NLD | USA | DNK | FRA | CHR |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| BEL | 1.00 | .94 | .83 | .93 | .95 |  |  |  |
| CAN | .94 | 1.00 | .83 | .93 | .92 |  |  |  |
| EST | .83 | .83 | 1.00 | .81 | .85 |  |  |  |
| NLD | .93 | .93 | .81 | 1.00 | .93 |  |  |  |
| USA | .95 | .92 | .85 | .93 | 1.00 |  |  |  |
| DNK |  |  |  |  |  |  |  |  |
| FRA |  |  |  |  |  |  |  |  |
| CHR |  |  |  |  |  |  |  |  |

## 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**

## 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. **

## 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**