Genetic correlation estimation procedure

Estimation of genetic correlations among countries takes place in test-runs and only when new or modified data are submitted from a country, according to the following procedure (as per Interbull technical workshop of January 2004, Uppsala, Sweden):

Step 1: Estimation of correlations

Data for estimation of genetic correlations are de-regressed breeding values for all AI bulls that have daughters in at least 10 herds. For mastitis and calving traits an additional requirement is that bulls have at least 50 daughters.

Correlations are estimated using the software package developed at Holstein Association USA (Klei & Weigel, 1998). Correlations are estimated simultaneously for all countries, except for Holstein, where subsets of 7 countries are considered. Countries are grouped into triplets, and per analysis correlations are estimated for countries in two triplets and the USA as link provider. Genetic correlation estimates for all country pairs are obtained by considering all possible combinations of triplets.

For each analysis only records from common bulls and bulls belonging to ¾-sib families with evaluations in multiple countries are used. Pedigree information is traced back until 1970; parents of ancestors born before 1970 are treated as missing and assigned to phantom parent groups. Phantom parent groups are defined according to origin, birth year of the bull and path of selection. Small groups are merged, where the first priority is given to combining birth years, and next to combining countries of origin. Genetic groups are treated as random effects.

Starting correlations for the REML procedure are the previously used correlations, and iterations are stopped when the relative change for all λ = Gij/√(Ri*Rj) is less than 10-6, where Gij is the sire covariance between country i and j, and Ri and Rj the residual variance in country i and j, respectively, or when the maximum change in correlation is less than 10-6. Aitken acceleration is used to speed up convergence.

Due to the country subsetting for Holstein, multiple estimates are obtained for the genetic correlation between some country pairs. The correlation matrix used in the next step (post-processing) is a combination of matrix of the maximum and average correlation estimates, weighted such to obtain the matrix with the highest smallest eigenvalue.

Step 2:Post processing

1. The following information sources are considered:
   1. the correlation estimate from step 1
   2. the correlation used in the previous run.
   3. own expectations
   4. correlations from Holsteins (only for non-Holstein breeds)
2. Estimates are required to fall within certain windows. For milk production traits, separate windows are maintained depending on the climate and whether or not countries predominantly have grazing system. Two countries with a similar climate and production system (grazing vs. non-grazing) are expected to be more correlated with each other than two countries with different climate or production system. If estimates are higher than the maximum (or lower than the minimum) value they are set to the maximum (or minimum) value. In addition, estimates are regressed towards a mean correlation within groups, the regression depending on the number of common bulls. Trait specific parameters are given below.
3. For breeds other than Holstein, and for some traits (production and udder health), estimates are combined with genetic correlations for Holstein. The approach to follow is similar to the one for Red Dairy Cattle conformation.
4. The two values (i.e. results from the preceding steps and the previously used correlations) are combined into a weighted average to avoid large changes in correlations between consecutive test runs. If the national evaluations for two countries have not changed, then the genetic correlation between these two countries is not expected to change much. However, if one of the countries introduced changes in their national evaluations, the genetic correlation between two countries may change. An increase in number of common bulls is expected to yield a more precise estimate of the genetic correlation, and more weight is given to the current estimate. This is done by increasing the weight on the current estimate proportionally to the increase in number of common bulls.

   	Current estimate	Previously used correlation
   No changes	1	3
   Minor change in at least one country (e.g., data edit, pedigree improvement)	1	1
   Major change in at least one country (e.g., new model or parameters)	1	0

5. Finally, the updated co)variance matrix is bended, using the bending procedure described by Jorjani et al. (2003).

Trait specific parameters:

Production

Minimum size of phantom parent groups: 30

Grouping of countries:

1. Australia, Ireland, New Zealand (grazing)
2. Israel (climate)
3. Other

Windows:

• Correlation between countries belonging to the same group: 0.85 – 0.98
• Correlation between countries belonging to different groups: 0.75 – 0.90

Regression:

r = (CBij · rGij + 10 · µij) /CBij + 10

where CBij is the number of common bulls between country i and j, rGij the genetic correlation between country i and j, and μij is either 0.92 or 0.82, depending on whether countries i and j belong to the same or different groups, respectively.

Conformation

Minimum size of phantom parent groups: 30

No windows imposed.

No regression applied.

Holstein prior information used for Red Dairy Cattle only.

Udder health

Minimum size of phantom parent groups: 30

Grouping of countries:

1. Somatic Cells (SCS): Australia, Ireland, New Zealand (grazing)
2. Somatic Cells (SCS): Israel (climate)
3. Somatic Cells (SCS): Other
4. Mastitis (MAS): Nordic countries, The Netherlands, Norway

Windows:

• Correlation between countries belonging to the same group (SCS): 0.85 – 0.98
• Correlation between countries belonging to the same group (MAS): 0.55 – 0.98
• Correlation between countries belonging to different groups (SCS): 0.75 – 0.90
• Correlation between countries belonging to different groups and traits: 0.35 – 0.85

Regression:

r = (CBij · rGij + 10 · µij) /CBij + 10

where CBij is the number of common bulls between country i and j, rGij the genetic correlation between country i and j, and μij is:

• 0.92 if countries i and j belong to the same group (SCS)
• 0.90 if countries i and j belong to the same group (MAS)
• 0.82 if countries i and j belong to different groups (SCS)
• 0.68 if countries i and j belong to different groups and traits

Longevity

Minimum size of phantom parent groups: 30

Grouping of countries:

1. All

Windows:

• Correlation between countries belonging to the same group: 0.30 – 0.98

No regression applied.

Calving

Minimum size of phantom parent groups: 30

Grouping of countries: DCE

1. Australia (grazing)
2. Other

MCE

1. All

DSB

1. Australia (grazing)
2. Countries with DSB information
3. Countries with DCE information

MSB

1. Countries with MSB information
2. Countries with MCE information

DCE

• Correlation between countries belonging to the same group: 0.60 – 0.98
• Correlation between countries belonging to different groups: 0.50 – 0.90

MCE

• Correlation between countries belonging to the same group: 0.55 – 0.98

DSB

• Correlation between countries belonging to the same group: 0.60 – 0.98
• Correlation between countries belonging to 1 and 2: 0.35 – 0.90
• Correlation between countries belonging to 1 and 3: 0.50 – 0.90
• Correlation between countries belonging to 2 and 3: 0.45 – 0.90

MSB

• Correlation between countries belonging to the same group: 0.55 – 0.98
• Correlation between countries belonging to the different groups: 0.40 – 0.90

Regression:

r = (CBij · rGij + 10 · µij) /CBij + 10

where CBij is the number of common bulls between country i and j, rGij the genetic correlation between country i and j, and μij is:

DCE

• Correlation between countries belonging to the same group: 0.80
• Correlation between countries belonging to different groups: 0.75

MCE

• Correlation between countries belonging to the same group: 0.75

DSB

• Correlation between countries belonging to the same group: 0.80
• Correlation between countries belonging to 1 and 2: 0.60
• Correlation between countries belonging to 1 and 3: 0.75
• Correlation between countries belonging to 2 and 3: 0.70

MSB

• Correlation between countries belonging to the same group: 0.75
• Correlation between countries belonging to the different groups: 0.65

Female Fertility Minimum size of phantom parent groups: 30

Regression

r = (CBij · rGij + 10 · µij) /CBij + 10

Where CBij is the number of common bulls between country i and j, rGij is the genetic correlation between country i and j, and μij is the mean correlation indicated above.

Female Fertility Trait Grouping and Correlation Windows

Fertility trait codes: interval calving-first insemination (CF), calving interval (CI), conception rate (CR), days open (DO), interval first insemination-conception (FC), interval first-last insemination (FL), number of inseminations (NI), non-return rate (NR), lactating cow's ability to start cycling (PM).

Workability Traits

Minimum size of phantom parent groups: 30

Grouping of countries:

1. Milking Speed (MSP): All
2. Temperament (TEM): All

Windows

• Correlation between countries belonging to the same group (MSP): 0.85 – 0.98
• Correlation between countries belonging to the same group (TEM): 0.70 – 0.95

Regression:

r = (CBij · rGij + 10 · µij) /CBij + 10

where CBij is the number of common bulls between country i and j, rGij the genetic correlation between country i and j, and μij is:

• 0.92 if countries i and j belong to the same group (MSP)
• 0.85 if countries i and j belong to the same group (TEM)