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Genetic correlation estimation procedure

Estimation of genetic correlations among countries takes place in test-runs 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 usually 7-8 countries are considered. Countries are grouped into triplets (sometimes quadruplets) according to their number of common bulls and a per analysis correlations are estimated between the countries belonging to two triplets plus a fixed set of countries, varying from trait to trait but always including USA, which are used as linked providers. 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 are considered:
   1. The correlation estimated from step 1
   2. The correlation used in the previous run.
   3. Magnitude of changes tested
   4. Correlations from Holsteins (only for non-Holstein breeds)
2. Estimates are required to fall within certain windows. For milk production traits, for example, 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 lower than the minimum window's value, they are set equal to the minimum window's value specified for that given group. In addition, estimates are regressed towards a mean correlation within groups, the regression depending on the number of common bulls. Trait specific windows' parameters are given below.
3. For breeds other than Holstein, estimates are combined with genetic correlations for Holstein and weighted by both the number of common bulls between the two countries and the prior (HOL) common bulls. If a specific country is not among the HOL evaluation, the prior correlations used are equal to the minimum value of all non-missing countries.
4. The results from the preceding step and the previously used correlations are combined into a weighted average to avoid large changes in correlations between consecutive test runs, weighted by the number of common bulls. 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 has 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.

• Type of Changes Tested	Weight on Previous Correlations
  No changes	2
  Minor change in at least one country (e.g., data edit, pedigree improvement)	1
  Major change in at least one country (e.g., new model or parameters)	0

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

Trait specific windows' parameters:

(Symmetrical matrices, only values for the upper triangular matrix are reported)

Production

Minimum size of phantom parent groups: 30

Grouping of countries:

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

* Only one country in the group, correlations not available

Windows:

MIL

FAT

PRO

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 the median which vary depending on whether countries i and j belong to the same or different groups, respectively.

Conformation

Minimum size of phantom parent groups: 30

Windows:

OCS

1. Other countries
2. AUS, NZL, IRL

OUS

1. Other countries
2. NZL, AUS, IRL

OFL

1. Other countries
2. AUS, IRL

Other Conformation Traits

1. All Countries

BSW additional traits

1. All Countries

Udder health

Minimum size of phantom parent groups: 30

Windows:

SCS:

1. Somatic Cells (SCS): Other Countries
2. Somatic Cells (SCS): Israel (climate)*
3. Somatic Cells (SCS): Australia, Ireland, New Zealand (grazing)

*Only one country in the group, correlations not available

MAS:

1. Somatic Cells (SCS): Other Countries
2. Somatic Cells (SCS): Israel (climate)*
3. Somatic Cells (SCS): New Zealand (grazing)*
4. Mastitis (MAS): country using real MAS data

*Only one country in the group, correlations not available

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 the median which vary depending on whether countries i and j belong to the same or different groups, respectively.

Longevity

Minimum size of phantom parent groups: 30

Grouping of countries:

1. All Countries

Windows:

No regression applied.

Calving

Minimum size of phantom parent groups: 30

Windows:

• DCE

• Other
• Australia (grazing)*

*Only one country in the group, correlations not available

MCE

1. All Countries

DSB

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

*Only one country in the group, correlations not available

MSB

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

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 the median which vary depending on whether countries i and j belong to the same or different groups, respectively.

Female Fertility
Minimum size of phantom parent groups: 30

Windows:

HCO

1. Countries providing NR
2. Countries providing CR

CRC

1. Countries providing CI/DO
2. Countries providing CF
3. Countries providing PM*

* Only one country in the group, correlations not available

CC1

1. Countries providing NR
2. Countries providing CR

CC2

1. Countries providing CI/DO
2. Countries providing FC/FL
3. Countries providing NR

INT

1. Countries providing CI/DO
2. Countries providing RC*

*Only one country in the group, correlations not available

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 median which vary depending on whether countries i and j belong to the same or different groups, respectively.

Workability Traits

Minimum size of phantom parent groups: 30

Windows:

MSP

1. All Countries

TEM

1. All Countries

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 the median which vary depending on whether countries i and j belong to the same or different groups, respectively.

SNP Training for Clinical Mastitis

Minimum size of phantom parent groups: 30

Windows:

CMA

1. All Countries

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 the median which vary depending on whether countries i and j belong to the same or different groups, respectively.