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.