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.