Conversion of breeding values for milk from foreign populations

An estimate of a transmitting ability for milk in population or Country 1 (T^A₂)might be converted to an estimate for Country or Population 2 (T^A₂) by the equation proposed by the International Dairy Federation (IDF): (T^A₂)=a+b (TA₂). In this paper the derivation of the IDF equation is given and three procedures to estimate the equation parameters, a and b, are discussed as alternatives for the least-squares procedure, which yields biased and inconsistent estimates in this case. In the first procedure, parameters are estimated from a functional relationship model, where sire contributions are considered to be fixed. The second procedure is a linear regression with bias correction. In the third procedure, the parameters for the IDF equation are computed from estimates of population means and sire variances. When these population parameters are repeatedly estimated and the genetic correlation between the traits in both countries/populations is unity, the equation parameters are easily obtained by Procedure 3. When a and b have to be estimated from a sample of sires used in both countries, Procedure 1 is recommended from a mathematical viewpoint.