Principal components and factorial approaches for estimating genetic correlations in international sire evaluation.

The increasing number of participating countries and the lack of genetic links among some of them lead to statistical and computational difficulties in estimating the genetic (co)variance matrix needed for international sire evaluation of milk yield. Reparameterization using principal components or factorial approaches is proposed to exploit patterns in the genetic correlation matrix in order to reduce the number of parameters to be estimated without much loss of information. A 2-step approach was used. First, the genetic matrix between 8 or 9 "base" countries was used to determine a reduced number of principal components or factors. Then, the contributions of the remaining countries to these principal components or factors were computed. The resulting genetic correlations for the 18 countries were compared with the "reference" genetic correlations obtained with a classical model. The impact of using reparameterized genetic correlation matrices on breeding value prediction was investigated for both approaches. A better agreement between predicted breeding values and stability of their rankings was found when an approximate factor analysis was used, whatever the number of factors considered. The estimation of genetic correlations among 18 countries using an approximate factorial approach with 5 factors taken into account led to a reduction of the number of parameters to estimate from 171 to 80. The average absolute deviation of the correlations estimated with an approximate factorial approach from the "reference" genetic correlations was 0.014, which is considered very satisfactory in light of the computational ease.