Estimation of genetic correlations among countries in international dairy sire evaluations with structural models

The increase in the number of participating countries and the lack of genetic ties between some countries has lead to statistical and computational difficulties in estimating the genetic (co)variance matrix needed for international sire evaluation of milk yield and other traits. Structural models have been proposed to reduce the number of parameters to estimate by exploiting patterns in the genetic correlation matrix. Genetic correlations between countries are described as a simple function of unspecified country characteristics that can be mapped in a space of limited dimensions. Two link functions equal to the exponential of minus the Euclidian distance between the coordinates of two countries and the exponential of minus the square of this Euclidian distance were used for the study on international simulated and field data. On simulated data, it was shown that structural models might allow an easier estimation of genetic correlations close to the border of the parameter space. This is not always possible with an unstructured model. On milk yield data, genetic correlations obtained from 22 countries for structural models based on 2 and 7 dimensions, respectively, were analyzed. Only a structural model with a large number of axes gave reasonable estimates of genetic correlations compared with correlations obtained for an unstructured model: 76.7% of correlations deviated by less than 0.030. Such a model reduces the number of parameters from 231 genetic correlations to 126 coordinates. On foot angle data, large deviations were observed between genetic correlations estimated with an unstructured model and correlations estimated with a structural model, regardless of the number of axes taken into account.