Application of a structural model to estimate genetic correlations between countries

One of the major problems of MACE is the computation of the genetic correlations between countries. An advantage of structural models is the option to reduce the number of parameters to estimate. The structural model used here defines the genetic correlations between 2 countries as an exponential function of the Euclidian distance between them. In this structural model, (k+1) countries can be represented in a k-dimensional space. The reduction of the number of dimensions of the space allows to reduce the number of parameters. For example, in a 3-dimensional space only 72 coordinates need to be estimated to compute 325 genetic correlations between 26 countries. This structural model was successfully tested on simulated data, and on the current genetic correlations matrix used by INTERBULL. The first aim of the present study was to compare results of the structural model used on international data with results of an "unstructured" model. The second . aim was to study the possible use of the coordinates of different structural models related to the same space, to calculate directly genetic correlations, without having to estimate them. The third aim was to analyze the influence of the choice of the axes countries. Deregressed national breeding values used for Holstein milk yield international evaluation of February 2003 were analyzed. Several subsets of countries were considered. The structural model and a classical model were applied to estimate the genetic correlations between countries, using an AI-REML algorithm implemented in the AIREMLF90 program. Countries chosen to define axes in the structural model were based on the results from a previous study that applied a cluster analysis: The Netherlands as centre of the space, USA to define the I" axis, New Zealand for the 2 axis and Hungary for the 3 axis. Genetic correlations estimated with the structural model were very close to those estimated with the classical model. Larger differences (e.g., 0.06 for the correlation between Denmark and New Zealand) concerned the least connected of the countries considered. The standard errors of genetic correlations ranged from 0.006 to 0.058 depending on the amount of genetic ties. The -210gL was slightly higher for the structural model than for the classical model, but Bayesian information criterion favoured the structural model because of the lower number of parameters. Combining the coordinates obtained from different structural models related to the same space gave similar genetic correlations (differences were lower than the standard errors) and similar -210gL compared to the joint analyses of the countries. By this way, the number of runs needed to estimate all the genetic correlations can be reduced drastically. The change of some of the axes countries shows that the estimated genetic correlations were more precise when the volume defined by the axes countries was large. Determination of the optimal number of countries to define the axes and the choice of the axes countries needs to be investigated further, using e.g. information criteria and volume of the space defined by axes countries.