Abstract
Since many countries use multiple lactation random regression test day models in national evaluations for milk production traits, a random regression multiple across-country evaluation (MACE) model permitting a variable number of correlated traits per country should be used in international dairy evaluations. In order to reduce the number of within country traits for international comparison, three different MACE models were implemented based on German daughter yield deviation data and compared to the random regression MACE. The multiple lactation MACE model analysed daughter yield deviations on a lactation basis reducing the rank from nine random regression coefficients to three lactations. The lactation breeding values were very accurate for old bulls, but not for the youngest bulls with daughters with short lactations. The other two models applied principal component analysis as the dimension reduction technique: one based on eigenvalues of a genetic correlation matrix and the other on eigenvalues of a combined lactation matrix. The first one showed that German data can be transformed from nine traits to five eigenfunctions without losing much accuracy in any of the estimated random regression coefficients. The second one allowed performing rank reductions to three eigenfunctions without having the problem of young bulls with daughters with short lactations.
Highlights
The multiple across country evaluation (MACE) [17] methodology is currently used for international dairy bull comparisons
Fact that only a single EBV per bull is permitted for each country in international genetic evaluation, the current MACE has a large number of equations, since each evaluated sire will, conceptually, have a breeding value for all traits, i.e. for all countries, it might have daughters only in one
The aim of this paper was to explore different methods to reduce the rank of the German regression test day model (RRTDM) in order to make multiple trait MACE (MT-MACE) applicable for joint French-German evaluation and/or international genetic evaluation involving a higher number of countries
Summary
The multiple across country evaluation (MACE) [17] methodology is currently used for international dairy bull comparisons. Restrictions on estimates are imposed only to ensure that estimates were within the parameter space, i.e. that all variances and conditional variances are positive, that all correlation estimates are in the range of –1 to +1, and that all partial correlations are consistent with each other [13]. In statistical terms, this is equivalent to the requirement that the estimated covariance matrix is positive semidefinite, i.e. that none of its eigenvalues is negative
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