Multiple-trait genetic evaluation for milk, fat and protein yields and persistency

Single-trait animal-models (ST-AM) [e.9., DucRocQ, 1990; VANRADEN and WIGGANS, l99l; LERoY et al., 1993f are currently being implemented all over the world for genetic evaluation of milk, fat and protein lactation yields. But such evaluations are only suboptimal as there are at least three reasons for the use of multiple-trait animal models (MTAM). Firs! such methods improve t}re precision of the evaluations as enor variances (PEV) of predictions are reduced [Scnnenren, 1984; THoMpsoN and MEvER, 1986], therefore gain from selection would be enhanced. Secondly, an MT-AM would reduce selection bias as selection for yield is done in dairy cattle on milk, fat and protein together but genetic evafuations are still single-tait IPoLLAK et al., 1984]. MT-AM can be adapted for missing values, therefore the fact that one or two traits are missing can be taken into account. Even if the advantages of multiple-trait models for milk, fat and protein lactation yields are only limited, such methods enable the introduction of other traits in the models, as e.g., somatic cell scores, productive life and persistency of lactation yields. The major inconveniences of MT-AM are the prograrrming and solving difticulties due to more complicated matrix structures. But recent advances around canonical transformation make new developments possible. SurrH and LrN proposed in 1990 multiple-diagonalization of (co)variance matrices. DucRoce and BEsBEs [993] found an easy approach to missing values. Approximate reliability estimation for such methods were described by GeNclen and MrszrAL [995b]. DucRoce and Csapurs [995] and Gerclen and MrszrAL [995b] proposed two different approaches to solve mixed model equations with different models per trait.