Integration of external estimated breeding values and associated reliabilities using correlations among traits and effects.

Based on a Bayesian view of linear mixed models, several studies showed the possibilities to integrate estimated breeding values (EBV) and associated reliabilities (REL) provided by genetic evaluations performed outside a given evaluation system into this genetic evaluation. Hereafter, the term "internal" refers to this given genetic evaluation system, and the term "external" refers to all other genetic evaluations performed outside the internal evaluation system. Bayesian approaches integrate external information (i.e., external EBV and associated REL) by altering both the mean and (co)variance of the prior distributions of the additive genetic effects based on the knowledge of this external information. Extensions of the Bayesian approaches to multivariate settings are interesting because external information expressed on other scales, measurement units, or trait definitions, or associated with different heritabilities and genetic parameters than the internal traits, could be integrated into a multivariate genetic evaluation without the need to convert external information to the internal traits. Therefore, the aim of this study was to test the integration of external EBV and associated REL, expressed on a 305-d basis and genetically correlated with a trait of interest, into a multivariate genetic evaluation using a random regression test-day model for the trait of interest. The approach we used was a multivariate Bayesian approach. Results showed that the integration of external information led to a genetic evaluation for the trait of interest for, at least, animals associated with external information, as accurate as a bivariate evaluation including all available phenotypic information. In conclusion, the multivariate Bayesian approaches have the potential to integrate external information correlated with the internal phenotypic traits, and potentially to the different random regressions, into a multivariate genetic evaluation. This allows the use of different scales, heritabilities, variance components, measurement units, or trait definitions for external and internal traits. However, one possible issue for implementing multivariate Bayesian approaches could be the availability or estimation of genetic correlations between external and internal traits.