Efficient implementation of multitrait random regression test-day models with external information for dairy cattle genomic evaluations

Random regression models (RRM) combined with single-step genomic best linear unbiased prediction (ssGBLUP) are widely used for genomic evaluations in dairy cattle. This study aimed to efficiently implement RRM with ssGBLUP for national dairy cattle evaluations. Data from the Czech Holstein population were used, including 30 million test-day records for milk yield across 3 lactations. The pedigree included 2.5 million animals, of which 54,000 were genotyped. To enhance model convergence, we used a reduced number of genetic groups by combining groups with few records, and treated them as random. Additionally, the algorithm for proven and young (APY) was applied. Mixed model equations were solved by the preconditioned conjugate gradient method using iteration on data. External information from Interbull was included as deregressed proofs (DRP) of cumulative 305-d multicountry evaluation approach (MACE) breeding values and weighted by effective record contributions (ERC). Reliabilities of 305-d GEBV combined the reliability of the average of cumulative 305-d GEBV across the 3 lactations without genomic information and the reliability from a genomic BLUP model in terms of ERC. The linear regression method was used to validate EBV and GEBV of average 305-d milk yield across lactations. For that, 2 datasets for test-day records from the first 3 lactations were used: a complete dataset containing records up to 2023, and a partial dataset cut off in 2018. All models successfully achieved convergence. The validation revealed bias close to zero, with dispersion ranging from 0.97 to 0.99, correlation between complete and partial (G)EBV between 0.95 and 0.98, and validation reliability ranging from 0.77 to 0.94. Applying APY resulted in a 10-fold increase in speed compared with ssGBLUP. The correlation between MACE reliabilities and national reliabilities increased by 3% and 2% from pre-integration to post-integration for BLUP and ssGBLUP, respectively. Our results demonstrate that the application of ssGBLUP to a multitrait RRM while integrating external MACE information is feasible and results in a highly efficient genomic evaluation system, with GEBV with desirable validation statistics.