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The multiple-lactation autoregressive test-day (AR) model is the adopted model for the national genetic evaluation of dairy cattle in Portugal. Under this model, animals' permanent environment effects are assumed to follow a first-order autoregressive process over the long (auto-correlations between parities) and short (auto-correlations between test-days within lactation) terms. Given the relevance of genomic prediction in dairy cattle, it is essential to include marker information in national genetic evaluations. In this context, we aimed to evaluate the feasibility of applying the single-step genomic (G)BLUP to analyze milk yield using the AR model in Portuguese Holstein cattle. In total, 11,434,294 test-day records from the first 3 lactations collected between 1994 and 2017 and 1,071 genotyped bulls were used in this study. Rank correlations and differences in reliability among bulls were used to compare the performance of the traditional (A-AR) and single-step (H-AR) models. These 2 modeling approaches were also applied to reduced data sets with records truncated after 2012 (deleting daughters of tested bulls) to evaluate the predictive ability of the H-AR. Validation scenarios were proposed, taking into account young and proven bulls. Average EBV reliabilities, empirical reliabilities, and genetic trends predicted from the complete and reduced data sets were used to validate the genomic evaluation. Average EBV reliabilities for H-AR (A-AR) using the complete data set were 0.52 (0.16) and 0.72 (0.62) for genotyped bulls with no daughters and bulls with 1 to 9 daughters, respectively. These results showed an increase in EBV reliabilities of 0.10 to 0.36 when genomic information was included, corresponding to a reduction of up to 43% in prediction error variance. Considering the 3 validation scenarios, the inclusion of genomic information improved the average EBV reliability in the reduced data set, which ranged, on average, from 0.16 to 0.26, indicating an increase in the predictive ability. Similarly, empirical reliability increased by up to 0.08 between validation tests. The H-AR outperformed A-AR in terms of genetic trends when unproven genotyped bulls were included. The results suggest that the single-step GBLUP AR model is feasible and may be applied to national Portuguese genetic evaluations for milk yield., (Copyright © 2019 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Daily milk yield over the course of the lactation follows a curvilinear pattern, so a suitable function is required to model this curve. In this study, 7 functions (Wood, Wilmink, Ali and Schaeffer, cubic splines, and 3 Legendre polynomials) were used to model the lactation curve at the phenotypic level, using both daily observations and data from commonly used recording schemes. The number of observations per lactation varied from 4 to 11. Several criteria based on the analysis of the real error were used to compare models. The performance of models showed few discrepancies in the comparison criteria when daily or 4-weekly (with first test at days in milk 8) data by lactation were used. The performance of the Wood, Wilmink, and Ali and Schaeffer models were highly affected by the reduction of the sample dimension. The results of this work support the idea that the performance of these models depends on the sample properties but also shows considerable variation within the sampling groups.