Autoregressive (AR) and random regression (RR) models were fitted to test‐day records from the first three lactations of Brazilian Holstein cattle with the objective of comparing their efficiency for national genetic evaluations. The data comprised 4,142,740 records of milk yield (MY) and somatic cell score (SCS) from 274,335 cows belonging to 2,322 herds. Although heritabilities were similar between models and traits, additive genetic variance estimates using AR were 7.0 (MY) and 22.2% (SCS) higher than those obtained from RR model. On the other hand, residual variances were lower in both traits when estimated through AR model. The rank correlation between EBV obtained from AR and RR models was 0.96 and 0.94 (MY) and 0.97 and 0.95 (SCS), respectively, for bulls (with 10 or more daughters) and cows. Estimated annual genetic gains for bulls (cows) obtained using AR were 46.11 (49.50) kg for MY and −0.019 (−0.025) score for SCS; whereas using RR these values were 47.70 (55.56) kg and −0.022 (−0.028) score. Akaike information criterion was lower for AR in both traits. Although AR model is more parsimonious, RR model assumes genetic correlations different from the unity within and across lactations. Thus, when these correlations are relatively high, these models tend to yield to similar predictions; otherwise, they will differ more and RR model would be theoretically sounder.
We investigated the efficiency of the autoregressive repeatability model (AR) for genetic evaluation of longitudinal reproductive traits in Portuguese Holstein cattle and compared the results with those from the conventional repeatability model (REP). The data set comprised records taken during the first four calving orders, corresponding to a total of 416, 766, 872 and 766 thousand records for interval between calving to first service, days open, calving interval and daughter pregnancy rate, respectively. Both models included fixed (month and age classes associated to each calving order) and random (herd-year-season, animal and permanent environmental) effects. For AR model, a first-order autoregressive (co)variance structure was fitted for the herd-year-season and permanent environmental effects. The AR outperformed the REP model, with lower Akaike Information Criteria, lower Mean Square Error and Akaike Weights close to unity. Rank correlations between estimated breeding values (EBV) with AR and REP models ranged from 0.95 to 0.97 for all studied reproductive traits, when the total bulls were considered. When considering only the top-100 selected bulls, the rank correlation ranged from 0.72 to 0.88. These results indicate that the re-ranking observed at the top level will provide more opportunities for selecting the best bulls. The EBV reliabilities provided by AR model was larger for all traits, but the magnitudes of the annual genetic progress were similar between two models. Overall, the proposed AR model was suitable for genetic evaluations of longitudinal reproductive traits in dairy cattle, outperforming the REP model.
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