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.

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We evaluated the inclusion of information on genetic relationship into the analysis of crude protein requirement in diets for pigs of Brazilian Piau breed, using Bayesian inference.The animals were assigned to treatments in a completely randomized design in factorial scheme 4 × 2 (crude protein levels × sex) with 12 repetitions per treatment. The evaluations were carried out in the initial, growing and finishing phases, and after slaughter. The traits evaluated were feed conversion (FC), backfat thickness (BF), daily weight gain (DWG), daily feed intake (DFI) and some carcass cuts. Three models were considered to evaluate the inclusion of information on genetic relationship into the analysis: Model I, a simple linear model; Model II, the same effects of Model I with addition of the independent random effect of animal; and Model III, the same effects of Model II, but including the genetic relationship between the animals. Model III presented the best fit and was considered for later inferences. Crude protein (CP) levels did not significantly influence any of the evaluated traits. The effect of sex was significant only for the growing phase, while its interaction with protein levels presented an opposite result for all evaluated traits. Additionally, CP levels of 10.2 %, 9.6 % and 9.0 % can be used in diets for pigs of Brazilian Piau breed in the initial, growing and finishing phases, respectively.

Over the years, increasing body weight has been the main selection objective of broiler breeding programs. The selection resulted in birds with higher growth rates and feed efficiency, while production costs were minimized (Alnahhas et al., 2016). However, changes in consumer preferences associated with new industries demands have increased the relevance of meat quality traits in the modern broiler market (Alnahhas et al., 2014). The inclusion

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Reproductive efficiency is major determinant of the dairy herd profitability. Thus, reproductive traits have been widely used as selection objectives in the current dairy cattle breeding programs. We aimed to evaluate strategies to model days open (DO), calving interval (CI) and daughter pregnancy rate (DPR) in Brazilian Holstein cattle. These reproductive traits were analysed by the autoregressive (AR) model and compared with classical repeatability (REP) model using 127,280, 173,092 and 127,280 phenotypic records, respectively. The first three calving orders of cows from 1,469 Holstein herds were used here. The AR model reported lower values for Akaike Information Criteria and Mean Square Errors, as well as larger model probabilities, for all evaluated traits. Similarly, larger additive genetic and lower residual variances were estimated from AR model. Heritability and repeatability estimates were similar for both models. Heritabilities for DO, CI and DPR were 0.04, 0.07 and 0.04; and 0.05, 0.06 and 0.04 for AR and REP models, respectively. Individual EBV reliabilities estimated from AR for DO, CI and DPR were, in average, 0.29, 0.30 and 0.29 units higher than those obtained from REP model. Rank correlation between EBVs obtained from AR and REP models considering the top 10 bulls ranged from 0.72 to 0.76; and increased from 0.98 to 0.99 for the top 100 bulls. The percentage of coincidence between selected bulls from both methods increased over the number of bulls included in the top groups. Overall, the results of model‐fitting criteria, genetic parameters estimates and EBV predictions were favourable to the AR model, indicating that it may be applied for genetic evaluation of longitudinal reproductive traits in Brazilian Holstein cattle.