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Objective: Considering the importance of dairy farming and the negative effects of heat stress, more tolerant genotypes need to be identified. The objective of this study was to investigate the effect of heat stress via temperature-humidity index (THI) and diurnal temperature variation (DTV) in the genetic evaluations for daily milk yield of Holstein dairy cattle, using random regression models. Methods: The data comprised 94,549 test-day records of 11,294 first parity Holstein cows from Brazil, collected from 1997 to 2013, and bioclimatic data (THI and DTV) from 18 weather stations. Least square linear regression models were used to determine the THI and DTV thresholds for milk yield losses caused by heat stress. In addition to the standard model (SM, without bioclimatic variables), THI and DTV were combined in various ways and tested for different days, totaling 41 models. Results: The THI and DTV thresholds for milk yield losses was THI = 74 (-0.106 kg/d/THI) and DTV = 13 (-0.045 kg/d/DTV). The model that included THI and DTV as fixed effects, considering the two-day average, presented better fit (-2logL, Akaike information criterion, and Bayesian information criterion). The estimated breeding values (EBVs) and the reliabilities of the EBVs improved when using this model. Conclusion: Sires are re-ranking when heat stress indicators are included in the model. Genetic evaluation using the mean of two days of THI and DTV as fixed effect, improved EBVs and EBVs reliability. [ABSTRACT FROM AUTHOR]

• Pioneer proposal to improve the modeling of fixed regression, including the heat stress level. • The results have potential economic impact in dairy chain. • Preliminary step in developing weighted genetic evaluations for heat stress. To date, no study has tested the inclusion of bioclimatic variables or heat stress indicators in the formation of fixed regression for the genetic evaluation of dairy cattle. The objective of the present study was to investigate the inclusion of heat stress level in modeling of fixed regression in random regression models to predict population response and individual genetic components for fat and protein yield in test-day, using data from Holstein cattle in tropical environment. The data comprised 52,012 test-day fat and protein records of 9,858 first-parity Holstein cows from Brazil, collected from 1997 to 2013, and bioclimatic data (temperature-humidity index – THI, and diurnal temperature variation – DTV) from 18 weather stations. Least square linear regression models were used to determine THI and DTV thresholds for fat and protein yield losses caused by heat stress. In addition to the standard model (SM, without bioclimatic variables), THI and DTV were analyzed as fixed effects (considering the average of two days before the test-day control), and heat stress level was considered in formation of fixed regression, totaling three models for each trait. THI and DTV thresholds for fat and protein losses was THI = 74 (−0.030 kg/day/ THI) and DTV = 16 (−0.020 kg/day/ DTV), for both traits. The model that included THI and DTV as fixed effects, and used heat stress level in formation of fixed regression (fixed curve), presented a better fit (Akaike's information criterion, Schwarz's Bayesian information criterion, and residual variance). Estimated breeding values (EBV) are improved when using this model, and there is an increase in reliability of estimates. There is an important reranking of sires when heat stress indicators are included in the model to evaluate fat and protein yield in test-day. The increase in reliability of EBV by including heat stress level in the fixed regression shows a better fit of model to the data. It is possible to conclude that the inclusion of heat stress level in the formation of fixed regression is an important factor to be considered in dairy cattle reared in tropical regions to minimize environmental effects and optimize the process of evaluation and genetic selection. [ABSTRACT FROM AUTHOR]

• Innovative proposal at national level in genetic evaluation of dairy cattle. • Somatic cell score is an early indicator of heat stress. • Current animal selection in dairy cattle does not consider heat stress. • The results have potential economic impact in dairy chain. Considering the importance of dairy farming and negative effects of heat stress, the objective of this study was to investigate the effect of heat stress via temperature-humidity index (THI) and diurnal temperature variation (DTV) for somatic cell score (SCS) of Holstein dairy cattle, using random regression models. Data were a total of 52,012 test-day records for SCS of 9,765 first parity Holstein cows from Brazil, collected from 1997 to 2013, along with weather records (THI and DTV) from 18 weather stations. Least square linear regression models were used to determine THI and DTV thresholds for SCS increase caused by heat stress. In addition to the standard model (SM; without bioclimatic variables), THI and DTV were combined in various ways and tested for different days, totaling 21 models. Thresholds of THI and DTV for SCS increase was 70 (0.09 score unit/THI) and 9 (0.03 score unit/DTV), respectively. The model that included THI and DTV as fixed effects, considering the two days average, presented better fit (AIC, BIC and -2logL). Estimated breeding values (EBVs) and reliability of EBVs improved when using this model. Changes on SCS may be an early indicator of heat stress in Holstein cattle reared in tropical conditions. The sires are re-ranked when bioclimatic variables are included in the model. More significant reclassifications of sires were observed when we increased selection pressure. This study provides strong evidence of a genotype by environment interaction on SCS. Genetic evaluation using average of two days of THI and DTV as fixed effects, improves EBVs and reliability of EBVs. [ABSTRACT FROM AUTHOR]