Tropical and sub-tropical climates are characterized by high temperature and humidity, during at least part of the year. Consequently, heat stress is common in Holstein cattle and productive and reproductive losses are frequent. Our objectives were as follows: (1) to quantify losses in production and quality of milk due to heat stress; (2) to estimate genetic correlations within and between milk yield (MY) and milk quality traits; and (3) to evaluate the trends of genetic components of tolerance to heat stress in multiple lactations of Brazilian Holstein cows. Thus, nine analyses using two-trait random regression animal models were carried out to estimate variance components and genetic parameters over temperature–humidity index (THI) values for MY and milk quality traits (three lactations: MY×fat percentage (F%), MY×protein percentage (P%) and MY×somatic cell score (SCS)) of Brazilian Holstein cattle. It was demonstrated that the effects of heat stress can be harmful for traits related to milk production and milk quality of Holstein cattle even though most herds were maintained in a modified environment, for example, with fans and sprinklers. For MY, the effect of heat stress was more detrimental in advanced lactations (−0.22 to −0.52 kg/day per increase of 1 THI unit). In general, the mean heritability estimates were higher for lower THI values and longer days in milk for all traits. In contrast, the heritability estimates for SCS increased with increasing THI values in the second and third lactation. For each trait studied, lower genetic correlations (different from unity) were observed between opposite extremes of THI (THI 47 v. THI 80) and in advanced lactations. The genetic correlations between MY and milk quality trait varied across the THI scale and lactations. The genotype×environment interaction due to heat stress was more important for MY and SCS, particularly in advanced lactations, and can affect the genetic relationship between MY and milk quality traits. Selection for higher MY, F% or P% may result in a poor response of the animals to heat stress, as a genetic antagonism was observed between the general production level and specific ability to respond to heat stress for these traits. Genetic trends confirm the adverse responses in the genetic components of heat stress over the years for milk production and quality. Consequently, the selection of Holstein cattle raised in modified environments in both tropical and sub-tropical regions should take into consideration the genetic variation in heat stress.

In an attempt to determine the possible detrimental effects of continuous selection for milk yield on the genetic tolerance of Zebu cattle to heat stress, genetic parameters and trends of the response to heat stress for 86,950 test-day (TD) milk yield records from 14,670 first lactations of purebred dairy Gir cows were estimated. A random regression model with regression on days in milk (DIM) and temperature-humidity index (THI) values was applied to the data. The most detrimental effect of THI on milk yield was observed in the stage of lactation with higher milk production, DIM 61 to 120 (-0.099kg/d per THI). Although modest variations were observed for the THI scale, a reduction in additive genetic variance as well as in permanent environmental and residual variance was observed with increasing THI values. The heritability estimates showed a slight increase with increasing THI values for any DIM. The correlations between additive genetic effects across the THI scale showed that, for most of the THI values, genotype by environment interactions due to heat stress were less important for the ranking of bulls. However, for extreme THI values, this type of genotype by environment interaction may lead to an important error in selection. As a result of the selection for milk yield practiced in the dairy Gir population for 3 decades, the genetic trend of cumulative milk yield was significantly positive for production in both high (51.81kg/yr) and low THI values (78.48kg/yr). However, the difference between the breeding values of animals at high and low THI may be considered alarming (355kg in 2011). The genetic trends observed for the regression coefficients related to general production level (intercept of the reaction norm) and specific ability to respond to heat stress (slope of the reaction norm) indicate that the dairy Gir population is heading toward a higher production level at the expense of lower tolerance to heat stress. These trends reflect the genetic antagonism between production and tolerance to heat stress demonstrated by the negative genetic correlation between these components (-0.23). Monitoring trends of the genetic component of heat stress would be a reasonable measure to avoid deterioration in one of the main traits of Zebu cattle (i.e., high tolerance to heat stress). On the basis of current genetic trends, the need for future genetic evaluation of dairy Zebu animals for tolerance to heat stress cannot be ruled out.

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records.