Production data obtained from AIPL USDA included 119,337 first-parity, test-day records of 15,012 Holsteins from 134 Georgia farms collected in 1990 to 1997. Weather information was obtained from the Georgia Automated Environmental Monitoring Network and included daily minimum, average, and maximum temperatures and humidity for 21 stations throughout the state. Each test-day record was augmented with weather information from the closest weather station. Analyses were based on models that included effects of herd-year-season, age, test day, milking frequency, and several types of heat and humidity. The best model used a temperature-humidity index. With this model, the average test-day yield for milk was about 26.3 kg for a temperature-humidity index <72 and decreased at about 0.2 kg per unit increase in the temperature-humidity index for a temperature-humidity index > or =72. For fat and protein, the test yield was 0.92 and 0.85 kg at a temperature-humidity index <72, respectively, and declined at a rate of 0.012 and 0.009 kg per degree of the temperature-humidity index, respectively. The temperature-humidity index calculated with the available weather information can be used to account for the effect of heat stress on production.

Our data included 119,205 first-parity, test-day records from 15,002 Holsteins in 134 Georgia farms with temperature and humidity data from 21 weather stations throughout Georgia. The test-day model included the effects of herd test date, days-in-milk (DIM) classes, age, milking frequency, general additive effect, random regression on the heat-humidity index for heat-tolerance additive effect, general permanent environment, and the random regression on the heat-humidity index for a permanent environment. The general effects, which corresponded to effects in the current repeatability models, were assumed to be correlated with the heat-tolerance effects. Variance components were estimated by REML. For heat-humidity indices below 72, heritability for milk was 0.17, and additive variance of heat tolerance was 0. For a heat-humidity index of 86 (which would correspond to temperatures of 36 degrees C at 50% humidity), the additive variance of heat tolerance was as high as for general effect, and the genetic correlation between the two effects was -0.36. Results for fat and protein were similar. Current selection for production reduces heat tolerance. Joint selection for heat tolerance and production is possible.

The objective of this study was to examine the relationship between reproductive traits and heat stress. Nonreturn rate at 45 d (NR45) was analyzed in a fixed-effect model that included the temperature-humidity index (THI) from a nearby weather station as a measurement of heat stress. Data consisted of 150,200 first inseminations at first and later parities of 110,860 Holstein cows from 550 herds in Georgia, Tennessee, and Florida with weather information from 16 weather stations. THI on the day of the insemination, 2 d prior, 5 d prior, 5, 10, 20, and 30 d after insemination were studied as independent variables. The THI on the day of insemination showed the highest effect on NR45, followed by 2 d prior, 5 d prior, and 5 d after insemination, but no relationship was found with THI at 10, 20, and 30 d after insemination. NR45 showed a decrease of 0.005 per unit increase in THI on the day of insemination for THI >68. First and later parities presented similar thresholds but responded differently to an increase in THI, with NR45 being significantly lower and more susceptible to increases of THI in cows in their first parity than in later parities (0.008 vs. 0.005 decrease). Threshold for sensitivity to heat stress changed with the states, with Florida, Georgia, and Tennessee having thresholds of 70, 70, and 66, respectively. The decrease in NR45 per unit increase of THI was 0.007, 0.005, and 0.006 for Florida, Georgia, and Tennessee, respectively. With respect to only the Florida data, the final fixed-effect model used was NR45 = herd(year) + month(year) + month(year) + age(parity) + days in milk + 100d milk + THI + error. Animals with more than 150 d in milk (DIM) had a 0.16 lower NR45 than animals with less than 60 DIM at insemination. Lower milk-producing animals showed 0.08 higher NR45 than higher-producing animals. A difference of 0.10 in NR45 was observed between THI lower than 70 and THI 84. This variation in NR45 caused by THI changes is sufficient to merit further studies to examine genetic components of heat tolerance for this trait.

The genetic component in heat tolerance for nonreturn rate in Holsteins was estimated using an animal linear model augmented by a random regression on a temperature-humidity index (THI). Data consisted of 18,059 nonreturn rates at 45,60, and 90 d after insemination and 81,674 first-parity test-day milk yields from 78 herds in Florida. The THI on the day of insemination or test day was added to each record. Only first-insemination records were used. The model for nonreturn rate included the effects of herd-year-season, age, days in milk, milk yield, THI as a covariable, regular additive effect, and random regression on THI for heat-tolerance additive effect. With a single-trait model, heritability estimates for NR45, NR60, and NR90 at THI = 70 for first-lactation cows were 0.006, 0.014, and 0.053, respectively. Genetic correlation between regular NR90 and heat tolerance was -0.95. A bivariate analysis for NR90 and test-day milk production yielded a correlation between regular merit and heat tolerance for NR90 of -0.35, substantially lower than by the univariate model, indicating a bias in the univariate estimates caused by ignored selection. The regular genetic correlation between NR90 and milk yield was -0.41. Genetic correlation between heat tolerance for NR90 and heat tolerance for milk yield was -0.04, indicating the need to separate selection.

Model‐based accuracy, defined as the theoretical correlation between true and estimated breeding value, can be obtained for each individual as a function of its prediction error variance (PEV) and inbreeding coefficient F, in BLUP, GBLUP and SSGBLUP genetic evaluations. However, for computational convenience, inbreeding is often ignored in two places. First, in the computation of reliability = 1‐PEV/(1 + F). Second, in the set‐up, using Henderson's rules, of the inverse of the pedigree‐based relationship matrix A. Both approximations have an effect in the computation of model‐based accuracy and result in wrong values. In this work, first we present a reminder of the theory and extend it to SSGBLUP. Second, we quantify the error of ignoring inbreeding with real data in three scenarios: BLUP evaluation and SSGBLUP in Uruguayan dairy cattle, and BLUP evaluations in a line of rabbit closed for >40 generations with steady increase of inbreeding up to an average of 0.30. We show that ignoring inbreeding in the set‐up of the A‐inverse is equivalent to assume that non‐inbred animals are actually inbred. This results in an increase of apparent PEV that is negligible for dairy cattle but considerable for rabbit. Ignoring inbreeding in reliability = 1‐PEV/(1 + F) leads to underestimation of reliability for BLUP evaluations, and this underestimation is very large for rabbit. For SSGBLUP in dairy cattle, it leads to both underestimation and overestimation of reliability, both for genotyped and non‐genotyped animals. We strongly recommend to include inbreeding both in the set‐up of A‐inverse and in the computation of reliability from PEVs.