Genetic variation of the weaning weight of beef cattle as a function of accumulated heat stress.

The objective of this study was to identify the genetic variation in the weaning weight (WW) of beef cattle as a function of heat stress. The WWs were recorded at approximately 205 days of age in three Brazilian beef cattle populations: Nelore (93,616), Brangus (18,906) and Tropical Composite (62,679). In view of the cumulative nature of WW, the effect of heat stress was considered as the accumulation of temperature and humidity index units (ACTHI) from the animal's birth to weaning. A reaction norm model was used to estimate the (co)variance components of WW across the ACTHI scale. The accumulation of THI units from birth to weaning negatively affected the WW. The definition of accumulated THI units as an environmental descriptor permitted to identify important genetic variation in the WW as a function of heat stress. As evidence of genotype by environment interaction, substantial heterogeneity was observed in the (co)variance components for WW across the environmental gradient. In this respect, the best animals in less stressful environments are not necessarily the best animals in more stressful environments. Furthermore, the response to selection for WW is expected to be lower in more stressful environments.

Inbreeding depression in Zebu cattle traits.

The productivity of herds may be negatively affected by inbreeding depression, and it is important to know how intense is this effect on the livestock performance. We performed a comprehensive analysis involving five Zebu breeds reared in Brazil to estimate inbreeding depression in productive and reproductive traits. Inbreeding depression was estimated for 13 traits by including the individual inbreeding rate as a linear covariate in the standard genetic evaluation models. For all breeds and for almost all traits (no effect was observed on gestation length), the performance of the animals was compromised by an increase in inbreeding. The average inbreeding depression was -0.222% and -0.859% per 1% of inbreeding for linear regression coefficients scaled on the percentage of mean (ßm ) and standard deviation (ßσ ), respectively. The means for ßm (and ßσ ) were -0.269% (-1.202%) for weight/growth traits and -0.174% (-0.546%) for reproductive traits. Hence, inbreeding depression is more pronounced in weight/growth traits than in reproductive traits. These findings highlight the need for the management of inbreeding in the respective breeding programmes of the breeds studied here.

Detrimental effect of selection for milk yield on genetic tolerance to heat stress in purebred Zebu cattle: Genetic parameters and trends.

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.

Random regression analysis of test-day milk yields in the first and second lactations of Brazilian Gyr cows.

The objective of the present study was to estimate the genetic parameters for test-day milk yields (TDMY) in the first and second lactations using random regression models (RRM) in order to contribute to the application of these models in genetic evaluation of milk yield in Gyr cattle. A total of 53,328 TDMY records from 7118 lactations of 5853 Gyr cows were analyzed. The model included the direct additive, permanent environmental, and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cows at calving were included as fixed effects. A random regression model fitting fourth-order Legendre polynomials for additive genetic and permanent environmental effects, with five classes of residual variance, was applied. In the first lactation, the heritabilities increased from early lactation (0.26) until TDMY3 (0.38), followed by a decrease until the end of lactation. In the second lactation, the estimates increased from the first (0.29) to the fifth test day (0.36), with a slight decrease thereafter, and again increased on the last two test days (0.34 and 0.41). There were positive and high genetic correlations estimated between first-lactation TDMY and the remaining TDMY of the two lactations. The moderate heritability estimates, as well as the high genetic correlations between half the first-lactation TDMY and all TDMY of the two lactations, suggest that the selection based only on first lactation TDMY is the best selection strategy to increase milk production across first and second lactations of Gyr cows.

Genetic parameters of test-day milk yield in Guzerá cattle under tropical conditions.

The objective of this study was to estimate genetic parameters for test-day milk yield (TDMY) in Guzerá cows using random regression models. Additive and permanent environmental random effects were modeled by random regression on fourth- and fifth-order orthogonal Legendre polynomials, respectively. The residual variances were heterogeneous, with seven classes. Heritability estimates for TDMY ranged from 0.24 to 0.52, with higher heritabilities for yields during early lactation. Genetic correlations between TDMYs ranged from -0.03 to 0.95. The phenotypic and permanent environmental correlations were all positive, and the highest estimates were between adjacent TDMYs. The results suggest that TDMYs obtained with random regression models may be used as selection criteria for Guzerá cattle.

Multivariate analysis of test-day and total milk yield in goats.

The objective of this study was to estimate genetic parameters for 305-day cumulative milk yield (MY305) and its association with test-day milk yield (TDMY) in Saanen and Alpine goats in order to provide information that allows the use of TDMY as selection criteria. This was done using standard multi-trait and reduced rank models. Data from 1157 lactations, including the first three kiddings, and 5435 test-day records from 683 Saanen and 449 Alpine goats were used. MY305 was analyzed together with TDMY by multi-trait analysis, from the first to tenth test-day, using records of the first three lactations as repeated measures. Three multi-trait models were used: a standard (SM) and two reduced rank models that fitted the first two (PC2) and three (PC3) genetic principal components. Akaike and Schwarz Bayesian information criteria were used to compare models. Heritability for TDMY estimated with the SM ranged from 0.20 to 0.66, whereas the range calculated from the PC2 model was 0.16 to 0.63. Genetic correlations between TDMY and MY305 were positive and moderate to high, ranging from 0.56 to 0.98 when estimated with the SM, and 0.91 to 1.00 when estimated with the PC2. The standard multi-trait model produced estimates that were more accurate than the reduced rank models. Although the SM provided the worst fit according to the two model selection criteria, it was the best in this dataset.

Random regression models using different functions to model milk flow in dairy cows.

We analyzed 75,555 test-day milk flow records from 2175 primiparous Holstein cows that calved between 1997 and 2005. Milk flow was obtained by dividing the mean milk yield (kg) of the 3 daily milking by the total milking time (min) and was expressed as kg/min. Milk flow was grouped into 43 weekly classes. The analyses were performed using a single-trait Random Regression Models that included direct additive genetic, permanent environmental, and residual random effects. In addition, the contemporary group and linear and quadratic effects of cow age at calving were included as fixed effects. Fourth-order orthogonal Legendre polynomial of days in milk was used to model the mean trend in milk flow. The additive genetic and permanent environmental covariance functions were estimated using random regression Legendre polynomials and B-spline functions of days in milk. The model using a third-order Legendre polynomial for additive genetic effects and a sixth-order polynomial for permanent environmental effects, which contained 7 residual classes, proved to be the most adequate to describe variations in milk flow, and was also the most parsimonious. The heritability in milk flow estimated by the most parsimonious model was of moderate to high magnitude.

Estimates of genetic parameters for total milk yield over multiple ages in Brazilian Murrah buffaloes using different models.

The objective of this study was to estimate variance components and genetic parameters for accumulated 305-day milk yield (MY305) over multiple ages, from 24 to 120 months of age, applying random regression (RRM), repeatability (REP) and multi-trait (MT) models. A total of 4472 lactation records from 1882 buffaloes of the Murrah breed were utilized. The contemporary group (herd-year-calving season) and number of milkings (two levels) were considered as fixed effects in all models. For REP and RRM, additive genetic, permanent environmental and residual effects were included as random effects. MT considered the same random effects as did REP and RRM with the exception of permanent environmental effect. Residual variances were modeled by a step function with 1, 4, and 6 classes. The heritabilities estimated with RRM increased with age, ranging from 0.19 to 0.34, and were slightly higher than that obtained with the REP model. For the MT model, heritability estimates ranged from 0.20 (37 months of age) to 0.32 (94 months of age). The genetic correlation estimates for MY305 obtained by RRM (L23.res4) and MT models were very similar, and varied from 0.77 to 0.99 and from 0.77 to 0.99, respectively. The rank correlation between breeding values for MY305 at different ages predicted by REP, MT, and RRM were high. It seems that a linear and quadratic Legendre polynomial to model the additive genetic and animal permanent environmental effects, respectively, may be sufficient to explain more parsimoniously the changes in MY305 genetic variation with age.

Longitudinal genetic dynamics of weaning index and implications for cow-calf production efficiency.

In beef cattle, the selection for higher weights at young ages has been questioned with the argument that this criterion may increase the adult weight of cows, resulting in higher costs. Therefore, selection criteria should be employed to increase weights at young ages with minimal impact on the adult weight of cows. Additionally, the relationship between measures of cow production efficiency and other well-established selection criteria in breeding programs remains poorly understood. The objective of this study was to longitudinally evaluate the relationship between the weaning index (WIndex) as a measure of efficiency and growth traits of the cows. Possible changes over time in WIndex due to selection applied for yearling weight (YW) were also investigated. The WIndex was proposed to maximize genetic response in the weaning weight of the calf while maintaining genetic gain in BW of the cow at zero. A random regression model was adopted to estimate correlations between WIndex, BW, hip height (HH), and body condition score (BCS) using records of Nelore cows from three lines. Genetic trends were calculated for the control line (NeC) and lines selected for greater YW (NeS and NeT). The age of 3 years was the most critical for the weaning efficiency of the cows. At this stage, young cows are still growing and wean lighter calves than their adult counterparts. The genetic correlation estimates between WIndex and BW (-0.58 to 0.04), HH (-0.05 to -0.34), and BCS (-0.51 to -0.17) were close to zero or negative. BW and HH were strongly correlated genetically across all ages (0.73-0.76). In general, HH exhibited a weak and negative genetic relationship with BCS. The genetic correlation between BW and BCS was stronger for advanced ages (0.45-0.68). In lines selected for YW, important increases in WIndex were observed. However, NeS has been selected since the 1980s until the present for YW, and thus, it showed a more pronounced trend of increasing BW and, consequently, a more modest trend of increasing WIndex compared to NeT. In contrast, WIndex exhibited a trend close to zero for NeC. In this context, monitoring HH and BCS can be useful to avoid losses in the weaning efficiency of cows. Furthermore, we suggest that one way to mitigate efficiency losses in calf production could involve stabilizing the BW of cows and increasing the weaning weight of calves using the WIndex.

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle.

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.

Genotype by environment interaction and model comparison for growth traits of Santa Ines sheep.

The objectives of the present study were to compare alternative models for the genetic evaluation and assess the importance of genotype by environment interaction (G×E) in the estimation of genetic parameters and genetic evaluation of birth weight (BW), weight at 60 days of age (W60) and weight at 180 days of age (W180) of Santa Ines sheep. Data comprise 7622 BW, 4673 W60 and 2830 W180 records from animals born in 44 Brazilian herds. Four models were used for the analyses: animal model (AM) with homogeneous residual variance (1), or heterogeneous residual variance (2), hierarchical reaction norms model (HRNM) with homogeneous (1) or heterogeneous residual variance (2). The models that best fit the BW, W60 and W180 data were AM2, HRNM1 and HRNM2 respectively. Thus, models for genetic evaluation that consider heterogeneity of variances are recommended to evaluate growth traits of sheep. The correlation between intercept and slope of the HRNM was higher than 0.70 for all traits studied, indicating that animals with higher average breeding values responded better to improvement in environmental conditions, a fact characterizing the scale effect of G×E. Therefore, G×E is an important factor to be considered in the estimation of genetic parameters and genetic evaluation of growth traits of sheep.

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle.

A total of 46,089 individual monthly test-day (TD) milk yields (10 test-days), from 7,331 complete first lactations of Holstein cattle were analyzed. A standard multivariate analysis (MV), reduced rank analyses fitting the first 2, 3, and 4 genetic principal components (PC2, PC3, PC4), and analyses that fitted a factor analytic structure considering 2, 3, and 4 factors (FAS2, FAS3, FAS4), were carried out. The models included the random animal genetic effect and fixed effects of the contemporary groups (herd-year-month of test-day), age of cow (linear and quadratic effects), and days in milk (linear effect). The residual covariance matrix was assumed to have full rank. Moreover, 2 random regression models were applied. Variance components were estimated by restricted maximum likelihood method. The heritability estimates ranged from 0.11 to 0.24. The genetic correlation estimates between TD obtained with the PC2 model were higher than those obtained with the MV model, especially on adjacent test-days at the end of lactation close to unity. The results indicate that for the data considered in this study, only 2 principal components are required to summarize the bulk of genetic variation among the 10 traits.

Population structure and effects of inbreeding on milk yield and quality of Murrah buffaloes.

To provide data for conservation, selection, and expansion programs of buffalo herds, this study evaluated the history of a population of Murrah buffaloes based on population structure and the effect of inbreeding on accumulated 305-d milk yield (MY), fat yield (FY), protein yield (PY), mozzarella production (MProd), and somatic cell score (SCS). The usefulness of including the individual inbreeding coefficient (F) or individual increase in inbreeding coefficient (ΔF) in the model to describe inbreeding depression was evaluated. Pedigree information from 8,054 animals born between 1976 and 2008 and 4,497 lactation records obtained from 12 herds were used. The realized effective population size was 40.10 ± 1.27, and the mean F of the entire population was 2.14%. The ratio between the number of founders and ancestors demonstrated the existence of a bottleneck in the pedigree of this population, which may contribute to a reduction of genetic diversity. The effect of F on MY, FY, PY, MProd, and SCS was -1.005 kg, -0.299 kg, -0.246 kg, -1.201 kg, and -0.002 units, and the effect of ΔF transformed to equivalent F (%) for a mean of 2.57 equivalent generations was -4.287 kg, -0.581 kg, -0.383 kg, -2.001 kg, and -0.007 units, respectively. The inbreeding depression observed may have important economic repercussions for production systems. The ΔF can be considered the better of the two indicators of inbreeding depression due to its properties that prevent underestimation of this effect. A designed mating system to avoid inbreeding may be applied to this population to maintain genetic diversity.

Effect of pregnancy on the genetic evaluation of dairy cattle.

We investigated the effect of stage of pregnancy on estimates of breeding values for milk yield and milk persistency in Gyr and Holstein dairy cattle in Brazil. Test-day milk yield records were analyzed using random regression models with or without the effect of pregnancy. Models were compared using residual variances, heritabilities, rank correlations of estimated breeding values of bulls and cows, and number of nonpregnant cows in the top 200 for milk yield and milk persistency. The estimates of residual variance and heritabilities obtained with the models with or without the effect of pregnancy were similar for the two breeds. Inclusion of the effect of pregnancy in genetic evaluation models for these populations did not affect the ranking of cows and sires based on their predicted breeding values for 305-day cumulative milk yield. In contrast, when we examined persistency of milk yield, lack of adjustment for the effect of pregnancy overestimated breeding values of nonpregnant cows and cows with a long days open period and underestimated breeding values of cows with a short days open period. We recommend that models include the effect of days of pregnancy for estimation of adjustment factors for the effect of pregnancy in genetic evaluations of Dairy Gyr and Holstein cattle.

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows.

We analyzed 152,145 test-day records from 7317 first lactations of Holstein cows recorded from 1995 to 2003. Our objective was to model variations in test-day milk yield during the first lactation of Holstein cows by random regression model (RRM), using various functions in order to obtain adequate and parsimonious models for the estimation of genetic parameters. Test-day milk yields were grouped into weekly classes of days in milk, ranging from 1 to 44 weeks. The contemporary groups were defined as herd-test-day. The analyses were performed using a single-trait RRM, including the direct additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. The mean trend of milk yield was modeled with a fourth-order orthogonal Legendre polynomial. The additive genetic and permanent environmental covariance functions were estimated by random regression on two parametric functions, Ali and Schaeffer and Wilmink, and on B-spline functions of days in milk. The covariance components and the genetic parameters were estimated by the restricted maximum likelihood method. Results from RRM parametric and B-spline functions were compared to RRM on Legendre polynomials and with a multi-trait analysis, using the same data set. Heritability estimates presented similar trends during mid-lactation (13 to 31 weeks) and between week 37 and the end of lactation, for all RRM. Heritabilities obtained by multi-trait analysis were of a lower magnitude than those estimated by RRM. The RRMs with a higher number of parameters were more useful to describe the genetic variation of test-day milk yield throughout the lactation. RRM using B-spline and Legendre polynomials as base functions appears to be the most adequate to describe the covariance structure of the data.

Estimation of genetic parameters for milk yield in Murrah buffaloes by Bayesian inference.

Random regression models were used to estimate genetic parameters for test-day milk yield in Murrah buffaloes using Bayesian inference. Data comprised 17,935 test-day milk records from 1,433 buffaloes. Twelve models were tested using different combinations of third-, fourth-, fifth-, sixth-, and seventh-order orthogonal polynomials of weeks of lactation for additive genetic and permanent environmental effects. All models included the fixed effects of contemporary group, number of daily milkings and age of cow at calving as covariate (linear and quadratic effect). In addition, residual variances were considered to be heterogeneous with 6 classes of variance. Models were selected based on the residual mean square error, weighted average of residual variance estimates, and estimates of variance components, heritabilities, correlations, eigenvalues, and eigenfunctions. Results indicated that changes in the order of fit for additive genetic and permanent environmental random effects influenced the estimation of genetic parameters. Heritability estimates ranged from 0.19 to 0.31. Genetic correlation estimates were close to unity between adjacent test-day records, but decreased gradually as the interval between test-days increased. Results from mean squared error and weighted averages of residual variance estimates suggested that a model considering sixth- and seventh-order Legendre polynomials for additive and permanent environmental effects, respectively, and 6 classes for residual variances, provided the best fit. Nevertheless, this model presented the largest degree of complexity. A more parsimonious model, with fourth- and sixth-order polynomials, respectively, for these same effects, yielded very similar genetic parameter estimates. Therefore, this last model is recommended for routine applications.

Genetic parameters for buffalo milk yield and milk quality traits using Bayesian inference.

The availability of accurate genetic parameters for important economic traits in milking buffaloes is critical for implementation of a genetic evaluation program. In the present study, heritabilities and genetic correlations for fat (FY305), protein (PY305), and milk (MY305) yields, milk fat (%F) and protein (%P) percentages, and SCS were estimated using Bayesian methodology. A total of 4,907 lactations from 1,985 cows were used. The (co)variance components were estimated using multiple-trait analysis by Bayesian inference method, applying an animal model, through Gibbs sampling. The model included the fixed effects of contemporary groups (herd-year and calving season), number of milking (2 levels), and age of cow at calving as (co)variable (quadratic and linear effect). The additive genetic, permanent environmental, and residual effects were included as random effects in the model. The posterior means of heritability distributions for MY305, FY305, PY305, %F, P%, and SCS were 0.22, 0.21, 0.23, 0.33, 0.39, and 0.26, respectively. The genetic correlation estimates ranged from -0.13 (between %P and SCS) to 0.94 (between MY305 and PY305). The permanent environmental correlation estimates ranged from -0.38 (between MY305 and %P) to 0.97 (between MY305 and PY305). Residual and phenotypic correlation estimates ranged from -0.26 (between PY305 and SCS) to 0.97 (between MY305 and PY305) and from -0.26 (between MY305 and SCS) to 0.97 (between MY305 and PY305), respectively. Milk yield, milk components, and milk somatic cells counts have enough genetic variation for selection purposes. The genetic correlation estimates suggest that milk components and milk somatic cell counts would be only slightly affected if increasing milk yield were the selection goal. Selecting to increase FY305 or PY305 will also increase MY305, %P, and %F.

Random regression models to estimate genetic parameters for test-day milk yield in Brazilian Murrah buffaloes.

The objective of this work was to estimate covariance functions for additive genetic and permanent environmental effects and, subsequently, to obtain genetic parameters for buffalo's test-day milk production using random regression models on Legendre polynomials (LPs). A total of 17 935 test-day milk yield (TDMY) from 1433 first lactations of Murrah buffaloes, calving from 1985 to 2005 and belonging to 12 herds located in São Paulo state, Brazil, were analysed. Contemporary groups (CGs) were defined by herd, year and month of milk test. Residual variances were modelled through variance functions, from second to fourth order and also by a step function with 1, 4, 6, 22 and 42 classes. The model of analyses included the fixed effect of CGs, number of milking, age of cow at calving as a covariable (linear and quadratic) and the mean trend of the population. As random effects were included the additive genetic and permanent environmental effects. The additive genetic and permanent environmental random effects were modelled by LP of days in milk from quadratic to seventh degree polynomial functions. The model with additive genetic and animal permanent environmental effects adjusted by quintic and sixth order LP, respectively, and residual variance modelled through a step function with six classes was the most adequate model to describe the covariance structure of the data. Heritability estimates decreased from 0.44 (first week) to 0.18 (fourth week). Unexpected negative genetic correlation estimates were obtained between TDMY records at first weeks with records from middle to the end of lactation, being the values varied from -0.07 (second with eighth week) to -0.34 (1st with 42nd week). TDMY heritability estimates were moderate in the course of the lactation, suggesting that this trait could be applied as selection criteria in milking buffaloes.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models.

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Genetic component of sensitivity to heat stress for nonreturn rate of Brazilian Holstein cattle.

The objectives of the present study were: 1) to investigate variation in the genetic component of heat stress for nonreturn rate at 56 days after first artificial insemination (NR56); 2) to identify and characterize the genotype by environment interaction (G × E) due to heat stress for NR56 of Brazilian Holstein cattle. A linear random regression model (reaction norm model) was applied to 51,748 NR56 records of 28,595 heifers and multiparous cows. The decline in NR56 due to heat stress was more pronounced in milking cows compared to heifers. The age of females at first artificial insemination and temperature-humidity index (THI) exerted an important influence on the genetic parameters of NR56. Several evidence of G × E on NR56 were found as the high slope/intercept ratio and frequent intersection of reaction norms. Additionally, the genetic correlation between NR56 at opposite extremes of the THI scale reached estimates below zero, indicating that few of the same genes are responsible for NR56 under conditions of thermoneutrality and heat stress. The genetic evaluation and selection for NR56 in Holstein cattle reared under (sub)tropical conditions should therefore take into consideration the genetic variation on age at insemination and G × E due to heat stress.