Variance components and breeding values for growth traits from different statistical models.

Estimates of genetic parameters resulting from various analytical models for birth weight (BWT, n = 4,155), 205-d weight (WWT, n = 3,884), and 365-d weight (YWT, n = 3,476) were compared. Data consisted of records for Line 1 Hereford cattle selected for postweaning growth from 1934 to 1989 at ARS-USDA, Miles City, MT. Twelve models were compared. Model 1 included fixed effects of year, sex, age of dam; covariates for birth day and inbreeding coefficients of animal and of dam; and random animal genetic and residual effects. Model 2 was the same as Model 1 but ignored inbreeding coefficients. Model 3 was the same as Model 1 and included random maternal genetic effects with covariance between direct and maternal genetic effects, and maternal permanent environmental effects. Model 4 was the same as Model 3 but ignored inbreeding. Model 5 was the same as Model 1 but with a random sire effect instead of animal genetic effect. Model 6 was the same as Model 5 but ignored inbreeding. Model 7 was a sire model that considered relationships among males. Model 8 was a sire model, assuming sires to be unrelated, but with dam effects as uncorrelated random effects to account for maternal effects. Model 9 was a sire and dam model but with relationships to account for direct and maternal genetic effects; dams also were included as uncorrelated random effects to account for maternal permanent environmental effects. Model 10 was a sire model with maternal grandsire and dam effects all as uncorrelated random effects. Model 11 was a sire and maternal grandsire model, with dams as uncorrelated random effects but with sires and maternal grandsires assumed to be related using male relationships. Model 12 was the same as Model 11 but with all pedigree relationships from the full animal model for sires and maternal grandsires. Rankings on predictions of breeding values were the same regardless of whether inbreeding coefficients for animal and dam were included in the models. Heritability estimates were similar regardless of whether inbreeding effects were in the model. Models 3 and 9 best fit the data for estimation of variances and covariances for direct, maternal genetic, and permanent environmental effects. Other models resulted in changes in ranking for predicted breeding values and for estimates of direct and maternal heritability. Heritability estimates of direct effects were smallest with sire and sire-maternal grandsire models.     

Genetic parameters for calving ease and survival at birth in Angus field data.

Calving performance records from the American Angus Herd Improvement Registry files were used to estimate variance components for calving ease and survival to 24 h. Genetic parameters for direct and maternal effects were estimated by using a sire-maternal grandsire model. Data included two independent samples of 19 and 34 herds with complete calving information. Maternal variance for calving ease was much larger than the variance for the direct effect of the sire. Maternal heritability for calving ease was .27 and .20 in the two samples of herds, respectively. Heritabilities for direct effects were .21 and .07. The genetic correlations between direct and maternal effects were -.93 and -.80. There was little genetic variation in survival at birth. Parameter estimates were within the allowable parameter space in the sample of 19 herds. Heritability for the direct effect of the sire on survival was .04. Maternal heritability was .09, and the direct-maternal correlation was -.85.     

Bayesian inference strategies for the prediction of genetic merit using threshold models with an application to calving ease scores in Italian Piemontese cattle

First parity calving difficulty scores from Italian Piemontese cattle were analysed using a threshold mixed effects model. The model included the fixed effects of age of dam and sex of calf and their interaction and the random effects of sire, maternal grandsire, and herd‐year‐season. Covariances between sire and maternal grandsire effects were modelled using a numerator relationship matrix based on male ancestors. Field data consisted of 23 953 records collected between 1989 and 1998 from 4741 herd‐year‐seasons. Variance and covariance components were estimated using two alternative approximate marginal maximum likelihood (MML) methods, one based on expectation‐maximization (EM) and the other based on Laplacian integration. Inferences were compared to those based on three separate runs or sequences of Markov Chain Monte Carlo (MCMC) sampling in order to assess the validity of approximate MML estimates derived from data with similar size and design structure. Point estimates of direct heritability were 0.24, 0.25 and 0.26 for EM, Laplacian and MCMC (posterior mean), respectively, whereas corresponding maternal heritability estimates were 0.10, 0.11 and 0.12, respectively. The covariance between additive direct and maternal effects was found to be not different from zero based on MCMC‐derived confidence sets. The conventional joint modal estimates of sire effects and associated standard errors based on MML estimates of variance and covariance components differed little from the respective posterior means and standard deviations derived from MCMC. Therefore, there may be little need to pursue computation‐intensive MCMC methods for inference on genetic parameters and genetic merits using conventional threshold sire and maternal grandsire models for large datasets on calving ease.     

The effectiveness of the best linear unbiased prediction of beef sires using field data collected from small farms.

Beef sire evaluation using BLUP was investigated under field conditions at small-scale farms. The 6,848 records on fattened Japanese Black cattle steers were obtained from 1981 through 1987. The average number of steers in the subclass of market-year-farm was 5.2. A sire-maternal grandsire mixed model with relationships was used to analyze the data to yield BLUP for the sire and maternal grandsire effects. The regression coefficients of the realized value of progeny on the predicted value calculated using BLUP procedures for daily gain, carcass weight, and marbling score were 1.027, 1.054, and .917, respectively (i.e., the regression almost equaled 1). Therefore, BLUP was shown to be very effective in predicting offspring performance, even using field records collected from small-scale farms.     

Threshold-linear versus linear-linear analysis of birth weight and calving ease using an animal model: II. Comparison of models.

Several models were evaluated in terms of predictive ability for calving difficulty. Data included birth weight and calving difficulty scores provided by the American Gelbvieh Association from 26,006 calves born to first-parity cows and five simulated populations of 6,200 animals each. Included in the model were fixed age of dam x sex interaction effects, random herd-year-season effects, and random animal direct and maternal effects. Bivariate linear-threshold and linear-linear models for birth weight/calving ease and univariate threshold and linear models for calving ease were applied to the data sets. For each data set and model, one-half of calving ease records were randomly discarded. Predictive ability of the different models was defined with the mean square error (MSE) for the difference between a deleted calving ease score and its prediction obtained from the remaining data. In terms of correlation between simulated and predicted breeding values, the threshold models had a 1% advantage for direct genetic effects and 3% for maternal genetic effects. In simulation, the average MSE was .29 for linear-threshold, .32 for linear-linear, .37 for threshold, and .39 for linear model. For the field data set, the MSE was .31, .33, .39, and .40, respectively. Although the bivariate models for calving ease/birth weight were more accurate than univariate models, the threshold models showed a greater advantage under the bivariate model. For the purpose of genetic evaluation for calving difficulty in beef cattle, the use of the linear-threshold model seems justified. In dairy cattle, the evaluation for calving ease can benefit from recording birth weight.     

Animal model for genetic evaluation of multibreed data.

Extension of beef cattle genetic evaluation procedures to multibreed data sets is proposed as a way to allow inclusion of crossbred animals into current analyses and to provide comparisons between purebred animals of different breeds. Previous papers dealing with multibreed BLUP have proposed sire or sire-maternal grandsire models. Because current models used in the beef industry are predominantly of the reduced animal model form, models were developed for animal model and reduced animal model mixed-model evaluations that would account for fixed and random additive genetic effects, along with fixed and random nonadditive genetic effects for populations with heterogeneous means and variances.     

Threshold-linear versus linear-linear analysis of birth weight and calving ease using an animal model: I. Variance component estimation.

Birth weight and calving difficulty were analyzed with Bayesian methodology using univariate linear models, a bivariate linear model, a threshold model for calving difficulty, and a joint threshold-linear model using a probit approach. Field data included 26,006 records of Gelbvieh cattle. Simulated populations were generated using parameters estimated from the field data. The Gibbs sampler was used to obtain estimates of the marginal posterior mean and standard deviation of the (co)variance components, heritabilities, and correlations. In the univariate analyses, the posterior mean of direct heritability for calving difficulty was .23 with the threshold model and .18 with the linear model. Maternal heritabilities were .10 and .08, respectively. In the bivariate analysis, posterior means of direct heritability for calving difficulty were .21 and .18 for the bivariate linear-threshold and linear-linear model, respectively. Maternal heritabilities were .09 and .06, respectively. Direct heritability for birth weight was .25 for the univariate model and .26 for bivariate models. Maternal heritability was .05 for the linear-threshold model and the univariate model and .06 for the bivariate linear model. Genetic correlation between direct genetic effects in both traits was .81 for the linear-threshold model and .79 for the bivariate linear. Residual correlation was .35 for the bivariate linear model and .50 for the bivariate linear-threshold. A simulation study confirmed that the posterior mean of the marginal distribution was suitable as a point estimate for univariate threshold and bivariate linear-threshold models.     

Bayesian analysis of birth weight and litter size in Baluchi sheep using Gibbs sampling

Variance and covariance components for birth weight (BWT), as a lamb trait, and litter size measured on ewes in the first, second, and third parities (LS1 through LS3) were estimated using a Bayesian application of the Gibbs sampler. Data came from Baluchi sheep born between 1966 and 1989 at the Abbasabad sheep breeding station, located northeast of Mashhad, Iran. There were 10,406 records of BWT recorded for all ewe lambs and for ram lambs that later became sires or maternal grandsires. All lambs that later became dams had records of LS1 through LS3. Separate bivariate analyses were done for each combination of BWT and one of the three variables LS1 through LS3. The Gibbs sampler with data augmentation was used to draw samples from the marginal posterior distribution for sire, maternal grandsire, and residual variances and the covariance between the sire and maternal grandsire for BWT, variances for the sire and residual variances for the litter size traits, and the covariances between sire effects for different trait combinations, sire and maternal grandsire effects for different combinations of BWT and LS1 through LS3, and the residual covariations between traits. Although most of the densities of estimates were slightly skewed, they seemed to fit the normal distribution well, because the mean, mode, and median were similar. Direct and maternal heritabilities for BWT were relatively high with marginal posterior modes of .14 and .13, respectively. The average of the three direct-maternal genetic correlation estimates for BWT was low, .10, but had a high standard deviation. Heritability increased from LS1 to LS3 and was relatively high, .29 to .37. Direct genetic correlations between BWT and LS1 and between BWT and LS3 were negative, -.32 and -.43, respectively. Otherwise, the same correlation between BWT and LS2 was positive and low, .06. Genetic correlations between maternal effects for BWT and direct effects for LS1 through LS3 were all highly negative and consistent for all parities, circa -.75. Environmental correlations between BWT and LS1 through LS3 were relatively low and ranged from .18 to .29 and had high standard errors.     

Breed effects on crossbred cow-calf performance

Effects of seven breeds of cow's sire and 12 breeds of cow's maternal grandsire on preweaning performance of crossbred cows and their calves were examined in data from two experiments conducted at the Roman L. Hruska U.S. Mean Animal Research Center. Data included 1,836 records over three to five parities for 516 cows by 143 sires and by 307 maternal grandsires. The statistical model fitted effects of calf sex, parity, cow birth-breeding year or cow-calf birth year, the breed effects and their interactions. Deviations of breed of sire or equivalent grandsire effects on each trait from the mean for Hereford x Angus cows ranged from -1.6 to 5.5 kg (P less than .001) for calf birth weights, -15 to 1% (P less than .001) for calving difficulty, nonsignificant for preweaning calf mortality and -2 to 27 kg (P less than .001) for calf weaning weight. Deviations were nonsignificant for conception rate and calves weaned per cow exposed to breeding, but -2 to 40 kg (P less than .001) for calf weight weaned per cow exposed for breeding, -7 to 78 kg (P less than .001) for cow weight and -20 to 2% (P less than .001) for body condition score. The advantages of Holstein and Brahman cross over Hereford x Angus cows of 23 and 13% in weight of calf weaned/cow-breeding exposure must be compared with the expected greater feed requirements from 7 or 8% heavier cows and at least 50% higher milk production, which emphasizes the need to include input measures and costs in breed evaluation schemes.     

Relationship between calving difficulty and fertility traits in first‐parity Iranian Holsteins under standard and recursive models

The main objective of this study was to estimate the genetic and phenotypic relationships between calving difficulty (CD) and fertility traits, including success at first service (SF), number of inseminations to conception (INS), interval from calving to first service (CTFS), interval between first and last service (IFL) and days open (DO), in first‐parity Iranian Holsteins under standard (SMMs) and recursive (RMMs) mixed models. The data analysed in this paper included 29 950 records on CD and fertility traits, collected in the time period from 1995 to 2014 by the Animal Breeding and Improvement Center of Iran. Under all observed SMMs and RMMs, five bivariate sire‐maternal grandsire models (ten bivariate analyses in total) were used for the analyses. Recursive models were applied with a view to consider that CD influences the fertility traits in the subsequent reproductive cycle and the genetic determination of CD and fertility traits by fitting CD as covariate for any of the fertility traits studied. The existence of such cause‐and‐effect is considered in RMMs but not in SMMs. Our results implied a statistically non‐zero magnitude of the causal relationships between CD and all the fertility traits studied, with the former influencing the latter. The causal effects of CD on SF (on the observed scale, %), INS, CTFS, IFL and DO were ?2.23%, 0.10 services, 1.93 days, 3.76 days and 5.61 days, respectively. Direct genetic correlations between CD and the fertility traits under both models were not statistically different from zero (95% HPD interval included zero), except for the correlation between CD and CTFS, which were 0.197 and 0.134 under SMM and RMM, respectively, indicating that genes associated with difficult births also increase intervals between calving and the first insemination afterwards. Comparison of both models by the deviance information criterion (DIC) demonstrated the plausibility of RMMs over SMMs.     

Investigating maternal effects on production traits in Duroc pigs using animal and sire models

Variance components for production traits were estimated using different models to evaluate maternal effects. Data analysed were records from the South African pig performance testing scheme on 22 224 pigs from 18 herds, tested between 1990 and 2008. The traits analysed were backfat thickness (BFAT), test period weight gain (TPG), lifetime weight gain (LTG), test period feed conversion ratio (FCR) and age at slaughter (AGES). Data analyses were performed by REML procedures in ASREML, where random effects were successively fitted into animal and sire models to produce different models. The first animal model had one random effect, the direct genetic effects, while the additional random effects were maternal genetic and maternal permanent environmental effects. In the sire model, the random effects fitted were sire and maternal grand sire effects. The best model considered the covariance between direct and maternal genetic effects or between sire and maternal grand sire effects. Fitting maternal genetic effects into the animal model reduced total additive variance, while the total additive variance increased when maternal grand sire effects were fitted into the sire model. The correlations between direct and maternal genetic effects were all negative, indicating antagonism between these effects, hence the need to consider both effects in selection programmes. Direct genetic correlations were higher than other correlations, except for maternal genetic correlations of FCR with TPG, LTG and AGES. There has been direct genetic improvement and almost constant maternal ability in production traits as shown by trends for estimated (EBVs) and maternal breeding values (MBVs), while phenotypic trends were similar to those for EBVs. These results suggest that maternal genetic effects should be included in selection programmes for these production traits. Therefore, the animal–maternal model may be the most appropriate model to use when estimating genetic parameters for production traits in this population.     

Evaluation models and genetic parameters for calving difficulty in beef cattle

Calving difficulty was analyzed under threshold and linear models considering either a fixed or random herd-year effect. The aim of the study was to compare models for predicting breeding values according to the size of herd-year groups. When simulating data sets with small herds, in order to obtain an unbiased evaluation under a nonrandom and negative association of sire and herd effects, the best model for a practical evaluation was the fixed linear model. Field data included 246,576 records of the largest Charolais herds in France. Models were compared using the correlations of estimated breeding values between the different models. Although the best model from a theoretical point of view was a threshold model with a fixed herd-year effect, a linear model with a fixed herd-year effect was the best choice from a practical point of view for predicting direct effects for calving difficulty in beef cattle and was a sufficient choice for predicting the associated maternal effects for data set with large herds. Correlations between direct estimated breeding values under the reference model and the fixed linear model and the random threshold model were 0.94 and 0.91, respectively. Correlations between the corresponding maternal estimated breeding values were 0.94 and 0.98. Heritabilities of direct effects were 0.27 and 0.14 under fixed threshold and fixed linear models, respectively. The corresponding heritabilities of maternal effects were 0.18 and 0.13, and the genetic correlation between direct and maternal effects were -0.36 and -0.34, respectively.     

Analysis of gestation length in American Simmental cattle

Records of gestation length (71,461) for Simmental cattle were distributed with mean 284.3 d and standard deviation 5.52 d. Gestation length was found to increase with percent Simmental and was 1.9 d longer for calves born to mature dams than for those born to heifer dams. Bull calves experienced gestation lengths 1.5 d longer than heifer calves. Sire, maternal grandsire, residual and total variances were estimated to be 2.42, .58, 22.78 and 25.78 d2, respectively, by Henderson's Method III. Heritability of gestation length was calculated to be .374 from the sire variance and .09 from the maternal grandsire variance. Direct additive genetic variance was considered to be of greater importance than maternal additive genetic variance. Correlations between the evaluations of sires for gestation length and heifer calving ease, birth weight and weaning weight were .26, .26 and .13, respectively.     

Effects of parent‐of‐origin models with different pedigree information on beef carcass traits and fatty acid composition in Japanese Black cattle

Genomic imprinting should be considered in animal breeding systems to avoid lead in bias in genetic parameter estimation. The objective of this study was to clarify the effects of pedigree information on imprinting variances for carcass traits and fatty acid composition in Japanese Black cattle. Carcass records [carcass weight, rib eye area, rib thickness (RT), subcutaneous fat thickness and beef marbling score (BMS)] and fatty acid composition were obtained for 11,855 Japanese Black feedlot cattle. To estimate and compare the imprinting variances for the traits, two imprinting models with different pedigree information [the sire–dam gametic relationship matrix (Model 1) and the sire–maternal grandsire (MGS) numerator relationship matrix (Model 2)] were fitted. The ratio of the imprinting variance to the total additive genetic variance for RT (6.33%) and BMS (19.00%) was significant in Model 1, but only that for BMS (21.09%) was significant in Model 2. This study revealed that fitting the sire–MGS model could be useful in estimating imprinting variance under certain conditions, such as when restricted pedigree information is available. Furthermore, the present result suggested that the maternal gametic effects on BMS should be included in breeding programmes for Japanese Black cattle to avoid selection bias caused by imprinting effects.     

Reproductive rates, birth weight, calving ease and 24-h calf survival in a four-breed diallel among Simmental, Limousin, Polled Hereford and Brahman beef cattle

Calving and weaning rates, birth weight, calving ease, and 24-h calf survival were evaluated in a four-breed diallel of Simmental (S), Limousin (L), Polled Hereford (H) and Brahman (B) beef cattle in five calf crops. Limousin dams tended to have the highest calving and weaning rates because they were able to have heavier calves with less calving difficulty and higher survival rates. Brahman-sired calves were the heaviest at birth (P less than .05) and B dams produced the lightest calves (P less than .001). Lower birth weights tended to be the limiting factor on survival of these calves. A linear comparison among means to evaluate purebred, additive, maternal and specific combining ability effects showed most of the reduction in birth weight from B dams was due to maternal effects. Breed of dam accounted for a higher proportion of variation in calving ease than did sire breed. Simmental sires had significantly heavier calves at birth and S and H dams tended to have more calving difficulty and lower survival rates. Heterosis for these traits was generally not significant. Correlations were generally positive and significant for birth weight and calving ease, but were more variable for birth weight and survival. Linear regressions of calving ease on birth weight both within years and within dam-breed-year subclasses were very similar in that the association of these two traits was reduced as dam age increased.     

Estimation of variance and covariance components to determine heritabilities and repeatability of weaning weight in American Simmental cattle

Components of (co)variance for weaning weight were estimated from field data provided by the American Simmental Association. These components were obtained for the observational components of variance corresponding to a sire, maternal grandsire, and dam within maternal grandsire model. From these estimates, direct additive genetic variance (Sigma2A), maternal additive genetic variance (Sigma2M), covariance between direct and maternal additive genetic effects (SigmaAM), variance of permanent environment(Sigma2pe) and temporary environment variance(Sigma2te) were determined. A procedure to approximate restricted maximum likelihood (REML) estimates of the observational components of variance based on the expectation-maximization (EM) algorithm is described. From these results, phenotypic variance ( ) of weaning weight was 667.88 kg2. Values forSigma2A, Sigma2M, Sigma2pe and Sigma2te were 79,30,58,38,49.45, and 469.97 kg2, respectively. Genetic correlation between direct and maternal additive genetic effects was .16.     

Symmetric differences squared and analysis of variance procedures for estimating genetic and environmental variances and covariances for beef cattle weaning weight: I. Comparison via simulation

Analysis of variance (ANOVA) and symmetric differences squared (SDS) methods for estimating genetic and environmental variances and covariances associated with beef cattle weaning weight were compared via simulation. Simulation was based on the pedigree and record structure of 503 beef weaning weights collected over 19 yr from a university herd. The SDS methodology was used with four models. The simplest model included direct (g) and maternal (gm) additive genetic effects, genetic covariance between direct and maternal additive genetic effects (sigma ggm), permanent maternal environmental effects (m) and temporary environmental effects (e). The second model also allowed for a nonzero environmental covariance (sigma mem) between dam and offspring weaning weights. Models 3 and 4 were models 1 and 2, respectively, expanded to include a grandmaternal genetic effect (gn) and covariances sigma ggn and sigma gmgn. Two ANOVA solution sets for the parameters of model 4 were obtained using sire, dam, maternal grandsire, maternal grandam and phenotypic variances and offspring-dam (covOD), offspring-sire (covOS), offspring-grandam (covOGD), and offspring-maternal half-aunt or uncle (covOMH) covariances. Four ANOVA solution sets for the parameters of model 2 were obtained using sire, dam, within dam and maternal grandsire variances, covOD and either covOS or covOGD. Two sets of 1,000 replicates of the data were simulated. These data were used to compare precision and accuracy of SDS and ANOVA estimators, to estimate correlations among SDS and ANOVA estimators, and to study the importance of taking inbreeding into account with SDS methodology. All ANOVA estimators for rho ggm were biased downward. The SDS procedure had a clear advantage over ANOVA. Averages of SDS estimates were closer to parameter values used to simulate the data and their standard deviations were generally smaller. The standard deviations of both SDS and ANOVA estimates of rho ggm were very large. It is important to allow for a nonzero sigma mem (at least when it is negative) when using SDS methods; otherwise estimators of sigma 2gm and sigma ggm are biased upward and downward, respectively.     

Direct and maternal (co)variance components and genetic parameters for growth and reproductive traits in the Boran cattle in Kenya

Direct and maternal (co)variance components and genetic parameters were estimated for growth and reproductive traits in the Kenya Boran cattle fitting univariate animal models. Data consisted of records on 4502 animals from 81 sires and 1010 dams collected between 1989 and 2004. The average number of progeny per sire was 56. Direct heritability estimates for growth traits were 0.34, 0.12, 0.19, 0.08 and 0.14 for birth weight (BW), weaning weight (WW), 12-month weight (12W), 18-month weight (18W) and 24-month weight (24W), respectively. Maternal heritability increased from 0.14 at weaning to 0.34 at 12 months of age but reduced to 0.11 at 24 months of age. The maternal permanent environmental effect contributed 16%, 4% and 10% of the total phenotypic variance for WW, 12W and 18W, respectively. Direct-maternal genetic correlations were negative ranging from −0.14 to −0.58. The heritability estimates for reproductive traits were 0.04, 0.00, 0.15, 0.00 and 0.00 for age at first calving (AFC), calving interval in the first, second, and third parity, and pooled calving interval. Selection for growth traits should be practiced with caution since this may lead to a reduction in reproduction efficiency, and direct selection for reproductive traits may be hampered by their low heritability.     

Variance and covariance estimates for weaning weight of Senepol cattle.

Variance and covariance components were estimated for weaning weight from Senepol field data for use in the reduced animal model for a maternally influenced trait. The 4,634 weaning records were used to evaluate 113 sires and 1,406 dams on the island of St. Croix. Estimates of direct additive genetic variance (sigma 2A), maternal additive genetic variance (sigma 2M), covariance between direct and maternal additive genetic effects (sigma AM), permanent maternal environmental variance (sigma 2PE), and residual variance (sigma 2 epsilon) were calculated by equating variances estimated from a sire-dam model and a sire-maternal grandsire model, with and without the inverse of the numerator relationship matrix (A-1), to their expectations. Estimates were sigma 2A, 139.05 and 138.14 kg2; sigma 2M, 307.04 and 288.90 kg2; sigma AM, -117.57 and -103.76 kg2; sigma 2PE, -258.35 and -243.40 kg2; and sigma 2 epsilon, 588.18 and 577.72 kg2 with and without A-1, respectively. Heritability estimates for direct additive (h2A) were .211 and .210 with and without A-1, respectively. Heritability estimates for maternal additive (h2M) were .47 and .44 with and without A-1, respectively. Correlations between direct and maternal (IAM) effects were -.57 and -.52 with and without A-1, respectively.     

Genetic relationships between calving and carcass traits for Charolais and Hereford cattle in Sweden

The objective of this study was to estimate genetic correlations between calving difficulty score and carcass traits in Charolais and Hereford cattle, treating first and later parity calvings as different traits. Genetic correlations between birth weight and carcass traits were also estimated. Field data on 59,182 Charolais and 27,051 Hereford calvings, and carcass traits of 5,260 Charolais and 1,232 Hereford bulls, were used in bivariate linear animal model analyses. Estimated heritabilities were moderate to high (0.22 to 0.50) for direct effects on birth weight, carcass weight, and (S)EUROP (European Community scale for carcass classification) grades for carcass fleshiness and fatness. Heritabilities of 0.07 to 0.18 were estimated for maternal effect on birth weight, and for direct and maternal effects on calving difficulty score at first parity. Lower heritabilities (0.01 to 0.05) were estimated for calving difficulty score at later parities. Carcass weight was positively genetically correlated (0.11 to 0.53) with both direct and maternal effects on birth weight and with direct effects on calving difficulty score. Carcass weight was, however, weakly or negatively (-0.70 to 0.07) correlated with maternal calving difficulty score. Higher carcass fatness grade was genetically associated with lower birth weight, and in most cases, also with less difficult calving. Genetic correlations with carcass fleshiness grade were highly variable. Moderately unfavorable correlations between carcass fleshiness grade and maternal calving difficulty score at first parity were estimated for both Charolais (0.42) and Hereford (0.54). This study found certain antagonistic genetic relationships between calving performance and carcass traits for both Charolais and Hereford cattle. Both direct and maternal calving performance, as well as carcass traits, should be included in the breeding goal and selected for in beef breeds.