Analysis of beef cattle longitudinal data applying a nonlinear model

The objective of this work was to evaluate the Nelore beef cattle, growth curve parameters using the Von Bertalanffy function in a nested Bayesian procedure that allowed estimation of the joint posterior distribution of growth curve parameters, their (co)variance components, and the environmental and additive genetic components affecting them. A hierarchical model was applied; each individual had a growth trajectory described by the nonlinear function, and each parameter of this function was considered to be affected by genetic and environmental effects that were described by an animal model. Random samples of the posterior distributions were drawn using Gibbs sampling and Metropolis-Hastings algorithms. The data set consisted of a total of 145,961 BW recorded from 15,386 animals. Even though the curve parameters were estimated for animals with few records, given that the information from related animals and the structure of systematic effects were considered in the curve fitting, all mature BW predicted were suitable. A large additive genetic variance for mature BW was observed. The parameter a of growth curves, which represents asymptotic adult BW, could be used as a selection criterion to control increases in adult BW when selecting for growth rate. The effect of maternal environment on growth was carried through to maturity and should be considered when evaluating adult BW. Other growth curve parameters showed small additive genetic and maternal effects. Mature BW and parameter k, related to the slope of the curve, presented a large, positive genetic correlation. The results indicated that selection for growth rate would increase adult BW without substantially changing the shape of the growth curve. Selection to change the slope of the growth curve without modifying adult BW would be inefficient because their genetic correlation is large. However, adult BW could be considered in a selection index with its corresponding economic weight to improve the overall efficiency of beef cattle production.     

Variational bayesian method of estimating variance components

We developed a Bayesian analysis approach by using a variational inference method, a so‐called variational Bayesian method, to determine the posterior distributions of variance components. This variational Bayesian method and an alternative Bayesian method using Gibbs sampling were compared in estimating genetic and residual variance components from both simulated data and publically available real pig data. In the simulated data set, we observed strong bias toward overestimation of genetic variance for the variational Bayesian method in the case of low heritability and low population size, and less bias was detected with larger population sizes in both methods examined. The differences in the estimates of variance components between the variational Bayesian and the Gibbs sampling were not found in the real pig data. However, the posterior distributions of the variance components obtained with the variational Bayesian method had shorter tails than those obtained with the Gibbs sampling. Consequently, the posterior standard deviations of the genetic and residual variances of the variational Bayesian method were lower than those of the method using Gibbs sampling. The computing time required was much shorter with the variational Bayesian method than with the method using Gibbs sampling.     

Investigation of Gibbs sampling conditions to estimate variance components from Japanese Black carcass field data

The genetic evaluation using the carcass field data in Japanese Black cattle has been carried out employing an animal model, implementing the restricted maximum likelihood (REML) estimation of additive genetic and residual variances. Because of rapidly increasing volumes of the official data sets and therefore larger memory spaces required, an alternative approach like the REML estimation could be useful. The purpose of this study was to investigate Gibbs sampling conditions for the single-trait variance component estimation using the carcass field data. As prior distributions, uniform and normal distributions and independent scaled inverted chi-square distributions were used for macro-environmental effects, breeding values, and the variance components, respectively. Using the data sets of different sizes, the influences of Gibbs chain length and thinning interval were investigated, after the burn-in period was determined using the coupling method. As would be expected, the chain lengths had obviously larger effects on the posterior means than those of thinning intervals. The posterior means calculated using every 10th sample from 90 000 of samples after 10 000 samples discarded as burn-in period were all considered to be reasonably comparable to the corresponding estimates by REML.     

Maternal animal model with correlation between maternal environmental effects of related dams

A procedure to take into account the nongenetic relationship between maternal effects in adjacent generations is presented. It considers a correlation between maternal environments provided by a dam and its daughters (lambda). The dispersion structure of the maternal animal model was modified to include a correlation matrix (E) that relates the maternal permanent environmental effects. The structures of the E matrix and its inverse (E(-1)) are described. Both matrices are completely defined by the correlation coefficient lambda. An algorithm to compute these matrices from pedigree information was also developed. Furthermore, a Bayesian analysis of this model including the lambda parameter was developed using Gibbs sampling, with Metropolis steps for the nonstandard conditional distributions. With simulated data, the proposed model reduced the bias in all estimates of dispersion parameters when an antagonism between the maternal effects received by a daughter and its future maternal environment existed. This model also provides an estimate of the environmental relationship between the maternal effects of dams and daughters by the lambda parameter. The same Bayesian analysis was also carried out with weaning weight data of the Bruna dels Pirineus breed. The posterior means (standard deviation) of (co)variance ratios were .214 (.081) for direct heritability (h2d), .107 (.033) for maternal heritability (h2m), .047 (.020) for the proportion of variance due to maternal environmental effects (c2m), and -.034 (.043) for the genetic correlation between direct and maternal effects (r(dm)). The posterior mean of lambda parameter was -.190, and 76% of its marginal posterior distribution took negative values. As occurred with simulated data, considering the maternal environmental correlation in the analysis implied higher h2m estimates, lower c2m and h2d estimates, and less negative values for the marginal posterior distribution of r(dm). These results were considered as evidence of the environmental antagonism between maternal effects provided by a dam and its daughters to weaning weight of their progeny in the Bruna dels Pirineus breed.     

Comparison of (co)variance component estimates in control populations of red flour beetle (Tribolium castaneum) using restricted maximum likelihood and Gibbs sampling

Mixed model (co)variance component estimates by REML and Gibbs sampling for two traits were compared for base populations and control lines of Red Flour Beetle (Tribolium castaneum). Two base populations (1296 records in the first replication, 1292 in the second) were sampled from laboratory stock. Control lines were derived from corresponding base populations with random selection and mating for 16 generations. The REML estimate of each (co)variance component for both pupa weight and family size was compared with the mean and 95% central interval of the particular (co)variance estimated by Gibbs sampling with three different weights on the given priors: ‘flat’, smallest, and 3.7% degrees of belief. Results from Gibbs sampling showed that flat priors gave a wider and more skewed marginal posterior distribution than the other two weights on priors for all parameters. In contrast, the 3.7% degree of belief on priors provided reasonably narrow and symmetric marginal posterior distributions. Estimation by REML does not have the flexibility of changing the weight on prior information as does the Bayesian analysis implemented by Gibbs sampling. In general, the 95% central intervals from the three different weights on priors in the base populations were similar to those in control lines. Most REML estimates in base populations differed from REML estimates in control lines. Insufficient information from the data, and confounding of random effects contributed to the variability of REML estimates in base populations. Evidence is presented showing that some (co)variance components were estimated with less precision than others. Results also support the hypothesis that REML estimates were equivalent to the joint mode of posterior distribution obtained from a Bayesian analysis with flat priors, but only when there was sufficient information from data, and no confounding among random effects.     

利用Bayesian-MCMC方法进行畜禽远交群多家系离散性状QTL连锁检测

利用Bayesian—MCMC方法对不同家系结构的畜禽远交群体的二级离散性状进行QTL连锁检测，在分析中，基于IBD方差组分的随机模型的定位策略，同时利用MCMC的3种不同抽样技术（Gibbs抽样、Metropolis抽样和Reversible jump MCMC抽样）产生相应QTL参数的后验样本，在此基础上进行目标参数的Bayesian统计推断。结果表明：Bayesian—MCMC方法能够对QTL数目进行准确估计，并且在不同家系结构下得到较为理想的参数估计结果。     

Identifiability of parameters and behaviour of MCMC chains: a case study using the reaction norm model

Markov chain Monte Carlo (MCMC) enables fitting complex hierarchical models that may adequately reflect the process of data generation. Some of these models may contain more parameters than can be uniquely inferred from the distribution of the data, causing non‐identifiability. The reaction norm model with unknown covariates (RNUC) is a model in which unknown environmental effects can be inferred jointly with the remaining parameters. The problem of identifiability of parameters at the level of the likelihood and the associated behaviour of MCMC chains were discussed using the RNUC as an example. It was shown theoretically that when environmental effects (covariates) are considered as random effects, estimable functions of the fixed effects, (co)variance components and genetic effects are identifiable as well as the environmental effects. When the environmental effects are treated as fixed and there are other fixed factors in the model, the contrasts involving environmental effects, the variance of environmental sensitivities (genetic slopes) and the residual variance are the only identifiable parameters. These different identifiability scenarios were generated by changing the formulation of the model and the structure of the data and the models were then implemented via MCMC. The output of MCMC sampling schemes was interpreted in the light of the theoretical findings. The erratic behaviour of the MCMC chains was shown to be associated with identifiability problems in the likelihood, despite propriety of posterior distributions, achieved by arbitrarily chosen uniform (bounded) priors. In some cases, very long chains were needed before the pattern of behaviour of the chain may signal the existence of problems. The paper serves as a warning concerning the implementation of complex models where identifiability problems can be difficult to detect a priori. We conclude that it would be good practice to experiment with a proposed model and to understand its features before embarking on a full MCMC implementation.     

Bayesian inference in a piecewise Weibull proportional hazards model with unknown change points

The main difference between parametric and non-parametric survival analyses relies on model flexibility. Parametric models have been suggested as preferable because of their lower programming needs although they generally suffer from a reduced flexibility to fit field data. In this sense, parametric survival functions can be redefined as piecewise survival functions whose slopes change at given points. It substantially increases the flexibility of the parametric survival model. Unfortunately, we lack accurate methods to establish a required number of change points and their position within the time space. In this study, a Weibull survival model with a piecewise baseline hazard function was developed, with change points included as unknown parameters in the model. Concretely, a Weibull log-normal animal frailty model was assumed, and it was solved with a Bayesian approach. The required fully conditional posterior distributions were derived. During the sampling process, all the parameters in the model were updated using a Metropolis-Hastings step, with the exception of the genetic variance that was updated with a standard Gibbs sampler. This methodology was tested with simulated data sets, each one analysed through several models with different number of change points. The models were compared with the Deviance Information Criterion, with appealing results. Simulation results showed that the estimated marginal posterior distributions covered well and placed high density to the true parameter values used in the simulation data. Moreover, results showed that the piecewise baseline hazard function could appropriately fit survival data, as well as other smooth distributions, with a reduced number of change points.     

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.     

Elliptical selection experiment for the estimation of genetic parameters of the growth rate and feed conversion ratio in rabbits

Two elliptical selection experiments were performed in two contemporary sire lines of rabbits (C and R) in order to optimize the experimental design for estimating the genetic parameters of the growth rate (GR) and feed conversion ratio (FCR). Twelve males and 19 females from line C, and 13 males and 23 females from line R, were selected from an ellipse defined by a quadratic index based on these traits. Data from 160 rabbits of each of the parental generations of lines C and R and their offspring (275 and 266 animals, respectively) were used for the analysis. A Bayesian framework was adopted for inference. Marginal posterior distributions of the genetic parameters were obtained by Gibbs sampling. An animal model including batch, parity order, litter size, and common environmental litter effects was assumed. Posterior means (posterior standard deviations) for heritabilities of GR and FCR were estimated to be 0.31 (0.10) and 0.31 (0.10), respectively, in line C and 0.21 (0.08) and 0.25 (0.12) in line R. Posterior means of the proportion of the variance due to common litter environmental effects were 0.14 (0.06) and 0.21 (0.06) for GR and FCR, respectively, in line C and 0.17 (0.06) and 0.22 (0.06) in line R. Posterior means of genetic correlation between both traits were -0.49 (0.25) in line C and -0.47 (0.32) in line R, indicating that selection for GR was expected to result in a similar correlated response in FCR in both lines.     

油脂对鸡蛋内容物含量影响的研究

为探讨不同油脂对蛋鸡生产性能及蛋黄多不饱和脂肪酸和胆固醇含量的影响,160只42周龄的海塞克斯蛋鸡随机分成四组,分别饲喂对照日粮、5%鱼油、5%棕榈油和5%豆油日粮,试验三周。结果表明,棕榈油组的产蛋量比豆油组高(P<0.05),而对照组的平均蛋重和蛋黄重明显低于鱼油组(P<0.05),鱼油组鸡的总增重明显高于豆油组(P<0.05);鱼油组的血清和蛋黄的胆固醇含量都低于棕榈油和对照组(P<0.01);鱼油组蛋黄中的C20:5n-3含量明显高于对照组和豆油组(P<0.01),鱼油组蛋黄中的C22:6n-3含量高于棕榈油组(P<0.01);豆油组的C18:1n-9含量最低,与棕榈油组的相比,差异显著(P<0.05);豆油组的C18:2n-6含量明显高于其它三组(P<0.01),又以对照组最低,与鱼油组相比,差异显著(P<0.05);鱼油组的C18:3n-3含量高于豆油组和棕榈油组(P<0.05);鱼油组的C20:1n-9含量明显高于其它三组(P<0.01)。     

Effects of grass species on grazing steers: I. Diet composition and ingestive mastication.

In traditional grazing trials, per animal and per hectare productivity are determined, but pasture and animal measurements are generally inadequate to address reasons for different treatment responses. This 2-yr study examined the diet and diet characteristics of steers grazing tall fescue (Festuca arundinacea Schreb.), switchgrass (Panicum virgatum L.), flaccidgrass (Pennisetum flaccidum Griseb.), and bermudagrass (Cynodon dactylon [L.] Pers.) pastures. A randomized complete block design was used with two agronomic replicates. In vitro DM disappearance (IVDMD) of masticates from tall fescue (TF), switchgrass (SG), and flaccidgrass (FG) generally were similar; all exceeded 70% (70.3 to 79.9%), except for bermudagrass (BG), which was lowest (63.5 to 65.0%). Sieving the masticate DM showed BG to contain the highest proportion (20 to 29%) of particles passing a .5-mm sieve and the lowest proportion (6 to 8%) of particles retained on a 2.8-mm sieve. This resulted in BG having the smallest mean (1.29 mm) and median (1.08 mm) particle sizes in yr 1 and a mean (1.10 mm) and median (.91 mm) particle size smaller than SG in yr 2. Except for BG, the IVDMD of the masticate DM was lowest for small particles. Canopies showed BG and SG to have the highest proportion of stem (47 and 52%, respectively); the BG canopy was composed of fractions that were consistently lowest in IVDMD. In general, BG offered the grazing animal a canopy inferior in IVDMD concentration and had canopy characteristics that limited the animals' selection of a diet with quality as high as that of TF, SG, or FG.     

The relative effect of genomic information on efficiency of Bayesian analysis of the mixed linear model with unknown variance

This work focuses on the effects of variable amount of genomic information in the Bayesian estimation of unknown variance components associated with single‐step genomic prediction. We propose a quantitative criterion for the amount of genomic information included in the model and use it to study the relative effect of genomic data on efficiency of sampling from the posterior distribution of parameters of the single‐step model when conducting a Bayesian analysis with estimating unknown variances. The rate of change of estimated variances was dependent on the amount of genomic information involved in the analysis, but did not depend on the Gibbs updating schemes applied for sampling realizations of the posterior distribution. Simulation revealed a gradual deterioration of convergence rates for the locations parameters when new genomic data were gradually added into the analysis. In contrast, the convergence of variance components showed continuous improvement under the same conditions. The sampling efficiency increased proportionally to the amount of genomic information. In addition, an optimal amount of genomic information in variance–covariance matrix that guaranty the most (computationally) efficient analysis was found to correspond a proportion of animals genotyped ***0.8. The proposed criterion yield a characterization of expected performance of the Gibbs sampler if the analysis is subject to adjustment of the amount of genomic data and can be used to guide researchers on how large a proportion of animals should be genotyped in order to attain an efficient analysis.     

Effects of grass species on grazing steers: II. Dry matter intake and digesta kinetics

Animal responses to treatments in grazing experiments frequently remain unexplained because of inadequate pasture and(or) animal measurements. This 2-yr study examined DMI, gastrointestinal tract fill of undigested DM (FILL), rate of digesta passage (ROP), and digesta mean retention time (MRT) for steers grazing tall fescue (Festuca arundinacea Schreb.), switchgrass (Panicum virgatum L.), flaccidgrass (Pennisetum flaccidum Griseb.), and bermudagrass (Cynodon dactylon [L.] Pers.). A randomized complete block design was used with two agronomic replicates. Comparisons in June (yr 1) among continuously grazed switchgrass (SG), flaccidgrass (FG), and bermudagrass (BG) or in May (yr 2) among tall fescue (TF), SG, and FG showed similar digesta kinetics, but different DMI (kg.d-1.100 kg BW-1), among these forages within each sampling. In the June evaluation, the DMI of SG and FG were similar (means = 3.09), DMI of bermudagrass (BG) was lowest (2.23), and fecal DM output (FO) was similar among forages. In the May evaluation, DMI by steers grazing SG (3.90) was higher than that by steers grazing FG (2.97); DMI of tall fescue (TF) was intermediate (3.41) but similar to DMI of FG. Differences in DMI were due to differences in diet in vitro DM disappearance (IVDMD) rather than to differences in digesta kinetics. In July (yr 2), the MRT was highest for BG (84 h) and similar for SG and FG (57 h). Steers grazing different forages exhibited similar ROP and FILL, but FO (kg.d-1.100 kg BW-1) among steers varied (.37 for steers fed BG; .74 for steers fed SG and FG).(ABSTRACT TRUNCATED AT 250 WORDS)     

Evaluation of chopped switchgrass and chopped bermudagrass as litter materials over multiple heavy broiler flocks

Chopped switchgrass (SG) and chopped bermudagrass (BG) were evaluated as alternatives to pine shavings (PS) for broiler litter over 3 flocks. Twenty-four pens were filled with the 3 litter types. Live performance parameters included mortality, BW, BW gain, feed consumption, and feed conversion. Mortality was not different for litter type or flock. All other live variables were different (P < 0.0001) for flock. Mean foot pad scores (FPS) were only different (P < 0.0001) for flock. Litter performance variables included litter and cake moisture content (MC), pH, litter ammonia concentration, and cake nutrient values [nitrogen, phosphorus, and potassium (N–P–K)]. Litter and cake MC differed by litter type and flock (P < 0.0001). Litter MC was 1% lower for SG than BG or PS. Cake depth observations were similar for litter type. Litter pH differed by flock (P = 0.008) while cake pH differed for both litter type (P = 0.05) and flock (P < 0.0001). Beginning and ending litter ammonia concentration were different for flock (P < 0.0001). Potassium was different for both litter type (P = 0.04) and flock (P < 0.0001) while nitrogen and phosphorus differed only by flock (P < 0.0001). Chopped SG and BG performed as well as PS as a litter material over 3 grow-out cycles. Based on the results of this study, chopped grass materials appear to be a viable alternative to PS for broiler bedding.     

Genetic parameters and evaluation of the Tunisian dairy cattle population for milk yield by Bayesian and BLUP analyses

A Markov Chain Monte Carlo Bayesian method and BLUP analyses were used on Tunisian dairy cattle data. Data included 92,106 lactation records collected on 37,536 animals over 19 freshening years, from 1983 to 2001. Each record was partitioned into the fixed effects of herd-year, month of calving, and age-parity, a permanent environmental effect, an additive genetic effect, and a residual effect.

Posterior conditional distributions were determined for variance components and model effects. Solutions (BLUE) and posterior means for levels of herd-year, month of calving, and age-parity showed similar patterns. Posterior means of heritability and repeatability were 0.17 ± 18 × 10^− 5 and 0.39 ± 8 × 10^− 5, respectively. Posterior means of bull's breeding values were compared to bull's BLUP solutions. BLUP solutions were obtained using 0.17 and 0.39, estimated from the data, and 0.25 and 0.40 estimates for heritability and repeatability, respectively. Rank correlations between bull's posterior means and BLUP breeding values were 0.998 and 0.994 using genetic parameters estimated from the data and from the literature, respectively. This correlation coefficient was 0.995 between bull's BLUP solutions using either of the two sets of genetic parameters.     

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.     

Impact of variation in length of individual testing periods on estimation of (co)variance components of a random regression model for feed intake of growing pigs

A simulation study was conducted to assess the influence of differences in the length of individual testing periods on estimates of (co)variance components of a random regression model for daily feed intake of growing pigs performance tested between 30 and 100 kg live weight. A quadratic polynomial in days on test with fixed regressions for sex, random regressions for additive genetic and permanent environmental effects and a constant residual variance was used for a bivariate simulation of feed intake and daily gain. (Co)variance components were estimated for feed intake only by means of a Bayesian analysis using Gibbs sampling and restricted maximum likelihood (REML). A single trait random regression model analogous to the one used for data simulation was used to analyse two versions of the data: full data sets with 18 weekly means of feed intake per animal and reduced data sets with the individual length of testing periods determined when tested animals reached 100 kg live weight. Only one significant difference between estimates from full and reduced data (REML estimate of genetic covariance between linear and quadratic regression parameters) and two significant differences from expected values (Gibbs estimates of permanent environmental variance of quadratic regression parameters) occurred. These differences are believed to be negligible, as the number lies within the expected range of type I error when testing at the 5% level. The course of test day variances calculated from estimates of additive genetic and permanent environmental covariance matrices also supports the conclusion that no bias in estimates of (co)variance components occurs due to the individual length of testing periods of performance‐tested growing pigs. A lower number of records per tested animal only results in more variation among estimates of (co)variance components from reduced compared with full data sets. Compared with the full data, the effective sample size of Gibbs samples from the reduced data decreased to 18% for residual variance and increased up to five times for other (co)variances. The data structure seems to influence the mixing of Gibbs chains.     

Comparison of methods for handling censored records in beef fertility data: simulation study

A simulation study was conducted to compare methods for handling censored records for days to calving in beef cattle data. Days to calving was defined as the time, in days, between when a bull is turned out in the pasture and the subsequent parturition. Simulated data were generated to have data structure and genetic relationships similar to an available field data set. Records were simulated for 33,176 daughters of 4,238 sires. Data were simulated using a mixed linear model that included the fixed effects of contemporary group and sex of calf, linear and quadratic covariates for age at mating, and random effects of animal and residual error. Two methods for handling censored records were evaluated, and two censoring rates of 12 and 20% were applied to assess the influence of higher censoring rates on inferences. Censored records were assigned penalty values on a within-contemporary group basis under the first method (DCPEN). Under the second method (DCSIM), censored records were drawn from their respective predictive distributions. A Bayesian approach via Gibbs sampling was used to estimate variance components and predict breeding values. Posterior means (PM) and standard deviations (SD) of additive genetic variance for DCPEN at 12 and 20% censoring were 23.2 (3.7) and 21.0 (3.6), respectively, whereas the same estimates for DCSIM at 12 and 20% censoring were 23.7(3.3) and 21.9 (3.4), respectively. In all cases, the true value of the genetic variance was within the high posterior density (HPD) interval (95%). The PM (SD) of residual variance for DCPEN at 12 and 20% censoring were 415.7 (4.7) and 440.0 (4.8) respectively, whereas the same estimates for DCSIM at 12 and 20% censoring were 371.0 (4.3) and 365.4 (4.4), respectively. The true value of the residual variance was within the HPD (95%) for DCSIM, but it was outside this interval for DCPEN at both censoring rates, indicating a systematic bias for this parameter. Bayes Factor and Deviance Information Criteria were used for model comparisons, and both criteria indicated the superiority of the DCSIM method. However, little difference was observed between the two methods for correlations between true breeding values and posterior means of animal effects for sires, indicating that no major reranking of sires would be expected. This finding suggests that either censored data handling technique can be successfully used in a genetic evaluation for days to calving.