Genetic parameters estimated with multitrait and linear spline-random regression models using Gelbvieh early growth data

Estimates of direct and maternal genetic parameters in beef cattle were obtained with a random regression model with a linear spline function (SFM) and were compared with those obtained by a multitrait model (MTM). Weight data of 18,900 Gelbvieh calves were used, of which 100, 75, and 17% had birth (BWT), weaning (WWT), and yearling (YWT) weights, respectively. The MTM analysis was conducted with a three-trait maternal animal model. The MTM included an overall linear partial fixed regression on age at recording for WWT and YWT, and direct-maternal genetic and maternal permanent environmental effects. The SFM included the same effects as MTM, plus a direct permanent environmental effect and heterogeneous residual variance. Three knots, or breakpoints, were set to 1, 205, and 365 d. (Co)variance components in both models were estimated with a Bayesian implementation via Gibbs sampling using flat priors. Because BWT had no variability of age at recording, there was good agreement between corresponding components of variance estimated from both models. For WWT and YWT, with the exception of the sum of direct permanent environmental and residual variances, there was a general tendency for SFM estimates of variances to be lower than MTM estimates. Direct and maternal heritability estimates with SFM tended to be lower than those estimated with MTM. For example, the direct heritability for YWT was 0.59 with MTM, and 0.48 with SFM. Estimated genetic correlations for direct and maternal effects with SFM were less negative than those with MTM. For example, the direct-maternal correlation for WWT was -0.43 with MTM and -0.33 with SFM. Estimates with SFM may be superior to MTM due to better modeling of age in both fixed and random effects.     

Influence of population structure on estimates of direct and maternal parameters.

The estimation of (co)variance components for multiple traits with maternal genetic effects was found to be influenced by population structure. Two traits in a closed breeding herd with random mating were simulated over nine generations. Population structures were simulated on the basis of different proportions of dams not having performance records (0, 0.1, 0.5, 0.8 and 0.9): three genetic correlations (-0.5, 0.0 and +0.5) between direct and maternal effects and three genetic correlations (0, 0.3 and 0.8) between two traits. Three ratios of direct to maternal genetic variances, (1:3, 1:1, 3:1), were also considered. Variance components were estimated by restricted maximum likelihood. The proportion of dams without records had an effect on the SE of direct-maternal covariance estimates when the proportion was 0.8 or 0.9 and the true correlation between direct and maternal effects was negative. The ratio of direct to maternal genetic variances influenced the SE of the (co)variance estimates more than the proportion of dams with missing records. The correlation between two traits did not have an effect on the SE of the estimates. The proportion of dams without records and the correlation between direct and maternal effects had the strongest effects on bias of estimates. The largest biases were obtained when the proportion of dams without records was high, the correlation between direct and maternal effects was positive, and the direct variance was greater than the maternal variance, as would be the situation for most growth traits in livestock. Total bias in all parameter estimates for two traits was large in the same situations. Poor population structure can affect both bias and SE of estimates of the direct-maternal genetic correlation, and can explain some of the large negative estimates often obtained.     

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 models to estimate genetic effects of weaning weight of Angus cattle

Weaning weights from nine sets of Angus field data from three regions of the United States were analyzed. Six animal models were used to compare two approaches to account for an environmental dam-offspring covariance and to investigate the effects of sire x herd-year interaction on the genetic parameters. Model 1 included random direct and maternal genetic, maternal permanent environmental, and residual effects. Age at weaning was a covariate. Other fixed effects were age of dam and a herd-year-management-sex combination. Possible influence of a dam's phenotype on her daughter's maternal ability was modeled by including a regression on maternal phenotype (fm) (Model 3) or by fitting grandmaternal genetic and grandmaternal permanent environmental effects (Model 5). Models 2, 4, and 6 were based on Models 1, 3, and 5, respectively, and additionally included sire x herd-year (SH) interaction effects. With Model 3, estimates of fm ranged from -.003 to .014, and (co)variance estimates were similar to those from Model 1. With Model 5, grandmaternal heritability estimates ranged from .02 to .07. Estimates of maternal heritability and direct-maternal correlation (r(am)) increased compared with Model 1. With models including SH, estimates of the fraction of phenotypic variance due to SH interaction effects were from .02 to .10. Estimates of direct and maternal heritability were smaller and estimates of r(am) were greater than with models without SH interaction effects. Likelihood values showed that SH interaction effects were more important than fm and grandmaternal effects. The comparisons of models suggest that r(am) may be biased downward if SH interaction and(or) grandmaternal effects are not included in models for weaning weight.     

Additive, dominance, and epistatic loss effects on preweaning weight gain of crossbred beef cattle from different Bos taurus breeds

(Co)variance components, direct and maternal breed additive, dominance, and epistatic loss effects on preweaning weight gain of beef cattle were estimated. Data were from 478,466 animals in Ontario, Canada, from 1986 to 1999, including records of both purebred and crossbred animals from Angus, Blonde d'Aquitaine, Charolais, Gelbvieh, Hereford, Limousin, Maine-Anjou, Salers, Shorthorn, and Simmental breeds. The genetic model included fixed direct and maternal breed additive, dominance, and epistatic loss effects, fixed environmental effects of age of the calf, contemporary group, and age of the dam x sex of the calf, random additive direct and maternal genetic effects, and random maternal permanent environment effects. Estimates of direct and maternal additive genetic, maternal permanent environmental and residual variances, expressed as proportions of the phenotypic variance, were 0.32, 0.20, 0.12, and 0.52, respectively. Correlation between direct and maternal additive genetic effects was -0.63. Breed ranking was similar to previous studies, but estimates showed large SE. The favorable effects of direct and maternal dominance (P < 0.05) on preweaning gain were equivalent to 1.3 and 2.3% of the phenotypic mean of purebred calves, respectively. The same features for direct and maternal epistatic loss effects were -2.2% (P < 0.05) and -0.1% (P > 0.05). The large SE of breed effects were likely due to multicollinearity among predictor variables and deficiencies in the dataset to separate direct and maternal effects and may result in a less reliable ranking of the animals for across breed comparisons. Further research to identify the causes of the instability of estimates of breed additive, dominance, and epistatic loss genetic effects, and application of alternative statistical methods is recommended.     

Estimation of direct, maternal, and grandmaternal genetic effects for weaning weight in several breeds of beef cattle.

Weaning weights from nine parental breeds and three composites were analyzed to estimate variance due to grandmaternal genetic effects and to compare estimates for variance due to maternal genetic effects from two different models. Number of observations ranged from 794 to 3,465 per population. Number of animals in the pedigree file ranged from 1,244 to 4,326 per population. Two single-trait animal models were used to obtain estimates of covariance components by REML using an average information method. Model 1 included random direct and maternal genetic, permanent maternal environmental, and residual environmental effects as well as fixed sex x year and age of dam effects. Model 2 in addition included random grandmaternal genetic and permanent grandmaternal environmental effects to account for maternal effects of a cow on her daughter's maternal ability. Non-zero estimates of proportion of variance due to grandmaternal effects were obtained for 7 of the 12 populations and ranged from .03 to .06. Direct heritability estimates in these populations were similar with both models. Existence of variance due to grandmaternal effects did not affect the estimates of maternal heritability (m2) or the correlation between direct and maternal genetic effects (r(am)) for Angus and Gelbvieh. For the other five populations, magnitude of estimates increased for both m2 and r(am) when estimates of variance due to grandmaternal effects were not zero. Estimates of the correlation between maternal and grandmaternal genetic effects were large and negative. These results suggest that grand-maternal effects exist in some populations, that when such effects are ignored in analyses maternal heritability may be underestimated, and that the correlation between direct and maternal genetic effects may be biased downward if grandmaternal effects are not included in the model for weaning weight of beef cattle.     

Effects of sire misidentification on estimates of genetic parameters for birth and weaning weights in Hereford cattle

Birth weights (4,155) and weaning weights (3,884) of Line 1 Herefords collected at the Fort Keogh Livestock and Range Research Laboratory in Miles City, MT, between the years of 1935 to 1989 were available. To study the effect of misidentification on estimates of genetic parameters, the sire identification of calf was randomly replaced by the identification of another sire based on the fraction of progeny each sire contributed to a yearly calf crop. Misidentification rates ranged from 5 to 50% with increments of 5%. For each rate of misidentification, 100 replicates were obtained and analyzed with single-trait and two-trait analyses with a restricted maximum likelihood (REML) algorithm. Two different models were used. Both models contained year x sex combinations and ages of dam as fixed effects, calendar birth date as a fixed covariate, and random animal and maternal genetic effects and maternal permanent environment effects. Model 2 also included sire x year combinations as random effects. As the rate of misidentification increased, estimates of the direct-maternal genetic correlation increased for both traits, with both models, for all analyses. With singletrait analyses, estimates of the fraction of variance that were due to sire x year interaction effects increased slightly for birth weight (near zero) and decreased slightly (0.015 to 0.004) for weaning weight as misidentification increased. With two-trait analyses, estimates of fraction of variance that were due to sire x year effects gradually decreased for weaning weight as misidentification increased. With the two-trait analyses, and with both models, as the level of sire misidentification increased, estimates of the genetic correlation between direct effects gradually increased, and estimates of the correlation between maternal effects gradually decreased. Estimates of the direct-maternal genetic correlation were more positive with Model 2 than with Model 1 for all levels of misidentification. Results of this study indicate that misidentification of sires would severely bias estimates of genetic parameters and would reduce genetic gain from selection.     

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.     

Evaluation of animal models to explore the influence of maternal genetic and maternal permanent environment effect on reproductive performance of Jersey crossbred cattle

The present study was conducted on 1,002 reproductive records of 430 Jersey crossbred cattle, descended from 57 sires and 198 dams, maintained at the Eastern Regional Station of ICAR-National Dairy Research Institute, Kalyani, Nadia, West Bengal, India to investigate the influence of direct genetic, maternal genetic and maternal permanent environmental effect on three most important reproductive traits viz., number of service per conception (NSPC), days open (DO) and calving interval (CI) of Jersey crossbred cattle. Six single-trait animal models (including or excluding maternal genetic or permanent environmental effects) were fitted to analyse these traits, and the best model was chosen after testing the significant increase in the log-likelihood values when additional parameters were added in the model. Direct heritability estimates for NSPC, DO and CI from the best model were 0.10, 0.14 and 0.20, respectively. The maternal permanent environmental (c²) effects on reproductive traits accounted for almost negligible fraction of the total phenotypic variance in this study. The maternal genetic effects (m²) also contributed very little (0%–3%) to the total phenotypic variance except for CI where it was important and accounted for 20% of phenotypic variance. A significantly large negative genetic correlation was observed between direct and maternal genetic effects for all traits, suggesting the presence of antagonistic relationship between dam's direct additive component and daughter's additive genetic component. Results suggest that both direct and maternal effects were important only for CI but not for other traits. Therefore, both direct additive effects and maternal genetic effect need to be considered for improving this trait by selection.     

Direct genetic, maternal genetic, and heterozygosity effects on weaning weight in a Colombian multibreed beef cattle population

The (co)variance components of BW at weaning (WW) were estimated for a Colombian multibreed beef cattle population. A single-trait animal model was used. The model included the fixed effect of contemporary group (sex, season, and year), and covariates including age of calf at weaning, age of cow, individual and maternal heterozygosity proportions, and breed percentage. Direct genetic, maternal genetic, permanent environmental, and residual effects were included as random effects. Direct, maternal, and total heritabilities were 0.23 +/- 0.047, 0.15 +/- 0.041, and 0.19, respectively. The genetic correlation between direct and maternal effects was -0.42 +/- 0.131, indicating that there may be antagonism among genes for growth and genes for maternal ability, which in turn suggests that improving WW by direct and maternal EPD may be difficult. A greater value for the direct heterosis effect compared with the maternal heterosis effect was found. Furthermore, the greater the proportion of Angus, Romosinuano, and Blanco Orejinegro breeds, the less the WW.     

Estimates of genetic parameters for worm resistance,wool and growth traits in Merino sheep of Uruguay

The genotype of an individual and the environment as the maternal ability of its dam have substantial effects on the phenotype expression of many production traits. The aim of the present study was to estimate the (co)variance components for worm resistance, wool and growth traits in Merino sheep, testing the importance of maternal effects and to determine the most appropriate model for each trait. The traits analyzed were Greasy Fleece Weight (GFW), Clean Fleece Weight (CFW), average Fibre Diameter (FD), Coefficient of Variation of FD (CVFD), Staple Length (SL), Comfort Factor (CF30), Weaning Weight (WWT), Yearling Body Weight (YWT) and Faecal worm Egg Count (FEC). The data were recorded during a 15-year period from 1995 to 2010, from Uruguayan Merino stud flocks. A Bayesian analysis was performed to estimate (co)variance components and genetic parameters. By ignoring or including maternal genetic or environmental effects, five different univariate models were fitted in order to determine the most effective for each trait. For CVFD and YWT, the model fitting the data best included direct additive effects as the only significant random source of variation. For GFW, CFW, FD, SL and CF30 the most appropriate model included direct-maternal covariance; while for FEC included maternal genetics effects with a zero direct-maternal covariance. The most suitable model for WWT included correlated maternal genetic plus maternal permanent environmental effects. The estimates of direct heritability were moderate to high and ranged from 0.15 for log transformed FEC to 0.74 for FD. Most of the direct additive genetic correlation (rg) estimations were in the expected range for Merino breed. However, the estimate of rg between FEC and FD was unfavourable (−0.18±0.03). In conclusion, there is considerable genetic variation in the traits analyzed, indicating the potential to make genetic progress on these traits. This study showed that maternal effects are influencing most of traits analyzed, thus these effects should be considered in Uruguayan Merino breeding programs; since the implementation of an appropriate model of analysis is critical to obtain accurate estimates.     

Maternal effects on docility in Limousin cattle

The objective of this study was to quantify the role of maternal effects on docility in Limousin cattle. Docility scores were obtained at weaning while animals were restrained in a squeeze chute. Scores 1 through 6 represented a docile to aggressive temperament, respectively, and were provided by the North American Limousin Foundation. Observations with unknown age of dam, contemporary groups containing less than 10 observations, contemporary groups with no variation, and single-sire contemporary groups were removed, leaving 21,932 observations. A 2-generation pedigree file compiled from animals with observations contained 49,459 animals. Fixed effects were weaning contemporary group and age of dam (2, > or =3 yr). Six animal models encompassed combinations of random factors: direct genetic, maternal genetic, and maternal permanent environmental effects. The model D was the most basic, containing direct genetic and residual effects, and it resembled the method currently used by the North American Limousin Foundation for genetic evaluation of docility. Maternal genetic or permanent environmental effects were separately added to the model D, denoted as models DM and DC, respectively. Model DMC contained all random factors. Models DM-Zero and DMC-Zero were equivalent to models DM and DMC, respectively, but with zero direct-maternal genetic covariance. Direct heritability estimates were moderate for all models (0.29 +/- 0.02 to 0.38 +/- 0.03). Maternal heritability estimates were low, ranging from 0.01 +/- 0.01 (DM-Zero) to 0.05 +/- 0.02 (DM). Negative direct-maternal genetic correlations of -0.41 +/- 0.09 and -0.55 +/- 0.09 were estimated for models DM and DMC, respectively. The proportion of phenotypic variance accounted for by maternal permanent environmental effects was 0.03 +/- 0.01, 0.04 +/- 0.01, and 0.02 +/- 0.01 for models DC, DMC, and DMC-Zero, respectively. Likelihood ratio tests indicated that model DMC best fit the data. Although maternal genetic and maternal permanent environmental effects were significant, they accounted for only 8% (model DMC) of the phenotypic variance, and a Spearman rank correlation of 0.99 between models D and DMC showed sires did not rank differently with or without inclusion of these effects. Given these results, inclusion of maternal effects to the genetic evaluation of docility in Limousin cattle does not seem warranted.     

Synthesis of direct and maternal genetic components of economically important traits from beef breed-cross evaluations

Published information on relative performance of beef breed crosses was used to derive combined estimates of purebred breed values for predominant temperate beef breeds. The sources of information were largely from the United States, Canada, and New Zealand, although some European estimates were also included. Emphasis was on maternal traits of potential economic importance to the suckler beef production system, but some postweaning traits were also considered. The estimates were taken from comparison studies undertaken in the 1970s, 1980s and 1990s, each with representative samples of beef breeds used in temperate agriculture. Weighting factors for breed-cross estimates were derived using the number of sires and offspring that contributed to that estimate. These weights were then used in a weighted multiple regression analysis to obtain single purebred breed effects. Both direct additive and maternal additive genetic effects were estimated for preweaning traits. Important genetic differences between the breeds were shown for many of the traits. Significant regression coefficients were estimated for the effect of mature weight on calving ease, both maternal and direct additive genetic, survival to weaning direct, and birth weight direct. The breeds with greater mature weight were found to have greater maternal genetic effects for calving ease but negative direct genetic effects on calving ease. A negative effect of mature weight on the direct genetic effect of survival to weaning was observed. A cluster analysis was done using 17 breeds for which information existed on nine maternal traits. Regression was used to predict breed-cross-specific heterosis using genetic distance. Only five traits, birth weight, survival to weaning, cow fertility, and preweaning and postweaning growth rate had enough breed-cross-specific heterosis estimates to develop a prediction model. The breed biological values estimated provide a basis to predict the biological value of crossbred suckler cows and their offspring.     

Genetic (co)variances for calving difficulty score in composite and parental populations of beef cattle: I. Calving difficulty score, birth weight, weaning weight, and postweaning gain

Heritability of 2-yr-old heifer calving difficulty score was estimated in nine purebred and three composite populations with a total of 5,986 calving difficulty scores from 520 sires and 388 maternal grandsires. Estimates were 0.43 for direct (calf) genetic effects and 0.23 for maternal (heifer) genetic effects. The correlation between direct and maternal effects was -0.26. Direct effects were strongly positively correlated with birth weight and moderately correlated with 200-d weight and postweaning gain. Smaller negative correlations of maternal calving difficulty with direct effects of birth weight, weaning weight, and postweaning gain were estimated. Calving difficulty was scored from 1 to 7. Predicted heritabilities using seven optimal scores were similar to those using four scores. The predicted heritability using only two categories was reduced 23%. Phenotypic and direct genetic variance increased with increasing average population calving difficulty score. The estimated direct and maternal heritabilities for 2-yr-old calving difficulty score were larger than many literature estimates. These estimates suggested substantial variance for direct and maternal genetic effects. The direct effects of 2-yr-old calving difficulty score seemed to be much more closely tied to birth weight than were maternal effects.     

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 nuclear and nonnuclear inheritance in three synthetic lines of beef cattle differing in mature size.

Genetic parameters for nuclear and cytoplasmic genetic effects were estimated from preweaning growth data collected on three synthetic lines of beef cattle differing in mature size. Lines of small-, medium-, and large-framed calves were represented in each of two research herds (Rhodes and McNay). Variance components were estimated separately by herd and size line for birth weight and 205-d weight (WW) by REML with an animal mode using an average of 847 and 427 calf records from Rhodes and McNay, respectively. Model 1 included effects of fixed year, sex of calf, age of dam, and random additive direct (a), additive maternal genetic (m), covariance (a,m), permanent environment affecting the dam, and residual error. Model 2 differed from Model 1 by including random cytoplasmic lineage effects and by ignoring permanent environmental effects. Model 1--direct (maternal) heritability estimates for birth weight at Rhodes were .62(.03) for small, .67(.06) for medium, and .30(.11) for large lines. Genetic correlations between direct and maternal effects for birth weight were .67, -.16, and .48 for the respective size groups. For WW at Rhodes, direct (maternal) heritability estimates were .30(.29), .30(.14), and .10(.16) for small, medium, and large lines, respectively, with genetic correlations of -.34 (small), -.12 (medium), and .17 (large). Heritability estimates at McNay were similar to those at Rhodes, except that maternal genetic heritabilities for WW were smaller (.10, small; .01, medium; .00, large). Model 2--estimates for nuclear genetic effects were consistent with the estimates from Model 1. Cytoplasmic variance accounted for 0 to 5% of the total random variance in birth weight. For WW, cytoplasmic variance was negligible at Rhodes and accounted for 4% of the total random variance in the large line at McNay, averaging less than the permanent environment. Results failed to indicate that cytoplasmic variance was important for preweaning performance.     

Bayesian inference for genetic parameter estimation on growth traits for Nelore cattle in Brazil,using the Gibbs sampler

This data set consisted of over 29 245 field records from 24 herds of registered Nelore cattle born between 1980 and 1993, with calves sires by 657 sires and 12 151 dams. The records were collected in south‐eastern and midwestern Brazil and animals were raised on pasture in a tropical climate. Three growth traits were included in these analyses: 205‐ (W205), 365‐ (W365) and 550‐day (W550) weight. The linear model included fixed effects for contemporary groups (herd‐year‐season‐sex) and age of dam at calving. The model also included random effects for direct genetic, maternal genetic and maternal permanent environmental (MPE) contributions to observations. The analyses were conducted using single‐trait and multiple‐trait animal models. Variance and covariance components were estimated by restricted maximum likelihood (REML) using a derivative‐free algorithm (DFREML) for multiple traits (MTDFREML). Bayesian inference was obtained by a multiple trait Gibbs sampling algorithm (GS) for (co)variance component inference in animal models (MTGSAM). Three different sets of prior distributions for the (co)variance components were used: flat, symmetric, and sharp. The shape parameters (ν) were 0, 5 and 9, respectively. The results suggested that the shape of the prior distributions did not affect the estimates of (co)variance components. From the REML analyses, for all traits, direct heritabilities obtained from single trait analyses were smaller than those obtained from bivariate analyses and by the GS method. Estimates of genetic correlations between direct and maternal effects obtained using REML were positive but very low, indicating that genetic selection programs should consider both components jointly. GS produced similar but slightly higher estimates of genetic parameters than REML, however, the greater robustness of GS makes it the method of choice for many applications.     

Genotypic expression with different ages of dams: III. Weight traits of sheep.

Correlations between genetic expression in lambs when dams were young (1 yr), middle-aged (2 and 3 yr), or older (older than 3 yr) were estimated with three-trait analyses for weight traits. Weights at birth (BWT) and weaning (WWT) and ADG from birth to weaning were used. Numbers of observations were 7,731, 9,518, 9,512, and 9,201 for Columbia (COLU), Polypay (POLY), Rambouillet (RAMB), and Targhee (TARG) breeds of sheep, respectively. When averaged, relative estimates for WWT and ADG were similar across breeds. Estimates were variable across breeds. On average, direct heritability was greater when environment was young dams (.44 for BWT and .34 for WWT) than when environment was dams of middle age or older (.24 and .28 for BWT and .20 and .16 for WWT, respectively). Maternal heritability was greater when dams were middle-aged or older (.28 and .22 vs .18) for BWT but was greater when dams were younger (.10 vs .05 and .04) for WWT. The estimates of genetic correlations for direct effects across age of dam environments averaged .32 for birth weight and averaged .70 for weaning weight. Average estimates of maternal genetic correlations across age of dam classes were .36 or less for both BWT and WWT. Average estimates of correlations among maternal permanent environmental effects were .49 or less across age of dam classes. Total maternal effects accounted for .33 to .42 of phenotypic variance for BWT and for .09 to .26 of phenotypic variance for WWT. The average estimates of genetic correlations between expressions of the same genotypes with different ages of dams suggest that measurements of BWT of lambs with dams in young, middle, and older age classes should be considered to be separate traits for genetic evaluation and that for WWT measurements with young age of dam class and combined middle and older age of dam classes should be considered to be separate traits for genetic evaluation.     

Comparison of models for estimation of genetic parameters for mature weight of Hereford cattle

Genetic parameters of mature weight are needed for effective selection and genetic evaluation. Data for estimating these parameters were collected from 1963 to 1985 and consisted of 32,018 mature weight records of 4,175 Hereford cows that were in one control and three selection lines that had been selected for weaning weight, for yearling weight, or for an index combining yearling weight and muscle score for 22 yr. Several models and subsets of the data were considered. The mature weight records consisted of a maximum of three seasonal weights taken each year, at brand clipping (February and March), before breeding (May and June), and at palpation (August and September). Heritability estimates were high (0.49 to 0.86) for all models considered, which suggests that selection to change mature weight could be effective. The model that best fit the data included maternal genetic and maternal permanent environmental effects in addition to direct genetic and direct permanent environmental effects. Estimates of direct heritability with this model ranged from 0.53 to 0.79, estimates of maternal heritability ranged from 0.09 to 0.21, and estimates of the genetic correlation between direct and maternal effects ranged from -0.16 to -0.67 for subsets of the data based on time of year that mature weight was measured. For the same subsets, estimates of the proportions of variance due to direct permanent environment and maternal permanent environment ranged from 0.00 to 0.09 and 0.00 to 0.06, respectively. Using a similar model that combined all records and included an added fixed effect of season of measurement of mature weight, direct heritability, maternal heritability, genetic correlation between direct and maternal effects, proportion of variance due to direct permanent environmental effects, and proportion of variance due to maternal permanent environmental effects were estimated to be 0.69, 0.13, -0.65, 0.00, and 0.04, respectively. Mature weight is a highly heritable trait that could be included in selection programs and maternal effects should not be ignored when analyzing mature weight data.     

Calving performance and calf mortality

The most important maternal factor influencing calving performance is parity. Among calf factors, birth weight seems the most important. There are large differences between breeds and, generally speaking, heavier beef and dual-purpose breeds present more problems than smaller cattle. Variation in calving performance and stillbirth may be attributed to characters of both the calf and the dam. Genetic variation in calving performance and stillbirth at first calving has been demonstrated in several investigations for both the direct (calf) and the maternal character.In a Swedish investigation a heritability of 10% was found for both the direct and the maternal character. For stillbirth values were on average 3%. A strong genetic relationship was found between calving performance and birth weight as direct characters (r_GD = 0.98) but for the maternal characters it was considerably weaker (r_GM = 0.60). Correlations between stillbirth rate and birth weight were generally weaker, because the relationship was non-linear. Estimations of the genetic correlations between direct and maternal effects gave values between zero and ?0.5 for the characters investigated, indicating an antagonistic relationship between the genetic make-up of the cow and the calf. This implies that, in the long run, selection will not be as effective as the heritabilities suggest.A substantial improvement in calving performance and calf mortality can be achieved, however, through selection within breeds, optimal organization of breeding structures, choice of appropriate beef breeds for cross-breeding on heifers and cows, respectively, and timing calving to occur at favourable ages and in favourable seasons.