The empirical bias of estimates by restricted maximum likelihood, Bayesian method, and method R under selection for additive, maternal, and dominance models.

Bayesian analysis via Gibbs sampling, restricted maximum likelihood (REML), and Method R were used to estimate variance components for several models of simulated data. Four simulated data sets that included direct genetic effects and different combinations of maternal, permanent environmental, and dominance effects were used. Parents were selected randomly, on phenotype across or within contemporary groups, or on BLUP of genetic value. Estimates by Bayesian analysis and REML were always empirically unbiased in large data sets. Estimates by Method R were biased only with phenotypic selection across contemporary groups; estimates of the additive variance were biased upward, and all the other estimates were biased downward. No empirical bias was observed for Method R under selection within contemporary groups or in data without contemporary group effects. The bias of Method R estimates in small data sets was evaluated using a simple direct additive model. Method R gave biased estimates in small data sets in all types of selection except BLUP. In populations where the selection is based on BLUP of genetic value or where phenotypic selection is practiced mostly within contemporary groups, estimates by Method R are likely to be unbiased. In this case, Method R is an alternative to single-trait REML and Bayesian analysis for analyses of large data sets when the other methods are too expensive to apply.     

Direct genetic, maternal and litter effects on behaviour in German shepherd dogs in Sweden

The aim of this study was to study genetic (co)variation of broader behavioural traits in German shepherd dogs and to test whether there is maternal and litter influence on these traits. Data were extracted from the Swedish Dog Mentality Assessment (DMA) from 1989 to 2001 on 5959 German shepherd dogs. Based on previous results, personality traits were created from the 15 behavioural variables extracted from the test. These personality traits were (1) Playfulness, (2) Chase-proneness, (3) Curiosity/Fearlessness, and (4) Aggressiveness. A trait Boldness was constructed from all behaviour variables except those included in Aggressiveness. Mixed linear models with fixed effects of sex, test type, test year, test month, age, and judge were used. Models with all combinations of random effects of animal (direct genetic), genetic and non-genetic maternal, and litter were tested. The best model included effects of animal and litter. Direct heritability estimates were between 0.09 and 0.23, highest for Playfulness and Curiosity/Fearlessness. Maternal heritabilities were all low (0.01-0.08), lowest and not significant if litter or non-genetic maternal effects were included in the model. Additive genetic correlations among Playfulness, Chase-proneness, and Curiosity/Fearlessness were higher (0.54-0.74) than genetic correlations with Aggressiveness (0.29-0.40). Litter variance ratios (c²) were larger than the maternal heritabilities (0.03-0.10). Boldness had a direct heritability estimate of 0.27 and a direct genetic correlation with Aggressiveness of 0.37. We conclude that there is substantial additive genetic variation, that the mother has rather little influence (both genetically and environmentally) and that the litter seems to have a larger influence than the mother for these personality traits. Genetic improvement in these behaviour traits is thus possible.     

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.     

Genetic parameters for individual birth and weaning weight and for litter size of Large White pigs

Data from a French experimental herd recorded between 1990 and 1997 were used to estimate genetic parameters for individual birth and weaning weight, as well as litter size of Large White pigs using restricted maximum likelihood (REML) methodology applied to a multivariate animal model. In addition to fixed effects the model included random common environment of litter, direct and maternal additive genetic effects. The data consisted of 1928 litters including individual weight observations from 18 151 animals for birth weight and from 15 360 animals for weaning weight with 5% of animals transferred to a nurse. Estimates of direct and maternal heritability and proportion of the common environmental variance for birth weight were 0.02, 0.21 and 0.11, respectively. The corresponding values for weaning weight were 0.08, 0.16 and 0.23 and for litter size 0.22, 0.02 and 0.06, respectively. The direct and the maternal genetic correlations between birth and weaning weight were positive (0.59 and 0.76). Weak positive (negative) genetic correlations between direct effects on weight traits and maternal effects on birth weight (weaning weight) were found. Negative correlations were found between direct genetic effect for litter size and maternal genetic effects on all three traits. The negative relationship between litter size and individual weight requires a combined selection for litter size and weight.     

Genetic parameters for individual birth and weaning weight and for litter size of Large White pigs

Data from a French experimental herd recorded between 1990 and 1997 were used to estimate genetic parameters for individual birth and weaning weight, as well as litter size of Large White pigs using restricted maximum likelihood (REML) methodology applied to a multivariate animal model. In addition to fixed effects the model included random common environment of litter, direct and maternal additive genetic effects. The data consisted of 1928 litters including individual weight observations from 18151 animals for birth weight and from 15360 animals for weaning weight with 5% of animals transferred to a nurse. Estimates of direct and maternal heritability and proportion of the common environmental variance for birth weight were 0.02, 0.21 and 0.11, respectively. The corresponding values for weaning weight were 0.08, 0.16 and 0.23 and for litter size 0.22, 0.02 and 0.06, respectively. The direct and the maternal genetic correlations between birth and weaning weight were positive (0.59 and 0.76). Weak positive (negative) genetic correlations between direct effects on weight traits and maternal effects on birth weight (weaning weight) were found. Negative correlations were found between direct genetic effect for litter size and maternal genetic effects on all three traits. The negative relationship between litter size and individual weight requires a combined selection for litter size and weight.     

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.     

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.     

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.     

Symmetric differences squared and analysis of variance procedures for estimating genetic and environmental variances and covariances for beef cattle weaning weight: II. Estimates from a data set

Analysis of variance (ANOVA) and symmetric differences squared (SDS) methods were used to estimate additive genetic and environmental variances and covariances associated with weaning weight. The two methods were applied to 503 beef records collected over 19 yr from a relatively unselected university Angus herd. The SDS methodology was used with four models. The first model included direct (g) and maternal (gm) additive genetic effects, the 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 based on 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 based on sire, dam, within dam and maternal grandsire variances, covOD and either covOS or covOGD. Symmetric differences squared estimates of h2g and h2gm averaged .30 and .16, respectively. All SDS estimates of rho ggm (correlation between direct and maternal genetic effects) were less than -1. Estimates of sigma mem were positive. Both SDS estimates and one of the two ANOVA estimates of the grandmaternal variance were negative. The ANOVA model 4 estimates of h2g were .33. The estimates of h2gm were .44 and .39, while the estimates for rho ggm were -.88 and -.80. Both estimates of sigma mem were positive. The four ANOVA model 2 estimates of h2g and h2gm averaged .33 and .48, respectively. Three of the four estimates of rho ggm were less than -.97; the fourth was .35. Three of the four estimates of sigma mem were positive. Expectations show the extent to which SDS and ANOVA estimators were biased by nonzero grandmaternal components that were not accounted for. The extent to which dominance components bias the ANOVA estimators also is shown. Nonzero grandmaternal effects need to be taken into account in either SDS or ANOVA solution sets, or important biases occur with most of the estimators. More numerous, and generally more severe, biases occur with ANOVA estimators than with SDS estimators in solution sets that do not account for grandmaternal 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.     

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.     

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.     

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.     

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.     

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.     

Estimation of genetic parameters for average daily gain using models with competition effects

Components of variance for ADG with models including competition effects were estimated from data provided by the Pig Improvement Company on 11,235 pigs from 4 selected lines of swine. Fifteen pigs with average age of 71 d were randomly assigned to a pen by line and sex and taken off test after approximately 89 d (off-test BW ranged from 61 to 158 kg). Models included fixed effects of line, sex, and contemporary group and initial test age as a covariate, with random direct genetic, competition (genetic and environmental), pen, litter, and residual effects. With the full model, variances attributable to direct, direct-competition, genetic competition, and litter (co)variance components could be partitioned; genetic competition variance was small but statistically significantly different from zero. Variances attributable to environmental competition, pen, and residual effects could not be partitioned, but combinations of these environmental variances were estimable. Variances could be partitioned with either pen effects or environmental competition effects in the model. Environmental competition effects seemed to be the source of variance associated with pens. With pen as a fixed effect and without environmental competition effects in the model, genetic components of variance could not be partitioned, but combinations of genetic (co)variances were estimable. With both pen and environmental competition effects ignored, estimates of direct-competition and genetic competition (co)variance components were greatly inflated. With competition (genetic and environmental) effects ignored, the estimate of pen variance increased by 39%, with little change in estimates of direct genetic or residual variance. When both pen and competition (genetic and environmental) effects were dropped from the model, variance attributable to direct genetic effects was inflated. Estimates of variance attributable to competition effects were small in this study. Including environmental competition effects as permanent environmental effects in the model did not change estimates of genetic (co)variances. We concluded that including either pen effects or environmental competition effects as random effects in the model avoids bias in estimates of genetic variances but that including pen effects is much easier.     

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.     

Genetic and phenotypic parameter estimates for growth traits in Boer goat

An understanding of influencing factors and genetic principles affecting the growth traits is needed to implement optimal breeding and selection programs. In this study, heritabilities (direct additive and maternal) of body weights at birth (BW0), 90 days (BW90) and 300 days (BW300) of age and average daily gains from birth to 90 days (ADG0-90), birth to 300 days (ADG0-300) and 90 days to 300 days (ADG90–300) of age in Boer goats were estimated on the basis of 1520 Boer goats at Boer Goat Breeding Station in Yidu, China, during 2002–2007. The parameters were estimated using a DFREML procedure by excluding or including maternal genetic or permanent maternal environmental effects, four analysis models were fitted in order to optimize the model for each trait. Influencing factors such as parity, litter size, kidding year and season, as well as sex of kids and some significant interactions among these factors were investigated as the fixed effects for the models. The results showed that the birth year and maternal genetic effects such as parity and litter size of dam were important determinants of the genetic parameter estimates for pre-weaning growth traits, and environmental effects such as birth year, season and sex of kids had some significant effect on post-weaning growth traits. The mean values and standard errors (SE) of direct additive heritability estimates calculated with the optimum model were 0.17 ± 0.07, 0.22 ± 0.08, 0.07 ± 0.07, 0.10 ± 0.08, 0.30 ± 0.12 and 0.08 ± 0.10 for BW0, BW90, ADG0-90, BW300, ADG0-300 and ADG90–300, respectively. For pre-weaning weights, correlation estimates between direct additive and maternal genetic (r_a–m) effect were high and negative ranging from − 0.74 to − 0.86.     

Estimation of Genetic Parameters and Variance Components for Growth Traits of Nguni Cattle in Limpopo Province,South Africa

Estimates of (co)variance and genetic parameters of birth, weaning (205 days) and yearling (365 days) weight were obtained using single-trait animal models. The data were analysed by restricted maximum likelihood, fitting an animal model that included direct and maternal genetic and permanent environmental effects. The data included records collected between 1976 and 2001. The pedigree information extended as far back as early 1960s. The heritabilities for direct effects of birth, weaning and yearling weights were 0.36, 0.29 and 0.25, respectively. Heritability estimates for maternal effects were 0.13, 0.16 and 0.15 for birth, weaning and yearling weights, respectively. The correlations between direct and maternal additive genetic effects were negative for all traits analysed. The results indicate that both direct and maternal effects should be included in a selection programme for all the traits analysed.     

Variance components and genetic parameters for weight and size at birth in the Boer goat

Variance components, heritability (direct additive and maternal) and correlations (additive genetic, phenotypic, maternal genetic and environmental) of body weight (BW) and body size including length (BL), height (BH) and chest girth (BCG) at birth in Boer goats were estimated on the basis of 5096 records obtained from a Boer Goat Breeding Station in Yidu, China, during 2001–2005. The parameters were estimated using a DFREML procedure by excluding or including maternal genetic or permanent maternal environmental effects, four different analysis models were fitted in order to determine the optimum model for each trait. The environmental factors such as year, season, sex and litter size (LS, number of kids) were investigated as the fixed effects. The results showed that the maternal effects were important determinants of estimated the genetic parameters for birth traits. Year and season had significant effect on birth traits. Single births and male kids had the heaviest live weight and the largest body size at birth. The mean values and standard deviation (SD) of BW, BL, BH and BCG were 3.87 ± 0.85 kg, 31.67 ± 2.87 cm, 32.92 ± 2.80 cm, 33.46 ± 3.21 cm. The mean values and standard error (SE) of direct additive heritability estimates for BW, BL, BH and BCG calculated with the optimum model were 0.19 ± 0.08, 0.14 ± 0.07, 0.24 ± 0.09 and 0.25 ± 0.10, respectively. For all the birth traits, estimates of the correlations between direct additive and maternal genetic (r_a–m) were negative. The estimates of additive genetic and phenotypic correlations among the birth traits were high and positive, and implied no genetic antagonisms among these traits analyzed. The estimates of maternal genetic correlations also were high and positive. Medium and positive environmental correlations indicated the important effects of environmental factors on early growth traits.