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

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

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.     

Effect of including relationships in the estimation of genetic parameters of beef calves.

Variances and covariances for birth weight, gain from birth to weaning (ADG), and 205-d weight were obtained from a sire-dam model and a sire-maternal grandsire model for a herd of Angus and a herd of Hereford cattle. 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 environmental variance (sigma 2PE), and residual variance (sigma 2e) were obtained both with and without the inverse of the numerator relationship matrix (A-1) included. Estimates of heritability for direct genetic effects (h2A), maternal genetic effects (h2M), and the correlation between direct and maternal effects (rAM) for birth weight were .37, .18, and -.01 in Angus and .53, .23, and -.19 in Herefords, respectively, for the analyses without A-1. For the analyses with A-1, estimates of h2A, h2M, and rAM were .42, .22, and -.12 for Angus and .58, .22, and -.13 for Herefords, respectively. Estimates of h2A, h2M, and rAM for ADG were .43, .15, and -.44 in Angus and .52, .38, and -.03 in Herefords, respectively, without A-1. With A-1, estimates of h2A, h2M, and rAM were .57, .15, and -.32 for Angus and .58, .39, and -.05 for Herefords, respectively. Estimates of h2A, h2M, and rAM for 205-d weight were .49, .15, and -.46 for Angus and .58, .43, and -.06 for Herefords, respectively, without A-1. With A-1, estimates of h2A, h2M, and rAM were .63, .16, and -.36 for Angus and .66, .43, and -.08 for Herefords, respectively. Estimates of h2A were higher with A-1 than without A-1, but estimates of h2M were similar. Using variances and covariances obtained from analyses including A-1 generally gave higher estimates of direct breeding values than using variances and covariances obtained from analyses not including A-1. Both Pearson product-moment and Spearman rank correlations were high (.99) between estimates of breeding values from the two analyses, although some changes in rank did occur.     

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.     

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.     

绵羊生长性状母本效应方差组分、遗传参数估计的研究

本文利用公畜母畜模型和公畜外祖父模型估计了初生重、断奶重的直接加性遗传方差、母本遗传方差和遗传参数,得出初生重的直接加性遗传效应、母本遗传效应和总的加性遗传效应的遗传力分别为:0.164、0.101、0.103;断奶重相应的各遗传力为:0.076、0.108、0.081。初生重和断奶重二性状加性遗传效应和母本遗传效应间的遗传相关为:-0.57和-0.36。     

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

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

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.     

Estimating maternal genetic effects in livestock

This study investigates the estimation of direct and maternal genetic (co)variances, accounting for environmental covariances between direct and maternal effects. Estimated genetic correlations between direct and maternal effects presented in the literature have often been strongly negative, and their validity has been questioned. Explanations of extreme estimates have focused on the existence of environmental covariances between dam and offspring. As a solution, models including a regression on dam-phenotype have been proposed, but have yielded biased estimates. The performance of models that implement the variance structure arising from the classical model of Willham, however, has not been evaluated. This study investigated the covariance structure of the parts of the residual term that arise from Willham's model. Results show that a correlation between the residual of the record of an individual and that of its dam is a direct consequence of combining Willham's model with the usual assumption that phenotypic covariances between different traits are the sum of additive genetic and environmental covariances. Stochastic simulations show that fitting this structure yields unbiased estimates of the genetic (co)variances. When correlated residuals were ignored in the cases investigated, the bias in the estimated genetic correlations was approximately equal to the value of the environmental correlation. In contrast to models including a regression on dam-phenotype, there were no difficulties with interpretation of results, and the approach was consistent with standard quantitative genetic theory. The use of Willham's model while accounting for correlated residuals is conceptually appealing and yields unbiased results, with no need for regression on dam phenotype. Inclusion of the ability to fit the residual variance structure required for maternal effects into existing software packages would be helpful to animal breeders.     

Estimates of genetic parameters for direct and maternal effects on embryonic survival in swine.

Survival of 16,838 potential embryos was determined by counting corpora lutea and fetuses at 50 d of gestation for 1,081 litters by 225 sires. These data, coded as 1 or 0 depending on whether an ovulation was represented by a fetus, were used to estimate direct and maternal additive genetic variances and their covariance for embryonic survival. Data were from first-parity gilts of a Large White-Landrace composite population subdivided into two lines, one selected for an index of ovulation rate and embryonic survival for seven generations and a contemporary control line. Variance components were obtained by ANOVA and expectations of covariances among relatives and by derivative-free restricted maximum likelihood (DFREML) in an animal model. As a trait of the embryo, heritability of direct effects obtained with ANOVA was 3.8%, heritability of maternal effects was 1.5%, and the genetic correlation between them was -.51. After adjustment of embryonic survival for ovulation rate, lower estimates of each parameter were obtained with ANOVA. Heritability of embryonic survival as a trait of the dam was 9 to 10%. Estimates of heritability of both direct and maternal effects obtained with DFREML were less than 1% and the genetic correlation between them was -.64. When survival of embryos from only those dams with 15 or more ovulations was analyzed, heritability of maternal effects was 4.4%. Estimates of common environmental effects on embryonic survival ranged from 5 to 7%.     

Estimation of direct and maternal genetic variance for litter size in Canadian Yorkshire and Landrace swine using an animal model

Estimates of additive direct heritability (h2a) for traits such as litter size may be biased by maternal effects. The size of these effects was estimated using a derivative-free restricted maximum likelihood procedure under an animal model. First-parity records from Yorkshire (Y) and Landrace (L) gilts were obtained from the Quebec Record of Performance sow productivity program for 21,127 litters born between 1977 and 1987. Direct (sigma 2a) and maternal (sigma 2m) additive genetic variances, their covariance (sigma am) and error variance (sigma 2e) were estimated for total numbers born (NOBN), born alive (NOBA) and weaned (NOWN). Analysis of purebred Y and crossbred litters indicated that estimates of sigma 2a were of similar magnitude for all traits, with h2a ranging from .06 to .13. Except for L litters, estimates of sigma 2m were relatively low for NOBN and NOBA, and increased in size for NOWN, with h2m ranging from 0 to .08. Also, estimates of sigma am were negative, except for NOBN and NOBA with crossbred litters, and became increasingly negative for NOWN. Results from purebred L litters indicated there was a stronger negative correlation between direct and maternal genetic effects for NOBN and NOBA than for NOWN.     

Parent‐of‐origin effects on carcass traits in Japanese Black cattle

Variances caused by the differential expression of paternally and maternally imprinted genes controlling carcass traits in Japanese Black cattle were estimated in this study. Data on marbling score (BMS), carcass weight, rib thickness, rib‐eye area (REA) and subcutaneous fat thickness (SFT) were collected from a total of 13,115 feedlot steers and heifers in a commercial population. A sire–maternal grandsire model was used to analyse the data, and then, imprinting parameters were derived by replacing the genetic effect of the dam with the effect of the maternal grandsire in the imprinting model to calculate the genetic parameter estimates. The proportions of the total genetic variance attributable to imprinted genes ranged from 8.7% (SFT) to 35.2% (BMS). The remarkably large imprinting variance of BMS was mainly contributed by maternally expressed inheritance because the maternal contribution of the trait was much larger than that of the paternal trait. The parent‐of‐origin effect originating from maternal gene expression was also observed for REA. The results suggested the existence of genomic imprinting effects on the traits of the Japanese Black cattle. Hence, the parent‐of‐origin effect should be considered for the genetic evaluation of Japanese Black cattle in breeding programmes.     

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.     

Analyses of growth curves of nellore cattle by multiple-trait and random regression models

The purpose of this study was to compare estimates of genetic parameters for sequential growth of beef cattle using two models and two data sets. Growth curves of Nellore cattle were analyzed using body weights measured at ages 1 (birth weight) to 733 d. Two data samples were created, one with 71,867 records sampled from all herds (MISS), and the other with 74,601 records sampled from herds with no missing traits (NMISS). Records preadjusted to a fixed age were analyzed by a multiple-trait model (MTM), which included the effects of contemporary group, age of dam class, additive direct, additive maternal, and maternal permanent environment. Analyses were by REML, with five traits at a time. The random regression model (RRM) included the effects of age of animal, contemporary group, age of dam class, additive direct, additive maternal, permanent environment, and maternal permanent environment. All effects were modeled as cubic Legendre polynomials. These analyses were also by REML. Shapes of estimates of variances by MTM were mostly similar for both data sets for all except late ages, where estimates for MISS were less regular, and for birth weight with MISS. Genetic correlations among ages for the direct and maternal effects were less smooth with MISS. Genetic correlations between direct and maternal effects were more negative for NMISS, where few sires were maternal grandsires. Parameter estimates with RRM were similar to MTM cept that estimates of variances showed more artifacts for MISS; the estimates of additive direct-maternal correlations were more negative with both data sets and approached -1.0 for some ages with NMISS. When parameters of a growth model obtained by used for genetic evaluation, these parameters should be examined for consistency with parameters from MTM and prior information, and adjustments may be required to eliminate artifacts.     

Estimates of repeatability and heritability of horn fly resistance in beef cattle.

Horn fly population density on 215 beef cows representing seven breed groups and 51 sires was used to obtain estimates of repeatability (rXX) and heritability (h2) for resistance to the horn fly (Haematobia irritans [L.] Diptera: Muscidae). Total horn fly densities were determined weekly on each cow beginning in May and ending in late October or early November of 1988, 1989, and 1990. No insecticides were used on cattle in this study. Estimates of h2 for horn fly resistance (low horn fly number per cow) were obtained by the paternal half-sib method (4 sigma 2S) and as twice the intrasire regression of offspring on dam (2bDD/S). Variance component estimates were obtained using a completely nested ANOVA that included overall mean, breed, sire/breed, cow/sire, and residual error. One hundred twenty-six daughter-dam pairs were available for regression analysis. In a preliminary analysis, the within-breed regression was nonsignificant (P greater than .05), implying that the regression was the same for all breeds; therefore, breed was deleted from the model. The regression model included an overall mean, year, and the intrasire regression of daughter on dam (bDD/S). The estimate of rXX was .47 +/- .02. Estimates of h2 were .78 +/- .16 and .59 +/- .10 from the 4 sigma 2S and 2bDD/S methods, respectively. Similar estimates of rXX and h2 were obtained when each observation of horn fly number per cow (x) was transformed to both log10 (x) and square root of x. These estimates suggest the possibility of selection procedures as an environmentally safe alternative to the use of chemical control.     

Maternal influence on growth of laboratory rats

Data from 2,089 laboratory rats utilized in selection experiments were used to estimate maternal influence on growth from weaning (21 d) to 16 wk of age. Adjustment factors were calculated for the effects of sex, generation, litter size, inbreeding of the dam and inbreeding of the offspring on the body weights. The effect of line of sire was included in the analysis of variance models. Covariances among paternal half-sibs, full-sibs, offspring-dam, and individuals with the same maternal grandsire were equated to theoretical causal components of variance in a series of simultaneous equations. From these, estimates of heritability, maternal influence and other environmental influences on the weights of the animals were calculated. Estimates of additive genetic effects were negative at weaning and increased to positive intermediate values during postweaning growth. Maternal influence due to additive genetic effects was of primary importance at weaning and tended to diminish at later stages of growth. An antagonism was indicated between maternal environment and genes affecting the offspring's growth. Maternal influence is an important factor at weaning and during the postweaning growth of a litter-bearing species such as the laboratory rat.     

Estimation of additive genetic variance when base populations are selected

A population of size 40 was simulated 1,000 times for 10 generations. Five out of twenty males were selected each generation, and each male was mated to four females to have two progeny. The additive genetic variance (sigma 2a) before selection was 10, and the initial heritability was .5. Due to covariances among animals, inbreeding and gametic disequilibrium, the genetic variance was reduced to 6.72 after 10 generations of selection. Reduction of variance was lower in another population simulated with size 400 and 10% of the males selected. Restricted Maximum Likelihood was used to estimate sigma 2a using an animal model. The estimate of sigma 2a was empirically unbiased when all data and all relationships were used. Omitting data from selected ancestors caused biased estimates of sigma 2a due to not accounting for all gametic disequilibrium. Including additional relationships between assumed base animals adjusted for inbreeding and for covariances. Bias from gametic disequilibrium decreased slightly with the use of more relationship information, and it was smaller in the small population and(or) when selection had been practiced for just a few generations.     

The impact of data structure on genetic (co)variance components of early growth in sheep,estimated using an animal model with maternal effects

Several studies have noted high negative correlations between maternal genetic and direct additive effects and their influence on additive and maternal heritability of early growth traits in sheep. Multigeneration data from the Suffolk Sire Reference Scheme (SSRS) were used to investigate the effect of data structure on estimates of direct and maternal (co)variances for lamb 8-wk weight. In all analyses the additive, maternal genetic, maternal environmental, and residual effects were fitted along with the covariance between direct and maternal additive effects. The contributions of particular genetic relationships to the estimates were studied by analyzing subsets of the SSRS data. A further eight subsets were formed having 10% or 50% of the dams with their own records and having one or two, three or four, five or six, and more than six offspring per dam. Analysis of data having only 10% of the dams with their own record and one or two offspring records yielded a high negative correlation (-0.99) between direct and maternal genetic effects. However, the seven other data sets with more records per dam or a higher proportion of dams with their own records produced values of -0.35 to -0.51. Data structure and the number of dams and granddams with records are important determinants of estimated direct and maternal effects in early growth traits.     

Comparison of methods of estimating variance components in pigs

Components of variance due to average effects of genes (sigma 2g), environmental effects common to littermates (sigma 2c), and environmental effects peculiar to individual pigs (sigma 2e) were estimated (--) by the Pseudo Expectation Approach (PE). Data were litter size (LS), backfat (BF; centimeter) and ADG (kilograms/day) collected from the Nebraska Gene Pool swine population between 1967 and 1986. Mean square errors (MSE) for h--2 and c--2 (sigma--2g and sigma--2c divided by phenotypic variance) by PE and nested ANOVA and h2 estimated by offspring on parent regression (REGOP) were evaluated using simulation of 200 repetitions of the Nebraska Gene Pool population. Parameter values for sigma 2g, sigma 2c, and sigma 2e used in simulations were PE estimates from the Gene Pool population. Estimates of h2 from PE were .18 +/- .06 for LS, .56 +/- .06 for BF, and .16 +/- .05 for ADG. Estimates of c2 from PE were .01 +/- .03 for LS, .09 +/- .02 for BF, and .19 +/- .03 for ADG. Compared with REGOP, PE yielded h--2 with smaller MSE for BF and ADG and larger MSE for LS. The MSE of PE was smaller than the MSE of the nested ANOVA estimate for all estimates and traits. These results were interpreted to suggest that considerable gains in precision in estimation of genetic parameters could be achieved by accounting for all relationships in lieu of accounting for only half- and full-sib relationships or parent-offspring relationships.     

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.