Estimation of genetic parameters for functional longevity in the South African Holstein cattle using a piecewise Weibull proportional hazards model

Non‐genetic factors influencing functional longevity and the heritability of the trait were estimated in South African Holsteins using a piecewise Weibull proportional hazards model. Data consisted of records of 161,222 of daughters of 2,051 sires calving between 1995 and 2013. The reference model included fixed time‐independent age at first calving and time‐dependent interactions involving lactation number, region, season and age of calving, within‐herd class of milk production, fat and protein content, class of annual variation in herd size and the random herd–year effect. Random sire and maternal grandsire effects were added to the model to estimate genetic parameters. The within‐lactation Weibull baseline hazards were assumed to change at 0, 270, 380 days and at drying date. Within‐herd milk production class had the largest contribution to the relative risk of culling. Relative culling risk increased with lower protein and fat per cent production classes and late age at first calving. Cows in large shrinking herds also had high relative risk of culling. The estimate of the sire genetic variance was 0.0472 ± 0.0017 giving a theoretical heritability estimate of 0.11 in the complete absence of censoring. Genetic trends indicated an overall decrease in functional longevity of 0.014 standard deviation from 1995 to 2007. There are opportunities for including the trait in the breeding objective for South African Holstein cattle.     

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.     

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.     

Comparison of threshold vs linear and animal vs sire models for predicting direct and maternal genetic effects on calving difficulty in beef cattle

This study compared the accuracy of several models for obtaining genetic evaluations of calving difficulty. The models were univariate threshold animal (TAM), threshold sire-maternal grandsire (TSM), linear animal (LAM), and linear sire-maternal grandsire (LSM) models and bivariate threshold-linear animal (TLAM), threshold-linear sire-maternal grandsire (TLSM), linear-linear animal (LLAM), and linear-linear sire-maternal grandsire (LLSM) models for calving difficulty and birth weight. Data were obtained from the American Gelbvieh Association and included 84,420 first-parity records of both calving difficulty and birth weight. Calving difficulty scores were distributed as 73.4% in the first category (no assistance), 18.7% in the second, 6.3% in the third, and 1.6% in the fourth. Included in the animal models were fixed sex of calf by age of dam subclasses, random herd-year-season effects, and random animal direct and maternal breeding values. Sire-maternal grandsire models were similar to the animal models, with animal and maternal effects replaced by sire and maternal grandsire effects. Models were compared using a data splitting technique based on the correlation of estimated breeding values from two samples, with one-half of the calving difficulty records discarded randomly in the first sample and the remaining calving difficulty records discarded in the second sample. Reported correlations are averages of 10 replicates. The results obtained using animal models confirmed the slight advantage of TAM over LAM (0.69 vs 0.63) and TLAM over LLAM (0.90 vs 0.86). Bivariate analyses greatly improved the accuracy of genetic prediction of direct effects on calving difficulty relative to univariate analyses. Similar ranking of the models was found for maternal effects, but smaller correlations were obtained for bivariate models. For sire-maternal grandsire models, no differences between sire or maternal grandsire correlations were observed for TLSM compared to LLSM, and small differences were observed between TSM and LSM. The threshold model offered advantages over the linear model in animal models but not in sire-maternal grandsire models. For genetic evaluation of calving difficulty in beef cattle, the threshold-linear animal model seems to be the best choice for predicting both direct and 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.     

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。     

Genetic analysis of the rates of conception using a longitudinal threshold model with random regression in dairy crossbreeding within a tropical environment

This study was designed to: (i) estimate genetic parameters and breeding values for conception rates (CR) using the repeatability threshold model (RP‐THM) and random regression threshold models (RR‐THM); and (ii) compare covariance functions for modeling the additive genetic (AG) and permanent environmental (PE) effects in the RR‐THM. The CR was defined as the outcome of an insemination. A data set of 130 592 first‐lactation insemination records of 55 789 Thai dairy cows, calving between 1996 and 2011, was used in the analyses. All models included fixed effects of year × month of insemination, breed × day in milk to insemination class and age at calving. The random effects consisted of herd × year interaction, service sire, PE, AG and residual. Variance components were estimated using a Bayesian method via Gibbs sampling. Heritability estimates of CR ranged from 0.032 to 0.067, 0.037 to 0.165 and 0.045 to 0.218 for RR‐THM with the second, third and fourth‐order of Legendre polynomials, respectively. The heritability estimated from RP‐THM was 0.056. Model comparisons based on goodness of fit, predictive abilities, predicted service results of animal, and pattern of genetic parameter estimates, indicated that the model which fit the desired outcome of insemination was the RR‐THM with two regression coefficients.     

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.     

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.     

Sire x herd interactions for weaning weight in beef cattle.

Weaning weight records of 44,357 Australian Angus calves produced by 1,020 sires in 90 herds were used to evaluate the importance of sire x herd interactions. Models fitted fixed effects of contemporary group (herd-year-date of weighing subclass), sex, calf age, and dam age and random effects of sire or of sire and sire x herd interaction using REML. Effects of standardizing the data, including sire relationships and including dam maternal breeding values (MBV) as a covariate were also investigated. Sire x herd interactions were found (P less than .05) in all cases and, in the most complete model, accounted for 3.3% of phenotypic variance. Across-herd heritabilities ranged from .19 to .28. Differential nonrandom mating among herds seemed to occur in the data. Significant sire x herd effects were observed for dam MBV, and adjustment for dam MBV yielded the smallest estimates of interaction variance and across-herd heritability. If sire x herd interactions were due only to genotype x environment interaction, within-herd heritabilities would range from .33 to .49. These estimates are larger than previously reported estimates. Thus, unreported environmental effects common to progeny of individual sires may also be involved in the observed interaction but could not be disentangled from true genotype x environment interaction effects using these data. Results of these analyses suggest that some accommodation of sire x herd interaction effects on weaning weight may be needed in beef cattle genetic evaluations, but a compelling case for development of herd-specific breeding value prediction cannot be made.     

Genetic parameters for direct and maternal calving ease in Walloon dairy cattle based on linear and threshold models

Calving ease scores from Holstein dairy cattle in the Walloon Region of Belgium were analysed using univariate linear and threshold animal models. Variance components and derived genetic parameters were estimated from a data set including 33 155 calving records. Included in the models were season, herd and sex of calf × age of dam classes × group of calvings interaction as fixed effects, herd × year of calving, maternal permanent environment and animal direct and maternal additive genetic as random effects. Models were fitted with the genetic correlation between direct and maternal additive genetic effects either estimated or constrained to zero. Direct heritability for calving ease was approximately 8% with linear models and approximately 12% with threshold models. Maternal heritabilities were approximately 2 and 4%, respectively. Genetic correlation between direct and maternal additive effects was found to be not significantly different from zero. Models were compared in terms of goodness of fit and predictive ability. Criteria of comparison such as mean squared error, correlation between observed and predicted calving ease scores as well as between estimated breeding values were estimated from 85 118 calving records. The results provided few differences between linear and threshold models even though correlations between estimated breeding values from subsets of data for sires with progeny from linear model were 17 and 23% greater for direct and maternal genetic effects, respectively, than from threshold model. For the purpose of genetic evaluation for calving ease in Walloon Holstein dairy cattle, the linear animal model without covariance between direct and maternal additive effects was found to be the best choice.     

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

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

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.     

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.     

Genetic parameters for calving rate and calf survival from linear, threshold, and logistic models in a multibreed beef cattle population

Generalized mixed linear, threshold, and logistic sire models and Markov chain, Monte Carlo simulation procedures were used to estimate genetic parameters for calving rate and calf survival in a multibreed beef cattle population. Data were obtained from a 5-generation rotational crossbreeding study involving Angus, Brahman, Charolais, and Hereford (1969 to 1995). Gelbvieh and Simmental bulls sired terminal-cross calves from a sample of generation 5 cows. A total of 1,458 cows sired by 158 bulls had a mean calving rate of 78% based on 4,808 calving records. Ninety-one percent of 5,015 calves sired by 260 bulls survived to weaning. Mean heritability estimates and standard deviations for daughter calving rate from posterior distributions were 0.063 +/- 0.024, 0.150 +/- 0.049, and 0.130 +/- 0.047 for linear, threshold, and logistic models, respectively. For calf survival, mean heritability estimates and standard deviations from posterior distributions were 0.049 +/- 0.022, 0.160 +/- 0.058, and 0.190 +/- 0.078 from linear, threshold, and logistic models, respectively. When transformed to an underlying normal scale, linear sire, mixed model, heritability estimates were similar to threshold and logistic sire mixed model estimates. Posterior density distributions of estimated heritabilities from all models were normal. Spearman rank correlations between sire EPD across statistical models were greater than 0.97 for daughter calving rate and for calf survival. Sire EPD had similar ranges across statistical models for daughter calving rate and for calf survival.     

Genetic parameter estimates for prenatal and postnatal mortality in Nellore cattle

The aim of this study was to estimate genetic parameters for prenatal (PRE) and postnatal (POS) mortality in Nellore cattle. A total of 13 141 (PRE) and 17 818 (POS) records from Nellore females were used. PRE and POS were recorded using binary scale scores: a score of ‘1’ was given to calves that were born alive (PRE) and those that were alive at weaning (POS), and a score of ‘0’ was given to calves that were not alive at or around birth (PRE), as well as to those weighed at birth but not at weaning (POS). The relationship matrix included 698 sires, 107 paternal grandsires and 69 maternal grandsires. Data were analysed using Bayesian inference and a sire–maternal grandsire threshold model, including contemporary groups as random effects, and the classes of dam age at the beginning of mating season (for PRE), and dam age at calving and birthweight (linear covariable) (for POS), as fixed effects. For both traits, the covariance between direct and maternal effects (r_D,M) was estimated (r_D,M≠ 0) or fixed at zero (r_D,M = 0). PRE and POS rates were 3.00 and 4.04%, respectively. Estimates of direct and maternal heritability were 0.07 and 0.17, respectively, for PRE, and 0.02 and 0.07, respectively, for POS, assuming r_D,M = 0. For r_D,M ≠ 0, these estimates were 0.07 and 0.12, respectively, for PRE, and 0.03 and 0.07, respectively, for POS. The correlation estimates between direct and maternal effects were ?0.71 (PRE) and ?0.33 (POS). PRE and POS show low genetic variability, indicating that these traits probably suffer major environmental influences. Additionally, our study shows that the maternal genetic component affects preweaning calf mortality twice as much (or more) as the direct genetic component. A large number of offspring per sire is necessary in progeny tests to genetically decrease calf mortality.     

Study of the effect of genotype–environment interaction on age at first calving and production traits in Nellore cattle using multi‐trait reaction norms and Bayesian inference

This study investigated the effects of genotype–environment interaction on yearling weight, age at first calving and post‐weaning weight gain in Nellore cattle using multi‐trait reaction norm models. The environmental gradient was defined as a function of the mean yearling weight of the contemporary groups. A first‐order random regression sire model with four classes of residual variance was used in the analyses and Bayesian methods were applied to estimate the (co)variance components. The heritability estimates ranged from 0.284 to 0.547, 0.222 to 0.316 and 0.256 to 0.522 for yearling weight, age at first calving and post‐weaning weight gain, respectively. The lowest genetic correlations between environment groups for each trait were 0.38, 0.02 and 0.04 for yearling weight, age at first calving and post‐weaning weight gain, respectively. Differences in the correlation estimates were observed between traits in the same environments, with the magnitude of the estimates tending toward zero as the environment improved. The results highlight the importance of including genotype–environment interactions in genetic evaluation programs considering the differences observed between environmental groups not only in terms of heritability, but also of genetic correlations.     

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.     

Dairy sire evaluation fitting some of the herd-year-season effects as random

Three models of sire evaluation using different environmental groupings were compared. Effects fitted were herd, period (either 6 or 12 months) within herd, season (either 1 or 2 or 4 months) within period within herd, sire and linear and quadratic regressions on age at calving. Models differed in fitting (1) the effect of herd-period-season fixed, or (2) herd-period fixed and herd-period-season random, or (3) herd fixed, herd-period and herd-period-season random. The overall effects of period and season of calving were regarded as fixed, and were removed by precorrection. Records of first lactation fat yield on 49 242 progeny of 69 widely used proven Friesian-Holstein sires in 1628 herds in England and Wales were used.Compared to Model 1, Model 2 required about four-fifths and Model 3 required two-thirds of the effective number of daughters to give the equivalent variance of the estimates of sire effects. Using random effects models the relative advantage, in terms of a smaller variance of sire effects, increased as the size of herd-period-season subclass decreased.In herd-period-season fixed effects models subclasses with a single of few records, or subclasses with all or almost all records of the same sire, contribute nothing or little to the progeny group comparisons. The random effects models could avoid these losses, and were considered to be useful especially where herds are small, provided sires can be assumed as randomly distributed over environmental subclasses.     

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.