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

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

Genetic evaluation of growth in a multibreed beef cattle population using random regression-linear spline models

The objective of this study was to examine the feasibility of using random regression-spline (RR-spline) models for fitting growth traits in a multibreed beef cattle population. To meet the objective, the results from the RR-spline model were compared with the widely used multitrait (MT) model when both were fit to a data set (1.8 million records and 1.1 million animals) provided by the American Gelbvieh Association. The effect of prior information on the EBV of sires was also investigated. In both RR-spline and MT models, the following effects were considered: individual direct and maternal additive genetic effects, contemporary group, age of the animal at measurement, direct and maternal heterosis, and direct and maternal additive genetic mean effect of the breed. Additionally, the RR-spline model included an individual direct permanent environmental effect. When both MT and RR-spline models were applied to a data set containing records for weaning weight (WWT) and yearling weight (YWT) within specified age ranges, the rankings of bulls' direct EBV (as measured via Pearson correlations) provided by both models were comparable, with slightly greater differences in the reranking of bulls observed for YWT evaluations (>or=0.99 for BWT and WWT and >or=0.98 for YWT); also, some bulls dropped from the top 100 list when these lists were compared across methods. For maternal effects, the estimated correlations were slightly smaller, particularly for YWT; again, some drops from the top 100 animals were observed. As in regular MT multibreed genetic evaluations, the heterosis effects and the additive genetic effects of the breed could not be estimated from field data, because there were not enough contemporary groups with the proper composition of purebred and crossbred animals; thus, prior information based on literature values had to be included. The inclusion of prior information had a negligible effect in the overall ranking for bulls with greater than 20 birth weight progeny records; however, the effect of prior information for breeds or groups poorly represented in the data was important. The Pearson correlations for direct and maternal WWT and YWT ranged from 0.95 to 0.98 when comparing evaluations of data sets for which the out-of-range age records were removed or retained. Random regression allows for avoiding the discarding of records that are outside the usual age ranges of measurement; thus, greater accuracies are achieved, and greater genetic progress could be expected.     

Threshold-linear versus linear-linear analysis of birth weight and calving ease using an animal model: II. Comparison of models.

Several models were evaluated in terms of predictive ability for calving difficulty. Data included birth weight and calving difficulty scores provided by the American Gelbvieh Association from 26,006 calves born to first-parity cows and five simulated populations of 6,200 animals each. Included in the model were fixed age of dam x sex interaction effects, random herd-year-season effects, and random animal direct and maternal effects. Bivariate linear-threshold and linear-linear models for birth weight/calving ease and univariate threshold and linear models for calving ease were applied to the data sets. For each data set and model, one-half of calving ease records were randomly discarded. Predictive ability of the different models was defined with the mean square error (MSE) for the difference between a deleted calving ease score and its prediction obtained from the remaining data. In terms of correlation between simulated and predicted breeding values, the threshold models had a 1% advantage for direct genetic effects and 3% for maternal genetic effects. In simulation, the average MSE was .29 for linear-threshold, .32 for linear-linear, .37 for threshold, and .39 for linear model. For the field data set, the MSE was .31, .33, .39, and .40, respectively. Although the bivariate models for calving ease/birth weight were more accurate than univariate models, the threshold models showed a greater advantage under the bivariate model. For the purpose of genetic evaluation for calving difficulty in beef cattle, the use of the linear-threshold model seems justified. In dairy cattle, the evaluation for calving ease can benefit from recording birth weight.     

Illustration of the maternal animal model used for genetic evaluation of beef cattle

National cattle evaluation programs for weaning weight in most beef breed associations involve implementation of the maternal animal model to predict direct and maternal EPD. With this model, direct breeding values are predicted for all animals with records or pedigree ties to animals with records, or both. Even though maternal genetic value is expressed only in animals that become dams, these effects are transmitted by all parents and inherited from parents by all animals, leading to maternal breeding values being predicted for all animals as well. A small example data set was simulated involving 12 parents, 8 nonparents, and 13 animals with weaning weight records. The pedigree was developed to include paternal and maternal half-sib families, full-sibs, and some inbreeding, similar to field populations of beef cattle. Assembly of the mixed model equations and solutions for the maternal animal model are illustrated explicitly to assist animal breeding students in their understanding of the properties of the maternal animal model and to explicitly implement the model. Model parameters and moments, fixed contemporary group solutions, adjustment of breeding values for merit of mates, interpretation of maternal permanent environmental effect solutions, and alternatives for the assembly of the equations are shown. This example should lead to increased student and producer understanding of genetic improvement programs for weaning weight in beef cattle.     

Inclusion of weaning management group as a random effect in the genetic evaluation of postweaning traits in Nellore cattle

The objective of this study was to evaluate the impact of including weaning management group (WMG) as an uncorrelated random effect in the genetic evaluation of postweaning traits. Data from 186,507 Nellore animals' sons to 1,734 sires and 75,016 cows were analyzed. Three single-trait models were studied. These models included the contemporary group (CG) as a fixed effect and age of animal at measurement and age of dam at calving as covariates, in addition to the direct additive breeding value as random effect. The CGs for postweaning traits varied between models which included or not WMG as part of the concatenation of fixed effects. In the model in which WMG was not part of the CG, the trait was included as an uncorrelated random effect. The results suggest that although no significant effects were observed on genetic parameter estimates or animal ranking, the inclusion of WMG as an uncorrelated random effect increased the number of observations per CG and contributed to maintaining animals in the analysis that would be discarded because they were in a CG with a small number of observations. This model could therefore be recommended for the genetic evaluation of this Nellore population.     

Use of random regression model as an alternative for multibreed relationship matrix

A random regression model is presented as an approximation for multibreed variance model. The approximation is derived using the splitted multibreed model where the single breeding value is split to the breed specific and their segregation terms. The random regression model allows extending the multibreed information easily to genomic data models. We present the approach by a simple example.     

Accounting for outliers and heteroskedasticity in multibreed genetic evaluations of postweaning gain of Nelore-Hereford cattle

The objectives of this study were to demonstrate the utility of hierarchical Bayesian models combining residual heteroskedasticity with robustness for outlier detection and muting and to evaluate the effects of such joint modeling in multibreed genetic evaluations. A 3 x 2 factorial specification of 6 residual variance models based on several distributional (Gaussian, Student's t, or Slash) and variability (homoskedastic or heteroskedastic) assumptions was used to analyze 22,717 postweaning gain records from a Nelore-Hereford population (40,082 animals in the pedigree). To illustrate the utility of the 2 robust distributional specifications (Student's t and Slash) for outlier detection and muting, 3 records from the same contemporary group (an extreme residual outlier, a mild residual outlier, and a near-zero residual) were chosen for further study. The posterior densities of the corresponding weighting variables of these records were used to assess their degree of Gaussian outlyingness and the ability of the robust models to mute the effects of deviant records. The Student's t heteroskedastic provided the best-fit model among the 6 specifications and was preferred for genetic merit inference. Kendall rank correlations of the posterior means of the additive genetic effects of the animals, used to compare the selection order of the Student's t and Gaussian models, were reasonably high across all animals within the most frequent genotypes, ranging from 0.83 to 0.91 and from 0.89 to 0.95 for the homoskedastic and the heteroskedastic versions, respectively. However, when considering only animals ranked in the top 10% by the customary Gaussian homoskedastic model, these rank correlations were reduced considerably, ranging from 0.29 to 0.57 and from 0.72 to 0.85 between the 2 residual densities within the homoskedastic and heteroskedastic versions, respectively. Rank correlations between the homoskedastic and heteroskedastic versions within each of the Gaussian and Student's t error models tended to be smaller, with a range from 0.68 to 0.90 across all animals and from 0.28 to 0.67 for animals ranked in the top 10%. These results support the implementation of robust models accounting for sources of heteroskedasticity to increase the precision and stability of multibreed genetic evaluations with proper statistical treatment of deviant records.     

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.     

Genetic associations between flight speed and growth traits in Nellore cattle

The aim of the present study was to estimate genetic parameters for flight speed and its association with growth traits in Nellore beef cattle. The flight speed (FS) of 7,402 yearling animals was measured, using a device composed of a pair of photoelectric cells. Time interval data (s) were converted to speed (m/s) and faster animals were regarded as more reactive. The growth traits analyzed were weaning weight (WW), ADG from weaning to yearling age, and yearling scrotal circumference (SC). The (co)variance components were estimated using REML in a multitrait analysis applying an animal model. The model included random direct additive genetic and residual effects, fixed effects of contemporary groups, age of dam (classes), and age of animal as covariable. For WW, the model also included maternal genetic and permanent environmental random effects. The direct heritability estimate for FS was 0.26 ± 0.05 and direct heritability estimates for WW, SC, and ADG were 0.30 ± 0.01, 0.48 ± 0.02, and 0.19 ± 0.01, respectively. Estimates of the genetic correlation between FS and the growth traits were -0.12 ± 0.07 (WW), -0.13 ± 0.08 (ADG), and -0.11 ± 0.07 (SC). Although the values were low, these correlations showed that animals with better temperaments (slower FS) tended to present better performance. It is possible to infer that longterm selection for weight and scrotal circumference can promote a positive genetic response in the temperament of animals. Nevertheless, to obtain faster genetic progress in temperament, it would be necessary to perform direct selection for such trait. Flight speed is an easily measured indicator of temperament and can be included as a selection criterion in breeding programs for Nellore cattle.     

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.     

Linear–threshold animal model for birth weight, gestation length and calving ease in United Kingdom Limousin beef cattle data

Breeding value evaluation for UK Limousin beef cattle data was carried out by multiple-trait linear–threshold animal model with variance components assumed to be known. Polychotomous calving ease with five categories was analysed with two continuous traits: birth weight and gestation length. Field data consisted of 220,799 animals with observations with every possible combination of traits, and 270,035 animals in the pedigree. The threshold model was solved either with Newton Raphson or Expectation Maximisation algorithm, and solutions were compared to evaluation by a linear model with original and normalised scores. There were insignificant differences in solutions between the two algorithms for threshold model analyses. Furthermore, solutions of the continuous traits were similar by the threshold and linear models. For the categorical trait, correlations for random effects from the threshold and linear models were high. In case of normalised scores (original scores case in brackets) correlations with solutions from the threshold and linear model were 0.97 (0.94) and 0.97 (0.93) for direct and maternal genetic effects and 0.95 (0.89) for permanent maternal effects. Even so, at least one third of the top 1% ranking of bulls differed between the linear and the threshold models. Predictive abilities as correlations between estimated breeding values and pedigree indices were almost equal between the linear and threshold models for both continuous and categorical traits. In conclusion, despite the higher computational demand, the linear–threshold animal model can be seen worthwhile in the genetic evaluation of the national UK beef cattle data set.     

Genotype × environment interaction for long-yearling weight in Canchim cattle quantified by reaction norm analysis

The objective of this study was to investigate the presence of genotype × environment interactions (G×E) for long-yearling weight in Canchim cattle (5/8 Charolais + 3/8 zebu) in Brazil using reaction norms (RN). The hierarchical RN model included the fixed effect of age of the animal (linear coefficient) and random effects of contemporary groups and additive animal genetic intercept and slope of the RN and contemporary group effects as random effects. Contemporary groups as the most elemental representation of management conditions in beef cattle were chosen to represent the environmental covariate of the RN. The deviance information criteria demonstrated that a homoskedastic residual RN model provided a better data fit compared with a heteroskedastic counterpart and with a traditional animal model, which had the worst fit. The environmental gradient for long-yearling weight based on contemporary group effects ranged from -105 to 150 kg. The additive direct variance and heritability estimates increased with increasing environmental gradient from 74.33 ± 22.32 to 1,922.59 ± 258.99 kg(2) and from 0.08 ± 0.02 to 0.68 ± 0.03, respectively. The high genetic correlation (0.90 ± 0.03) between the intercept and the slope of the RN shows that animals with the greatest breeding values best responded to environmental improvement, characterizing scale effect as the source of G×E for long-yearling weight. The phenotypic plasticity demonstrated by the slope of the RN of the animal indicates the possibility to change genotype expression along the environmental gradient through selection. The results demonstrate the importance of accounting for G×E in the genetic evaluation of this population.     

Random regression models on Legendre polynomials to estimate genetic parameters for weights from birth to adult age in Canchim cattle*

The objective of this work was to estimate covariance functions for direct and maternal genetic effects, animal and maternal permanent environmental effects, and subsequently, to derive relevant genetic parameters for growth traits in Canchim cattle. Data comprised 49 011 weight records on 2435 females from birth to adult age. The model of analysis included fixed effects of contemporary groups (year and month of birth and at weighing) and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Residual variances were allowed to vary and were modelled by a step function with 1, 4 or 11 classes based on animal’s age. The model fitting four classes of residual variances was the best. A total of 12 random regression models from second to seventh order were used to model direct and maternal genetic effects, animal and maternal permanent environmental effects. The model with direct and maternal genetic effects, animal and maternal permanent environmental effects fitted by quadric, cubic, quintic and linear Legendre polynomials, respectively, was the most adequate to describe the covariance structure of the data. Estimates of direct and maternal heritability obtained by multi‐trait (seven traits) and random regression models were very similar. Selection for higher weight at any age, especially after weaning, will produce an increase in mature cow weight. The possibility to modify the growth curve in Canchim cattle to obtain animals with rapid growth at early ages and moderate to low mature cow weight is limited.     

Evaluation models and genetic parameters for calving difficulty in beef cattle

Calving difficulty was analyzed under threshold and linear models considering either a fixed or random herd-year effect. The aim of the study was to compare models for predicting breeding values according to the size of herd-year groups. When simulating data sets with small herds, in order to obtain an unbiased evaluation under a nonrandom and negative association of sire and herd effects, the best model for a practical evaluation was the fixed linear model. Field data included 246,576 records of the largest Charolais herds in France. Models were compared using the correlations of estimated breeding values between the different models. Although the best model from a theoretical point of view was a threshold model with a fixed herd-year effect, a linear model with a fixed herd-year effect was the best choice from a practical point of view for predicting direct effects for calving difficulty in beef cattle and was a sufficient choice for predicting the associated maternal effects for data set with large herds. Correlations between direct estimated breeding values under the reference model and the fixed linear model and the random threshold model were 0.94 and 0.91, respectively. Correlations between the corresponding maternal estimated breeding values were 0.94 and 0.98. Heritabilities of direct effects were 0.27 and 0.14 under fixed threshold and fixed linear models, respectively. The corresponding heritabilities of maternal effects were 0.18 and 0.13, and the genetic correlation between direct and maternal effects were -0.36 and -0.34, respectively.     

Estimation of genetic parameters for ultrasound-predicted percentage of intramuscular fat in Angus cattle using random regression models

The present study included 3,358 observations of 675 bulls and heifers from the Iowa State University beef cattle breeding project. Data were collected over a 3-yr period between 1998 and 2000. Each year, cattle were scanned four to six times for ultrasound-predicted percentage of intramuscular fat (UPFAT) and other ultrasound traits, starting at a minimum age of 28 wk. The objective of the current study was to estimate variance components, heritability, and repeatability of UPFAT in young bulls and heifers. Data were subjected to random-regression animal models that included fixed effects of contemporary group, fixed Legendre polynomial of age at measurement, and random regression coefficients on Legendre polynomial of age at measurement for animals' direct genetic and direct permanent environmental effects. Phenotypic and genetic models involving different levels of polynomial fit for the animal component were considered. A model fitting a linear effect of Legendre polynomial of age at a measurement for animal direct genetic and direct permanent environmental effects and a homogeneous error variance described the present data adequately. Heritability of UPFAT ranged from 0.32 at 28 wk of age to a maximum of 0.53 at 63 wk. Repeatability of UPFAT increased from a minimum of 0.60 at ages of 28 to 39 wk to a maximum of 0.80 at ages 61 to 63 wk. Heritability and repeatability of yearling UPFAT were 0.50 and 0.71, respectively. With the exception of minor differences at earlier ages, fitting heterogeneous error variances did not have an effect on genetic parameter estimates for most ages of measurement. The present results showed an optimal heritability and repeatability of UPFAT measures around 52 wk and through at least 63 wk of age. This suggested that differences in UPFAT measures during this period also are good measures of differences in marbling genetic potential of Angus cattle.     

Use of an animal model in situations of limited subclass numbers and high degrees of relationships

Breeding value estimation procedures for two traits with moderate and high heritability were evaluated by using a single-trait animal model and computer-simulated data designs. Of interest were the effects of differing numbers of animals and degrees of relationships among animals within and across contemporary groups (tests). Test effects were assumed fixed and animal effects were assumed random. Family size, number of families per contemporary group, and degree of genetic relationships within and across contemporary groups were varied to determine interrelationships among the factors. Results were compared on the basis of accuracy by using both the correlation of true and estimated breeding values and the prediction error variance obtained from the inverse of the coefficient matrix of the mixed-model equations. Small contemporary groups in conjunction with evaluation of closely related families caused average accuracy to decrease relative to that obtained with the same number of unrelated animals because genetically related animals were less accurately evaluated relative to one another. Connecting contemporary groups with a genetic relationship matrix formed a large set of interdependent equations and improved the average accuracy of predicted breeding values. The slight decrease in accuracy for genetically related animals was more than offset by the increase in accuracy of evaluation for their unrelated test mates because the proportion of fixed effects to random effects was smaller. Care must be exercised in designing evaluation schemes involving small populations, and the decision of which fixed effects to include in the model is critical.     

Genetic parameters for various random regression models to describe total sperm cells per ejaculate over the reproductive lifetime of boars

The objective of this study was to model the variances and covariances of total sperm cells per ejaculate (TSC) over the reproductive lifetime of AI boars. Data from boars (n = 834) selected for AI were provided by Smithfield Premium Genetics. The total numbers of records and animals were 19,629 and 1,736, respectively. Parameters were estimated for TSC by age of boar classification with a random regression model using the Simplex method and DxMRR procedures. The model included breed, collector, and year-season as fixed effects. Random effects were additive genetic, permanent environmental effect of boar, and residual. Observations were removed when the number of data at a given age of boar classification was < 10 records. Preliminary evaluations showed the best fit with fifth-order polynomials, indicating that the best model would have fifth-order fixed regression and fifth-order random regressions for animal and permanent environmental effects. Random regression models were fitted to evaluate all combinations of first- through seventh-order polynomial covariance functions. Goodness of fit for the models was tested using Akaike's Information Criterion and the Schwarz Criterion. The maximum log likelihood value was observed for sixth-, fifth-, and seventh-order polynomials for fixed, additive genetic, and permanent environmental effects, respectively. However, the best fit as determined by Akaike's Information Criterion and the Schwarz Criterion was by fitting sixth-, fourth-, and seventh-order polynomials; and fourth-, second-, and seventh-order polynomials for fixed, additive genetic, and permanent environmental effects, respectively. Heritability estimates for TSC ranged from 0.27 to 0.48 across age of boar classifications. In addition, heritability for TSC tended to increase with age of boar classification.     

Assessment of Poisson, probit and linear models for genetic analysis of presence and number of black spots in Corriedale sheep

Black skin spots are associated with pigmented fibres in wool, an important quality fault. Our objective was to assess alternative models for genetic analysis of presence (BINBS) and number (NUMBS) of black spots in Corriedale sheep. During 2002-08, 5624 records from 2839 animals in two flocks, aged 1 through 6 years, were taken at shearing. Four models were considered: linear and probit for BINBS and linear and Poisson for NUMBS. All models included flock-year and age as fixed effects and animal and permanent environmental as random effects. Models were fitted to the whole data set and were also compared based on their predictive ability in cross-validation. Estimates of heritability ranged from 0.154 to 0.230 for BINBS and 0.269 to 0.474 for NUMBS. For BINBS, the probit model fitted slightly better to the data than the linear model. Predictions of random effects from these models were highly correlated, and both models exhibited similar predictive ability. For NUMBS, the Poisson model, with a residual term to account for overdispersion, performed better than the linear model in goodness of fit and predictive ability. Predictions of random effects from the Poisson model were more strongly correlated with those from BINBS models than those from the linear model. Overall, the use of probit or linear models for BINBS and of a Poisson model with a residual for NUMBS seems a reasonable choice for genetic selection purposes in Corriedale sheep.     

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.     

Multiple-breed genetic inference using heavy-tailed structural models for heterogeneous residual variances

Multiple-breed genetic models recently have been demonstrated to account for the heterogenous genetic variances that exist between different beef cattle breed groups. We extend these models to allow for residual heteroskedasticity (heterogeneous residual variances), specified as a function of fixed effects (e.g., sex, breed proportion, breed group heterozygosity) and random effects such as contemporary groups (CG). We additionally specify the residual distributions to be either Gaussian or based on heavier-tailed alternatives such as the Student's t or Slash densities. For each of these three residual densities using either homoskedastic (homogeneous variance) or heteroskedastic error specifications, we analyzed 22,717 postweaning gain records from a Nelore-Hereford population based on a Markov chain Monte Carlo animal model implementation. The heteroskedastic Student's t error model (with estimated df = 7.33 +/- 0.48) was clearly the best-fitting model based on a pseudo-Bayes factor criterion. Breed group heterozygosity and, to a lesser extent, calf sex seemed to be marginally important sources of residual heteroskedasticity. Specifically, the residual variance in F1 animals was estimated to be 0.70 +/- 0.16 times that for purebreds, whereas the male residual variance was estimated to be 1.13 +/- 0.09 times that for females. The CG effects were important random sources of residual heteroskedasticity (i.e., the coefficient of variation of CG-specific residual variances was estimated to be 0.72 +/- 0.06). Purebred Nelores were estimated to have a larger genetic variance (124.84 +/- 21.75 kg2) compared with Herefords (40.89 +/- 6.70 kg2) under the heteroskedastic Student's t error model; however, the converse was observed from results based on a homoskedastic Student's t error model (46.24 +/- 10.90 kg2 and 60.11 +/- 8.54 kg2, respectively). These results indicate that allowing for robustness to outliers and accounting for heteroskedasticity of residual variances has potentially important implications for variance component and genetic parameter estimates from data on multiple-breed populations.