Use of robust multivariate linear mixed models for estimation of genetic parameters for carcass traits in beef cattle.

Assumptions of normality of residuals for carcass evaluation may make inferences vulnerable to the presence of outliers, but heavy-tail densities are viable alternatives to normal distributions and provide robustness against unusual or outlying observations when used to model the densities of residual effects. We compare estimates of genetic parameters by fitting multivariate Normal (MN) or heavy-tail distributions (multivariate Student's t and multivariate Slash, MSt and MS) for residuals in data of hot carcass weight (HCW), longissimus muscle area (REA) and 12th to 13th rib fat (FAT) traits in beef cattle using 2475 records from 2007 to 2008 from a large commercial operation in Nebraska. Model comparisons using deviance information criteria (DIC) favoured MSt over MS and MN models, respectively. The posterior means (and 95% posterior probability intervals, PPI) of v for the MSt and MS models were 5.89 ± 0.90 (4.35, 7.86) and 2.04 ± 0.18 (1.70, 2.41), respectively. Smaller values of posterior densities of v for MSt and MS models confirm that the assumption of normally distributed residuals is not adequate for the analysis of the data set. Posterior mean (PM) and posterior median (PD) estimates of direct genetic variances were variable with MSt having the highest mean value followed by MS and MN, respectively. Posterior inferences on genetic variance were, however, comparable among the models for FAT. Posterior inference on additive heritabilities for HCW, REA and FAT using MN, MSt and MS models indicated similar and moderate heritability comparable with the literature. Posterior means of genetic correlations for carcass traits were variable but positive except for between REA and FAT, which showed an antagonistic relationship. We have demonstrated that genetic evaluation and selection strategies will be sensitive to the assumed model for residuals.

Application of multivariate heavy-tailed distributions to residuals in the estimation of genetic parameters of growth traits in beef cattle.

Assumptions of normality in most animal breeding applications may make inferences vulnerable to the presence of outliers. Heavy-tail densities are viable alternatives to normal distributions and provide robustness against unusual or outlying observations when used to model the densities of residual effects. Our objective is to compare estimates of genetic parameters by fitting multivariate normal (MN) or heavy-tail distributions [multivariate Student's t (MSt) and multivariate slash (MS)] for residuals in data of body birth weight (BBW), weaning (WW), and yearling (YW) weight traits in beef cattle. A total of 17,019 weight records for BBW, WW, and YW from 1998 through 2010 from a large commercial cow/calf operation in the sand hills of Nebraska were analyzed. Models included fixed effects of contemporary group and sire breed whereas animal and maternal effects were random and the degrees of freedom (v) was treated as unknown for MSt and MS. Model comparisons using deviance information criteria (DIC) favored MSt over MS and MN models, respectively. The posterior means [and 95% posterior probability intervals (PPI)] of v for the MSt and MS models were 5.28 (4.80, 5.85) and 1.88 (1.76, 2.00), respectively. Smaller values of posterior densities of v for MSt and MS models confirm that the assumption of normally distributed residuals is not adequate for the analysis of BBW, WW, and YW datasets. Posterior mean (PM) and posterior median (PD) estimates of direct and maternal genetic variances were the same and posterior densities of these parameters were found to be symmetric. The 95% PPI estimates from MN and MSt models for BBW did not overlap, which indicates significant difference between PM estimates from MN or MSt models. The observed antagonistic relationship between additive direct and additive maternal effects indicated that genetic evaluation and selection strategies will be sensitive to the assumed model for residuals.