Technical note: how to use Winbugs to draw inferences in animal models.

This paper deals with Bayesian inferences of animal models using Gibbs sampling. First, we suggest a general and efficient method for updating additive genetic effects, in which the computational cost is independent of the pedigree depth and increases linearly only with the size of the pedigree. Second, we show how this approach can be used to draw inferences from a wide range of animal models using the computer package Winbugs. Finally, we illustrate the approach in a simulation study, in which the data are generated and analyzed using Winbugs according to a linear model with i.i.d errors having Student's t distributions. In conclusion, Winbugs can be used to make inferences in small-sized, quantitative, genetic data sets applying a wide range of animal models that are not yet standard in the animal breeding literature.

The effect of ignoring individual heterogeneity in Weibull log-normal sire frailty models.

The objective of this study was, by means of simulation, to quantify the effect of ignoring individual heterogeneity in Weibull sire frailty models on parameter estimates and to address the consequences for genetic inferences. Three simulation studies were evaluated, which included 3 levels of individual heterogeneity combined with 4 levels of censoring (0, 25, 50, or 75%). Data were simulated according to balanced half-sib designs using Weibull log-normal animal frailty models with a normally distributed residual effect on the log-frailty scale. The 12 data sets were analyzed with 2 models: the sire model, equivalent to the animal model used to generate the data (complete sire model), and a corresponding model in which individual heterogeneity in log-frailty was neglected (incomplete sire model). Parameter estimates were obtained from a Bayesian analysis using Gibbs sampling, and also from the software Survival Kit for the incomplete sire model. For the incomplete sire model, the Monte Carlo and Survival Kit parameter estimates were similar. This study established that when unobserved individual heterogeneity was ignored, the parameter estimates that included sire effects were biased toward zero by an amount that depended in magnitude on the level of censoring and the size of the ignored individual heterogeneity. Despite the biased parameter estimates, the ranking of sires, measured by the rank correlations between true and estimated sire effects, was unaffected. In comparison, parameter estimates obtained using complete sire models were consistent with the true values used to simulate the data. Thus, in this study, several issues of concern were demonstrated for the incomplete sire model.

Genetic parameters for within-litter variation in piglet birth weight and change in within-litter variation during suckling.

The objective of this study was to ascertain whether maternal additive genetic variance exists for within-litter variation in birth weight and for change in within-litter variation in piglet weight during suckling. A further objective was to estimate maternal genetic correlations of these two traits with mortality, birth weight, growth, and number of piglets born alive. Data were obtained from Lövsta research station, Swedish University of Agricultural Sciences, and included 22,521 piglets born in 2,003 litters by 1,074 Swedish Yorkshire sows. No cross fostering was used in the herd. The following seven traits were analysed in a multivariate animal (sow) model: number of piglets born alive, within-litter SD in birth weight, within-litter SD in piglet weight at 3 wk of age, mean weight at birth, mean weight at 3 wk of age, proportion of stillborn piglets, and proportion of dead piglets during suckling. Maternal genetic variance for the change in within-litter SD in piglet weight during suckling was assessed from the estimated additive genetic covariance components by conditioning on within-litter SD in birth weight. Similarly, mean growth of piglets during suckling was assessed from the additive genetic covariance components by conditioning on mean weight at birth. The heritability for within-litter SD in birth weight was 0.08 and 0.06 for within-litter SD in piglet weight at 3 wk. The genetic correlation between these two traits was 0.71. Little maternal genetic variance was found for the change in within-litter SD in piglet weight during suckling, and opportunity for genetic improvement of this trait by selective breeding seems limited. The genetic correlation of within-litter SD in birth weight with proportion of dead piglets during suckling was 0.25 and of within-litter SD in birth weight with mean growth of piglets was -0.31. The maternal genetic variance and heritability found for within-litter SD in birth weight indicates that genetic improvement of this trait by selective breeding is possible. In addition, selection for sows' capacity to give birth to homogeneous litters may be advantageous for piglet survival, piglet growth, and litter homogeneity at weaning.