Bayesian analysis of quantitative traits using skewed distributions

Statistical models for genetic evaluation often make use of Gaussian distributions. However, some new statistical developments allow the use of an asymmetric distribution for the residuals. Within this context, we analysed three different patterns for the residual term on a data set consisting of 63 208 litter-size records, belonging to 19 255 sows, with a pedigree including 27 911 individuals. The three different residual distributions were: (1) Gaussian distribution, (2) asymmetric Gaussian distribution and (3) asymmetric Gaussian distribution with a hierarchical scheme for the asymmetry parameter. The operational model always included order of parity and herd-year-season as systematic effects, and the permanent environmental and infinitesimal genetic effect of each sow as random effects. The most suitable model using the deviance information criterion (DIC) and posterior predictive checking was model 3. This implies systematic, additive genetic and permanent environmental control of both litter size and the asymmetry parameter of the residual distribution. The asymmetry parameter can be understood as a measure of sensitivity to negative (or positive) environmental influences on phenotypes. The posterior mean (standard deviation) of the additive genetic variance was 0.28 (0.06) for litter size and 0.07 (0.01) for the asymmetry parameter. The posterior mean (standard deviation) of the additive genetic correlation between litter size and the asymmetry parameter was 0.21 (0.07).