Bayesian analysis of quantitative traits using skewed distributions.

Area of Science:

• Animal Genetics
• Statistical Modeling
• Quantitative Genetics

Background:

• Traditional genetic evaluation models often assume Gaussian residual distributions.
• Recent statistical advancements enable the use of asymmetric distributions for residuals.
• Understanding residual distribution is crucial for accurate genetic parameter estimation.

Purpose of the Study:

• To analyze three residual distribution patterns (Gaussian, asymmetric Gaussian, hierarchical asymmetric Gaussian) for litter size in sows.
• To identify the most suitable statistical model for genetic evaluation incorporating asymmetric residuals.
• To investigate the genetic control of litter size and the asymmetry parameter.

Main Methods:

• Analysis of 63,208 litter-size records from 19,255 sows with a 27,911-individual pedigree.
• Comparison of three models: Gaussian, asymmetric Gaussian, and hierarchical asymmetric Gaussian residual distributions.
• Model selection using the deviance information criterion (DIC) and posterior predictive checking.

Main Results:

• The hierarchical asymmetric Gaussian distribution model (Model 3) was identified as the most suitable.
• Evidence suggests systematic, additive genetic, and permanent environmental control over both litter size and the asymmetry parameter.
• Posterior means (SD) for additive genetic variance were 0.28 (0.06) for litter size and 0.07 (0.01) for asymmetry.
• Posterior mean (SD) for additive genetic correlation between litter size and asymmetry was 0.21 (0.07).

Conclusions:

• The use of asymmetric residual distributions provides a more accurate genetic evaluation for traits like litter size.
• The asymmetry parameter reflects sensitivity to environmental influences, which is itself under genetic control.
• Findings support the integration of asymmetric distributions in statistical models for genetic evaluation.