Bayesian inference about parameters of a longitudinal trajectory when selection operates on a correlated trait

Area of Science:

• Quantitative Genetics
• Statistical Modeling
• Animal Breeding

Background:

• Selection bias in cross-sectional data can distort inferences about longitudinal trait distributions.
• Longitudinal data is often unavailable for early generations, complicating joint analysis with cross-sectional data.

Purpose of the Study:

• To present a hierarchical model for inferring joint distributions of longitudinal and selected cross-sectional traits.
• To provide a Bayesian implementation using Markov Chain Monte Carlo (MCMC) procedures.
• To analyze correlated responses in growth curve parameters in a selected rabbit population.

Main Methods:

• Developed a hierarchical statistical model for joint trait distribution analysis.
• Utilized Bayesian inference with Markov Chain Monte Carlo (MCMC) procedures.
• Explored alternative residual covariance structures.
• Applied the model to rabbit growth data selected for increased growth rate.

Main Results:

• The model successfully inferred parameters for joint trait distributions under selection.
• Analysis of rabbit growth data revealed correlated responses in growth curve parameters.
• Results were consistent with previous studies using selected and control populations.
• Identified slow MCMC mixing, leading to small effective sample sizes and high Monte Carlo standard errors.

Conclusions:

• The hierarchical Bayesian model is effective for analyzing longitudinal and selected cross-sectional traits.
• The model aids in understanding correlated genetic and phenotypic responses.
• Computational challenges, such as slow MCMC mixing, require attention for accurate parameter estimation.