Copula miss-specification in REML multivariate genetic animal model estimation.

Area of Science:

• Animal Genetics
• Quantitative Genetics
• Statistical Genetics

Background:

• Linear mixed models are standard in animal genetics for estimating genetic and environmental effects.
• Restricted maximum likelihood (REML) is commonly used for variance component estimation, assuming multivariate normality.
• Non-Gaussian dependence structures (copulas) can violate REML assumptions even with normal marginal distributions.

Purpose of the Study:

• To evaluate the impact of non-Gaussian copulas on REML estimation of variance components in bivariate animal models.
• To assess how selection strategies influence the robustness of REML under non-normality.

Main Methods:

• Simulations of bivariate phenotypes in selected animal populations.
• Incorporation of various copulas to model error component dependence.
• Comparison of REML estimates with true parameters under random and truncation selection schemes.
• Analysis of two scenarios: two traits measured vs. one trait measured on candidates.

Main Results:

• Random selection showed no significant bias in REML estimates, regardless of copula type.
• Truncation selection with two measured traits exhibited systematic bias in variance components for non-Gaussian distributions, particularly with heavy-tailed or asymmetric distributions.
• When only one trait was measured under truncation selection, REML estimates were unaffected by non-Gaussian distributions.

Conclusions:

• REML is robust for estimating breeding values in multivariate cases under random selection or when only one trait is measured, even with non-normal phenotypes.
• Violation of normality assumptions, specifically non-Gaussian copulas, can introduce significant biases in REML variance-covariance component estimations when two traits are measured and truncation selection is applied.