Sampling distributions, biases, variances, and confidence intervals for genetic correlations

Area of Science:

• Quantitative genetics
• Statistical genetics
• Bioinformatics

Background:

• Genetic correlations (rho_g) are crucial for understanding trait evolution and breeding.
• Current methods for estimating rho_g and their precision lack comprehensive statistical evaluation.

Purpose of the Study:

• To assess the statistical properties of multivariate analysis of variance (MANOVA), restricted maximum likelihood (REML), and maximum likelihood (ML) estimators of genetic correlations.
• To evaluate the accuracy of variance and confidence interval estimators for rho_g using parametric, jackknife, and bootstrap methods.

Main Methods:

• Simulated bivariate normal samples for a one-way balanced linear model.
• Estimated probabilities of non-positive definite matrices for MANOVA.
• Calculated biases and variances for MANOVA, REML, and ML estimators of rho_g.
• Assessed accuracy of variance and confidence interval estimators.

Main Results:

• All estimators (MANOVA, REML, ML) exhibited bias in estimating genetic correlations.
• MANOVA estimator showed less bias under low heritability, genotype numbers, and replication numbers.
• REML and ML estimators demonstrated skewed distributions for higher genetic correlations.
• Bootstrapping provided accurate variance estimates for REML and ML, with reliable confidence intervals.
• MANOVA's bootstrap confidence intervals were less accurate compared to REML and ML.

Conclusions:

• REML and ML methods, particularly with bootstrap confidence intervals, are recommended for estimating genetic correlations due to their better accuracy and reliability.
• MANOVA can be less biased in specific low-data scenarios but provides less precise variance estimation.
• Further research into bias reduction and improved precision for all estimators is warranted.