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

Genetic correlations (rho ( g )) are frequently estimated from natural and experimental populations, yet many of the statistical properties of estimators of rho ( g ) are not known, and accurate methods have not been described for estimating the precision of estimates of rho ( g ). Our objective was to assess the statistical properties of multivariate analysis of variance (MANOVA), restricted maximum likelihood (REML), and maximum likelihood (ML) estimators of rho ( g ) by simulating bivariate normal samples for the one-way balanced linear model. We estimated probabilities of non-positive definite MANOVA estimates of genetic variance-covariance matrices and biases and variances of MANOVA, REML, and ML estimators of rho ( g ), and assessed the accuracy of parametric, jackknife, and bootstrap variance and confidence interval estimators for rho ( g ). MANOVA estimates of rho ( g ) were normally distributed. REML and ML estimates were normally distributed for rho ( g ) = 0.1, but skewed for rho ( g ) = 0.5 and 0.9. All of the estimators were biased. The MANOVA estimator was less biased than REML and ML estimators when heritability (H), the number of genotypes (n), and the number of replications (r) were low. The biases were otherwise nearly equal for different estimators and could not be reduced by jackknifing or bootstrapping. The variance of the MANOVA estimator was greater than the variance of the REML or ML estimator for most H, n, and r. Bootstrapping produced estimates of the variance of rho ( g ) close to the known variance, especially for REML and ML. The observed coverages of the REML and ML bootstrap interval estimators were consistently close to stated coverages, whereas the observed coverage of the MANOVA bootstrap interval estimator was unsatisfactory for some H, rho ( g ), n, and r. The other interval estimators produced unsatisfactory coverages. REML and ML bootstrap interval estimates were narrower than MANOVA bootstrap interval estimates for most H, rho ( g ), n, and r.