SAMPLING DISTRIBUTIONS, BIASES, VARIANCES, AND CONFIDENCE-INTERVALS FOR GENETIC CORRELATIONS

Genetic correlations (rho(g)) are frequently estimated from natural an d 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 ob jective was to assess the statistical properties of multivariate analy sis of variance (MANOVA), restricted maximum likelihood (REML), and ma ximum likelihood (ML) estimators of rho(g) by simulating bivariate nor mal samples for the one-way balanced linear model. We estimated probab ilities of non-positive definite MANOVA estimates of genetic variance- covariance matrices and biases and variances of MANOVA, REML, and ML e stimators of rho(g), and assessed the accuracy of parametric, jackknif e, and bootstrap variance and confidence interval estimators for rho(g ). MANOVA estimates of rho(g) were normally distributed. REML and ML e stimates were normally distributed for rho(g) = 0.1, but skewed for rh o(g) = 0.5 and 0.9. All of the estimators were biased. The MANOVA esti mator was less biased than REML and ML estimators when heritability (H ), the number of genotypes (n), and the number of replications (r) wer e low. The biases were otherwise nearly equal for different estimators and could not be reduced by jackknifing or bootstrapping. The varianc e of the MANOVA estimator was greater than the variance of the REML or ML estimator for most H, n, and r. Bootstrapping produced estimates o f the variance of rho(g) close to the known variance, especially for R EML and ML. The observed coverages of the REML and ML bootstrap interv al estimators were consistently close to stated coverages, whereas the observed coverage of the MANOVA bootstrap interval estimator was unsa tisfactory for some H, rho(g), n, and r. The other interval estimators produced unsatisfactory coverages. REML and ML bootstrap interval est imates were narrower than MANOVA bootstrap interval estimates for most H, rho(g), n, and r.