Comparison of (co)variance component estimates in control populations of red flour beetle (Tribolium castaneum) using restricted maximum likelihood and Gibbs sampling

Mixed model (co)variance component estimates by REML and Gibbs sampling for two traits were compared for base populations and control lines of Red Flo ur Beetle (Tribolium castaneum). Two base populations (1296 records in the first replication, 1292 in the second) were sampled from laboratory stock. Control lines were derived from corresponding base populations with random selection and mating for 16 generations. The REML estimate of each (co)vari ance component for both pupa weight and family size was compared with the m ean and 95% central interval of the particular (co)variance estimated by Gi bbs sampling with three different weights on the given priors: 'flat', smal lest, and 3.7% degrees of belief. Results from Gibbs sampling showed that f lat priors gave a wider and more skewed marginal posterior distribution tha n the other two weights on priors for all parameters. In contrast, the 3.7% degree of belief on priors provided reasonably narrow and symmetric margin al posterior distributions. Estimation by REML does not have the flexibilit y of changing the weight on prior information as does the Bayesian analysis implemented by Gibbs sampling. In general, the 95% central intervals from the three different weights on priors in the base populations were similar to those in control lines. Most REML estimates in base populations differed from REML estimates in control lines. Insufficient information from the da ta, and confounding of random effects contributed to the variability of REM L estimates in base populations. Evidence is presented showing that some (c o)variance components were estimated with less precision than others. Resul ts also support the hypothesis that REML estimates were equivalent to the j oint mode of posterior distribution obtained from a Bayesian analysis with flat priors, but only when there was sufficient information from data, and no confounding among random effects.