"Bending" and beyond: Better estimates of quantitative genetic parameters?

Multivariate estimation of genetic parameters involving more than a handful of traits can be afflicted by problems arising through substantial sampling variation. We present a review of underlying causes and proposals to improve estimates, focusing on linear mixed model-based estimation via restricted maximum likelihood (REML). Both full multivariate analyses and pooling of results from overlapping subsets of traits are considered. It is suggested to impose a penalty on the likelihood designed to reduce sampling variances at the expense of a little additional bias. Simulation results are discussed which demonstrate that this can yield REML estimates that are on average closer to the population values than their unpenalized counterparts. Suitable penalties can be obtained based on assumed prior distributions of selected parameters. Necessary choices of penalty functions and of the stringency of penalization are examined. We argue that scale-free penalty functions lend themselves to a simple scheme imposing a mild, default penalty which can yield "better" estimates without being likely to incur detrimental effects.