title: Estimating sampling error of evolutionary statistics based on genetic covariance matrices using maximum likelihood.
abstract: We explore the estimation of uncertainty in evolutionary parameters using a recently devised approach for resampling entire additive genetic variance-covariance matrices (G). Large-sample theory shows that maximum-likelihood estimates (including restricted maximum likelihood, REML) asymptotically have a multivariate normal distribution, with covariance matrix derived from the inverse of the information matrix, and mean equal to the estimated G. This suggests that sampling estimates of G from this distribution can be used to assess the variability of estimates of G, and of functions of G. We refer to this as the REML-MVN method. This has been implemented in the mixed-model program WOMBAT. Estimates of sampling variances from REML-MVN were compared to those from the parametric bootstrap and from a Bayesian Markov chain Monte Carlo (MCMC) approach (implemented in the R package MCMCglmm). We apply each approach to evolvability statistics previously estimated for a large, 20-dimensional data set for Drosophila wings. REML-MVN and MCMC sampling variances are close to those estimated with the parametric bootstrap. Both slightly underestimate the error in the best-estimated aspects of the G matrix. REML analysis supports the previous conclusion that the G matrix for this population is full rank. REML-MVN is computationally very efficient, making it an attractive alternative to both data resampling and MCMC approaches to assessing confidence in parameters of evolutionary interest.
authors.affiliation: Department of Biological Science, Florida State University, Tallahassee, FL, USA.
authors.forename: D
authors.initials: D
authors.lastname: Houle
authors.affiliation: Animal Genetics and Breeding Unit, University of New England, Armidale, NSW, Australia.
authors.forename: K
authors.initials: K
authors.lastname: Meyer
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D005075:Biological Evolution; D004330:Drosophila / Q000033:anatomy & histology / Q000235:genetics*; D014644:Genetic Variation; D016013:Likelihood Functions; D008390:Markov Chains; D008957:Models, Genetic; D009010:Monte Carlo Method; D014921:Wings, Animal / Q000033:anatomy & histology*
keywords: G matrix; evolution; evolvability; quantitative genetics; restricted maximum likelihood; sampling error