title: Bayesian models for comparative analysis integrating phylogenetic uncertainty.
abstract: BACKGROUND
  Uncertainty in comparative analyses can come from at least two sources: a) phylogenetic uncertainty in the tree topology or branch lengths, and b) uncertainty due to intraspecific variation in trait values, either due to measurement error or natural individual variation. Most phylogenetic comparative methods do not account for such uncertainties. Not accounting for these sources of uncertainty leads to false perceptions of precision (confidence intervals will be too narrow) and inflated significance in hypothesis testing (e.g. p-values will be too small). Although there is some application-specific software for fitting Bayesian models accounting for phylogenetic error, more general and flexible software is desirable.
  
  
  METHODS
  We developed models to directly incorporate phylogenetic uncertainty into a range of analyses that biologists commonly perform, using a Bayesian framework and Markov Chain Monte Carlo analyses.
  
  
  RESULTS
  We demonstrate applications in linear regression, quantification of phylogenetic signal, and measurement error models. Phylogenetic uncertainty was incorporated by applying a prior distribution for the phylogeny, where this distribution consisted of the posterior tree sets from Bayesian phylogenetic tree estimation programs. The models were analysed using simulated data sets, and applied to a real data set on plant traits, from rainforest plant species in Northern Australia. Analyses were performed using the free and open source software OpenBUGS and JAGS.
  
  
  CONCLUSIONS
  Incorporating phylogenetic uncertainty through an empirical prior distribution of trees leads to more precise estimation of regression model parameters than using a single consensus tree and enables a more realistic estimation of confidence intervals. In addition, models incorporating measurement errors and/or individual variation, in one or both variables, are easily formulated in the Bayesian framework. We show that BUGS is a useful, flexible general purpose tool for phylogenetic comparative analyses, particularly for modelling in the face of phylogenetic uncertainty and accounting for measurement error or individual variation in explanatory variables. Code for all models is provided in the BUGS model description language.
authors: School of Biological Sciences, University of Queensland, Brisbane, 4072 Queensland, Australia.
authors: Pierre
authors: P
authors: de Villemereuil
authors: Jessie A
authors: JA
authors: Wells
authors: Robert D
authors: RD
authors: Edwards
authors: Simon P
authors: SP
authors: Blomberg
mesh_terms: D001315:Australia; D001499:Bayes Theorem; D003198:Computer Simulation; D016014:Linear Models; D008390:Markov Chains; D008957:Models, Genetic; D009010:Monte Carlo Method; D010802:Phylogeny; D012984:Software; D014197:Trees / Q000235:genetics; D035501:Uncertainty