[Draft] Manual BayesTraits Mark Pagel and Andrew Meade School of Biological Sciences University of Reading Reading RG6 6AJ www.evolution.rdg.ac.ukBayesTraits is a computer package for performing analyses of trait evolution among groups of species for which a phylogeny or sample of phylogenies is available. It can be applied to the analysis of traits that adopt a finite number of discrete states, or to the analysis of continuously varying traits. Hypotheses can be tested about models of evolution, about ancestral states and about correlations among pairs of traits. History BayesTraits combines a number of computer programs that we have previously made available, including MultiState, MultiAns, Discrete and Continuous. We will increasingly support only this package and so users are encouraged to switch to BayesTraits if currently using one of these older versions. The methods in BayesTraits are described in a series of papers that we will refer to throughout this manual (see also references at end). The computer code is all written in C and was produced by Dr Andrew Meade. We would be grateful if you use BayesTraits in your published research if you cite one or more of the relevant articles and indicate that the software is available from www.evolution.rdg.ac.uk. Methods and Approach BayesTraits uses Markov chain Monte Carlo (MCMC) methods to derive posterior distributions and maximum likelihood (ML) methods to derive point estimates of, log-likelihoods, the parameters of statistical models, and the values of traits at ancestral nodes of phylogenies. The user can select either standard or conventional MCMC or reversible-jump MCMC. In the latter case the Markov chain searches the posterior distribution of different models of evolution as well as the posterior distributions of the parameters of these models (see below). BayesTraits can be used with a single phylogenetic tree in which case only uncertainty about model parameters is explored, or, it can be applied to suitable samples of trees such that models are estimated and hypotheses are tested taking phylogenetic uncertainty into account. Our BayesPhylogenies package (www.evolution.rdg.ac.uk) can be used to generate posterior distributions of phylogenetic trees when a gene-sequence alignment or other data set is available. BayesTraits makes available several methods: • BayesMultiState is used to reconstruct how traits that adopt a finite number of discrete states evolve on phylogenetic trees. It is useful for reconstructing ancestral states and for testing models of trait evolution. It can be applied to traits that adopt two or more discrete states (see Pagel, M., Meade, A. and Barker, D. 2004. Systematic Biology, 53, 673-684; • BayesDiscrete is used to analyse correlated evolution between pairs of discrete binary traits. Most commonly the two binary states refer to the presence or absence of some feature, but could also include “low” and “high”, or any two distinct features. Its uses might include tests of correlation among behavioural, morphological, genetic or cultural characters (see Pagel, M. and Meade, A. 2006. American Naturalist, 167, 808-825.) Once recent use of BayesDiscrete is to test for functional linkage among pairs of genes (Barker, D. and Pagel, M. 2005. PLoS Computational Biology, 1, 24-31. DOI: 10.1371/journal.pcbi.0010003); • BayesContinuous is for the analysis of the evolution of continuously varying traits. It can be used to model the evolution of a single trait, to study correlations among pairs of traits, or to study the regression of one trait on two or more other traits (see Pagel, M. 1999. Nature, 401, 877-884). This manual is designed to show how to use the programs that implement these models. Detailed information about the methods can be found in the papers listed at the end (some are available as pdfs on our website). Syntax and a description of all of the commands in BayesTraits can be found in the list of commands in the Appendix to the manual. THE CONTINUOUS-TIME MARKOV MODELS OF TRAIT EVOLUTION FOR DISCRETE TRAITS Multistate and Discrete fit continuous-time Markov models to the discrete character data. This model allows the trait to change from the state it is in at any given moment to any other state overinfinitesimally small intervals of time. The rate parameters of the model estimate these transition rates (see Pagel, 1994 for further discussion). The model traverses the tree estimating transition rates and the likelihood associated with different states at each node. The table shows an example of the model of evolution for a trait that can adopt three states, 0,1, and 2. The qij are the transition rates among the three states, and these are what the method estimates on the tree, based on the distribution of states among the species. If these rates differ from zero, this indicates that they are a significant component of the model. The main diagonal elements are not estimated but are a function of the other values in their row. Example of the model of evolution for a trait that adopts three states State 0 1 2 0 -- q01 q02 1 q01 -- q12 2 q20 q21 -- For a trait that adopts four states, the matrix would have twelve entries, for a binary trait the matrix would have just two entries. Discrete tests for correlated evolution in two binary traits by comparing the fit (log-likelihood) of two of these continuous-time Markov models. One of these is a model in which the two traits evolve independently on the tree. Each trait is described by a 2 × 2 matrix in the same format as the one above, but in which the trait adopts just two states, “0” and “1”. This creates two rate coefficients per trait. The other model, allows the traits to evolve in a correlated fashion such that the rate of change in one trait depends upon the background state of the other. The dependent model can adopt four states, one for each combination of the two binary traits (0,0; 0,1; 1,0; 1,1). It is represented in the program as shown below and the transition rates describe all possible changes in one state holding the other constant. The main diagonal elements are estimated from the other values in their row as before. The other diagonal elements are set to zero as the model does not allow ‘dual’ transitions to occur, the logic being that these are instantaneous transition rates and the probability of two traits changing at
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