Bayesian Phylogenetic Analysis of Combined Data

Abstract

The recent development of Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC) techniques has facilitated the exploration of parameter-rich evolutionary models. At the same time, stochastic models have become more realistic (and complex) and have been extended to new types of data, such as morphology. Based on this foundation, we developed a Bayesian MCMC approach to the analysis of combined data sets and explored its utility in inferring relationships among gall wasps based on data from morphology and four genes (nuclear and mitochondrial, ribosomal and protein coding). Examined models range in complexity from those recognizing only a morphological and a molecular partition to those having complex substitution models with independent parameters for each gene. Bayesian MCMC analysis deals efficiently with complex models: convergence occurs faster and more predictably for complex models, mixing is adequate for all parameters even under very complex models, and the parameter update cycle is virtually unaffected by model partitioning across sites. Morphology contributed only 5% of the characters in the data set but nevertheless influenced the combined-data tree, supporting the utility of morphological data in multigene analyses. We used Bayesian criteria (Bayes factors) to show that process heterogeneity across data partitions is a significant model component, although not as important as among-site rate variation. More complex evolutionary models are associated with more topological uncertainty and less conflict between morphology and molecules. Bayes factors sometimes favor simpler models over considerably more parameter-rich models, but the best model overall is also the most complex and Bayes factors do not support exclusion of apparently weak parameters from this model. Thus, Bayes factors appear to be useful for selecting among complex models, but it is still unclear whether their use strikes a reasonable balance between model complexity and error in parameter estimates.

Dynamic evolution of venom proteins in squamate reptiles

“…17) was used to estimate effective sample sizes for all parameters and to construct plots of ln(L) against generation to verify the point of convergence (burnin); trees generated before the completion of burnin were discarded. To avoid potential overparameterisation as a result of implementing multiple codon models of sequence evolution 37,38 , we compared Bayes factors generated by Bayesian inference analysis of codon partitioned and unpartitioned (utilising a single model of sequence evolution selected by MrModelTest 15 and, second, utilising a mixed model) data sets in Tracer 17,39 . Bayes factors are defined as the likelihood of data under a particular model after parameter estimation from two competing hypotheses -comparisons of Bayes factors can be interpreted as the success of each hypothesis at predicting the data 40,41 .…”

Age and biogeography of major clades in sturgeons and paddlefishes (Pisces: Acipenseriformes)

“…Under the partitioning strategy, the data set was divided into 10 partitions: Two rRNAs and eight protein-coding genes. The best-Wtting nucleotide substitution models for each of the 10 partitions were selected by using the Akaike Information Criterion (AIC) implemented in MrModeltest version 2.2 (Nylander et al, 2004). Metropolis-coupled Markov chain Monte Carlo (MCMC) analyses (with random starting trees) were run with one cold and three heated chains (temperature set to default 0.2) for one million generations and sampled every 100 generations.…”

Molecular phylogeny of the brachyuran crab superfamily Majoidea indicates close congruence with trees based on larval morphology

“…To examine phylogenetic hypotheses based on morphological studies, we used Bayes factor analysis (Nylander et al, 2004;Ronquist and Hulsenbeck, 2003) to compare the posterior odds of unconstrained Bayesian tree topologies relative to Bayesian trees where we constrained the monophyly of majoid families or family groupings. We tested support for hypotheses based on both larval morphology (Clark and Webber, 1991;Pohle, 1998, 2003;Rice, 1983Rice, , 1988 and adult morphology, i.e., monophyly of traditional majoid families (Martin and Davis, 2001;McLaughlin et al, 2005).…”

“…We ran MCMC searches with four chains for 1 Â 10 6 generations (standard deviation of split frequencies 6 0.01) and obtained the harmonic mean of tree likelihood values by sampling the post burn-in posterior distribution (sump command). We then calculated Bayes factors for each tree (B 10 ) using the difference between the marginal likelihood values of the unconstrained topology (representing H 1 ) and the monophyly-constrained topology (representing H 0 ) (following Nylander et al, 2004, Ronquist andHulsenbeck, 2003). We used these Bayes factors to evaluate whether there was evidence against constrained trees (i.e., different hypotheses based on larval or adult morphology) using the test statistic 2 log e (B 10 ) and the criteria described by Kass and Raftery (1995).…”

“…We used these Bayes factors to evaluate whether there was evidence against constrained trees (i.e., different hypotheses based on larval or adult morphology) using the test statistic 2 log e (B 10 ) and the criteria described by Kass and Raftery (1995). Under this criteria, a value for the test statistic 2 log e (B 10 ) between 0 and 2 indicates no evidence against H 0 ; values from 2 to 6 indicate positive evidence against H 0 ; values from 6 to 10 indicate strong evidence against H 0 ; and values >10 indicate very strong evidence against H 0 (Kass and Raftery, 1995;Nylander et al, 2004).…”