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235
Model Selection and Model Averaging in Phylogenetics: Advantages of Akaike Information Criterion and Bayesian Approaches Over Likelihood Ratio Tests
, 2004
"... Model selection is a topic of special relevance in molecular phylogenetics that affects many, if not all, stages of phylogenetic inference. Here we discuss some fundamental concepts and techniques of model selection in the context of phylogenetics. We start by reviewing different aspects of the sel ..."
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Cited by 407 (8 self)
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Model selection is a topic of special relevance in molecular phylogenetics that affects many, if not all, stages of phylogenetic inference. Here we discuss some fundamental concepts and techniques of model selection in the context of phylogenetics. We start by reviewing different aspects of the selection of substitution models in phylogenetics from a theoretical, philosophical and practical point of view, and summarize this comparison in table format. We argue that the most commonly implemented model selection approach, the hierarchical likelihood ratio test, is not the optimal strategy for model selection in phylogenetics, and that approaches like the Akaike Information Criterion (AIC) and Bayesian methods offer important advantages. In particular, the latter two methods are able to simultaneously compare multiple nested or nonnested models, assess model selection uncertainty, and allow for the estimation of phylogenies and model parameters using all available models (model-averaged inference or multimodel inference). We also describe how the relative importance of the different parameters included in substitution models can be depicted. To illustrate some of these points, we have applied AIC-based model averaging to 37 mitochondrial DNA sequences from the subgenus Ohomopterus (genus Carabus) ground beetles described by Sota and Vogler (2001).
Approximate likelihood ratio test for branches: a fast, accurate and powerful alternative
- SYSTEMATIC BIOLOGY
, 2006
"... We revisit statistical tests for branches of evolutionary trees reconstructed upon molecular data. A new, fast, approximate likelihood-ratio test (aLRT) for branches is presented here as a competitive alternative to nonparametric bootstrap and Bayesian estimation of branch support. The aLRT is based ..."
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Cited by 275 (9 self)
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We revisit statistical tests for branches of evolutionary trees reconstructed upon molecular data. A new, fast, approximate likelihood-ratio test (aLRT) for branches is presented here as a competitive alternative to nonparametric bootstrap and Bayesian estimation of branch support. The aLRT is based on the idea of the conventional LRT, with the null hypothesis corresponding to the assumption that the inferred branch has length 0. We show that the LRT statistic is asymptotically distributed as a maximum of three random variables drawn from the 1 2 1 2 χ 2 0 + χ
Model selection in ecology and evolution.
- Trends in Ecology and Evolution
, 2004
"... Recently, researchers in several areas of ecology and evolution have begun to change the way in which they analyze data and make biological inferences. Rather than the traditional null hypothesis testing approach, they have adopted an approach called model selection, in which several competing hypo ..."
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Cited by 218 (0 self)
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Recently, researchers in several areas of ecology and evolution have begun to change the way in which they analyze data and make biological inferences. Rather than the traditional null hypothesis testing approach, they have adopted an approach called model selection, in which several competing hypotheses are simultaneously confronted with data. Model selection can be used to identify a single best model, thus lending support to one particular hypothesis, or it can be used to make inferences based on weighted support from a complete set of competing models. Model selection is widely accepted and well developed in certain fields, most notably in molecular systematics and markrecapture analysis. However, it is now gaining support in several other areas, from molecular evolution to landscape ecology. Here, we outline the steps of model selection and highlight several ways that it is now being implemented. By adopting this approach, researchers in ecology and evolution will find a valuable alternative to traditional null hypothesis testing, especially when more than one hypothesis is plausible. Science is a process for learning about nature in which competing ideas about how the world works are evaluated against observations Two basic approaches have been used to draw biological inferences. The dominant paradigm is to generate a null hypothesis (typically one with little biological meaning How model selection works Generating biological hypotheses as candidate models Model selection is underpinned by a philosophical view that understanding can best be approached by simultaneously weighing evidence for multiple working hypotheses
Bayesian phylogenetic analysis of combined data
- Syst. Biol
, 2004
"... 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 typ ..."
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Cited by 203 (12 self)
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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
Bayesian estimation of ancestral character states on phylogenies
- Syst. Biol
, 2004
"... Abstract.—Biologists frequently attempt to infer the character states at ancestral nodes of a phylogeny from the distribution of traits observed in contemporary organisms. Because phylogenies are normally inferences from data, it is desirable to account for the uncertainty in estimates of the tree a ..."
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Cited by 170 (4 self)
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Abstract.—Biologists frequently attempt to infer the character states at ancestral nodes of a phylogeny from the distribution of traits observed in contemporary organisms. Because phylogenies are normally inferences from data, it is desirable to account for the uncertainty in estimates of the tree and its branch lengths when making inferences about ancestral states or other comparative parameters. Here we present a general Bayesian approach for testing comparative hypotheses across statistically justified samples of phylogenies, focusing on the specific issue of reconstructing ancestral states. The method uses Markov chain Monte Carlo techniques for sampling phylogenetic trees and for investigating the parameters of a statistical model of trait evolution. We describe how to combine information about the uncertainty of the phylogeny with uncertainty in the estimate of the ancestral state. Our approach does not constrain the sample of trees only to those that contain the ancestral node or nodes of interest, and we show how to reconstruct ancestral states of uncertain nodes using a most-recent-common-ancestor approach. We illustrate the methods with data on ribonuclease evolution in the Artiodactyla. Software implementing the methods (BayesMultiState) is available from the authors. [Ancestral states; comparative methods; maximum likelihood; MCMC; phylogeny.] Given a collection of species, information on their at-tributes, and a phylogeny that describes their shared hi-erarchy of descent, the prospect is raised of inferring the
Bayes or bootstrap? A simulation study comparing the performance of Bayesian Markov chain Monte Carlo sampling and bootstrapping in assessing phylogenetic conWdence.
- Mol. Biol. Evol.
, 2003
"... Bayesian Markov chain Monte Carlo sampling has become increasingly popular in phylogenetics as a method for both estimating the maximum likelihood topology and for assessing nodal confidence. Despite the growing use of posterior probabilities, the relationship between the Bayesian measure of confid ..."
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Cited by 140 (5 self)
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Bayesian Markov chain Monte Carlo sampling has become increasingly popular in phylogenetics as a method for both estimating the maximum likelihood topology and for assessing nodal confidence. Despite the growing use of posterior probabilities, the relationship between the Bayesian measure of confidence and the most commonly used confidence measure in phylogenetics, the nonparametric bootstrap proportion, is poorly understood. We used computer simulation to investigate the behavior of three phylogenetic confidence methods: Bayesian posterior probabilities calculated via Markov chain Monte Carlo sampling (BMCMC-PP), maximum likelihood bootstrap proportion (ML-BP), and maximum parsimony bootstrap proportion (MP-BP). We simulated the evolution of DNA sequence on 17-taxon topologies under 18 evolutionary scenarios and examined the performance of these methods in assigning confidence to correct monophyletic and incorrect monophyletic groups, and we examined the effects of increasing character number on support value. BMCMC-PP and ML-BP were often strongly correlated with one another but could provide substantially different estimates of support on short internodes. In contrast, BMCMC-PP correlated poorly with MP-BP across most of the simulation conditions that we examined. For a given threshold value, more correct monophyletic groups were supported by BMCMC-PP than by either ML-BP or MP-BP. When threshold values were chosen that fixed the rate of accepting incorrect monophyletic relationship as true at 5%, all three methods recovered most of the correct relationships on the simulated topologies, although BMCMC-PP and ML-BP performed better than MP-BP. BMCMC-PP was usually a less biased predictor of phylogenetic accuracy than either bootstrapping method. BMCMC-PP provided high support values for correct topological bipartitions with fewer characters than was needed for nonparametric bootstrap.
A phylogenetic mixture model for detecting pattern-heterogeneity in gene sequence or character-state data. Syst. Biol
, 2004
"... Abstract.—We describe a general likelihood-based ‘mixture model ’ for inferring phylogenetic trees from gene-sequence or other character-state data. The model accommodates cases in which different sites in the alignment evolve in qualitatively distinct ways, but does not require prior knowledge of t ..."
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Cited by 136 (3 self)
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Abstract.—We describe a general likelihood-based ‘mixture model ’ for inferring phylogenetic trees from gene-sequence or other character-state data. The model accommodates cases in which different sites in the alignment evolve in qualitatively distinct ways, but does not require prior knowledge of these patterns or partitioning of the data. We call this qualitative variability in the pattern of evolution across sites “pattern-heterogeneity ” to distinguish it from both a homogenous process of evolution and from one characterized principally by differences in rates of evolution. We present studies to show that the model correctly retrieves the signals of pattern-heterogeneity from simulated gene-sequence data, and we apply the method to protein-coding genes and to a ribosomal 12S data set. The mixture model outperforms conventional partitioning in both these data sets. We implement the mixture model such that it can simultaneously detect rate- and pattern-heterogeneity. The model simplifies to a homogeneous model or a rate-variability model as special cases, and therefore always performs at least as well as these two approaches, and often considerably improves upon them. We make the model available within a Bayesian Markov-chain Monte Carlo framework for phylogenetic inference, as an easy-to-use computer program. [Bayesian inference; MCMC; mixture model; phylogeny; rate-heterogeneity; secondary structure; sequence evolution] The conventional likelihood-based approach to infer-ring phylogenetic trees from aligned gene-sequence or other data is to apply a single substitutional model to
Modeling compositional heterogeneity
- Syst Biol
, 2004
"... Abstract.—Compositional heterogeneity among lineages can compromise phylogenetic analyses, because models in common use assume compositionally homogeneous data. Models that can accommodate compositional heterogeneity with few extra parameters are described here, and used in two examples where the tr ..."
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Cited by 74 (0 self)
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Abstract.—Compositional heterogeneity among lineages can compromise phylogenetic analyses, because models in common use assume compositionally homogeneous data. Models that can accommodate compositional heterogeneity with few extra parameters are described here, and used in two examples where the true tree is known with confidence. It is shown using likelihood ratio tests that adequate modeling of compositional heterogeneity can be achieved with few composition parameters, that the data may not need to be modelled with separate composition parameters for each branch in the tree. Tree searching and placement of composition vectors on the tree are done in a Bayesian framework using Markov chain Monte Carlo (MCMC) methods. Assessment of fit of the model to the data is made in both maximum likelihood (ML) and Bayesian frameworks. In an ML framework, overall model fit is assessed using the Goldman-Cox test, and the fit of the composition implied by a (possibly heterogeneous) model to the composition of the data is assessed using a novel tree-and model-based composition fit test. In a Bayesian framework, overall model fit and composition fit are assessed using posterior predictive simulation. It is shown that when composition is not accommodated, then the model does not fit, and incorrect trees are found; but when composition is accommodated, the model then fits, and the known correct phylogenies are obtained. [Compositional heterogeneity; Markov chain Monte Carlo; maximum likelihood; model assessment; model selection; phylogenetics.] Markov process models used for phylogenetic analysis
Parallel Metropolis coupled Markov chain Monte Carlo for Bayesian phylogenetic inference. Bioinformatics
, 2004
"... Motivation: Bayesian estimation of phylogeny is based on the posterior probability distribution of trees. Currently, the only numerical method that can effectively approximate posterior probabilities of trees is Markov chain Monte Carlo (MCMC). Standard implementations of MCMC can be prone to entrap ..."
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Cited by 73 (0 self)
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Motivation: Bayesian estimation of phylogeny is based on the posterior probability distribution of trees. Currently, the only numerical method that can effectively approximate posterior probabilities of trees is Markov chain Monte Carlo (MCMC). Standard implementations of MCMC can be prone to entrapment in local optima. Metropolis coupled MCMC [(MC) 3], a variant of MCMC, allows multiple peaks in the landscape of trees to be more readily explored, but at the cost of increased execution time. Results: This paper presents a parallel algorithm for (MC) 3. The proposed parallel algorithm retains the ability to explore multiple peaks in the posterior distribution of trees while maintaining a fast execution time. The algorithm has been implemented using two popular parallel programming models: message passing and shared memory. Performance results indicate nearly linear speed improvement in both programming models for small and large data sets. Availability: MrBayes v3.0 is available at
Comparison of site-specific rate-inference methods for protein sequences: empirical Bayesian methods are superior. Mol Biol Evol,
, 2004
"... The degree to which an amino acid site is free to vary is strongly dependent on its structural and functional importance. An amino acid that plays an essential role is unlikely to change over evolutionary time. Hence, the evolutionary rate at an amino acid site is indicative of how conserved this s ..."
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Cited by 65 (11 self)
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The degree to which an amino acid site is free to vary is strongly dependent on its structural and functional importance. An amino acid that plays an essential role is unlikely to change over evolutionary time. Hence, the evolutionary rate at an amino acid site is indicative of how conserved this site is and, in turn, allows evaluation of its importance in maintaining the structure/function of the protein. When using probabilistic methods for site-specific rate inference, few alternatives are possible. In this study we use simulations to compare the maximum-likelihood and Bayesian paradigms. We study the dependence of inference accuracy on such parameters as number of sequences, branch lengths, the shape of the rate distribution, and sequence length. We also study the possibility of simultaneously estimating branch lengths and sitespecific rates. Our results show that a Bayesian approach is superior to maximum-likelihood under a wide range of conditions, indicating that the prior that is incorporated into the Bayesian computation significantly improves performance. We show that when branch lengths are unknown, it is better first to estimate branch lengths and then to estimate site-specific rates. This procedure was found to be superior to estimating both the branch lengths and sitespecific rates simultaneously. Finally, we illustrate the difference between maximum-likelihood and Bayesian methods when analyzing site-conservation for the apoptosis regulator protein Bcl-x L .
