Branch-length prior influences Bayesian posterior probability of phylogeny

The Bayesian method for estimating species phylogenies from molecular sequence data provides an attractive alternative to maximum likelihood with nonparametric bootstrap due to the easy interpretation of posterior probabilities for trees and to availability of efficient computational algorithms. However, for many data sets it produces extremely high posterior probabilities, sometimes for apparently incorrect clades. Here we use both computer simulation and empirical data analysis to examine the effect of the prior model for internal branch lengths. We found that posterior probabilities for trees and clades are sensitive to the prior for internal branch lengths, and priors assuming long internal branches cause high posterior probabilities for trees. In particular, uniform priors with high upper bounds bias Bayesian clade probabilities in favor of extreme values. We discuss possible remedies to the problem, including empirical and full Bayesian methods and subjective procedures suggested in Bayesian hypothesis testing. Our results also suggest that the bootstrap proportion and Bayesian posterior probability are different measures of accuracy, and that the bootstrap proportion, if interpreted as the probability that the clade is true, can be either too liberal or too conservative.     

Measures of clade confidence do not correlate with accuracy of phylogenetic trees

Metrics of phylogenetic tree reliability, such as parametric bootstrap percentages or Bayesian posterior probabilities, represent internal measures of the topological reproducibility of a phylogenetic tree, while the recently introduced aLRT (approximate likelihood ratio test) assesses the likelihood that a branch exists on a maximum-likelihood tree. Although those values are often equated with phylogenetic tree accuracy, they do not necessarily estimate how well a reconstructed phylogeny represents cladistic relationships that actually exist in nature. The authors have therefore attempted to quantify how well bootstrap percentages, posterior probabilities, and aLRT measures reflect the probability that a deduced phylogenetic clade is present in a known phylogeny. The authors simulated the evolution of bacterial genes of varying lengths under biologically realistic conditions, and reconstructed those known phylogenies using both maximum likelihood and Bayesian methods. Then, they measured how frequently clades in the reconstructed trees exhibiting particular bootstrap percentages, aLRT values, or posterior probabilities were found in the true trees. The authors have observed that none of these values correlate with the probability that a given clade is present in the known phylogeny. The major conclusion is that none of the measures provide any information about the likelihood that an individual clade actually exists. It is also found that the mean of all clade support values on a tree closely reflects the average proportion of all clades that have been assigned correctly, and is thus a good representation of the overall accuracy of a phylogenetic tree.     

Comparison of Bayesian and maximum likelihood bootstrap measures of phylogenetic reliability

Owing to the exponential growth of genome databases, phylogenetic trees are now widely used to test a variety of evolutionary hypotheses. Nevertheless, computation time burden limits the application of methods such as maximum likelihood nonparametric bootstrap to assess reliability of evolutionary trees. As an alternative, the much faster Bayesian inference of phylogeny, which expresses branch support as posterior probabilities, has been introduced. However, marked discrepancies exist between nonparametric bootstrap proportions and Bayesian posterior probabilities, leading to difficulties in the interpretation of sometimes strongly conflicting results. As an attempt to reconcile these two indices of node reliability, we apply the nonparametric bootstrap resampling procedure to the Bayesian approach. The correlation between posterior probabilities, bootstrap maximum likelihood percentages, and bootstrapped posterior probabilities was studied for eight highly diverse empirical data sets and were also investigated using experimental simulation. Our results show that the relation between posterior probabilities and bootstrapped maximum likelihood percentages is highly variable but that very strong correlations always exist when Bayesian node support is estimated on bootstrapped character matrices. Moreover, simulations corroborate empirical observations in suggesting that, being more conservative, the bootstrap approach might be less prone to strongly supporting a false phylogenetic hypothesis. Thus, apparent conflicts in topology recovered by the Bayesian approach were reduced after bootstrapping. Both posterior probabilities and bootstrap supports are of great interest to phylogeny as potential upper and lower bounds of node reliability, but they are surely not interchangeable and cannot be directly compared.     

Systematics and morphological evolution within the moss family Bryaceae: a comparison between parsimony and Bayesian methods for reconstruction of ancestral character states

The Bryaceae are a large cosmopolitan moss family including genera of significant morphological and taxonomic complexity. Phylogenetic relationships within the Bryaceae were reconstructed based on DNA sequence data from all three genomic compartments. In addition, maximum parsimony and Bayesian inference were employed to reconstruct ancestral character states of 38 morphological plus four habitat characters and eight insertion/deletion events. The recovered phylogenetic patterns are generally in accord with previous phylogenies based on chloroplast DNA sequence data and three major clades are identified. The first clade comprises Bryum bornholmense, B. rubens, B. caespiticium, and Plagiobryum. This corroborates the hypothesis suggested by previous studies that several Bryum species are more closely related to Plagiobryum than to the core Bryum species. The second clade includes Acidodontium, Anomobryum, and Haplodontium, while the third clade contains the core Bryum species plus Imbribryum. Within the latter clade, B. subapiculatum and B. tenuisetum form the sister clade to Imbribryum. Reconstructions of ancestral character states under maximum parsimony and Bayesian inference suggest fourteen morphological synapomorphies for the ingroup and synapomorphies are detected for most clades within the ingroup. Maximum parsimony and Bayesian reconstructions of ancestral character states are mostly congruent although Bayesian inference shows that the posterior probability of ancestral character states may decrease dramatically when node support is taken into account. Bayesian inference also indicates that reconstructions may be ambiguous at internal nodes for highly polymorphic characters.     

An examination of the monophyly of morning glory taxa using Bayesian phylogenetic inference

The objective of this study was to obtain a quantitative assessment of the monophyly of morning glory taxa, specifically the genus Ipomoea and the tribe Argyreieae. Previous systematic studies of morning glories intimated the paraphyly of Ipomoea by suggesting that the genera within the tribe Argyreieae are derived from within Ipomoea; however, no quantitative estimates of statistical support were developed to address these questions. We applied a Bayesian analysis to provide quantitative estimates of monophyly in an investigation of morning glory relationships using DNA sequence data. We also explored various approaches for examining convergence of the Markov chain Monte Carlo (MCMC) simulation of the Bayesian analysis by running 18 separate analyses varying in length. We found convergence of the important components of the phylogenetic model (the tree with the maximum posterior probability, branch lengths, the parameter values from the DNA substitution model, and the posterior probabilities for clade support) for these data after one million generations of the MCMC simulations. In the process, we identified a run where the parameter values obtained were often outside the range of values obtained from the other runs, suggesting an aberrant result. In addition, we compared the Bayesian method of phylogenetic analysis to maximum likelihood and maximum parsimony. The results from the Bayesian analysis and the maximum likelihood analysis were similar for topology, branch lengths, and parameters of the DNA substitution model. Topologies also were similar in the comparison between the Bayesian analysis and maximum parsimony, although the posterior probabilities and the bootstrap proportions exhibited some striking differences. In a Bayesian analysis of three data sets (ITS sequences, waxy sequences, and ITS + waxy sequences) no supoort for the monophyly of the genus Ipomoea, or for the tribe Argyreieae, was observed, with the estimate of the probability of the monophyly of these taxa being less than 3.4 x 10(-7).     

Clade support measures and their adequacy

In addition to hypothesis optimality, the evaluation of clade (group, edge, split, node) support is an important aspect of phylogenetic analysis. Here we clarify the logical relationship between support and optimality and formulate adequacy conditions for support measures. Support, S, and optimality, O, are both empirical knowledge claims about the strength of hypotheses, h₁, h₂, …h_n, in relation to evidence, e, given background knowledge, b. Whereas optimality refers to the absolute strength of hypotheses, support refers to the relative strength of hypotheses. Consequently, support and optimality are logically related such that they vary in direct proportion to each other, S(h | e,b) ∝ O(h | e,b). Furthermore, in order for a support measure to be objective it must quantify support as a function of explanatory power. For example, Goodman–Bremer support and ratio of explanatory power (REP) support satisfy the adequacy requirement S(h | e,b) ∝ O(h | e,b) and calculate support as a function of explanatory power. As such, these are adequate measures of objective support. The equivalent measures for statistical optimality criteria are the likelihood ratio (or log‐likelihood difference) and likelihood difference support measures for maximum likelihood and the posterior probability ratio and posterior probability difference support measures for Bayesian inference. These statistical support measures satisfy the adequacy requirement S(h | e,b) ∝ O(h | e,b) and to that extent are internally consistent; however, they do not quantify support as a function of explanatory power and therefore are not measures of objective support. Neither the relative fit difference (RFD; relative GB support) nor any of the parsimony (bootstrap and jackknife character resampling) or statistical [bootstrap character resampling, Markov chain Monte Carlo (MCMC) clade frequencies] support measures based on clade frequencies satisfy the adequacy condition S(h | e,b) ∝ O(h | e,b) or calculate support as a function of explanatory power. As such, they are not adequate support measures. © The Willi Hennig Society 2008.     

Contributions of rpb2 and tef1 to the phylogeny of mushrooms and allies (Basidiomycota, Fungi)

A phylogeny of the fungal phylum Basidiomycota is presented based on a survey of 160 taxa and five nuclear genes. Two genes, rpb2, and tef1, are presented in detail. The rpb2 gene is more variable than tef1 and recovers well-supported clades at shallow and deep taxonomic levels. The tef1 gene recovers some deep and ordinal-level relationships but with greater branch support from nucleotides compared to amino acids. Intron placement is dynamic in tef1, often lineage-specific, and diagnostic for many clades. Introns are fewer in rpb2 and tend to be highly conserved by position. When both protein-coding loci are combined with sequences of nuclear ribosomal RNA genes, 18 inclusive clades of Basidiomycota are strongly supported by Bayesian posterior probabilities and 16 by parsimony bootstrapping. These numbers are greater than produced by single genes and combined ribosomal RNA gene regions. Combination of nrDNA with amino acid sequences, or exons with third codon positions removed, produces strong measures of support, particularly for deep internodes of Basidiomycota, which have been difficult to resolve with confidence using nrDNA data alone. This study produces strong boostrap support and significant posterior probabilities for the first time for the following monophyletic groups: (1) Ustilaginomycetes plus Hymenomycetes, (2) an inclusive cluster of hymenochaetoid, corticioid, polyporoid, Thelephorales, russuloid, athelioid, Boletales, and euagarics clades, (3) Thelephorales plus the polyporoid clade, (4) the polyporoid clade, and (5) the cantharelloid clade. Strong support is also recovered for the basal position of the Dacrymycetales in the Hymenomycetidae and paraphyly of the Exobasidiomycetidae.     

Strange bayes indeed: uniform topological priors imply non-uniform clade priors

While Bayesian analysis has become common in phylogenetics, the effects of topological prior probabilities on tree inference have not been investigated. In Bayesian analyses, the prior probability of topologies is almost always considered equal for all possible trees, and clade support is calculated from the majority rule consensus of the approximated posterior distribution of topologies. These uniform priors on tree topologies imply non-uniform prior probabilities of clades, which are dependent on the number of taxa in a clade as well as the number of taxa in the analysis. As such, uniform topological priors do not model ignorance with respect to clades. Here, we demonstrate that Bayesian clade support, bootstrap support, and jackknife support from 17 empirical studies are significantly and positively correlated with non-uniform clade priors resulting from uniform topological priors. Further, we demonstrate that this effect disappears for bootstrap and jackknife when data sets are free from character conflict, but remains pronounced for Bayesian clade supports, regardless of tree shape. Finally, we propose the use of a Bayes factor to account for the fact that uniform topological priors do not model ignorance with respect to clade probability.     

Unringing a bell: metazoan phylogenomics and the partition bootstrap

Several large phylogenomic analyses have recently cast doubt on long‐held beliefs about early metazoan phylogenetic patterns. Those data sets, and the relative bootstrap support for various controversial clades, are reanalysed in the context of parsimony, yielding results that are at considerable odds with the original likelihood or Bayesian findings. Discrepancies are considered in light of the tendency of RAxML to overestimate support values by virtue (sic) of its lazy search algorithm and its autocorrelated pseudoreplication as well as the extraordinary ability for Bayesian analyses to be led astray by missing data. In addition to standard nonparametric bootstrapping as a measure of support, a new strategy involving resampling loci as units, partition bootstrap support, is introduced as a more defensible alternative to resampling nonindependent sites. © The Willi Hennig Society 2009.     

Phylogeny of eusocial Lasioglossum reveals multiple losses of eusociality within a primitively eusocial clade of bees (Hymenoptera: Halictidae)

We performed a phylogenetic analysis of the species, species groups, and subgenera within the predominantly eusocial lineage of Lasioglossum (the Hemihalictus series) based on three protein coding genes: mitochondrial cytochrome oxidase I, nuclear elongation factor 1alpha and long-wavelength rhodopsin. The entire data set consisted of 3421 aligned nucleotide sites, 854 of which were parsimony informative. Analyses by equal weights parsimony, maximum likelihood, and Bayesian methods yielded good resolution among the 53 taxa/populations, with strong bootstrap support and high posterior probabilities for most nodes. There was no significant incongruence among genes, and parsimony, maximum likelihood, and Bayesian methods yielded congruent results. We mapped social behavior onto the resulting tree for 42 of the taxa/populations to infer the likely history of social evolution within Lasioglossum. Our results indicate that eusociality had a single origin within Lasioglossum. Within the predominantly eusocial clade, however, there have been multiple (six) reversals from eusociality to solitary nesting, social polymorphism, or social parasitism, suggesting that these reversals may be more common in primitively eusocial Hymenoptera than previously anticipated. Our results support the view that eusociality is hard to evolve but easily lost. This conclusion is potentially important for understanding the early evolution of the advanced eusocial insects, such as ants, termites, and corbiculate bees.     

Reliability of Bayesian posterior probabilities and bootstrap frequencies in phylogenetics

Many empirical studies have revealed considerable differences between nonparametric bootstrapping and Bayesian posterior probabilities in terms of the support values for branches, despite claimed predictions about their approximate equivalence. We investigated this problem by simulating data, which were then analyzed by maximum likelihood bootstrapping and Bayesian phylogenetic analysis using identical models and reoptimization of parameter values. We show that Bayesian posterior probabilities are significantly higher than corresponding nonparametric bootstrap frequencies for true clades, but also that erroneous conclusions will be made more often. These errors are strongly accentuated when the models used for analyses are underparameterized. When data are analyzed under the correct model, nonparametric bootstrapping is conservative. Bayesian posterior probabilities are also conservative in this respect, but less so.     

Phylogenetics of advanced snakes (Caenophidia) based on four mitochondrial genes

Phylogenetic relationships among advanced snakes (Acrochordus + Colubroidea = Caenophidia) and the position of the genus Acrochordus relative to colubroid taxa are contentious. These concerns were investigated by phylogenetic analysis of fragments from four mitochondrial genes representing 62 caenophidian genera and 5 noncaenophidian taxa. Four methods of phylogeny reconstruction were applied: matrix representation with parsimony (MRP) supertree consensus, maximum parsimony, maximum likelihood, and Bayesian analysis. Because of incomplete sampling, extensive missing data were inherent in this study. Analyses of individual genes retrieved roughly the same clades, but branching order varied greatly between gene trees, and nodal support was poor. Trees generated from combined data sets using maximum parsimony, maximum likelihood, and Bayesian analysis had medium to low nodal support but were largely congruent with each other and with MRP supertrees. Conclusions about caenophidian relationships were based on these combined analyses. The Xenoderminae, Viperidae, Pareatinae, Psammophiinae, Pseudoxyrophiinae, Homalopsinae, Natricinae, Xenodontinae, and Colubrinae (redefined) emerged as monophyletic, whereas Lamprophiinae, Atractaspididae, and Elapidae were not in one or more topologies. A clade comprising Acrochordus and Xenoderminae branched closest to the root, and when Acrochordus was assessed in relation to a colubroid subsample and all five noncaenophidians, it remained associated with the Colubroidea. Thus, Acrochordus + Xenoderminae appears to be the sister group to the Colubroidea, and Xenoderminae should be excluded from Colubroidea. Within Colubroidea, Viperidae was the most basal clade. Other relationships appearing in all final topologies were (1) a clade comprising Psammophiinae, Lamprophiinae, Atractaspididae, Pseudoxyrophiinae, and Elapidae, within which the latter four taxa formed a subclade, and (2) a clade comprising Colubrinae, Natricinae, and Xenodontinae, within which the latter two taxa formed a subclade. Pareatinae and Homalopsinae were the most unstable clades.     

Molecular systematics of Middle American harvest mice Reithrodontomys (Muridae), estimated from mitochondrial cytochrome b gene sequences

We estimated phylogenetic relationships among 16 species of harvest mice using sequences from the mitochondrial cytochrome b (cyt b) gene. Gene phylogenies constructed using maximum parsimony (MP), maximum likelihood (ML) and Bayesian inference (BI) optimality criteria were largely congruent and arranged taxa into two groups corresponding to the two recognized subgenera (Aporodon and Reithrodontomys). All analyses also recovered R. mexicanus and R. microdon as polyphyletic, although greater resolution was obtained using ML and BI approaches. Within R. mexicanus, three clades were identified with high nodal support (MP and ML bootstrap, Bremer decay and Bayesian posterior probabilities). One represented a subspecies of R. mexicanus from Costa Rica (R. m. cherrii) and a second was distributed in the Sierra Madre Oriental of Mexico. The third R. mexicanus clade consisted of mice from southern Mexico southward to South America. Polyphyly between the two moieties of R. microdon corresponded to the Isthmus of Tehuantepec in southern Mexico. Populations of R. microdon microdon to the east of the isthmus (Chiapas, Mexico) grouped with R. tenuirostris, whereas samples of R. m. albilabris to the west in Oaxaca, Mexico, formed a clade with R. bakeri. Within the subgenus Reithrodontomys, all analyses recovered R. montanus and R. raviventris as sister taxa, a finding consistent with earlier studies based on allozymes and cyt b data. There was also strong support (ML and BI criteria) for a clade consisting of ((R. megalotis, R. zacatecae) (R. sumichrasti)). In addition, cytb gene phylogenies (MP, ML, and BI) recovered R. fulvescens and R. hirsutus (ML and BI) as basal taxa within the subgenus Reithrodontomys. Constraint analyses demonstrated that tree topologies treating the two subgenera (Aporodon and Reithrodontomys) as monophyletic (ML criterion) was significantly better (p>0.036) and supported polyphyly of R. mexicanus (both ML and MP criteria - p>0.013) and R. microdon (MP criterion only for certain topologies; p>0.02). Although several species-level taxa were identified based on multiple, independent data sets, we recommended a conservative approach which will involve thorough analyses of museum specimens including material from type localities together with additional sampling and data from multiple, nuclear gene markers.     

Effects of branch length uncertainty on Bayesian posterior probabilities for phylogenetic hypotheses

In Bayesian phylogenetics, confidence in evolutionary relationships is expressed as posterior probability--the probability that a tree or clade is true given the data, evolutionary model, and prior assumptions about model parameters. Model parameters, such as branch lengths, are never known in advance; Bayesian methods incorporate this uncertainty by integrating over a range of plausible values given an assumed prior probability distribution for each parameter. Little is known about the effects of integrating over branch length uncertainty on posterior probabilities when different priors are assumed. Here, we show that integrating over uncertainty using a wide range of typical prior assumptions strongly affects posterior probabilities, causing them to deviate from those that would be inferred if branch lengths were known in advance; only when there is no uncertainty to integrate over does the average posterior probability of a group of trees accurately predict the proportion of correct trees in the group. The pattern of branch lengths on the true tree determines whether integrating over uncertainty pushes posterior probabilities upward or downward. The magnitude of the effect depends on the specific prior distributions used and the length of the sequences analyzed. Under realistic conditions, however, even extraordinarily long sequences are not enough to prevent frequent inference of incorrect clades with strong support. We found that across a range of conditions, diffuse priors--either flat or exponential distributions with moderate to large means--provide more reliable inferences than small-mean exponential priors. An empirical Bayes approach that fixes branch lengths at their maximum likelihood estimates yields posterior probabilities that more closely match those that would be inferred if the true branch lengths were known in advance and reduces the rate of strongly supported false inferences compared with fully Bayesian integration.     

Homology assessment in parsimony and model‐based analyses: two sides of the same coin

The present paper is mainly concerned with homology assessment through phylogenetic analyses. It raises a fundamental question: What are the epistemological differences between modern parsimony and model‐based analyses in relation to homology assessment and phylogenetic inference? Although these methods usually achieve concordant topological results, they may generate discordant inferences of character evolution from the same datasets. This indicates that method selection has serious implications for evolutionary scenarios and classificatory arrangements. Notwithstanding that parsimony and model‐based approaches use the Hennigian concepts of monophyly and synapomorphy, they employ different epistemological ways of dealing with the monophyly/synapomorphy relationship. Independently of their differences, these analyses should take into account all relevant evidence in support of the phylogenetic inferences. A focus on morphological homologues means that they must be included in data matrices, evaluated as part of the phylogenetic analysis, and cannot be ignored in calculation of the tree(s) length (parsimony), maximum‐likelihood (maximum‐likelihood), and posterior probabilities (Bayes).     

Relationships of the temperate Australasian labrid fish tribe Odacini (Perciformes; Teleostei)

The labrid tribe Odacini comprises four genera and 12 species of fishes that inhabit shallow kelp forest and seagrass areas in temperate waters of Australia and New Zealand. Odacines are morphologically disparate, but share synapomorphies in fin structure and fusion of teeth into a beak-like oral jaw. A phylogenetic analysis of odacines was conducted to investigate their relationships to other labrid fishes, the relationships of species within the tribe, and the evolution of herbivory within the group. Fragments from two mitochondrial genes, 12S rDNA and 16S rDNA, and two nuclear genes, Tmo4C4 and RAG2, were sequenced for seven odacine species (representing all four genera), eight species representing the other major labrid lineages, and three outgroup species. Maximum likelihood and maximum parsimony analyses on the resulting 2338 bp of DNA sequence produced nearly identical topologies differing only in the placement of a clade containing the cheiline Cheilinus fasciatus and the scarine Cryptotomus roseus. The remaining clades received strong bootstrap support under maximum parsimony, and all clades in the maximum likelihood analysis received high bootstrap proportions and high posterior probabilities. The hypsigenyine labrid Choerodon anchorago formed the sister group to the odacines. Within the odacines, Odax cyanoallix+Odax pullus formed the sister to the remaining odacines, with Odax acroptilus, Odax cyanomelas, and Siphonognathus argyrophanes forming successively closer sister groups to the clade Haletta semifasciatus+Neoodax balteatus. Either herbivory evolved twice in the odacines, or herbivory evolved once with two reversions to carnivory. The latter hypothesis appears more likely in the light of odacine feeding biology.     

Probabilistic methods surpass parsimony when assessing clade support in phylogenetic analyses of discrete morphological data

Fossil taxa are critical to inferences of historical diversity and the origins of modern biodiversity, but realizing their evolutionary significance is contingent on restoring fossil species to their correct position within the tree of life. For most fossil species, morphology is the only source of data for phylogenetic inference; this has traditionally been analysed using parsimony, the predominance of which is currently challenged by the development of probabilistic models that achieve greater phylogenetic accuracy. Here, based on simulated and empirical datasets, we explore the relative efficacy of competing phylogenetic methods in terms of clade support. We characterize clade support using bootstrapping for parsimony and Maximum Likelihood, and intrinsic Bayesian posterior probabilities, collapsing branches that exhibit less than 50% support. Ignoring node support, Bayesian inference is the most accurate method in estimating the tree used to simulate the data. After assessing clade support, Bayesian and Maximum Likelihood exhibit comparable levels of accuracy, and parsimony remains the least accurate method. However, Maximum Likelihood is less precise than Bayesian phylogeny estimation, and Bayesian inference recaptures more correct nodes with higher support compared to all other methods, including Maximum Likelihood. We assess the effects of these findings on empirical phylogenies. Our results indicate probabilistic methods should be favoured over parsimony.     

Polytomies and Bayesian phylogenetic inference

Bayesian phylogenetic analyses are now very popular in systematics and molecular evolution because they allow the use of much more realistic models than currently possible with maximum likelihood methods. There are, however, a growing number of examples in which large Bayesian posterior clade probabilities are associated with very short branch lengths and low values for non-Bayesian measures of support such as nonparametric bootstrapping. For the four-taxon case when the true tree is the star phylogeny, Bayesian analyses become increasingly unpredictable in their preference for one of the three possible resolved tree topologies as data set size increases. This leads to the prediction that hard (or near-hard) polytomies in nature will cause unpredictable behavior in Bayesian analyses, with arbitrary resolutions of the polytomy receiving very high posterior probabilities in some cases. We present a simple solution to this problem involving a reversible-jump Markov chain Monte Carlo (MCMC) algorithm that allows exploration of all of tree space, including unresolved tree topologies with one or more polytomies. The reversible-jump MCMC approach allows prior distributions to place some weight on less-resolved tree topologies, which eliminates misleadingly high posteriors associated with arbitrary resolutions of hard polytomies. Fortunately, assigning some prior probability to polytomous tree topologies does not appear to come with a significant cost in terms of the ability to assess the level of support for edges that do exist in the true tree. Methods are discussed for applying arbitrary prior distributions to tree topologies of varying resolution, and an empirical example showing evidence of polytomies is analyzed and discussed.     

A Bayesian perspective on a non-parsimonious parsimony model

Several stochastic models of character change, when implemented in a maximum likelihood framework, are known to give a correspondence between the maximum parsimony method and the method of maximum likelihood. One such model has an independently estimated branch-length parameter for each site and each branch of the phylogenetic tree. This model--the no-common-mechanism model--has many parameters, and, in fact, the number of parameters increases as fast as the alignment is extended. We take a Bayesian approach to the no-common-mechanism model and place independent gamma prior probability distributions on the branch-length parameters. We are able to analytically integrate over the branch lengths, and this allowed us to implement an efficient Markov chain Monte Carlo method for exploring the space of phylogenetic trees. We were able to reliably estimate the posterior probabilities of clades for phylogenetic trees of up to 500 sequences. However, the Bayesian approach to the problem, at least as implemented here with an independent prior on the length of each branch, does not tame the behavior of the branch-length parameters. The integrated likelihood appears to be a simple rescaling of the parsimony score for a tree, and the marginal posterior probability distribution of the length of a branch is dependent upon how the maximum parsimony method reconstructs the characters at the interior nodes of the tree. The method we describe, however, is of potential importance in the analysis of morphological character data and also for improving the behavior of Markov chain Monte Carlo methods implemented for models in which sites share a common branch-length parameter.     

Molecular phylogeny of the carnivora (mammalia): assessing the impact of increased sampling on resolving enigmatic relationships

This study analyzed 76 species of Carnivora using a concatenated sequence of 6243 bp from six genes (nuclear TR-i-I, TBG, and IRBP; mitochondrial ND2, CYTB, and 12S rRNA), representing the most comprehensive sampling yet undertaken for reconstructing the phylogeny of this clade. Maximum parsimony and Bayesian methods were remarkably congruent in topologies observed and in nodal support measures. We recovered all of the higher level carnivoran clades that had been robustly supported in previous analyses (by analyses of morphological and molecular data), including the monophyly of Caniformia, Feliformia, Arctoidea, Pinnipedia, Musteloidea, Procyonidae + Mustelidae sensu stricto, and a clade of (Hyaenidae + (Herpestidae + Malagasy carnivorans)). All of the traditional "families," with the exception of Viverridae and Mustelidae, were robustly supported as monophyletic groups. We further have determined the relative positions of the major lineages within the Caniformia, which previous studies could not resolve, including the first robust support for the phylogenetic position of marine carnivorans (Pinnipedia) within the Arctoidea (as the sister-group to musteloids [sensu lato], with ursids as their sister group). Within the pinnipeds, Odobenidae (walrus) was more closely allied with otariids (sea lions/fur seals) than with phocids ("true" seals). In addition, we recovered a monophyletic clade of skunks and stink badgers (Mephitidae) and resolved the topology of musteloid interrelationships as: Ailurus (Mephitidae (Procyonidae, Mustelidae [sensu stricto])). This pattern of interrelationships of living caniforms suggests a novel inference that large body size may have been the primitive condition for Arctoidea, with secondary size reduction evolving later in some musteloids. Within Mustelidae, Bayesian analyses are unambiguous in supporting otter monophyly (Lutrinae), and in both MP and Bayesian analyses Martes is paraphyletic with respect to Gulo and Eira, as has been observed in some previous molecular studies. Within Feliformia, we have confirmed that Nandinia is the outgroup to all other extant feliforms, and that the Malagasy Carnivora are a monophyletic clade closely allied with the mongooses (Herpestidae [sensu stricto]). Although the monophyly of each of the three major feliform clades (Viverridae sensu stricto, Felidae, and the clade of Hyaenidae + (Herpestidae + Malagasy carnivorans)) is robust in all of our analyses, the relative phylogenetic positions of these three lineages is not resolvable at present. Our analyses document the monophyly of the "social mongooses," strengthening evidence for a single origin of eusociality within the Herpestidae. For a single caniform node, the position of pinnipeds relative to Ursidae and Musteloidea, parsimony analyses of data for the entire Carnivora did not replicate the robust support observed for both parsimony and Bayesian analyses of the caniform ingroup alone. More detailed analyses and these results demonstrate that outgroup choice can have a considerable effect on the strength of support for a particular topology. Therefore, the use of exemplar taxa as proxies for entire clades with diverse evolutionary histories should be approached with caution.The Bayesian analysis likelihood functions generally were better able to reconstruct phylogenetic relationships (increased resolution and more robust support for various nodes) than parsimony analyses when incompletely sampled taxa were included. Bayesian analyses were not immune, however, to the effects of missing data; lower resolution and support in those analyses likely arise from non-overlap of gene sequence data among less well-sampled taxa. These issues are a concern for similar studies, in which different gene sequences are concatenated in an effort to increase resolving power.