Likelihood and Inconsistency

Parsimony can be inconsistent, but not maximum likelihood—likelihood advocates often say. This difference and conclusions drawn from it have provided the main reasons advanced by likelihoodists against the use of parsimony. Recent statistical research, however, shows that maximum likelihood estimation of phylogenetic trees can become inconsistent in all but the simplest cases, so that under realistic conditions the consistency of maximum likelihood cannot be assured. If likelihoodists wish to dispose of parsimony, they will have to find another argument.     

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.     

The relative performance of Bayesian and parsimony approaches when sampling characters evolving under homogeneous and heterogeneous sets of parameters

We tested whether it is beneficial for the accuracy of phylogenetic inference to sample characters that are evolving under different sets of parameters, using both Bayesian MCMC (Markov chain Monte Carlo) and parsimony approaches. We examined differential rates of evolution among characters, differential character-state frequencies and character-state space, and differential relative branch lengths among characters. We also compared the relative performance of parsimony and Bayesian analyses by progressively incorporating more of these heterogeneous parameters and progressively increasing the severity of this heterogeneity. Bayesian analyses performed better than parsimony when heterogeneous simulation parameters were incorporated into the substitution model. However, parsimony outperformed Bayesian MCMC when heterogeneous simulation parameters were not incorporated into the Bayesian substitution model. The higher the rate of evolution simulated, the better parsimony performed relative to Bayesian analyses. Bayesian and parsimony analyses converged in their performance as the number of simulated heterogeneous model parameters increased. Up to a point, rate heterogeneity among sites was generally advantageous for phylogenetic inference using both approaches. In contrast, branch-length heterogeneity was generally disadvantageous for phylogenetic inference using both parsimony and Bayesian approaches. Parsimony was found to be more conservative than Bayesian analyses, in that it resolved fewer incorrect clades.
© The Willi Hennig Society 2006.     

Reconstructing ancestral patterns of colonization and dispersal in the Hawaiian understory tree genus Psychotria (Rubiaceae): a comparison of parsimony and likelihood approaches

Systematic and biogeographical relationships within the Hawaiian clade of the pantropical understory shrub genus Psychotria (Rubiaceae) were investigated using phylogenetic analysis of 18S-26S ribosomal DNA internal (ITS) and external (ETS) transcribed spacers. Phylogenetic analyses strongly suggest that the Hawaiian Psychotria are monophyletic and the result of a single introduction to the Hawaiian Islands. The results of phylogenetic analyses of ITS and ETS partitions alone give slightly different topologies among basal lineages of the Hawaiian clade; however, such differences are not well supported. Relationships in the section Straussia clade in particular are not well resolved because of few nucleotide changes on internal branches, suggesting extremely rapid radiation in the lineage. Parsimony and likelihood reconstructions of ancestral geographical distributions using the topologies inferred from both parsimony and likelihood analysis of combined data and using different combinations of models and branch lengths gave highly congruent results. However, for one internal node (corresponding to the majority of the "greenwelliae" clade), parsimony reconstructions were unable to distinguish between three possible island states, whereas likelihood reconstructions resulted in clear ordering of possible states, with the island of Oàhu slightly more probable than other islands under all but one model and branch length combination considered (the Jukes-Cantor-like model with branch lengths inferred under parsimony, under which conditions Maui Nui is more probable). A pattern of colonization from oldest to youngest islands was inferred from the phylogeny, using maximum parsimony and maximum likelihood. Additionally, a much higher incidence of intraisland versus interisland speciation was inferred.     

Phylogenetic analysis and intraspecific variation: performance of parsimony,likelihood, and distance methods

Intraspecific variation is abundant in all types of systematic characters but is rarely addressed in simulation studies of phylogenetic method performance. We compared the accuracy of 15 phylogenetic methods using simulations to (1) determine the most accurate method(s) for analyzing polymorphic data (under simplified conditions) and (2) test if generalizations about the performance of phylogenetic methods based on previous simulations of fixed (nonpolymorphic) characters are robust to a very different evolutionary model that explicitly includes intraspecific variation. Simulated data sets consisted of allele frequencies that evolved by genetic drift. The phylogenetic methods included eight parsimony coding methods, continuous maximum likelihood, and three distance methods (UPGMA, neighbor joining, and Fitch-Margoliash) applied to two genetic distance measures (Nei's and the modified Cavalli-Sforza and Edwards chord distance). Two sets of simulations were performed. The first examined the effects of different branch lengths, sample sizes (individuals sampled per species), numbers of characters, and numbers of alleles per locus in the eight-taxon case. The second examined more extensively the effects of branch length in the four-taxon, two-allele case. Overall, the most accurate methods were likelihood, the additive distance methods (neighbor joining and Fitch-Margoliash), and the frequency parsimony method. Despite the use of a very different evolutionary model in the present article, many of the results are similar to those from simulations of fixed characters. Similarities include the presence of the "Felsenstein zone," where methods often fail, which suggests that long-branch attraction may occur among closely related species through genetic drift. Differences between the results of fixed and polymorphic data simulations include the following: (1) UPGMA is as accurate or more accurate than nonfrequency parsimony methods across nearly all combinations of branch lengths, and (2) likelihood and the additive distance methods are not positively misled under any combination of branch lengths tested (even when the assumptions of the methods are violated and few characters are sampled). We found that sample size is an important determinant of accuracy and affects the relative success of methods (i.e., distance and likelihood methods outperform parsimony at small sample sizes). Attempts to generalize about the behavior of phylogenetic methods should consider the extreme examples offered by fixed-mutation models of DNA sequence data and genetic-drift models of allele frequencies.     

Estimating phylogenetic trees from pairwise likelihoods and posterior probabilities of substitution counts

The field of phylogenetic tree estimation has been dominated by three broad classes of methods: distance-based approaches, parsimony and likelihood-based methods (including maximum likelihood (ML) and Bayesian approaches). Here we introduce two new approaches to tree inference: pairwise likelihood estimation and a distance-based method that estimates the number of substitutions along the paths through the tree. Our results include the derivation of the formulae for the probability that two leaves will be identical at a site given a number of substitutions along the path connecting them. We also derive the posterior probability of the number of substitutions along a path between two sequences. The calculations for the posterior probabilities are exact for group-based, symmetric models of character evolution, but are only approximate for more general models.     

A simulation comparison of phylogeny algorithms under equal and unequal evolutionary rates [published erratum appears in Mol Biol Evol 1995 May;12(3):525]

Using simulated data, we compared five methods of phylogenetic tree estimation: parsimony, compatibility, maximum likelihood, Fitch- Margoliash, and neighbor joining. For each combination of substitution rates and sequence length, 100 data sets were generated for each of 50 trees, for a total of 5,000 replications per condition. Accuracy was measured by two measures of the distance between the true tree and the estimate of the tree, one measure sensitive to accuracy of branch lengths and the other not. The distance-matrix methods (Fitch- Margoliash and neighbor joining) performed best when they were constrained from estimating negative branch lengths; all comparisons with other methods used this constraint. Parsimony and compatibility had similar results, with compatibility generally inferior; Fitch- Margoliash and neighbor joining had similar results, with neighbor joining generally slightly inferior. Maximum likelihood was the most successful method overall, although for short sequences Fitch- Margoliash and neighbor joining were sometimes better. Bias of the estimates was inferred by measuring whether the independent estimates of a tree for different data sets were closer to the true tree than to each other. Parsimony and compatibility had particular difficulty with inaccuracy and bias when substitution rates varied among different branches. When rates of evolution varied among different sites, all methods showed signs of inaccuracy and bias.      

Weighted parsimony outperforms other methods of phylogenetic inference under models appropriate for morphology

One of the lasting controversies in phylogenetic inference is the degree to which specific evolutionary models should influence the choice of methods. Model‐based approaches to phylogenetic inference (likelihood, Bayesian) are defended on the premise that without explicit statistical models there is no science, and parsimony is defended on the grounds that it provides the best rationalization of the data, while refraining from assigning specific probabilities to trees or character‐state reconstructions. Authors who favour model‐based approaches often focus on the statistical properties of the methods and models themselves, but this is of only limited use in deciding the best method for phylogenetic inference—such decision also requires considering the conditions of evolution that prevail in nature. Another approach is to compare the performance of parsimony and model‐based methods in simulations, which traditionally have been used to defend the use of models of evolution for DNA sequences. Some recent papers, however, have promoted the use of model‐based approaches to phylogenetic inference for discrete morphological data as well. These papers simulated data under models already known to be unfavourable to parsimony, and modelled morphological evolution as if it evolved just like DNA, with probabilities of change for all characters changing in concert along tree branches. The present paper discusses these issues, showing that under reasonable and less restrictive models of evolution for discrete characters, equally weighted parsimony performs as well or better than model‐based methods, and that parsimony under implied weights clearly outperforms all other methods.     

Philosophy and phylogenetic inference: a comparison of likelihood and parsimony methods in the context of Karl Popper's writings on corroboration

Advocates of cladistic parsimony methods have invoked the philosophy of Karl Popper in an attempt to argue for the superiority of those methods over phylogenetic methods based on Ronald Fisher's statistical principle of likelihood. We argue that the concept of likelihood in general, and its application to problems of phylogenetic inference in particular, are highly compatible with Popper's philosophy. Examination of Popper's writings reveals that his concept of corroboration is, in fact, based on likelihood. Moreover, because probabilistic assumptions are necessary for calculating the probabilities that define Popper's corroboration, likelihood methods of phylogenetic inference--with their explicit probabilistic basis--are easily reconciled with his concept. In contrast, cladistic parsimony methods, at least as described by certain advocates of those methods, are less easily reconciled with Popper's concept of corroboration. If those methods are interpreted as lacking probabilistic assumptions, then they are incompatible with corroboration. Conversely, if parsimony methods are to be considered compatible with corroboration, then they must be interpreted as carrying implicit probabilistic assumptions. Thus, the non-probabilistic interpretation of cladistic parsimony favored by some advocates of those methods is contradicted by an attempt by the same authors to justify parsimony methods in terms of Popper's concept of corroboration. In addition to being compatible with Popperian corroboration, the likelihood approach to phylogenetic inference permits researchers to test the assumptions of their analytical methods (models) in a way that is consistent with Popper's ideas about the provisional nature of background knowledge.     

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).     

以雾灵山夜蛾科为材料评估进化模型对DNA条码分类的影响

为了探究进化模型对DNA条形码分类的影响, 本研究以雾灵山夜蛾科44个种的标本为材料, 获得COI基因序列。使用邻接法（neighbor-joining）、 最大简约法（maximum parsimony）、 最大似然法（maximum likelihood）以及贝叶斯法（Bayesian inference）构建系统发育树, 并且对邻接法的12种模型、 最大似然法的7种模型、 贝叶斯法的2种模型进行模型成功率的评估。结果表明, 邻接法的12种模型成功率相差不大, 较稳定; 最大似然法及贝叶斯法的不同模型成功率存在明显差异, 不稳定; 最大简约法不基于模型, 成功率比较稳定。邻接法及最大似然法共有6种相同的模型, 这6种模型在不同的方法中成功率存在差异。此外, 分子数据中存在单个物种仅有一条序列的情况, 显著降低了模型成功率, 表明在DNA条形码研究中, 每个物种需要有多个样本。     

Efficacy or convenience? Model‐based approaches to phylogeny estimation using morphological data

Model‐based approaches (e.g. maximum likelihood, Bayesian inference) are widely used with molecular data, where they might be more appropriate than maximum parsimony for estimating phylogenies under various models of molecular evolution. Recently, there has been an increase in the application of model‐based approaches with morphological (mainly fossil) data; however, there is some doubt as to the effectiveness of the model of morphological evolution. The input parameters (prior probabilities) for the model are unclear, particularly when concerned with unobserved character states. Despite this, some systematists are suggesting superiority of these model‐based methods over maximum parsimony based on, for example, increased resolution or, in the current study, the preferred phylogenetic placement of an iconic taxon. Here, we revisit a recently published analysis implying such superiority and document the discrepancies between parsimony‐based and model‐based approaches to phylogeny estimation. We find that although some taxa are shifted back to their “traditional” phylogenetic placement, other clades are disturbed. The model‐based phylogenies are better resolved; however, due to the lack of an appropriate model of morphological evolution, the increase in resolving power is probably not meaningful. Similarly, some of the preferred phylogenetic positions of taxa, particularly of labile taxa such as Archaeopteryx, are based solely on analyses employing maximum parsimony as the optimality criterion. Poor resolution and labile taxa indicate a need for further examination of the morphology and not a change in method.     

Estimating trees from filtered data: Identifiability of models for morphological phylogenetics

As an alternative to parsimony analyses, stochastic models have been proposed ( [Lewis, 2001] and [Nylander et al., 2004]) for morphological characters, so that maximum likelihood or Bayesian analyses may be used for phylogenetic inference. A key feature of these models is that they account for ascertainment bias, in that only varying, or parsimony-informative characters are observed. However, statistical consistency of such model-based inference requires that the model parameters be identifiable from the joint distribution they entail, and this issue has not been addressed.Here we prove that parameters for several such models, with finite state spaces of arbitrary size, are identifiable, provided the tree has at least eight leaves. If the tree topology is already known, then seven leaves suffice for identifiability of the numerical parameters. The method of proof involves first inferring a full distribution of both parsimony-informative and non-informative pattern joint probabilities from the parsimony-informative ones, using phylogenetic invariants. The failure of identifiability of the tree parameter for four-taxon trees is also investigated.     

STATISTICAL COVARIANCE AS A MEASURE OF PHYLOGENETIC RELATIONSHIP

Abstract— The method of parsimony in phylogenetic inference is often taken to mean two things: (1) that one should favor the genealogical hypothesis that minimizes the required number of homoplasies ( matchings of independently evolved derived character states ), and (2) that symplesiomorphies (matchings of primitive character states) have little or no evidential value for phylogenetic relationship. This paper shows both theses to be false by undermining recent likelihood arguments for them and by providing a more secure likelihood proof of a new method, which is incompatible with both (1) and (2).     

Failed refutations: further comments on parsimony and likelihood methods and their relationship to Popper's degree of corroboration

Kluge's (2001, Syst. Biol. 50:322-330) continued arguments that phylogenetic methods based on the statistical principle of likelihood are incompatible with the philosophy of science described by Karl Popper are based on false premises related to Kluge's misrepresentations of Popper's philosophy. Contrary to Kluge's conjectures, likelihood methods are not inherently verificationist; they do not treat every instance of a hypothesis as confirmation of that hypothesis. The historical nature of phylogeny does not preclude phylogenetic hypotheses from being evaluated using the probability of evidence. The low absolute probabilities of hypotheses are irrelevant to the correct interpretation of Popper's concept termed degree of corroboration, which is defined entirely in terms of relative probabilities. Popper did not advocate minimizing background knowledge; in any case, the background knowledge of both parsimony and likelihood methods consists of the general assumption of descent with modification and additional assumptions that are deterministic, concerning which tree is considered most highly corroborated. Although parsimony methods do not assume (in the sense of entailing) that homoplasy is rare, they do assume (in the sense of requiring to obtain a correct phylogenetic inference) certain things about patterns of homoplasy. Both parsimony and likelihood methods assume (in the sense of implying by the manner in which they operate) various things about evolutionary processes, although violation of those assumptions does not always cause the methods to yield incorrect phylogenetic inferences. Test severity is increased by sampling additional relevant characters rather than by character reanalysis, although either interpretation is compatible with the use of phylogenetic likelihood methods. Neither parsimony nor likelihood methods assess test severity (critical evidence) when used to identify a most highly corroborated tree(s) based on a single method or model and a single body of data; however, both classes of methods can be used to perform severe tests. The assumption of descent with modification is insufficient background knowledge to justify cladistic parsimony as a method for assessing degree of corroboration. Invoking equivalency between parsimony methods and likelihood models that assume no common mechanism emphasizes the necessity of additional assumptions, at least some of which are probabilistic in nature. Incongruent characters do not qualify as falsifiers of phylogenetic hypotheses except under extremely unrealistic evolutionary models; therefore, justifications of parsimony methods as falsificationist based on the idea that they minimize the ad hoc dismissal of falsifiers are questionable. Probabilistic concepts such as degree of corroboration and likelihood provide a more appropriate framework for understanding how phylogenetics conforms with Popper's philosophy of science. Likelihood ratio tests do not assume what is at issue but instead are methods for testing hypotheses according to an accepted standard of statistical significance and for incorporating considerations about test severity. These tests are fundamentally similar to Popper's degree of corroboration in being based on the relationship between the probability of the evidence e in the presence versus absence of the hypothesis h, i.e., between p(e|hb) and p(e|b), where b is the background knowledge. Both parsimony and likelihood methods are inductive in that their inferences (particular trees) contain more information than (and therefore do not follow necessarily from) the observations upon which they are based; however, both are deductive in that their conclusions (tree lengths and likelihoods) follow necessarily from their premises (particular trees, observed character state distributions, and evolutionary models). For these and other reasons, phylogenetic likelihood methods are highly compatible with Karl Popper's philosophy of science and offer several advantages over parsimony methods in this context.     

A likelihood approach to estimating phylogeny from discrete morphological character data

Evolutionary biologists have adopted simple likelihood models for purposes of estimating ancestral states and evaluating character independence on specified phylogenies; however, for purposes of estimating phylogenies by using discrete morphological data, maximum parsimony remains the only option. This paper explores the possibility of using standard, well-behaved Markov models for estimating morphological phylogenies (including branch lengths) under the likelihood criterion. An important modification of standard Markov models involves making the likelihood conditional on characters being variable, because constant characters are absent in morphological data sets. Without this modification, branch lengths are often overestimated, resulting in potentially serious biases in tree topology selection. Several new avenues of research are opened by an explicitly model-based approach to phylogenetic analysis of discrete morphological data, including combined-data likelihood analyses (morphology + sequence data), likelihood ratio tests, and Bayesian analyses.     

Relationships among seed plants inferred from highly conserved genes: sorting conflicting phylogenetic signals among ancient lineages

Phylogenetic studies based on different types and treatment of data provide substantially conflicting hypotheses of relationships among seed plants. We conducted phylogenetic analyses of sequences of two highly conserved chloroplast genes, psaA and psbB, for a comprehensive taxonomic sample of seed plants and land plants. Parsimony analyses of two different codon position partitions resulted in well-supported, but significantly conflicting, phylogenetic trees. First and second codon positions place angiosperms and gymnosperms as sister clades and Gnetales as sister to Pinaceae. Third positions place Gnetales as sister to all other seed plants. Maximum likelihood trees for the two partitions are also in conflict. Relationships among the main seed plant clades according to first and second positions are similar to those found in parsimony analysis for the same data, but the third position maximum likelihood tree is substantially different from the corresponding parsimony tree, although it agrees partially with the first and second position trees in placing Gnetales as the sister group of Pinaceae. Our results document high rate heterogeneity among lineages, which, together with the greater average rate of substitution for third positions, may reduce phylogenetic signal due to long-branch attraction in parsimony reconstructions. Whereas resolution of relationships among major seed plant clades remains pending, this study provides increased support for relationships within major seed plant clades.     

A penalty of using anonymous dominant markers (AFLPs, ISSRs, and RAPDs) for phylogenetic inference

AFLPs (and to a lesser extent ISSRs and RAPDs) are increasingly being used for phylogenetic inference among closely related species. Presence/absence characters for each AFLP allele treat all absences as homologous to one another. With three or more alleles, terminals are grouped by their shared absence of alleles in character-based phylogenetic-inference methods in a manner that is not redundant with their shared presence of an alternative allele. We conducted simulations to quantify how severe the negative effect of using presence/absence characters of individual bands is for phylogenetic inference relative to standard multistate characters. We examined alternative tree topologies, relative branch lengths, numbers of characters, rates of evolution, and numbers of alternative alleles, using both parsimony and Nei-and-Li distance analyses. Multistate parsimony generally outperformed presence/absence parsimony, which in turn outperformed Nei-and-Li distance. Increasing the character-state space (i.e., the number of alternative character states available) was found to be advantageous for all three methods of analysis examined, but was most advantageous for multistate parsimony. However, the advantage of multistate parsimony relative to Nei-and-Li distance decreased when applied to more divergent characters. More parsimony-informative variation generally alleviated the problem associated with scoring multistate characters as presence/absence characters. The ensemble consistency index was lower for presence/absence characters relative to multistate characters.     

Phylogenetic analysis using parsimony and likelihood methods

The assumptions underlying the maximum-parsimony (MP) method of phylogenetic tree reconstruction were intuitively examined by studying the way the method works. Computer simulations were performed to corroborate the intuitive examination. Parsimony appears to involve very stringent assumptions concerning the process of sequence evolution, such as constancy of substitution rates between nucleotides, constancy of rates across nucleotide sites, and equal branch lengths in the tree. For practical data analysis, the requirement of equal branch lengths means similar substitution rates among lineages (the existence of an approximate molecular clock), relatively long interior branches, and also few species in the data. However, a small amount of evolution is neither a necessary nor a sufficient requirement of the method. The difficulties involved in the application of current statistical estimation theory to tree reconstruction were discussed, and it was suggested that the approach proposed by Felsenstein (1981,J. Mol. Evol. 17: 368–376) for topology estimation, as well as its many variations and extensions, differs fundamentally from the maximum likelihood estimation of a conventional statistical parameter. Evidence was presented showing that the Felsenstein approach does not share the asymptotic efficiency of the maximum likelihood estimator of a statistical parameter. Computer simulations were performed to study the probability that MP recovers the true tree under a hierarchy of models of nucleotide substitution; its performance relative to the likelihood method was especially noted. The results appeared to support the intuitive examination of the assumptions underlying MP. When a simple model of nucleotide substitution was assumed to generate data, the probability that MP recovers the true topology could be as high as, or even higher than, that for the likelihood method. When the assumed model became more complex and realistic, e.g., when substitution rates were allowed to differ between nucleotides or across sites, the probability that MP recovers the true topology, and especially its performance relative to that of the likelihood method, generally deteriorates. As the complexity of the process of nucleotide substitution in real sequences is well recognized, the likelihood method appears preferable to parsimony. However, the development of a statistical methodology for the efficient estimation of the tree topology remains a difficult open problem.     

Rabbits, if anything, are likely Glires

Rodentia (e.g., mice, rats, dormice, squirrels, and guinea pigs) and Lagomorpha (e.g., rabbits, hares, and pikas) are usually grouped into the Glires. Status of this controversial superorder has been evaluated using morphology, paleontology, and mitochondrial plus nuclear DNA sequences. This growing corpus of data has been favoring the monophyly of Glires. Recently, Misawa and Janke [Mol. Phylogenet. Evol. 28 (2003) 320] analyzed the 6441 amino acids of 20 nuclear proteins for six placental mammals (rat, mouse, rabbit, human, cattle, and dog) and two outgroups (chicken and xenopus), and observed a basal position of the two murine rodents among the former. They concluded that "the Glires hypothesis was rejected." We here reanalyzed [loc. cit.] data set under maximum likelihood and Bayesian tree-building approaches, using phylogenetic models that take into account among-site variation in evolutionary rates and branch-length variation among proteins. Our observations support both the association of rodents and lagomorphs and the monophyly of Euarchontoglires (=Supraprimates) as the most likely explanation of the protein alignments. We conducted simulation studies to evaluate the appropriateness of lissamphibian and avian outgroups to root the placental tree. When the outgroup-to-ingroup evolutionary distance increases, maximum parsimony roots the topology along the long Mus-Rattus branch. Maximum likelihood, in contrast, roots the topology along different branches as a function of their length. Maximum likelihood appears less sensitive to the "long-branch attraction artifact" than is parsimony. Our phylogenetic conclusions were confirmed by the analysis of a different protein data set using a similar sample of species but different outgroups. We also tested the effect of the addition of afrotherian and xenarthran taxa. Using the linearized tree method, [loc. cit.] estimated that mice and rats diverged about 35 million years ago. Molecular dating based on the Bayesian relaxed molecular clock method suggests that the 95% credibility interval for the split between mice and rats is 7-17 Mya. We here emphasize the need for appropriate models of sequence evolution (matrices of amino acid replacement, taking into account among-site rate variation, and independent parameters across independent protein partitions) and for a taxonomically broad sample, and conclude on the likelihood that rodents and lagomorphs together constitute a monophyletic group (Glires).