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.     

Testing the accuracy of methods for reconstructing ancestral states of continuous characters.

Many methods are available for estimating ancestral values of continuous characteristics, but little is known about how well these methods perform. Here we compare six methods: linear parsimony, squared-change parsimony, one-parameter maximum likelihood (Brownian motion), two-parameter maximum likelihood (Ornstein-Uhlenbeck process), and independent comparisons with and without branch-length information. We apply these methods to data from 20 morphospecies of Pleistocene planktic Foraminifera in order to estimate ancestral size and shape variables, and compare these estimates with measurements on fossils close to the phylogenetic position of 13 ancestors. No method produced accurate estimates for any variable: estimates were consistently less good as predictors of the observed values than were the averages of the observed values. The two-parameter maximum-likelihood model consistently produces the most accurate size estimates overall. Estimation of ancestral sizes is confounded by an evolutionary trend towards increasing size. Shape showed no trend but was still estimated very poorly: we consider possible reasons. We discuss the implications of our results for the use of estimates of ancestral characteristics.     

Different gymnosperm outgroups have (mostly) congruent signal regarding the root of flowering plant phylogeny

We examined multiple plastid genes from a diversity of gymnosperm lineages to explore the consistency of signal among different outgroups for rooting flowering plant phylogeny. For maximum parsimony (MP), most outgroups attach on a branch of the underlying ingroup tree that leads to Amborella. Maximum likelihood (ML) analyses either root angiosperms on a nearby branch or find split support for these neighboring root placements, depending on the outgroup. The inclusion of two species of Hydatellaceae, recently recognized as an ancient line of angiosperms, does not aid in inference of the root. Cost profiles for placing the root in suboptimal locations are highly correlated across most outgroup comparisons, even comparing MP and ML profiles. Those for Gnetales are the most deviant of all those considered. This divergent outgroup either attaches on a long eudicot branch with moderate bootstrap support in MP analyses or supports no particular root location in ML analysis. Removing the most rapidly evolving sites in rate classifications based on two divergent angiosperm root placements with Gnetales yields strongly conflicting root placements in MP analysis, despite substantial overlap in the estimated sets of conservative sites. However, the generally high consistency in rooting signal among distantly related gymnosperm clades suggests that the long branch connecting angiosperms to their extant relatives may not interfere substantially with inference of the angiosperm root.     

Reconstructing ancestral ecologies: challenges and possible solutions

There are several ways to extract information about the evolutionary ecology of clades from their phylogenies. Of these, character state optimization and 'ancestor reconstruction' are perhaps the most widely used despite their being fraught with assumptions and potential pitfalls. Requirements for robust inferences of ancestral traits in general (i.e. those applicable to all types of characters) include accurate and robust phylogenetic hypotheses, complete species-level sampling and the appropriate choice of optimality criterion. Ecological characters, however, also require careful consideration of methods for accounting for intraspecific variability. Such methods include 'Presence Coding' and 'Polymorphism Coding' for discrete ecological characters, and 'Range Coding' and 'MaxMin Coding' for continuously variable characters. Ultimately, however, historical inferences such as these are, as with phylogenetic inference itself, associated with a degree of uncertainty. Statistically based uncertainty estimates are available within the context of model-based inference (e.g. maximum likelihood and Bayesian); however, these measures are only as reliable as the chosen model is appropriate. Although generally thought to preclude the possibility of measuring relative uncertainty or support for alternative possible reconstructions, certain useful non-statistical support measures (i.e. 'Sharkey support' and 'Parsimony support') are applicable to parsimony reconstructions.     

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).     

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.     

Estimating the phylogeny in mollusc Littorina saxatilis (Olivi) from enzyme data: methodological considerations

The evolutionary history of 19 populations of Littorina saxatilis (Olivi) was estimated by four different approaches. Three of these operate upon a population by population matrix of genetic distances: average linkage clustering, and two versions of the Fitch-Margoliash method. The fourth method was a maximum likelihood estimate based on differences in allele frequencies between populations. The study aims to assess how well each method estimates the phylogeny by including seven populations of the closely related species L. arcana Hannaford Ellis. The rationale behind this is that a good estimation technique should be able to separate these two monophyletic taxa.The results show that, by our criteria, the maximum likelihood method yields the best estimate and the unconstrained Fitch-Margoliash technique gives reasonable estimates. Both average-linkage clustering and the Fitch-Margoliash method with evolutionary clock perform less well. We argue that this is expected since both these techniques are based on probably unrealistic assumptions such as the overall rate of evolutionary divergence being homogeneous over phyletic lines.     

Ancestral inference and the study of codon bias evolution: implications for molecular evolutionary analyses of the Drosophila melanogaster subgroup

Reliable inference of ancestral sequences can be critical to identifying both patterns and causes of molecular evolution. Robustness of ancestral inference is often assumed among closely related species, but tests of this assumption have been limited. Here, we examine the performance of inference methods for data simulated under scenarios of codon bias evolution within the Drosophila melanogaster subgroup. Genome sequence data for multiple, closely related species within this subgroup make it an important system for studying molecular evolutionary genetics. The effects of asymmetric and lineage-specific substitution rates (i.e., varying levels of codon usage bias and departures from equilibrium) on the reliability of ancestral codon usage was investigated. Maximum parsimony inference, which has been widely employed in analyses of Drosophila codon bias evolution, was compared to an approach that attempts to account for uncertainty in ancestral inference by weighting ancestral reconstructions by their posterior probabilities. The latter approach employs maximum likelihood estimation of rate and base composition parameters. For equilibrium and most non-equilibrium scenarios that were investigated, the probabilistic method appears to generate reliable ancestral codon bias inferences for molecular evolutionary studies within the D. melanogaster subgroup. These reconstructions are more reliable than parsimony inference, especially when codon usage is strongly skewed. However, inference biases are considerable for both methods under particular departures from stationarity (i.e., when adaptive evolution is prevalent). Reliability of inference can be sensitive to branch lengths, asymmetry in substitution rates, and the locations and nature of lineage-specific processes within a gene tree. Inference reliability, even among closely related species, can be strongly affected by (potentially unknown) patterns of molecular evolution in lineages ancestral to those of interest.     

Parsimony, likelihood, and simplicity

The latest charge against parsimony in phylogenetic inference is that it involves estimating too many parameters. The charge is derived from the fact that, when each character is allowed a branch length vector of its own (instead of the homogeneous branch lengths assumed in current likelihood models), the results for likelihood and parsimony are identical. Parsimony, however, can also be derived from simpler models, involving fewer parameters. Therefore, parsimony provides (as many authors had argued before) the simplest explanation of the data, or the most realistic, depending on one's views. If (as argued by likelihoodists) phylogenetic inference is to use the simplest model that provides sufficient explanation of the data, the starting point of phylogenetic analyses should be parsimony, not maximum likelihood. If the addition of new parameters (which increase the likelihood) to a parsimony estimation is seen as desirable, this may lead to a preference for results based on current likelihood models. If the addition of parameters is continued, however, the results will eventually come back to the same place where they had started, since allowing each character a branch length of its own also produces parsimony. Parsimony can be justified by very different types of models—either very complex or very simple. This suggests that parsimony does have a unique place among methods of phylogenetic estimation.     

INTEGRATING FOSSILS WITH MOLECULAR PHYLOGENIES IMPROVES INFERENCE OF TRAIT EVOLUTION

Comparative biologists often attempt to draw inferences about tempo and mode in evolution by comparing the fit of evolutionary models to phylogenetic comparative data consisting of a molecular phylogeny with branch lengths and trait measurements from extant taxa. These kinds of approaches ignore historical evidence for evolutionary pattern and process contained in the fossil record. In this article, we show through simulation that incorporation of fossil information dramatically improves our ability to distinguish among models of quantitative trait evolution using comparative data. We further suggest a novel Bayesian approach that allows fossil information to be integrated even when explicit phylogenetic hypotheses are lacking for extinct representatives of extant clades. By applying this approach to a comparative dataset comprising body sizes for caniform carnivorans, we show that incorporation of fossil information not only improves ancestral state estimates relative to those derived from extant taxa alone, but also results in preference of a model of evolution with trend toward large body size over alternative models such as Brownian motion or Ornstein–Uhlenbeck processes. Our approach highlights the importance of considering fossil information when making macroevolutionary inference, and provides a way to integrate the kind of sparse fossil information that is available to most evolutionary biologists.     

Ancestral sequence reconstruction in primate mitochondrial DNA: compositional bias and effect on functional inference

Reconstruction of ancestral DNA and amino acid sequences is an important means of inferring information about past evolutionary events. Such reconstructions suggest changes in molecular function and evolutionary processes over the course of evolution and are used to infer adaptation and convergence. Maximum likelihood (ML) is generally thought to provide relatively accurate reconstructed sequences compared to parsimony, but both methods lead to the inference of multiple directional changes in nucleotide frequencies in primate mitochondrial DNA (mtDNA). To better understand this surprising result, as well as to better understand how parsimony and ML differ, we constructed a series of computationally simple "conditional pathway" methods that differed in the number of substitutions allowed per site along each branch, and we also evaluated the entire Bayesian posterior frequency distribution of reconstructed ancestral states. We analyzed primate mitochondrial cytochrome b (Cyt-b) and cytochrome oxidase subunit I (COI) genes and found that ML reconstructs ancestral frequencies that are often more different from tip sequences than are parsimony reconstructions. In contrast, frequency reconstructions based on the posterior ensemble more closely resemble extant nucleotide frequencies. Simulations indicate that these differences in ancestral sequence inference are probably due to deterministic bias caused by high uncertainty in the optimization-based ancestral reconstruction methods (parsimony, ML, Bayesian maximum a posteriori). In contrast, ancestral nucleotide frequencies based on an average of the Bayesian set of credible ancestral sequences are much less biased. The methods involving simpler conditional pathway calculations have slightly reduced likelihood values compared to full likelihood calculations, but they can provide fairly unbiased nucleotide reconstructions and may be useful in more complex phylogenetic analyses than considered here due to their speed and flexibility. To determine whether biased reconstructions using optimization methods might affect inferences of functional properties, ancestral primate mitochondrial tRNA sequences were inferred and helix-forming propensities for conserved pairs were evaluated in silico. For ambiguously reconstructed nucleotides at sites with high base composition variability, ancestral tRNA sequences from Bayesian analyses were more compatible with canonical base pairing than were those inferred by other methods. Thus, nucleotide bias in reconstructed sequences apparently can lead to serious bias and inaccuracies in functional predictions.     

A method for molecular phylogeny construction by direct use of nucleotide sequence data

Summary A method for molecular phylogeny construction is newly developed. The method, called the stepwise ancestral sequence method, estimates molecular phylogenetic trees and ancestral sequences simultaneously on the basis of parsimony and sequence homology. For simplicity the emphasis is placed more on parsiomony than on sequence homology in the present study, though both are certainly important. Because parsimony alone will sometimes generate plural candidate trees, the method retains not one but five candidates from which one can then single out the final tree taking other criteria into account.The properties and performance of the method are then examined by simulating an evolving gene along a model phylogenetic tree. The estimated trees are found to lie in a narrow range of the parsimony criteria used in the present study. Thus, other criteria such as biological evidence and likelihood are necessary to single out the correct tree among them, with biological evidence taking precedence over any other criterion. The computer simulation also reveals that the method satisfactorily estimates both tree topology and ancestral sequences, at least for the evolutionary model used in the present study.     

Heterotachy and tree building: a case study with plastids and eubacteria

The nature of heterotachy at the center of recent controversy over the relative performance of tree-building methods is different from the form of heterotachy that has been inferred in empirical studies. The latter have suggested that proportions of variable sites (p(var)) vary among orthologues and among paralogues. However, the strength of this inference, describing what may be one of the most important evolutionary properties of sequence data, has remained weak. Consequently, other models of sequence evolution have been proposed to explain some long-branch attraction (LBA) problems that could be attributed to differences in p(var). For an empirical case with plastid and eubacterial RNA polymerase sequences, we confirm using capture-recapture estimates and simulations that p(var) can differ among orthologues in anciently diverged evolutionary lineages. We find that parsimony and a least squares distance method that implements an overly simple model of sequence evolution are susceptible to LBA induced by this form of heterotachy. Although homogeneous maximum likelihood inference was found to be robust to model misspecification in our specific example, we caution against assuming that it will always be so.     

Convergent evolution of a complex fruit structure in the tribe Brassiceae (Brassicaceae)

? Premise of study: Many angiosperms have fruit morphologies that result in seeds from the same plant having different dispersal capabilities. A prime example is found in the Brassiceae (Brassicaceae), which has many members with segmented or heteroarthrocarpic fruits. Since only 40% of the genera are heteroarthrocarpic, this tribe provides an opportunity to study the evolution of an ecologically significant novelty and its variants. ? Methods: We analyzed nuclear (PHYA) and plastid (matK) sequences from 66 accessions using maximum parsimony, maximum likelihood, and Bayesian inference approaches. The evolution of heteroarthrocarpy and its variants was evaluated using maximum parsimony and maximum likelihood ancestral state reconstructions. ? Key results: Although nuclear and plastid phylogenies are incongruent with each other, the following findings are consistent: (1) Cakile, Crambe, Vella, and Zilla lineages are monophyletic; (2) the Nigra lineage is not monophyletic; and (3) within the Cakile clade, Cakile, Didesmus, and Erucaria are paraphyletic. Despite differences in the matK and PHYA topologies at both deep and shallow nodes, similar patterns of morphological evolution emerge. Heteroarthrocarpy, a complex morphological trait, has evolved multiple times across the tribe. Moreover, there are convergent transitions in dehiscence capabilities and fruit disarticulation across the tribe. ? Conclusions: We present the first explicit analysis of fruit evolution within the Brassiceae, which exemplifies evolutionary lability. The repeated loss and gain of segment dehiscence and disarticulation suggests conservation in the genetic pathway controlling abscission with differential expression across taxa. This study provides a strong foundation for future studies of mechanisms underlying variation in dispersal capabilities of Brassiceae.     

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.     

Maximum likelihood inference of geographic range evolution by dispersal, local extinction, and cladogenesis

In historical biogeography, model-based inference methods for reconstructing the evolution of geographic ranges on phylogenetic trees are poorly developed relative to the diversity of analogous methods available for inferring character evolution. We attempt to rectify this deficiency by constructing a dispersal-extinction-cladogenesis (DEC) model for geographic range evolution that specifies instantaneous transition rates between discrete states (ranges) along phylogenetic branches and apply it to estimating likelihoods of ancestral states (range inheritance scenarios) at cladogenesis events. Unlike an earlier version of this approach, the present model allows for an analytical solution to probabilities of range transitions as a function of time, enabling free parameters in the model, rates of dispersal, and local extinction to be estimated by maximum likelihood. Simulation results indicate that accurate parameter estimates may be difficult to obtain in practice but also show that ancestral range inheritance scenarios nevertheless can be correctly recovered with high success if rates of range evolution are low relative to the rate of cladogenesis. We apply the DEC model to a previously published, exemplary case study of island biogeography involving Hawaiian endemic angiosperms in Psychotria (Rubiaceae), showing how the DEC model can be iteratively refined from inspecting inferences of range evolution and also how geological constraints involving times of island origin may be imposed on the likelihood function. The DEC model is sufficiently similar to character models that it might serve as a gateway through which many existing comparative methods for characters could be imported into the realm of historical biogeography; moreover, it might also inspire the conceptual expansion of character models toward inclusion of evolutionary change as directly coincident, either as cause or consequence, with cladogenesis events. The DEC model is thus an incremental advance that highlights considerable potential in the nascent field of model-based historical biogeographic inference.     

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.     

To what extent do new fossil discoveries change our understanding of clade evolution? A cautionary tale from burying beetles (Coleoptera: Nicrophorus)

Divergence time estimates derived from phylogenies are crucial to infer historical biogeography and diversification dynamics. Yet, the impact of fossil record incompleteness on macroevolutionary reconstructions remains equivocal. Here, we investigate to what extent gaps in the fossil record can impinge downstream evolutionary inferences in the beetle family Silphidae. Recent discoveries have pushed back the fossil record of this group from the Eocene into the Jurassic. We estimated the divergence times of the family using both its currently understood fossil record and the fossil record known prior to these recent discoveries. All fossil calibrations were informed with different parametric distributions to investigate the weight of priors on posterior age estimates. Based on time‐calibrated trees, we assessed the impact of fossil calibrations on the inference of ancestral ranges and diversification rate dynamics in the genus Nicrophorus. Depending upon the selected sets of fossil constraints, the age discrepancies had a major impact on the macroevolutionary inferences: the biogeographic extrapolations relative to paleogeography are markedly contrasting, and the calculated rates at which species form or go extinct (and when they varied) are strikingly different. We show that soft prior distributions do not necessarily alleviate such shortcomings therefore preventing the inference of reliable macroevolutionary patterns in groups presenting a taphonomic bias in their fossil record.     

Dynamic homology and the likelihood criterion

The use of likelihood as an optimality criterion is explored in the context of dynamic homology. Simple models and procedures are described to allow the analysis of large variable length sequence data sets, alone and in combination with qualitative information (such as morphology). Several approaches are discussed that have different likelihood interpretations in terms of maximum parsimony likelihood and maximum average likelihood. Implementation is discussed and an example in arthropod systematics presented. Topological congruence comparisons with parsimony are made.
© The Willi Hennig Society 2006.     

Compositional statistics: An improvement of evolutionary parsimony and its application to deep branches in the tree of life

Summary We present compositional statistics, a new method of phylogenetic inference, which is an extension of evolutionary parsimony. Compositional statistics takes account of the base composition of the compared sequences by using nucleotide positions that evolutionary parsimony ignores. It shares with evolutionary parsimony the features of rate invariance and the fundamental distinction between transitions and transversions. Of the presently available methods of phylogenetic inference, compositional statistics is based on the fewest and mildest assumptions about the mode of DNA sequence evolution. It is therefore applicable to phylogenetic studies of the most distantly related organisms or molecules. This was illustrated by analyzing conservative positions in the DNA sequences of the large subunit of RNA polymerase from three archaebacterial groups, a eubacterium, a chloroplast, and the three eukaryotic polymerases. Internally consistent results, which are in accord with our knowledge of organelle origin and archaebacterial physiology, were achieved.