Likelihood, parsimony, and heterogeneous evolution

Evolutionary rates vary among sites and across the phylogenetic tree (heterotachy). A recent analysis suggested that parsimony can be better than standard likelihood at recovering the true tree given heterotachy. The authors recommended that results from parsimony, which they consider to be nonparametric, be reported alongside likelihood results. They also proposed a mixture model, which was inconsistent but better than either parsimony or standard likelihood under heterotachy. We show that their main conclusion is limited to a special case for the type of model they study. Their mixture model was inconsistent because it was incorrectly implemented. A useful nonparametric model should perform well over a wide range of possible evolutionary models, but parsimony does not have this property. Likelihood-based methods are therefore the best way to deal with heterotachy.     

Artifactual phylogenies caused by correlated distribution of substitution rates among sites and lineages: the good, the bad, and the ugly

Despite the advances in understanding molecular evolution, current phylogenetic methods barely take account of a fraction of the complexity of evolution. We are chiefly constrained by our incomplete knowledge of molecular evolutionary processes and the limits of computational power. These limitations lead to the establishment of either biologically simplistic models that rarely account for a fraction of the complexity involved or overfitting models that add little resolution to the problem. Such oversimplified models may lead us to assign high confidence to an incorrect tree (inconsistency). Rate-across-site (RAS) models are commonly used evolutionary models in phylogenetic studies. These account for heterogeneity in the evolutionary rates among sites but do not account for changing within-site rates across lineages (heterotachy). If heterotachy is common, using RAS models may lead to systematic errors in tree inference. In this work we show possible misleading effects in tree inference when the assumption of constant within-site rates across lineages is violated using maximum likelihood. Using a simulation study, we explore the ways in which gamma stationary models can lead to wrong topology or to deceptive bootstrap support values when the within-site rates change across lineages. More precisely, we show that different degrees of heterotachy mislead phylogenetic inference when the model assumed is stationary. Finally, we propose a geometry-based approach to visualize and to test for the possible existence of bias due to heterotachy.     

Heterotachy, an important process of protein evolution.

Because of functional constraints, substitution rates vary among the positions of a protein but are usually assumed to be constant at a given site during evolution. The distribution of the rates across the sequence positions generally fits a Gamma distribution. Models of sequence evolution were accordingly designed and led to improved phylogenetic reconstruction. However, it has been convincingly demonstrated that the evolutionary rate of a given position is not always constant throughout time. We called such within-site rate variations heterotachy (for "different speed" in Greek). Yet, heterotachy was found among homologous sequences of distantly related organisms, often with different functions. In such cases, the functional constraints are likely different, which would explain the different distribution of variable sites. To evaluate the importance of heterotachy, we focused on amino acid sequences of mitochondrial cytochrome b, for which the function is likely the same in all vertebrates. Using 2,038 sequences, we demonstrate that 95% of the variable positions are heterotachous, i.e., underwent dramatic variations of substitution rate among vertebrate lineages. Heterotachy even occurs at small evolutionary scale, and in these cases it is very unlikely to be related to functional changes. Since a large number of sequences are required to efficiently detect heterotachy, the extent of this phenomenon could not be estimated for all proteins yet. It could be as large as for cytochrome b, since this protein is not a peculiar case. The observations made here open several new avenues of research, such as the understanding of the evolution of functional constraints or the improvement of phylogenetic reconstruction methods.     

Variation in modes and rates of evolution in nuclear and mitochondrial ribosomal DNA in the mushroom genus Amanita (Agaricales, Basidiomycota): phylogenetic implications

Modes and rates of molecular evolution, and congruence and combinability for phylogenetic reconstruction, of portions of the nuclear large ribosomal subunit (nLSU-rDNA) and mitochondrial small subunit (mtSSU-rDNA) genes were investigated in the mushroom genus Amanita. The AT content was higher in the mtSSU-rDNA than in the nLSU-rDNA. A transition bias in which AT substitutions were as frequent as transitions was present in the mtSSU-rDNA but not in the nLSU-rDNA. Among-sites rate variation in nucleotide substitutions at variable sites was present in the nLSU-rDNA but not in the mtSSU-rDNA. Likelihood ratio tests indicated very different models of evolution for the two molecules. A molecular clock could be rejected for both data sets. Rates of molecular evolution in the two molecules were uncoupled: faster evolutionary rates in the mtSSU-rDNA and nLSU-rDNA were not observed for the same taxa. In separate phylogenetic analyses, the nLSU-rDNA data set had higher phylogenetic resolution. The partition homogeneity test and statistical bootstrap support for branches indicated absence of conflict in the phylogenetic signal in the two data sets; however, tree topologies produced from the separate data sets were not congruent. Heterogeneity in modes and rates of evolution in the two molecules pose difficulties for a combined analysis of the two data sets: the use of equally weighted parsimony is not fully satisfactory when rate heterogeneity is present, and it is impractical to determine a model for maximum-likelihood analysis that fits simultaneously two heterogeneous data sets. Overall topologies produced from either the separated or the combined analyses using various tree reconstruction methods were identical for nearly all statistically significant branches.     

A random effects branch-site model for detecting episodic diversifying selection

Adaptive evolution frequently occurs in episodic bursts, localized to a few sites in a gene, and to a small number of lineages in a phylogenetic tree. A popular class of "branch-site" evolutionary models provides a statistical framework to search for evidence of such episodic selection. For computational tractability, current branch-site models unrealistically assume that all branches in the tree can be partitioned a priori into two rigid classes--"foreground" branches that are allowed to undergo diversifying selective bursts and "background" branches that are negatively selected or neutral. We demonstrate that this assumption leads to unacceptably high rates of false positives or false negatives when the evolutionary process along background branches strongly deviates from modeling assumptions. To address this problem, we extend Felsenstein's pruning algorithm to allow efficient likelihood computations for models in which variation over branches (and not just sites) is described in the random effects likelihood framework. This enables us to model the process at every branch-site combination as a mixture of three Markov substitution models--our model treats the selective class of every branch at a particular site as an unobserved state that is chosen independently of that at any other branch. When benchmarked on a previously published set of simulated sequences, our method consistently matched or outperformed existing branch-site tests in terms of power and error rates. Using three empirical data sets, previously analyzed for episodic selection, we discuss how modeling assumptions can influence inference in practical situations.     

Fast statistical tests for detecting heterotachy in protein evolution

The w statistic introduced by Lockhart et al. (1998. A covariotide model explains apparent phylogenetic structure of oxygenic photosynthetic lineages. Mol Biol Evol. 15:1183-1188) is a simple and easily calculated statistic intended to detect heterotachy by comparing amino acid substitution patterns between two monophyletic groups of protein sequences. It is defined as the difference between the fraction of varied sites in both groups and the fraction of varied sites in each group. The w test has been used to distinguish a covarion process from equal rates and rates variation across sites processes. Using simulation we show that the w test is effective for small data sets and for data sets that have low substitution rates in the groups but can have difficulties when these conditions are not met. Using site entropy as a measure of variability of a sequence site, we modify the w statistic to a w' statistic by assigning as varied in one group those sites that are actually varied in both groups but have a large entropy difference. We show that the w' test has more power to detect two kinds of heterotachy processes (covarion and bivariate rate shifts) in large and variable data. We also show that a test of Pearson's correlation of the site entropies between two monophyletic groups can be used to detect heterotachy and has more power than the w' test. Furthermore, we demonstrate that there are settings where the correlation test as well as w and w' tests do not detect heterotachy signals in data simulated under a branch length mixture model. In such cases, it is sometimes possible to detect heterotachy through subselection of appropriate taxa. Finally, we discuss the abilities of the three statistical tests to detect a fourth mode of heterotachy: lineage-specific changes in proportion of variable sites.     

The devil in the details: interactions between the branch-length prior and likelihood model affect node support and branch lengths in the phylogeny of the Psoraceae

In popular use of Bayesian phylogenetics, a default branch-length prior is almost universally applied without knowing how a different prior would have affected the outcome. We performed Bayesian and maximum likelihood (ML) inference of phylogeny based on empirical nucleotide sequence data from a family of lichenized ascomycetes, the Psoraceae, the morphological delimitation of which has been controversial. We specifically assessed the influence of the combination of Bayesian branch-length prior and likelihood model on the properties of the Markov chain Monte Carlo tree sample, including node support, branch lengths, and taxon stability. Data included two regions of the mitochondrial ribosomal RNA gene, the internal transcribed spacer region of the nuclear ribosomal RNA gene, and the protein-coding largest subunit of RNA polymerase II. Data partitioning was performed using Bayes' factors, whereas the best-fitting model of each partition was selected using the Bayesian information criterion (BIC). Given the data and model, short Bayesian branch-length priors generate higher numbers of strongly supported nodes as well as short and topologically similar trees sampled from parts of tree space that are largely unexplored by the ML bootstrap. Long branch-length priors generate fewer strongly supported nodes and longer and more dissimilar trees that are sampled mostly from inside the range of tree space sampled by the ML bootstrap. Priors near the ML distribution of branch lengths generate the best marginal likelihood and the highest frequency of "rogue" (unstable) taxa. The branch-length prior was shown to interact with the likelihood model. Trees inferred under complex partitioned models are more affected by the stretching effect of the branch-length prior. Fewer nodes are strongly supported under a complex model given the same branch-length prior. Irrespective of model, internal branches make up a larger proportion of total tree length under the shortest branch-length priors compared with longer priors. Relative effects on branch lengths caused by the branch-length prior can be problematic to downstream phylogenetic comparative methods making use of the branch lengths. Furthermore, given the same branch-length prior, trees are on average more dissimilar under a simple unpartitioned model compared with a more complex partitioned models. The distribution of ML branch lengths was shown to better fit a gamma or Pareto distribution than an exponential one. Model adequacy tests indicate that the best-fitting model selected by the BIC is insufficient for describing data patterns in 5 of 8 partitions. More general substitution models are required to explain the data in three of these partitions, one of which also requires nonstationarity. The two mitochondrial ribosomal RNA gene partitions need heterotachous models. We found no significant correlations between, on the one hand, the amount of ambiguous data or the smallest branch-length distance to another taxon and, on the other hand, the topological stability of individual taxa. Integrating over several exponentially distributed means under the best-fitting model, node support for the family Psoraceae, including Psora, Protoblastenia, and the Micarea sylvicola group, is approximately 0.96. Support for the genus Psora is distinctly lower, but we found no evidence to contradict the current classification.     

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.     

Bayesian Inference of Reticulate Phylogenies under the Multispecies Network Coalescent

The multispecies coalescent (MSC) is a statistical framework that models how gene genealogies grow within the branches of a species tree. The field of computational phylogenetics has witnessed an explosion in the development of methods for species tree inference under MSC, owing mainly to the accumulating evidence of incomplete lineage sorting in phylogenomic analyses. However, the evolutionary history of a set of genomes, or species, could be reticulate due to the occurrence of evolutionary processes such as hybridization or horizontal gene transfer. We report on a novel method for Bayesian inference of genome and species phylogenies under the multispecies network coalescent (MSNC). This framework models gene evolution within the branches of a phylogenetic network, thus incorporating reticulate evolutionary processes, such as hybridization, in addition to incomplete lineage sorting. As phylogenetic networks with different numbers of reticulation events correspond to points of different dimensions in the space of models, we devise a reversible-jump Markov chain Monte Carlo (RJMCMC) technique for sampling the posterior distribution of phylogenetic networks under MSNC. We implemented the methods in the publicly available, open-source software package PhyloNet and studied their performance on simulated and biological data. The work extends the reach of Bayesian inference to phylogenetic networks and enables new evolutionary analyses that account for reticulation.     

ImOSM: intermittent evolution and robustness of phylogenetic methods

Among the criteria to evaluate the performance of a phylogenetic method, robustness to model violation is of particular practical importance as complete a priori knowledge of evolutionary processes is typically unavailable. For studies of robustness in phylogenetic inference, a utility to add well-defined model violations to the simulated data would be helpful. We therefore introduce ImOSM, a tool to imbed intermittent evolution as model violation into an alignment. Intermittent evolution refers to extra substitutions occurring randomly on branches of a tree, thus changing alignment site patterns. This means that the extra substitutions are placed on the tree after the typical process of sequence evolution is completed. We then study the robustness of widely used phylogenetic methods: maximum likelihood (ML), maximum parsimony (MP), and a distance-based method (BIONJ) to various scenarios of model violation. Violation of rates across sites (RaS) heterogeneity and simultaneous violation of RaS and the transition/transversion ratio on two nonadjacent external branches hinder all the methods recovery of the true topology for a four-taxon tree. For an eight-taxon balanced tree, the violations cause each of the three methods to infer a different topology. Both ML and MP fail, whereas BIONJ, which calculates the distances based on the ML estimated parameters, reconstructs the true tree. Finally, we report that a test of model homogeneity and goodness of fit tests have enough power to detect such model violations. The outcome of the tests can help to actually gain confidence in the inferred trees. Therefore, we recommend using these tests in practical phylogenetic analyses.     

Phylogenetic mixtures on a single tree can mimic a tree of another topology

Phylogenetic mixtures model the inhomogeneous molecular evolution commonly observed in data. The performance of phylogenetic reconstruction methods where the underlying data are generated by a mixture model has stimulated considerable recent debate. Much of the controversy stems from simulations of mixture model data on a given tree topology for which reconstruction algorithms output a tree of a different topology; these findings were held up to show the shortcomings of particular tree reconstruction methods. In so doing, the underlying assumption was that mixture model data on one topology can be distinguished from data evolved on an unmixed tree of another topology given enough data and the "correct" method. Here we show that this assumption can be false. For biologists, our results imply that, for example, the combined data from two genes whose phylogenetic trees differ only in terms of branch lengths can perfectly fit a tree of a different topology.     

The effect of heterotachy in multigene analysis using the neighbor joining method

Sequence alignments of multiple genes are routinely used to infer phylogenetic relationships among species. The analysis of their concatenation is more likely to give correct results under an assumption of homotachy (i.e., the evolutionary rates within lineages in each of the concatenated genes are constant during evolution). Here, we examine how the violation of homotachy (i.e., presence of within-site rate variation, called heterotachy) distorts species phylogenies. A theoretical examination has been conducted using a four taxon case and the neighbor joining (NJ) method, concluding that NJ recovers the incorrect tree when concatenated genes exhibit heterotachy. The application of average and weighted-average distance approaches, where gene boundaries are kept intact, overcomes the detrimental effect of heterotachy in multigene analysis using the NJ method.     

A model-based approach for detecting coevolving positions in a molecule

We present a new method for detecting coevolving sites in molecules. The method relies on a set of aligned sequences (nucleic acid or protein) and uses Markov models of evolution to map the substitutions that occurred at each site onto the branches of the underlying phylogenetic tree. This mapping takes into account the uncertainty over ancestral states and among-site rate variation. We then build, for each site, a "substitution vector" containing the posterior estimates of the number of substitutions in each branch. The amount of coevolution for a pair of sites is then measured as the Pearson correlation coefficient between the two corresponding substitution vectors and compared to the expectation under the null hypothesis of independence. We applied the method to a 79-species bacterial ribosomal RNA data set, for which extensive structural characterization has been done over the last 30 years. More than 95% of the intramolecular predicted pairs of sites correspond to known interacting site pairs.     

A mixed branch length model of heterotachy improves phylogenetic accuracy

Evolutionary relationships are typically inferred from molecular sequence data using a statistical model of the evolutionary process. When the model accurately reflects the underlying process, probabilistic phylogenetic methods recover the correct relationships with high accuracy. There is ample evidence, however, that models commonly used today do not adequately reflect real-world evolutionary dynamics. Virtually all contemporary models assume that relatively fast-evolving sites are fast across the entire tree, whereas slower sites always evolve at relatively slower rates. Many molecular sequences, however, exhibit site-specific changes in evolutionary rates, called "heterotachy." Here we examine the accuracy of 2 phylogenetic methods for incorporating heterotachy, the mixed branch length model--which incorporates site-specific rate changes by summing likelihoods over multiple sets of branch lengths on the same tree--and the covarion model, which uses a hidden Markov process to allow sites to switch between variable and invariable as they evolve. Under a variety of simple heterogeneous simulation conditions, the mixed model was dramatically more accurate than homotachous models, which were subject to topological biases as well as biases in branch length estimates. When data were simulated with strong versions of the types of heterotachy observed in real molecular sequences, the mixed branch length model was more accurate than homotachous techniques. Analyses of empirical data sets confirmed that the mixed branch length model can improve phylogenetic accuracy under conditions that cause homotachous models to fail. In contrast, the covarion model did not improve phylogenetic accuracy compared with homotachous models and was sometimes substantially less accurate. We conclude that a mixed branch length approach, although not the solution to all phylogenetic errors, is a valuable strategy for improving the accuracy of inferred trees.     

Interactive analysis of phylogeny and character evolution using the computer program MacClade

Computer programs for phylogenetic analysis have been important tools in systematics and evolutionary biology, but most have been designed primarily for the reconstruction of phylogenetic trees and not the interpretation of patterns of character evolution. Described here is the computer program MacClade, designed for interactive analysis of character evolution and phylogeny. For a given tree and a matrix of character data, MacClade displays its reconstruction of character evolution by shading the branches of the tree to indicate ancestral states. Trees can be manipulated for instance by picking up and moving branches. Assumptions underlying the reconstruction of character evolution can be varied extensively. With these manipulations and MacClade's graphical feedback, one can explore the relationships among phylogenetic trees, character data, assumptions and interpretations of character evolution. MacClade has extensive facilities for editing data, displaying various summaries of character evolution in charts and diagrams, and printing.     

TESTING FOR UNEQUAL AMOUNTS OF EVOLUTION IN A CONTINUOUS CHARACTER ON DIFFERENT BRANCHES OF A PHYLOGENETIC TREE USING LINEAR AND SQUARED-CHANGE PARSIMONY: AN EXAMPLE USING LESSER ANTILLEAN ANOLIS LIZARDS

Although a large body of work investigating tests of correlated evolution of two continuous characters exists, hypotheses such as character displacement are really tests of whether substantial evolutionary change has occurred on a particular branch or branches of the phylogenetic tree. In this study, we present a methodology for testing such a hypothesis using ancestral character state reconstruction and simulation. Furthermore, we suggest how to investigate the robustness of the hypothesis test by varying the reconstruction methods or simulation parameters. As a case study, we tested a hypothesis of character displacement in body size of Caribbean Anolis lizards. We compared squared-change, weighted squared-change, and linear parsimony reconstruction methods, gradual Brownian motion and speciational models of evolution, and several resolution methods for linear parsimony. We used ancestor reconstruction methods to infer the amount of body size evolution, and tested whether evolutionary change in body size was greater on branches of the phylogenetic tree in which a transition from occupying a single-species island to a two-species island occurred. Simulations were used to generate null distributions of reconstructed body size change. The hypothesis of character displacement was tested using Wilcoxon Rank-Sums. When tested against simulated null distributions, all of the reconstruction methods resulted in more significant P-values than when standard statistical tables were used. These results confirm that P-values for tests using ancestor reconstruction methods should be assessed via simulation rather than from standard statistical tables. Linear parsimony can produce an infinite number of most parsimonious reconstructions in continuous characters. We present an example of assessing the robustness of our statistical test by exploring the sample space of possible resolutions. We compare ACCTRAN and DELTRAN resolutions of ambiguous character reconstructions in linear parsimony to the most and least conservative resolutions for our particular hypothesis.     

Robustness of compound Dirichlet priors for Bayesian inference of branch lengths

We modified the phylogenetic program MrBayes 3.1.2 to incorporate the compound Dirichlet priors for branch lengths proposed recently by Rannala, Zhu, and Yang (2012. Tail paradox, partial identifiability and influential priors in Bayesian branch length inference. Mol. Biol. Evol. 29:325-335.) as a solution to the problem of branch-length overestimation in Bayesian phylogenetic inference. The compound Dirichlet prior specifies a fairly diffuse prior on the tree length (the sum of branch lengths) and uses a Dirichlet distribution to partition the tree length into branch lengths. Six problematic data sets originally analyzed by Brown, Hedtke, Lemmon, and Lemmon (2010. When trees grow too long: investigating the causes of highly inaccurate Bayesian branch-length estimates. Syst. Biol. 59:145-161) are reanalyzed using the modified version of MrBayes to investigate properties of Bayesian branch-length estimation using the new priors. While the default exponential priors for branch lengths produced extremely long trees, the compound Dirichlet priors produced posterior estimates that are much closer to the maximum likelihood estimates. Furthermore, the posterior tree lengths were quite robust to changes in the parameter values in the compound Dirichlet priors, for example, when the prior mean of tree length changed over several orders of magnitude. Our results suggest that the compound Dirichlet priors may be useful for correcting branch-length overestimation in phylogenetic analyses of empirical data sets.     

Pitfalls of heterogeneous processes for phylogenetic reconstruction

Different genes often have different phylogenetic histories. Even within regions having the same phylogenetic history, the mutation rates often vary. We investigate the prospects of phylogenetic reconstruction when all the characters are generated from the same tree topology, but the branch lengths vary (with possibly different tree shapes). Furthering work of Kolaczkowski and Thornton (2004, Nature 431: 980-984) and Chang (1996, Math. Biosci. 134: 189-216), we show examples where maximum likelihood (under a homogeneous model) is an inconsistent estimator of the tree. We then explore the prospects of phylogenetic inference under a heterogeneous model. In some models, there are examples where phylogenetic inference under any method is impossible - despite the fact that there is a common tree topology. In particular, there are nonidentifiable mixture distributions, i.e., multiple topologies generate identical mixture distributions. We address which evolutionary models have nonidentifiable mixture distributions and prove that the following duality theorem holds for most DNA substitution models. The model has either: (i) nonidentifiability - two different tree topologies can produce identical mixture distributions, and hence distinguishing between the two topologies is impossible; or (ii) linear tests - there exist linear tests which identify the common tree topology for character data generated by a mixture distribution. The theorem holds for models whose transition matrices can be parameterized by open sets, which includes most of the popular models, such as Tamura-Nei and Kimura's 2-parameter model. The duality theorem relies on our notion of linear tests, which are related to Lake's linear invariants.     

BEST-FIT MAXIMUM-LIKELIHOOD MODELS FOR PHYLOGENETIC INFERENCE: EMPIRICAL TESTS WITH KNOWN PHYLOGENIES

Despite the proliferation of increasingly sophisticated models of DNA sequence evolution, choosing among models remains a major problem in phylogenetic reconstruction. The choice of appropriate models is thought to be especially important when there is large variation among branch lengths. We evaluated the ability of nested models to reconstruct experimentally generated, known phylogenies of bacteriophage T7 as we varied the terminal branch lengths. Then, for each phylogeny we determined the best-fit model by progressively adding parameters to simpler models. We found that in several cases the choice of best-fit model was affected by the parameter addition sequence. In terms of phylogenetic performance, there was little difference between models when the ratio of short: long terminal branches was 1:3 or less. However, under conditions of extreme terminal branch-length variation, there were not only dramatic differences among models, but best-fit models were always among the best at overcoming long-branch attraction. The performance of minimum-evolution-distance methods was generally lower than that of discrete maximum-likelihood methods, even if maximum-likelihood methods were used to generate distance matrices. Correcting for among-site rate variation was especially important for overcoming long-branch attraction. The generality of our conclusions is supported by earlier simulation studies and by a preliminary analysis of mitochondrial and nuclear sequences from a well-supported four-taxon amniote phylogeny.     

Discordance of species trees with their most likely gene trees: the case of five taxa

Under a coalescent model for within-species evolution, gene trees may differ from species trees to such an extent that the gene tree topology most likely to evolve along the branches of a species tree can disagree with the species tree topology. Gene tree topologies that are more likely to be produced than the topology that matches that of the species tree are termed anomalous, and the region of branch-length space that gives rise to anomalous gene trees (AGTs) is the anomaly zone. We examine the occurrence of anomalous gene trees for the case of five taxa, the smallest number of taxa for which every species tree topology has a nonempty anomaly zone. Considering all sets of branch lengths that give rise to anomalous gene trees, the largest value possible for the smallest branch length in the species tree is greater in the five-taxon case (0.1934 coalescent time units) than in the previously studied case of four taxa (0.1568). The five-taxon case demonstrates the existence of three phenomena that do not occur in the four-taxon case. First, anomalous gene trees can have the same unlabeled topology as the species tree. Second, the anomaly zone does not necessarily enclose a ball centered at the origin in branch-length space, in which all branches are short. Third, as a branch length increases, it is possible for the number of AGTs to increase rather than decrease or remain constant. These results, which help to describe how the properties of anomalous gene trees increase in complexity as the number of taxa increases, will be useful in formulating strategies for evading the problem of anomalous gene trees during species tree inference from multilocus data.