The Use (and Misuse) of Phylogenetic Trees in Comparative Behavioral Analyses

Phylogenetic comparative methods play a critical role in our understanding of the adaptive origin of primate behaviors. To incorporate evolutionary history directly into comparative behavioral research, behavioral ecologists rely on strong, well-resolved phylogenetic trees. Phylogenies provide the framework on which behaviors can be compared and homologies can be distinguished from similarities due to convergent or parallel evolution. Phylogenetic reconstructions are also of critical importance when inferring the ancestral state of behavioral patterns and when suggesting the evolutionary changes that behavior has undergone. Improvements in genome sequencing technologies have increased the amount of data available to researchers. Recently, several primate phylogenetic studies have used multiple loci to produce robust phylogenetic trees that include hundreds of primate species. These trees are now commonly used in comparative analyses and there is a perception that we have a complete picture of the primate tree. But how confident can we be in those phylogenies? And how reliable are comparative analyses based on such trees? Herein, we argue that even recent molecular phylogenies should be treated cautiously because they rely on many assumptions and have many shortcomings. Most phylogenetic studies do not model gene tree diversity and can produce misleading results, such as strong support for an incorrect species tree, especially in the case of rapid and recent radiations. We discuss implications that incorrect phylogenies can have for reconstructing the evolution of primate behaviors and we urge primatologists to be aware of the current limitations of phylogenetic reconstructions when applying phylogenetic comparative methods.     

Phylogenetic supertrees: Assembling the trees of life

Systematists and comparative biologists commonly want to make statements about relationships among taxa that have never been collectively included in any single phylogenetic analysis. Construction of phylogenetic 'supertrees' provides one solution. Supertrees are estimates of phylogeny assembled from sets of smaller estimates (source trees) sharing some but not necessarily all their taxa in common. If certain conditions are met, supertrees can retain all or most of the information from the source trees and also make novel statements about relationships of taxa that do not co-occur on any one source tree. Supertrees have commonly been constructed using subjective and informal approaches, but several explicit approaches have recently been proposed.     

Is there a star tree paradox?

Concerns have been raised that posterior probabilities on phylogenetic trees can be unreliable when the true tree is unresolved or has very short internal branches, because existing methods for Bayesian phylogenetic analysis do not explicitly evaluate unresolved trees. Two recent papers have proposed that evaluating only resolved trees results in a "star tree paradox": when the true tree is unresolved or close to it, posterior probabilities were predicted to become increasingly unpredictable as sequence length grows, resulting in inflated confidence in one resolved tree or another and an increasing risk of false-positive inferences. Here we show that this is not the case; existing Bayesian methods do not lead to an inflation of statistical confidence, provided the evolutionary model is correct and uninformative priors are assumed. Posterior probabilities do not become increasingly unpredictable with increasing sequence length, and they exhibit conservative type I error rates, leading to a low rate of false-positive inferences. With infinite data, posterior probabilities give equal support for all resolved trees, and the rate of false inferences falls to zero. We conclude that there is no star tree paradox caused by not sampling unresolved trees.     

A fully resolved consensus between fully resolved phylogenetic trees

Nowadays, there are many phylogeny reconstruction methods, each with advantages and disadvantages. We explored the advantages of each method, putting together the common parts of trees constructed by several methods, by means of a consensus computation. A number of phylogenetic consensus methods are already known. Unfortunately, there is also a taboo concerning consensus methods, because most biologists see them mainly as comparators and not as phylogenetic tree constructors. We challenged this taboo by defining a consensus method that builds a fully resolved phylogenetic tree based on the most common parts of fully resolved trees in a given collection. We also generated results showing that this consensus is in a way a kind of "median" of the input trees; as such it can be closer to the correct tree in many situations.     

Estimating phylogenetic relationships despite discordant gene trees across loci: the species tree of a diverse species group of feather mites (Acari: Proctophyllodidae)

With the increased availability of multilocus sequence data, the lack of concordance of gene trees estimated for independent loci has focused attention on both the biological processes producing the discord and the methodologies used to estimate phylogenetic relationships. What has emerged is a suite of new analytical tools for phylogenetic inference--species tree approaches. In contrast to traditional phylogenetic methods that are stymied by the idiosyncrasies of gene trees, approaches for estimating species trees explicitly take into account the cause of discord among loci and, in the process, provides a direct estimate of phylogenetic history (i.e. the history of species divergence, not divergence of specific loci). We illustrate the utility of species tree estimates with an analysis of a diverse group of feather mites, the pinnatus species group (genus Proctophyllodes). Discord among four sequenced nuclear loci is consistent with theoretical expectations, given the short time separating speciation events (as evident by short internodes relative to terminal branch lengths in the trees). Nevertheless, many of the relationships are well resolved in a Bayesian estimate of the species tree; the analysis also highlights ambiguous aspects of the phylogeny that require additional loci. The broad utility of species tree approaches is discussed, and specifically, their application to groups with high speciation rates--a history of diversification with particular prevalence in host/parasite systems where species interactions can drive rapid diversification.     

Inferring phylogenetic relationships avoiding forbidden rooted triplets

To construct a phylogenetic tree or phylogenetic network for describing the evolutionary history of a set of species is a well-studied problem in computational biology. One previously proposed method to infer a phylogenetic tree/network for a large set of species is by merging a collection of known smaller phylogenetic trees on overlapping sets of species so that no (or as little as possible) branching information is lost. However, little work has been done so far on inferring a phylogenetic tree/network from a specified set of trees when in addition, certain evolutionary relationships among the species are known to be highly unlikely. In this paper, we consider the problem of constructing a phylogenetic tree/network which is consistent with all of the rooted triplets in a given set C and none of the rooted triplets in another given set F. Although NP-hard in the general case, we provide some efficient exact and approximation algorithms for a number of biologically meaningful variants of the problem.     

The Tree versus the Forest: The Fungal Tree of Life and the Topological Diversity within the Yeast Phylome

A recurrent topic in phylogenomics is the combination of various sequence alignments to reconstruct a tree that describes the evolutionary relationships within a group of species. However, such approach has been criticized for not being able to properly represent the topological diversity found among gene trees. To evaluate the representativeness of species trees based on concatenated alignments, we reconstruct several fungal species trees and compare them with the complete collection of phylogenies of genes encoded in the Saccharomyces cerevisiae genome. We found that, despite high levels of among-gene topological variation, the species trees do represent widely supported phylogenetic relationships. Most topological discrepancies between gene and species trees are concentrated in certain conflicting nodes. We propose to map such information on the species tree so that it accounts for the levels of congruence across the genome. We identified the lack of sufficient accuracy of current alignment and phylogenetic methods as an important source for the topological diversity encountered among gene trees. Finally, we discuss the implications of the high levels of topological variation for phylogeny-based orthology prediction strategies.     

Multilocus phylogenetics of a rapid radiation in the genus Thomomys (Rodentia: Geomyidae)

Species complexes undergoing rapid radiation present a challenge in molecular systematics because of the possibility that ancestral polymorphism is retained in component gene trees. Coalescent theory has demonstrated that gene trees often fail to match lineage trees when taxon divergence times are less than the ancestral effective population sizes. Suggestions to increase the number of loci and the number of individuals per taxon have been proposed; however, phylogenetic methods to adequately analyze these data in a coalescent framework are scarce. We compare two approaches to estimating lineage (species) trees using multiple individuals and multiple loci: the commonly used partitioned Bayesian analysis of concatenated sequences and a modification of a newly developed hierarchical Bayesian method (BEST) that simultaneously estimates gene trees and species trees from multilocus data. We test these approaches on a phylogeny of rapidly radiating species wherein divergence times are likely to be smaller than effective population sizes, and incomplete lineage sorting is known, in the rodent genus, Thomomys. We use seven independent noncoding nuclear sequence loci (total approximately 4300 bp) and between 1 and 12 individuals per taxon to construct a phylogenetic hypothesis for eight Thomomys species. The majority-rule consensus tree from the partitioned concatenated analysis included 14 strongly supported bipartitions, corroborating monophyletic species status of five of the eight named species. The BEST tree strongly supported only the split between the two subgenera and showed very low support for any other clade. Comparison of both lineage trees to individual gene trees revealed that the concatenation method appears to ignore conflicting signals among gene trees, whereas the BEST tree considers conflicting signals and downweights support for those nodes. Bayes factor analysis of posterior tree distributions from both analyses strongly favor the model underlying the BEST analysis. This comparison underscores the risks of overreliance on results from concatenation, and ignoring the properties of coalescence, especially in cases of recent, rapid radiations.     

An optimization-based sampling scheme for phylogenetic trees

Much modern work in phylogenetics depends on statistical sampling approaches to phylogeny construction to estimate probability distributions of possible trees for any given input data set. Our theoretical understanding of sampling approaches to phylogenetics remains far less developed than that for optimization approaches, however, particularly with regard to the number of sampling steps needed to produce accurate samples of tree partition functions. Despite the many advantages in principle of being able to sample trees from sophisticated probabilistic models, we have little theoretical basis for concluding that the prevailing sampling approaches do in fact yield accurate samples from those models within realistic numbers of steps. We propose a novel approach to phylogenetic sampling intended to be both efficient in practice and more amenable to theoretical analysis than the prevailing methods. The method depends on replacing the standard tree rearrangement moves with an alternative Markov model in which one solves a theoretically hard but practically tractable optimization problem on each step of sampling. The resulting method can be applied to a broad range of standard probability models, yielding practical algorithms for efficient sampling and rigorous proofs of accurate sampling for heated versions of some important special cases. We demonstrate the efficiency and versatility of the method by an analysis of uncertainty in tree inference over varying input sizes. In addition to providing a new practical method for phylogenetic sampling, the technique is likely to prove applicable to many similar problems involving sampling over combinatorial objects weighted by a likelihood model.     

Phylogenetic uncertainty revisited: Implications for ecological analyses

Ecologists and biogeographers usually rely on a single phylogenetic tree to study evolutionary processes that affect macroecological patterns. This approach ignores the fact that each phylogenetic tree is a hypothesis about the evolutionary history of a clade, and cannot be directly observed in nature. Also, trees often leave out many extant species, or include missing species as polytomies because of a lack of information on the relationship among taxa. Still, researchers usually do not quantify the effects of phylogenetic uncertainty in ecological analyses. We propose here a novel analytical strategy to maximize the use of incomplete phylogenetic information, while simultaneously accounting for several sources of phylogenetic uncertainty that may distort statistical inferences about evolutionary processes. We illustrate the approach using a clade‐wide analysis of the hummingbirds, evaluating how different sources of uncertainty affect several phylogenetic comparative analyses of trait evolution and biogeographic patterns. Although no statistical approximation can fully substitute for a complete and robust phylogeny, the method we describe and illustrate enables researchers to broaden the number of clades for which studies informed by evolutionary relationships are possible, while allowing the estimation and control of statistical error that arises from phylogenetic uncertainty. Software tools to carry out the necessary computations are offered.     

Fair-balance paradox, star-tree paradox, and Bayesian phylogenetics

The star-tree paradox refers to the conjecture that the posterior probabilities for the three unrooted trees for four species (or the three rooted trees for three species if the molecular clock is assumed) do not approach 1/3 when the data are generated using the star tree and when the amount of data approaches infinity. It reflects the more general phenomenon of high and presumably spurious posterior probabilities for trees or clades produced by the Bayesian method of phylogenetic reconstruction, and it is perceived to be a manifestation of the deeper problem of the extreme sensitivity of Bayesian model selection to the prior on parameters. Analysis of the star-tree paradox has been hampered by the intractability of the integrals involved. In this article, I use Laplacian expansion to approximate the posterior probabilities for the three rooted trees for three species using binary characters evolving at a constant rate. The approximation enables calculation of posterior tree probabilities for arbitrarily large data sets. Both theoretical analysis of the analogous fair-coin and fair-balance problems and computer simulation for the tree problem confirmed the existence of the star-tree paradox. When the data size n --> infinity, the posterior tree probabilities do not converge to 1/3 each, but they vary among data sets according to a statistical distribution. This distribution is characterized. Two strategies for resolving the star-tree paradox are explored: (1) a nonzero prior probability for the degenerate star tree and (2) an increasingly informative prior forcing the internal branch length toward zero. Both appear to be effective in resolving the paradox, but the latter is simpler to implement. The posterior tree probabilities are found to be very sensitive to the prior.     

Euclidean nature of phylogenetic distance matrices

Phylogenies are fundamental to comparative biology as they help to identify independent events on which statistical tests rely. Two groups of phylogenetic comparative methods (PCMs) can be distinguished: those that take phylogenies into account by introducing explicit models of evolution and those that only consider phylogenies as a statistical constraint and aim at partitioning trait values into a phylogenetic component (phylogenetic inertia) and one or multiple specific components related to adaptive evolution. The way phylogenetic information is incorporated into the PCMs depends on the method used. For the first group of methods, phylogenies are converted into variance-covariance matrices of traits following a given model of evolution such as Brownian motion (BM). For the second group of methods, phylogenies are converted into distance matrices that are subsequently transformed into Euclidean distances to perform principal coordinate analyses. Here, we show that simply taking the elementwise square root of a distance matrix extracted from a phylogenetic tree ensures having a Euclidean distance matrix. This is true for any type of distances between species (patristic or nodal) and also for trees harboring multifurcating nodes. Moreover, we illustrate that this simple transformation using the square root imposes less geometric distortion than more complex transformations classically used in the literature such as the Cailliez method. Given the Euclidean nature of the elementwise square root of phylogenetic distance matrices, the positive semidefinitiveness of the phylogenetic variance-covariance matrix of a trait following a BM model, or related models of trait evolution, can be established. In that way, we build a bridge between the two groups of statistical methods widely used in comparative analysis. These results should be of great interest for ecologists and evolutionary biologists performing statistical analyses incorporating phylogenies.     

Evolutionarily distinctive species often capture more phylogenetic diversity than expected

Evolutionary distinctiveness measures of how evolutionarily isolated a species is relative to other members of its clade. Recently, distinctiveness metrics that explicitly incorporate time have been proposed for conservation prioritization. However, we found that such measures differ qualitatively in how well they capture the total amount of evolution (termed phylogenetic diversity, or PD) represented by a set of species. We used simulation and simple graph theory to explore this relationship with reference to phylogenetic tree shape. Overall, the distinctiveness measures capture more PD on more unbalanced trees and on trees with many splits near the present. The rank order of performance was robust across tree shapes, with apportioning measures performing best and node-based measures performing worst. A sample of 50 ultrametric trees from the literature showed the same patterns. Taken together, this suggests that distinctiveness metrics may be a useful addition to other measures of value for conservation prioritization of species. The simplest measure, the age of a species, performed surprisingly well, suggesting that new measures that focus on tree shape near the tips may provide a transparent alternative to more complicated full-tree approaches.     

Fels-Rand: an Xlisp-Stat program for the comparative analysis of data under phylogenetic uncertainty

MOTIVATION: Currently available programs for the comparative analysis of phylogenetic data do not perform optimally when the phylogeny is not completely specified (i.e. the phylogeny contains polytomies). Recent literature suggests that a better way to analyse the data would be to create random trees from the known phylogeny that are fully-resolved but consistent with the known tree. A computer program is presented, Fels-Rand, that performs such analyses. A randomisation procedure is used to generate trees that are fully resolved but whose structure is consistent with the original tree. Statistics are then calculated on a large number of these randomly-generated trees. Fels-Rand uses the object-oriented features of Xlisp-Stat to manipulate internal tree representations. Xlisp-Stat's dynamic graphing features are used to provide heuristic tools to aid in analysis, particularly outlier analysis. The usefulness of Xlisp-Stat as a system for phylogenetic computation is discussed. AVAILABILITY: Available from the author or at http://www.uq.edu.au/~ansblomb/Fels-Rand.sit.hqx. Xlisp-Stat is available from http://stat.umn.edu/~luke/xls/xlsinfo/xlsinfo.html. CONTACT: s.blomberg@abdn.ac.uk     

Computational methods for Gene Orthology inference

Accurate inference of orthologous genes is a pre-requisite for most comparative genomics studies, and is also important for functional annotation of new genomes. Identification of orthologous gene sets typically involves phylogenetic tree analysis, heuristic algorithms based on sequence conservation, synteny analysis, or some combination of these approaches. The most direct tree-based methods typically rely on the comparison of an individual gene tree with a species tree. Once the two trees are accurately constructed, orthologs are straightforwardly identified by the definition of orthology as those homologs that are related by speciation, rather than gene duplication, at their most recent point of origin. Although ideal for the purpose of orthology identification in principle, phylogenetic trees are computationally expensive to construct for large numbers of genes and genomes, and they often contain errors, especially at large evolutionary distances. Moreover, in many organisms, in particular prokaryotes and viruses, evolution does not appear to have followed a simple 'tree-like' mode, which makes conventional tree reconciliation inapplicable. Other, heuristic methods identify probable orthologs as the closest homologous pairs or groups of genes in a set of organisms. These approaches are faster and easier to automate than tree-based methods, with efficient implementations provided by graph-theoretical algorithms enabling comparisons of thousands of genomes. Comparisons of these two approaches show that, despite conceptual differences, they produce similar sets of orthologs, especially at short evolutionary distances. Synteny also can aid in identification of orthologs. Often, tree-based, sequence similarity- and synteny-based approaches can be combined into flexible hybrid methods.     

The probability of a gene tree topology within a phylogenetic network with applications to hybridization detection

Gene tree topologies have proven a powerful data source for various tasks, including species tree inference and species delimitation. Consequently, methods for computing probabilities of gene trees within species trees have been developed and widely used in probabilistic inference frameworks. All these methods assume an underlying multispecies coalescent model. However, when reticulate evolutionary events such as hybridization occur, these methods are inadequate, as they do not account for such events. Methods that account for both hybridization and deep coalescence in computing the probability of a gene tree topology currently exist for very limited cases. However, no such methods exist for general cases, owing primarily to the fact that it is currently unknown how to compute the probability of a gene tree topology within the branches of a phylogenetic network. Here we present a novel method for computing the probability of gene tree topologies on phylogenetic networks and demonstrate its application to the inference of hybridization in the presence of incomplete lineage sorting. We reanalyze a Saccharomyces species data set for which multiple analyses had converged on a species tree candidate. Using our method, though, we show that an evolutionary hypothesis involving hybridization in this group has better support than one of strict divergence. A similar reanalysis on a group of three Drosophila species shows that the data is consistent with hybridization. Further, using extensive simulation studies, we demonstrate the power of gene tree topologies at obtaining accurate estimates of branch lengths and hybridization probabilities of a given phylogenetic network. Finally, we discuss identifiability issues with detecting hybridization, particularly in cases that involve extinction or incomplete sampling of taxa.     

Encoding phylogenetic trees in terms of weighted quartets

One of the main problems in phylogenetics is to develop systematic methods for constructing evolutionary or phylogenetic trees. For a set of species X, an edge-weighted phylogenetic X-tree or phylogenetic tree is a (graph theoretical) tree with leaf set X and no degree 2 vertices, together with a map assigning a non-negative length to each edge of the tree. Within phylogenetics, several methods have been proposed for constructing such trees that work by trying to piece together quartet trees on X, i.e. phylogenetic trees each having four leaves in X. Hence, it is of interest to characterise when a collection of quartet trees corresponds to a (unique) phylogenetic tree. Recently, Dress and Erdös provided such a characterisation for binary phylogenetic trees, that is, phylogenetic trees all of whose internal vertices have degree 3. Here we provide a new characterisation for arbitrary phylogenetic trees.     

A chain is no stronger than its weakest link: double decay analysis of phylogenetic hypotheses

In decay analyses the support for a particular split in most-parsimonious trees is its decay index, that is, the extra steps required of the shortest trees that do not include the split. By focusing solely on the support for splits, traditional decay analysis may provide an incomplete and potentially misleading summary of the support for phylogenetic relationships common to the most-parsimonious tree or trees. Here, we introduce double decay analysis, a new approach to assessing support for phylogenetic relationships. Double decay analysis is the determination of the decay indices of all n-taxon statements/partitions common to the most-parsimonious tree. The results of double decay analyses are presented in a partition table, but various approaches to graphical representation of the results, including the use of reduced consensus support trees, are also discussed. Double decay analysis provides a more comprehensive summary and facilitates a better understanding of the strengths and weaknesses of complex phylogenetic hypotheses than does traditional decay analysis. The limitations of traditional decay analyses and the utility of double decay analyses are illustrated with both contrived data and real data for sauropod dinosaurs.