Representing and extending ensembles of parsimonious evolutionary histories with a directed acyclic graph.

In many situations, it would be useful to know not just the best phylogenetic tree for a given data set, but the collection of high-quality trees. This goal is typically addressed using Bayesian techniques, however, current Bayesian methods do not scale to large data sets. Furthermore, for large data sets with relatively low signal one cannot even store every good tree individually, especially when the trees are required to be bifurcating. In this paper, we develop a novel object called the "history subpartition directed acyclic graph" (or "history sDAG" for short) that compactly represents an ensemble of trees with labels (e.g. ancestral sequences) mapped onto the internal nodes. The history sDAG can be built efficiently and can also be efficiently trimmed to only represent maximally parsimonious trees. We show that the history sDAG allows us to find many additional equally parsimonious trees, extending combinatorially beyond the ensemble used to construct it. We argue that this object could be useful as the "skeleton" of a more complete uncertainty quantification.

Maximum parsimony reconciliation in the DTLOR model.

BACKGROUND: Analyses of microbial evolution often use reconciliation methods. However, the standard duplication-transfer-loss (DTL) model does not account for the fact that species trees are often not fully sampled and thus, from the perspective of reconciliation, a gene family may enter the species tree from the outside. Moreover, within the genome, genes are often rearranged, causing them to move to new syntenic regions. RESULTS: We extend the DTL model to account for two events that commonly arise in the evolution of microbes: origin of a gene from outside the sampled species tree and rearrangement of gene syntenic regions. We describe an efficient algorithm for maximum parsimony reconciliation in this new DTLOR model and then show how it can be extended to account for non-binary gene trees to handle uncertainty in gene tree topologies. Finally, we describe preliminary experimental results from the integration of our algorithm into the existing xenoGI tool for reconstructing the histories of genomic islands in closely related bacteria. CONCLUSIONS: Reconciliation in the DTLOR model can offer new insights into the evolution of microbes that is not currently possible under the DTL model.

Assessing topological congruence among concatenation-based phylogenomic approaches in empirical datasets.

Assessing the effect of methodological decisions on the resulting hypotheses is critical in phylogenetics. Recent studies have focused on evaluating how model selection, orthology definition and confounding factors affect phylogenomic results. Here, we compare the results of three concatenated phylogenetic methods (Maximum Likelihood, ML; Bayesian Inference, BI; Maximum Parsimony, MP) in 157 empirical phylogenomic datasets. The resulting trees were very similar, with 96.7% of all nodes shared between BI and ML (90.6% for ML-MP and 89.1% for BI-MP). Differing nodes were predominantly those of lower support. The main conclusions of most of the studies agreed for the three phylogenetic methods and the discordance involved nodes considered as recalcitrant problems in systematics. The differences between methods were proportionally larger in datasets that analyze the relationships at higher taxonomic levels (particularly phyla and kingdoms), and independent of the number of characters included in the datasets. Note: a spanish version of this article is available in the Supplementary material (Supplementary material online).

Comparison of Different Reweighting Approaches for the Calculation of Conformational Variability of Macromolecules from Molecular Simulations.

Conformational variability and heterogeneity are crucial determinants of the function of biological macromolecules. The possibility of accessing this information experimentally suffers from severe under-determination of the problem, since there are a few experimental observables to be accounted for by a (potentially) infinite number of available conformational states. Several computational methods have been proposed over the years in order to circumvent this theoretically insurmountable obstacle. A large share of these strategies is based on reweighting an initial conformational ensemble which arises from, for example, molecular simulations of different qualities and levels of theory. In this work, we compare the outcome of three reweighting approaches based on radically different views of the conformational heterogeneity problem, namely Maximum Entropy, Maximum Parsimony and Maximum Occurrence, and we do so using the same experimental data. In this comparison we find both expected as well as unexpected similarities.

A Third Strike Against Perfect Phylogeny.

Perfect phylogenies are fundamental in the study of evolutionary trees because they capture the situation when each evolutionary trait emerges only once in history; if such events are believed to be rare, then by Occam's Razor such parsimonious trees are preferable as a hypothesis of evolution. A classical result states that 2-state characters permit a perfect phylogeny precisely if each subset of 2 characters permits one. More recently, it was shown that for 3-state characters the same property holds but for size-3 subsets. A long-standing open problem asked whether such a constant exists for each number of states. More precisely, it has been conjectured that for any fixed number of states $r$ there exists a constant $f(r)$ such that a set of $r$-state characters $C$ has a perfect phylogeny if and only if every subset of at most $f(r)$ characters has a perfect phylogeny. Informally, the conjecture states that checking fixed-size subsets of characters is enough to correctly determine whether input data permits a perfect phylogeny, irrespective of the number of characters in the input. In this article, we show that this conjecture is false. In particular, we show that for any constant $t$, there exists a set $C$ of $8$-state characters such that $C$ has no perfect phylogeny, but there exists a perfect phylogeny for every subset of at most $t$ characters. Moreover, there already exists a perfect phylogeny when ignoring just one of the characters, independent of which character you ignore. This negative result complements the two negative results ("strikes") of Bodlaender et al. (1992,2000). We reflect on the consequences of this third strike, pointing out that while it does close off some routes for efficient algorithm development, many others remain open.

Most Parsimonious Likelihood Exhibits Multiple Optima for Compatible Characters.

Maximum likelihood estimators are a popular method for scoring phylogenetic trees to best explain the evolutionary histories of biomolecular sequences. In 1994, Steel showed that, given an incompatible set of binary characters and a fixed tree topology, there exist multiple sets of branch lengths that are optima of the maximum average likelihood estimator. Since parsimony techniques-another popular method of scoring evolutionary trees-tend to exhibit favorable behavior on data compatible with the tree, Steel asked if the same is true for likelihood estimators, or if multiple optima can occur for compatible sequences. We show that, despite exhibiting behavior similar to parsimony, multiple local optima can occur for compatible characters for the most parsimonious likelihood estimator. We caution that thorough understanding of likelihood criteria is necessary before they are used to analyze biological data.

An efficient exact algorithm for computing all pairwise distances between reconciliations in the duplication-transfer-loss model.

BACKGROUND: Maximum parsimony reconciliation in the duplication-transfer-loss model is widely used in studying the evolutionary histories of genes and species and in studying coevolution of parasites and their hosts and pairs of symbionts. While efficient algorithms are known for finding maximum parsimony reconciliations, the number of reconciliations can grow exponentially in the size of the trees. An understanding of the space of maximum parsimony reconciliations is necessary to determine whether a single reconciliation can adequately represent the space or whether multiple representative reconciliations are needed. RESULTS: We show that for any instance of the reconciliation problem, the distribution of pairwise distances can be computed exactly by an efficient polynomial-time algorithm with respect to several different distance metrics. We describe the algorithm, analyze its asymptotic worst-case running time, and demonstrate its utility and viability on a large biological dataset. CONCLUSIONS: This result provides new insights into the structure of the space of maximum parsimony reconciliations. These insights are likely to be useful in the wide range of applications that employ reconciliation methods.

Hierarchical clustering of maximum parsimony reconciliations.

BACKGROUND: Maximum parsimony reconciliation in the duplication-transfer-loss model is a widely-used method for analyzing the evolutionary histories of pairs of entities such as hosts and parasites, symbiont species, and species and genes. While efficient algorithms are known for finding maximum parsimony reconciliations, the number of such reconciliations can be exponential in the size of the trees. Since these reconciliations can differ substantially from one another, making inferences from any one reconciliation may lead to conclusions that are not supported, or may even be contradicted, by other maximum parsimony reconciliations. Therefore, there is a need to find small sets of best representative reconciliations when the space of solutions is large and diverse. RESULTS: We provide a general framework for hierarchical clustering the space of maximum parsimony reconciliations. We demonstrate this framework for two specific linkage criteria, one that seeks to maximize the average support of the events found in the reconciliations in each cluster and the other that seeks to minimize the distance between reconciliations in each cluster. We analyze the asymptotic worst-case running times and provide experimental results that demonstrate the viability and utility of this approach. CONCLUSIONS: The hierarchical clustering algorithm method proposed here provides a new approach to find a set of representative reconciliations in the potentially vast and diverse space of maximum parsimony reconciliations.

On the uniqueness of the maximum parsimony tree for data with up to two substitutions: An extension of the classic Buneman theorem in phylogenetics.

One of the main aims of phylogenetics is the reconstruction of the correct evolutionary tree when data concerning the underlying species set are given. These data typically come in the form of DNA, RNA or protein alignments, which consist of various characters (also often referred to as sites). Often, however, tree reconstruction methods based on criteria like maximum parsimony may fail to provide a unique tree for a given dataset, or, even worse, reconstruct the 'wrong' tree (i.e. a tree that differs from the one that generated the data). On the other hand it has long been known that if the alignment consists of all the characters that correspond to edges of a particular tree, i.e. they all require exactly k=1 substitution to be realized on that tree, then this tree will be recovered by maximum parsimony methods. This is based on Buneman's theorem in mathematical phylogenetics. It is the goal of the present manuscript to extend this classic result as follows: We prove that if an alignment consists of all characters that require exactly k=2 substitutions on a particular tree, this tree will always be the unique maximum parsimony tree (and we also show that this can be generalized to characters which require at most k=2 substitutions). In particular, this also proves a conjecture based on a recently published observation by Goloboff et al. affirmatively for the special case of k=2.

Statistical Inconsistency of Maximum Parsimony for k-Tuple-Site Data.

One of the main aims of phylogenetics is to reconstruct the "Tree of Life." In this respect, different methods and criteria are used to analyze DNA sequences of different species and to compare them in order to derive the evolutionary relationships of these species. Maximum parsimony is one such criterion for tree reconstruction, and it is the one which we will use in this paper. However, it is well known that tree reconstruction methods can lead to wrong relationship estimates. One typical problem of maximum parsimony is long branch attraction, which can lead to statistical inconsistency. In this work, we will consider a blockwise approach to alignment analysis, namely the so-called k-tuple analyses. For four taxa, it has already been shown that k-tuple-based analyses are statistically inconsistent if and only if the standard character-based (site-based) analyses are statistically inconsistent. So, in the four-taxon case, going from individual sites to k-tuples does not lead to any improvement. However, real biological analyses often consider more than only four taxa. Therefore, we analyze the case of five taxa for 2- and 3-tuple-site data and consider alphabets with two and four elements. We show that the equivalence of single-site data and k-tuple-site data then no longer holds. Even so, we can show that maximum parsimony is statistically inconsistent for k-tuple-site data and five taxa.

Quantifying the accuracy of ancestral state prediction in a phylogenetic tree under maximum parsimony.

In phylogenetic studies, biologists often wish to estimate the ancestral discrete character state at an interior vertex v of an evolutionary tree T from the states that are observed at the leaves of the tree. A simple and fast estimation method-maximum parsimony-takes the ancestral state at v to be any state that minimises the number of state changes in T required to explain its evolution on T. In this paper, we investigate the reconstruction accuracy of this estimation method further, under a simple symmetric model of state change, and obtain a number of new results, both for 2-state characters, and r-state characters ([Formula: see text]). Our results rely on establishing new identities and inequalities, based on a coupling argument that involves a simpler 'coin toss' approach to ancestral state reconstruction.

Finding a most parsimonious or likely tree in a network with respect to an alignment.

Phylogenetic networks are often constructed by merging multiple conflicting phylogenetic signals into a directed acyclic graph. It is interesting to explore whether a network constructed in this way induces biologically-relevant phylogenetic signals that were not present in the input. Here we show that, given a multiple alignment A for a set of taxa X and a rooted phylogenetic network N whose leaves are labelled by X, it is NP-hard to locate a most parsimonious phylogenetic tree displayed by N (with respect to A) even when the level of N-the maximum number of reticulation nodes within a biconnected component-is 1 and A contains only 2 distinct states. (If, additionally, gaps are allowed the problem becomes APX-hard.) We also show that under the same conditions, and assuming a simple binary symmetric model of character evolution, finding a most likely tree displayed by the network is NP-hard. These negative results contrast with earlier work on parsimony in which it is shown that if A consists of a single column the problem is fixed parameter tractable in the level. We conclude with a discussion of why, despite the NP-hardness, both the parsimony and likelihood problem can likely be well-solved in practice.

MPBoot: fast phylogenetic maximum parsimony tree inference and bootstrap approximation.

BACKGROUND: The nonparametric bootstrap is widely used to measure the branch support of phylogenetic trees. However, bootstrapping is computationally expensive and remains a bottleneck in phylogenetic analyses. Recently, an ultrafast bootstrap approximation (UFBoot) approach was proposed for maximum likelihood analyses. However, such an approach is still missing for maximum parsimony. RESULTS: To close this gap we present MPBoot, an adaptation and extension of UFBoot to compute branch supports under the maximum parsimony principle. MPBoot works for both uniform and non-uniform cost matrices. Our analyses on biological DNA and protein showed that under uniform cost matrices, MPBoot runs on average 4.7 (DNA) to 7 times (protein data) (range: 1.2-20.7) faster than the standard parsimony bootstrap implemented in PAUP*; but 1.6 (DNA) to 4.1 times (protein data) slower than the standard bootstrap with a fast search routine in TNT (fast-TNT). However, for non-uniform cost matrices MPBoot is 5 (DNA) to 13 times (protein data) (range:0.3-63.9) faster than fast-TNT. We note that MPBoot achieves better scores more frequently than PAUP* and fast-TNT. However, this effect is less pronounced if an intensive but slower search in TNT is invoked. Moreover, experiments on large-scale simulated data show that while both PAUP* and TNT bootstrap estimates are too conservative, MPBoot bootstrap estimates appear more unbiased. CONCLUSIONS: MPBoot provides an efficient alternative to the standard maximum parsimony bootstrap procedure. It shows favorable performance in terms of run time, the capability of finding a maximum parsimony tree, and high bootstrap accuracy on simulated as well as empirical data sets. MPBoot is easy-to-use, open-source and available at http://www.cibiv.at/software/mpboot .

Review Paper: The Shape of Phylogenetic Treespace.

Trees are a canonical structure for representing evolutionary histories. Many popular criteria used to infer optimal trees are computationally hard, and the number of possible tree shapes grows super-exponentially in the number of taxa. The underlying structure of the spaces of trees yields rich insights that can improve the search for optimal trees, both in accuracy and in running time, and the analysis and visualization of results. We review the past work on analyzing and comparing trees by their shape as well as recent work that incorporates trees with weighted branch lengths.

On the Accuracy of Ancestral Sequence Reconstruction for Ultrametric Trees with Parsimony.

We examine a mathematical question concerning the reconstruction accuracy of the Fitch algorithm for reconstructing the ancestral sequence of the most recent common ancestor given a phylogenetic tree and sequence data for all taxa under consideration. In particular, for the symmetric four-state substitution model which is also known as Jukes-Cantor model, we answer affirmatively a conjecture of Li, Steel and Zhang which states that for any ultrametric phylogenetic tree and a symmetric model, the Fitch parsimony method using all terminal taxa is more accurate, or at least as accurate, for ancestral state reconstruction than using any particular terminal taxon or any particular pair of taxa. This conjecture had so far only been answered for two-state data by Fischer and Thatte. Here, we focus on answering the biologically more relevant case with four states, which corresponds to ancestral sequence reconstruction from DNA or RNA data.

Varestrongylus (Nematoda: Protostrongylidae), lungworms of ungulates: a phylogenetic framework based on comparative morphology.

Varestrongylus Bhalerao, 1932 comprises ten valid lungworm species infecting wild and domestic ungulates from Eurasia and North America. Here, we present a phylogenetic hypothesis for the genus based on morphological characters in a broader context for the family Protostrongylidae and discuss species relationships and aspects of character evolution. Phylogenetic analysis of 25 structural attributes, including binary and multistate characters, among the 10 species of Varestrongylus resulted in one fully resolved most parsimonious tree (61 steps; consistency index = 0.672, retention index = 0.722, and consistency index excluding uninformative characters = 0.667). Varestrongylus forms a monophyletic clade and is the sister of Pneumostrongylus, supporting recognition of the subfamily Varestrongylinae. Monophyly for Varestrongylus is diagnosed by six unequivocal synapomorphies, all associated with structural characters of the copulatory system of males. Varestrongylus pneumonicus is basal, and sister to all other species within the genus, which form two subclades. The subclade I contains V. sagittatus + V. tuvae and V. qinghaiensis + V. longispiculatus. Subclade II contains V. alpenae, V. capricola, V. capreoli, and V. eleguneniensis + V. alces. Both subclades are diagnosed by two unambiguous synapomorphies. Highlighted is the continuing importance of phylogenetic assessments based on comparative morphology as a foundation to explore the structure of the biosphere across space and time.

Convex recoloring as an evolutionary marker.

With the availability of enormous quantities of genetic data it has become common to construct very accurate trees describing the evolutionary history of the species under study, as well as every single gene of these species. These trees allow us to examine the evolutionary compliance of given markers (characters). A marker compliant with the history of the species investigated, has undergone mutations along the species tree branches, such that every subtree of that tree exhibits a different state. Convex recoloring (CR) uses combinatorial representation to measure the adequacy of a taxonomic classifier to a given tree. Despite its biological origins, research on CR has been almost exclusively dedicated to mathematical properties of the problem, or variants of it with little, if any, relationship to taxonomy. In this work we return to the origins of CR. We put CR in a statistical framework and introduce and learn the notion of the statistical significance of a character. We apply this measure to two data sets - Passerine birds and prokaryotes, and four examples. These examples demonstrate various applications of CR, from evolutionary relatedness, through lateral evolution, to supertree construction. The above study was done with a new software that we provide, containing algorithmic improvement with a graphical output of a (optimally) recolored tree. AVAILABILITY: A code implementing the features and a README is available at http://research.haifa.ac.il/ssagi/software/convexrecoloring.zip.

Cases in which ancestral maximum likelihood will be confusingly misleading.

Ancestral maximum likelihood (AML) is a phylogenetic tree reconstruction criteria that "lies between" maximum parsimony (MP) and maximum likelihood (ML). ML has long been known to be statistically consistent. On the other hand, Felsenstein (1978) showed that MP is statistically inconsistent, and even positively misleading: There are cases where the parsimony criteria, applied to data generated according to one tree topology, will be optimized on a different tree topology. The question of weather AML is statistically consistent or not has been open for a long time. Mossel et al. (2009) have shown that AML can "shrink" short tree edges, resulting in a star tree with no internal resolution, which yields a better AML score than the original (resolved) model. This result implies that AML is statistically inconsistent, but not that it is positively misleading, because the star tree is compatible with any other topology. We show that AML is confusingly misleading: For some simple, four taxa (resolved) tree, the ancestral likelihood optimization criteria is maximized on an incorrect (resolved) tree topology, as well as on a star tree (both with specific edge lengths), while the tree with the original, correct topology, has strictly lower ancestral likelihood. Interestingly, the two short edges in the incorrect, resolved tree topology are of length zero, and are not adjacent, so this resolved tree is in fact a simple path. While for MP, the underlying phenomenon can be described as long edge attraction, it turns out that here we have long edge repulsion.

Ancestral Sequence Reconstruction with Maximum Parsimony.

One of the main aims in phylogenetics is the estimation of ancestral sequences based on present-day data like, for instance, DNA alignments. One way to estimate the data of the last common ancestor of a given set of species is to first reconstruct a phylogenetic tree with some tree inference method and then to use some method of ancestral state inference based on that tree. One of the best-known methods both for tree inference and for ancestral sequence inference is Maximum Parsimony (MP). In this manuscript, we focus on this method and on ancestral state inference for fully bifurcating trees. In particular, we investigate a conjecture published by Charleston and Steel in 1995 concerning the number of species which need to have a particular state, say a, at a particular site in order for MP to unambiguously return a as an estimate for the state of the last common ancestor. We prove the conjecture for all even numbers of character states, which is the most relevant case in biology. We also show that the conjecture does not hold in general for odd numbers of character states, but also present some positive results for this case.

Time-Dependent-Asymmetric-Linear-Parsimonious Ancestral State Reconstruction.

The time-dependent-asymmetric-linear parsimony is an ancestral state reconstruction method which extends the standard linear parsimony (a.k.a. Wagner parsimony) approach by taking into account both branch lengths and asymmetric evolutionary costs for reconstructing quantitative characters (asymmetric costs amount to assuming an evolutionary trend toward the direction with the lowest cost). A formal study of the influence of the asymmetry parameter shows that the time-dependent-asymmetric-linear parsimony infers states which are all taken among the known states, except for some degenerate cases corresponding to special values of the asymmetry parameter. This remarkable property holds in particular for the Wagner parsimony. This study leads to a polynomial algorithm which determines, and provides a compact representation of, the parametric reconstruction of a phylogenetic tree, that is for all the unknown nodes, the set of all the possible reconstructed states associated with the asymmetry parameters leading to them. The time-dependent-asymmetric-linear parsimony is finally illustrated with the parametric reconstruction of the body size of cetaceans.