Performance of flip supertree construction with a heuristic algorithm

Supertree methods are used to assemble separate phylogenetic trees with shared taxa into larger trees (supertrees) in an effort to construct more comprehensive phylogenetic hypotheses. In spite of much recent interest in supertrees, there are still few methods for supertree construction. The flip supertree problem is an error correction approach that seeks to find a minimum number of changes (flips) to the matrix representation of the set of input trees to resolve their incompatibilities. A previous flip supertree algorithm was limited to finding exact solutions and was only feasible for small input trees. We developed a heuristic algorithm for the flip supertree problem suitable for much larger input trees. We used a series of 48- and 96-taxon simulations to compare supertrees constructed with the flip supertree heuristic algorithm with supertrees constructed using other approaches, including MinCut (MC), modified MC (MMC), and matrix representation with parsimony (MRP). Flip supertrees are generally far more accurate than supertrees constructed using MC or MMC algorithms and are at least as accurate as supertrees built with MRP. The flip supertree method is therefore a viable alternative to other supertree methods when the number of taxa is large.     

Novel versus unsupported clades: assessing the qualitative support for clades in MRP supertrees

Matrix representation with parsimony (MRP) supertree construction has been criticized because the supertree may specify clades that are contradicted by every source tree contributing to it. Such unsupported clades may also occur using other supertree methods; however, their incidence is largely unknown. In this study, I investigated the frequency of unsupported clades in both simulated and empirical MRP supertrees. Here, I propose a new index, QS, to quantify the qualitative support for a supertree and its clades among the set of source trees. Results show that unsupported clades are very rare in MRP supertrees, occurring most often when there are few source trees that all possess the same set of taxa. However, even under these conditions the frequency of unsupported clades was <0.2%. Unsupported clades were absent from both the Carnivora and Lagomorpha supertrees, reflecting the use of large numbers of source trees for both. The proposed QS indices are correlated broadly with another measure of quantitative clade support (bootstrap frequencies, as derived from resampling of the MRP matrix) but appear to be more sensitive. More importantly, they sample at the level of the source trees and thus, unlike the bootstrap, are suitable for summarizing the support of MRP supertree clades.     

Comparative performance of supertree algorithms in large data sets using the soapberry family (Sapindaceae) as a case study

For the last 2 decades, supertree reconstruction has been an active field of research and has seen the development of a large number of major algorithms. Because of the growing popularity of the supertree methods, it has become necessary to evaluate the performance of these algorithms to determine which are the best options (especially with regard to the supermatrix approach that is widely used). In this study, seven of the most commonly used supertree methods are investigated by using a large empirical data set (in terms of number of taxa and molecular markers) from the worldwide flowering plant family Sapindaceae. Supertree methods were evaluated using several criteria: similarity of the supertrees with the input trees, similarity between the supertrees and the total evidence tree, level of resolution of the supertree and computational time required by the algorithm. Additional analyses were also conducted on a reduced data set to test if the performance levels were affected by the heuristic searches rather than the algorithms themselves. Based on our results, two main groups of supertree methods were identified: on one hand, the matrix representation with parsimony (MRP), MinFlip, and MinCut methods performed well according to our criteria, whereas the average consensus, split fit, and most similar supertree methods showed a poorer performance or at least did not behave the same way as the total evidence tree. Results for the super distance matrix, that is, the most recent approach tested here, were promising with at least one derived method performing as well as MRP, MinFlip, and MinCut. The output of each method was only slightly improved when applied to the reduced data set, suggesting a correct behavior of the heuristic searches and a relatively low sensitivity of the algorithms to data set sizes and missing data. Results also showed that the MRP analyses could reach a high level of quality even when using a simple heuristic search strategy, with the exception of MRP with Purvis coding scheme and reversible parsimony. The future of supertrees lies in the implementation of a standardized heuristic search for all methods and the increase in computing power to handle large data sets. The latter would prove to be particularly useful for promising approaches such as the maximum quartet fit method that yet requires substantial computing power.     

Fast local search for unrooted Robinson-Foulds supertrees

A Robinson-Foulds (RF) supertree for a collection of input trees is a tree containing all the species in the input trees that is at minimum total RF distance to the input trees. Thus, an RF supertree is consistent with the maximum number of splits in the input trees. Constructing RF supertrees for rooted and unrooted data is NP-hard. Nevertheless, effective local search heuristics have been developed for the restricted case where the input trees and the supertree are rooted. We describe new heuristics, based on the Edge Contract and Refine (ECR) operation, that remove this restriction, thereby expanding the utility of RF supertrees. Our experimental results on simulated and empirical data sets show that our unrooted local search algorithms yield better supertrees than those obtained from MRP and rooted RF heuristics in terms of total RF distance to the input trees and, for simulated data, in terms of RF distance to the true tree.     

A New Genus of Rhynchonellid Brachiopod from the Lower Triassic of South China and Implications for Timing the Recovery of Brachiopoda After the End-Permian Mass Extinction

A new genus, Meishanorhynchia , is proposed based on new material from the Lower Triassic of the Meishan section, South China. It is of a late Griesbachian age based on both associated biozones (ammonoids and bivalves) and radiometric dates of the intercalated volcanic ash beds. Comparison with both Palaeozoic and Mesozoic–Cenozoic-related genera suggests that it may represent the first radiation of progenitor brachiopods in the aftermath of the end-Permian extinction. The lowest brachiopod horizon that contains the genus is estimated to be about 250.1 ± 0.3 Ma. This implies that the initial stage of recovery of Brachiopoda in the Early Triassic was probably about 1.3 ± 0.3 myr after the major pulse of the end-Permian mass extinction (dated as 251.4 ± 0.3 Ma). This is in agreement with Hallam's expectancy that biotic recovery typically begins within one million years or so of major mass extinctions, in contrast to current views on the end-Permian extinction event which propose that the recovery of most if not all biotic groups in the Early Triassic was severely delayed and only began about five million years after the end-Permian extinction.     

Semi-strict supertrees

A method to calculate semi‐strict supertrees is proposed. The semi‐strict supertrees are calculated by creating the matrix that represents all the groups in the source trees (as done in already existing techniques), and then finding the trees determined by the ultra‐clique. The ultra‐clique is defined as the set of characters where each possible subset is compatible with each possible subset from the entire matrix. Finding the ultra‐clique is computationally complex (since in most cases many of the characters have missing entries), but a heuristic method yields reliable results. When the trees have no conflict, or when there are only two trees, the method produces the exact result for any ordering of the input trees and any ordering of the groups within them; when there are more than two trees and they have conflict, a single ordering or sequence can create some spurious groups, but doing multiple sequences eliminates the spurious groups. The method uses only state set operations, and is thus easily implemented in computer programs. Unlike any existing type of supertree, semi‐strict supertrees display all the groups, and only those groups, that are implied by at least some combination of the input trees and contradicted by none. The idea that supertrees should take into account the number of occurences of a given group, so as to retain some groups even in the case of conflict, is discussed; it is argued that a conceptual equivalent of the majority rule consensus is not possible when the sets of taxa differ among trees. Also, when pruning taxa from a set of trees, the supertree can display groups that contradict the consensus for the entire trees, suggesting that supertrees for matrices with very dissimilar sets of taxa should be interpreted with caution. If (for any valid reason) the data cannot be combined in a single matrix, it is advisable that the taxon sets in the matrices be as similar as possible.     

The shape of supertrees to come: tree shape related properties of fourteen supertree methods

Using a simple example and simulations, we explore the impact of input tree shape upon a broad range of supertree methods. We find that input tree shape can affect how conflict is resolved by several supertree methods and that input tree shape effects may be substantial. Standard and irreversible matrix representation with parsimony (MRP), MinFlip, duplication-only Gene Tree Parsimony (GTP), and an implementation of the average consensus method have a tendency to resolve conflict in favor of relationships in unbalanced trees. Purvis MRP and the average dendrogram method appear to have an opposite tendency. Biases with respect to tree shape are correlated with objective functions that are based upon unusual asymmetric tree-to-tree distance or fit measures. Split, quartet, and triplet fit, most similar supertree, and MinCut methods (provided the latter are interpreted as Adams consensus-like supertrees) are not revealed to have any bias with respect to tree shape by our example, but whether this holds more generally is an open problem. Future development and evaluation of supertree methods should consider explicitly the undesirable biases and other properties that we highlight. In the meantime, use of a single, arbitrarily chosen supertree method is discouraged. Use of multiple methods and/or weighting schemes may allow practical assessment of the extent to which inferences from real data depend upon methodological biases with respect to input tree shape or size.     

Building supertrees: an empirical assessment using the grass family (Poaceae)

Large and comprehensive phylogenetic trees are desirable for studying macroevolutionary processes and for classification purposes. Such trees can be obtained in two different ways. Either the widest possible range of taxa can be sampled and used in a phylogenetic analysis to produce a "big tree," or preexisting topologies can be used to create a supertree. Although large multigene analyses are often favored, combinable data are not always available, and supertrees offer a suitable solution. The most commonly used method of supertree reconstruction, matrix representation with parsimony (MRP), is presented here. We used a combined data set for the Poaceae to (1) assess the differences between an approach that uses combined data and one that uses different MRP modifications based on the character partitions and (2) investigate the advantages and disadvantages of these modifications. Baum and Ragan and Purvis modifications gave similar results. Incorporating bootstrap support associated with pre-existing topologies improved Baum and Ragan modification and its similarity with a combined analysis. Finally, we used the supertree reconstruction approach on 55 published phylogenies to build one of most comprehensive phylogenetic trees published for the grass family including 403 taxa and discuss its strengths and weaknesses in relation to other published hypotheses.     

Towards a Supertree of Arthropoda: A Species-Level Supertree of the Spiny,Slipper and Coral Lobsters (Decapoda: Achelata)

While supertrees have been built for many vertebrate groups (notably birds, mammals and dinosaurs), invertebrates have attracted relatively little attention. The paucity of supertrees of arthropods is particularly surprising given their economic and ecological importance, as well as their overwhelming contribution to biodiversity. The absence of comprehensive archives of machine-readable source trees, coupled with the need for software implementing repeatable protocols for managing them, has undoubtedly impeded progress. Here we present a supertree of Achelata (spiny, slipper and coral lobsters) as a proof of concept, constructed using new supertree specific software (the Supertree Toolkit; STK) and following a published protocol. We also introduce a new resource for archiving and managing published source trees. Our supertree of Achelata is synthesised from morphological and molecular source trees, and represents the most complete species-level tree of the group to date. Our findings are consistent with recent taxonomic treatments, confirming the validity of just two families: Palinuridae and Scyllaridae; Synaxidae were resolved within Palinuridae. Monophyletic Silentes and Stridentes lineages are recovered within Palinuridae, and all sub-families within Scyllaridae are found to be monophyletic with the exception of Ibacinae. We demonstrate the feasibility of building larger supertrees of arthropods, with the ultimate objective of building a complete species-level phylogeny for the entire phylum using a divide and conquer strategy.     

The End-Permian mass extinction: What really happened and did it matter?

Marine communities of the Paleozoic differ markedly from those of the post-Paleozoic, a dichotomy long recognized as the most fundamental change between the Cambrian metazoan radiation and the present. The end-Permian mass extinction of about 54% of marine families eliminated many of the groups that dominated Paleozoic communities. Correlative changes occurred in terrestrial vertebrate and plant communities, but there is no clear evidence that these changes are related to the marine extinction. The marine extinction occurred during a period of physical change, and a variety of extinction mechanisms have been proposed, most related to a major Late Permian marine regression or to climatic changes. Unfortunately, the regression has made it difficult to gather data on the rate, timing and pattern of extinction, and the available data exclude only a few hypotheses. Thus the largest mass extinction, and the one with the greatest evolutionary importance, is also the most poorly understood.     

Problems with supertrees based on the subtree prune‐and‐regraft distance,with comments on majority rule supertrees

This paper examines a recent proposal to calculate supertrees by minimizing the sum of subtree prune‐and‐regraft distances to the input trees. The supertrees thus calculated may display groups present in a minority of the input trees but contradicted by the majority, or groups that are not supported by any input tree or combination of input trees. The proponents of the method themselves stated that these are serious problems of “matrix representation with parsimony”, but they can in fact occur in their own method. The majority rule supertrees, being explicitly clade‐based, cannot have these problems, and seem much more suited to retrieving common clades from a set of trees with different taxon sets. However, it is dubious that so‐called majority rule supertrees can always be interpreted as displaying those clades present (or compatible with) with a majority of the trees. The majority rule consensus is always a median tree, in terms of the Robinson–Foulds distances (i.e. it minimizes the sum of Robinson–Foulds distances to the input trees). In contrast, majority rule supertrees may not be median—different, contradictory trees may minimize Robinson–Foulds distances, while their strict consensus does not. If being “majority” results from being median in Robinson–Foulds distances, this means that in the supertree setting a “majority” is ambiguously defined, sometimes achievable only by mutually contradictory trees.     

Robinson-Foulds Supertrees

Background  

Supertree methods synthesize collections of small phylogenetic trees with incomplete taxon overlap into comprehensive trees, or supertrees, that include all taxa found in the input trees. Supertree methods based on the well established Robinson-Foulds (RF) distance have the potential to build supertrees that retain much information from the input trees. Specifically, the RF supertree problem seeks a binary supertree that minimizes the sum of the RF distances from the supertree to the input trees. Thus, an RF supertree is a supertree that is consistent with the largest number of clusters (or clades) from the input trees.     

Reconstructing the Fungal Tree of Life Using Phylogenomics and a Preliminary Investigation of the Distribution of Yeast Prion-Like Proteins in the Fungal Kingdom

We have used three independent phylogenomic approaches (concatenated alignments, single-, and multi-gene supertrees) to reconstruct the fungal tree of life (FTOL) using publicly available fungal genomes. This is the first time multi-gene families have been used in fungal supertree reconstruction and permits us to use up to 66% of the 1,001,217 genes in our fungal database. Our analyses show that different phylogenomic datasets derived from varying clustering criteria and alignment orientation do not have a major effect on phylogenomic supertree reconstruction. Overall the resultant phylogenomic trees are relatively congruent with one another and successfully recover the major fungal phyla, subphyla and classes. We find that where incongruences do occur, the inferences are usually poorly supported. Within the Ascomycota phylum, our phylogenies reconstruct monophyletic Saccharomycotina and Pezizomycotina subphyla clades and infer a sister group relationship between these to the exclusion of the Taphrinomycotina. Within the Pezizomycotina subphylum, all three phylogenies infer a sister group relationship between the Leotiomycetes and Sordariomycetes classes. However, there is conflict regarding the relationships with the Dothideomycetes and Eurotiomycetes classes. Within the Basidiomycota phylum, supertrees derived from single- and multi-gene families infer a sister group relationship between the Pucciniomycotina and Agaricomycotina subphyla while the concatenated phylogeny infers a poorly supported relationship between the Agaricomycotina and Ustilagomycotina. The reconstruction of a robust FTOL is important for future fungal comparative analyses. We illustrate this point by performing a preliminary investigation into the phyletic distribution of yeast prion-like proteins in the fungal kingdom.     

Minority rule supertrees? MRP,Compatibility, and Minimum Flip may display the least frequent groups

New examples are presented, showing that supertree methods such as matrix representation with parsimony, minimum flip trees, and compatibility analysis of the matrix representing the input trees, produce supertrees that cannot be interpreted as displaying the groups present in the majority of the input trees. These methods may produce a supertree displaying some groups present in the minority of the trees, and contradicted by the majority. Of the three methods, compatibility analysis is the least used, but it seems to be the one that differs the least from majority rule consensus. The three methods are similar in that they choose the supertree(s) that best fit the set of input trees (quantified as some measure of the fit to the matrix representation of the input trees); in the case of complete trees, it is argued that, for a supertree method to be equivalent to majority rule or frequency difference consensus, two necessary (but not sufficient) conditions must be met. First, the measure of fit between a supertree and an input tree must be symmetrical. Second, the fit for a character representing a group must be measured as absolute: either it fits or it does not fit. In the restricted case of complete and equally resolved input trees, compatibility analysis (unlike MRP and minimum flipping) fulfils these two conditions: it is symmetrical (i.e., as long as the trees have the same taxon sets and are equally resolved, the number of characters in the matrix representation of tree A that require homoplasy in tree B is always the same as the number of characters in the matrix representation of tree B that require homoplasy in tree A) and it measures fit as all‐or‐none. In the case of just two complete and equally resolved input trees, the two conditions (symmetry and absolute fit) are necessary and sufficient, which explains why the compatibility analysis of such trees behaves as majority consensus. With more than two such trees, these conditions are still necessary but no longer sufficient for the equivalence; in such cases, the compatibility supertree may differ significantly from the majority rule consensus, even when these conditions apply (as shown by example). MRP and minimum flipping are asymmetric and measure various degrees of fit for each character, which explains why they often behave very differently from majority rule procedures, and why they are very likely to have groups contradicted by each of the input trees, or groups supported by a minority of the input trees. © The Willi Hennig Society 2005.     

Battenizyga, a new Early Triassic gastropod genus with a discussion of the caenogastropod evolution at the Permian/Triassic boundary

Battenizyga, a new Early Triassic gastropod genus from the Moenkopi Formation of Utah, is described and the speciesAnoptychia eotriassica Batten & Stokes, 1986 is placed in it. The new genus has an axially ribbed planktonic larval shell and a teleoconch with an angulated periphery. This character combination is unknown from the Palaeozoic. Therefore,Battenizyga represents additional evidence that recovery from the end-Permian mass extinction was connected with a faunal turnover. Additionally, the extinction of diverse Palaeozoic groups of the Caenogastropoda in the Permian (e.g., the Pseudozygopleuridae) suggest a turnover. All caenogastropod genera that hold Early Triassic species, have post-Palaeozoic type species and most were not reported from the Palaeozoic. This corroborates the view that there was an intense faunal turnover within the Caenogastropoda.Battenizyga is probably a caenogastropod that is closely related to the superfamily Zygopleuroidea which is abundant in the late Palaeozoic and early Mesozoic.      

MRL and SuperFine+MRL: new supertree methods

Background

Supertree methods combine trees on subsets of the full taxon set together to produce a tree on the entire set of taxa. Of the many supertree methods, the most popular is MRP (Matrix Representation with Parsimony), a method that operates by first encoding the input set of source trees by a large matrix (the "MRP matrix") over {0,1, ?}, and then running maximum parsimony heuristics on the MRP matrix. Experimental studies evaluating MRP in comparison to other supertree methods have established that for large datasets, MRP generally produces trees of equal or greater accuracy than other methods, and can run on larger datasets. A recent development in supertree methods is SuperFine+MRP, a method that combines MRP with a divide-and-conquer approach, and produces more accurate trees in less time than MRP. In this paper we consider a new approach for supertree estimation, called MRL (Matrix Representation with Likelihood). MRL begins with the same MRP matrix, but then analyzes the MRP matrix using heuristics (such as RAxML) for 2-state Maximum Likelihood.

Results

We compared MRP and SuperFine+MRP with MRL and SuperFine+MRL on simulated and biological datasets. We examined the MRP and MRL scores of each method on a wide range of datasets, as well as the resulting topological accuracy of the trees. Our experimental results show that MRL, coupled with a very good ML heuristic such as RAxML, produced more accurate trees than MRP, and MRL scores were more strongly correlated with topological accuracy than MRP scores.

Conclusions

SuperFine+MRP, when based upon a good MP heuristic, such as TNT, produces among the best scores for both MRP and MRL, and is generally faster and more topologically accurate than other supertree methods we tested.     

PhySIC_IST: cleaning source trees to infer more informative supertrees

Background  

Supertree methods combine phylogenies with overlapping sets of taxa into a larger one. Topological conflicts frequently arise among source trees for methodological or biological reasons, such as long branch attraction, lateral gene transfers, gene duplication/loss or deep gene coalescence. When topological conflicts occur among source trees, liberal methods infer supertrees containing the most frequent alternative, while veto methods infer supertrees not contradicting any source tree, i.e. discard all conflicting resolutions. When the source trees host a significant number of topological conflicts or have a small taxon overlap, supertree methods of both kinds can propose poorly resolved, hence uninformative, supertrees.     

Survival patterns of macrobenthic marine assemblages during the end-Permian mass extinction in the western Tethys (Dolomites, Italy)

The ecological competition between brachiopods and bivalves is analysed by means of a quantitative palaeoecologic method applied on four assemblages located within a short stratigraphic interval, approximately 2 m thick, in the lower Tesero Member of the Werfen Formation (in the Southern Alps). The assemblages originate from the Tesero, Bulla and Sass de Putia sections. The analysed stratigraphic interval, uppermost Changhsingian in age, is located between the early and heaviest phase of the end-Permian mass extinction, which occurred across the Bellerophon/Werfen formational boundary (Event Boundary), and the Permian/Triassic boundary (Chronological Boundary), when nearly all the Permian stenotopic holdovers disappeared.These assemblages are characterised by small sized skeletons (“Lilliput effect”), which represent an adaptive survival strategy in stressed and harsh habitats resulting from the climatic and palaeoceanographic changes connected with the mass extinction. The Tesero assemblages are dominated by rhynchonelliform brachiopod Orbicoelia (bed CNT10) or Streptorhynchus (bed CNT11A), which were mostly attached at the top of shallow microbialitic mounds. These assemblages are again dominated by Permian stenotopic taxa and show a Palaeozoic structure. The Tesero habitat, which again permitted the survival of brachiopods, represented one of the last refuges in the western Tethys. On the contrary, the Bulla (BU9-10) and Sass de Putia (wPK13A) assemblages are bivalve-dominated, and thus show an ecologic structure typical of Early Triassic post-extinction marine benthic communities or Palaeozoic stressed marine communities. The bivalve-dominated assemblages proliferated in prevailing muddy siliciclastic substrates, with brief episodes of microbial algal growth. The most important environmental limiting factors and leading causes of end-Permian mass extinction are discussed in terms of palaeoautecologic and palaeosynecologic analysis.The different taxonomic composition and ecologic structure of the assemblages is related to palaeogeography, including water depth and connections with the open sea. The brachiopod-dominated assemblage, exclusive of the Tesero section, proliferated in microbial carbonate habitats in near-shore environments. The bivalve-dominated assemblages, which were more widespread than the brachiopod assemblages in the Dolomites and also occurred in other western Tethys localities, occur in more open and deeper marine environments. In the western Tethys margins, the local distribution of mixed faunas suggests that the extinction of Permian stenotopic taxa was caused by the onset of poisonous water on the shelves originating from deep marine environments.This extinction pattern appears to be a regional phenomenon and does not seem be applicable on a global scale. The extinction events were controlled by a complex network of interactive factors and the survival of faunal elements was probably stochastic.     

Increasing data transparency and estimating phylogenetic uncertainty in supertrees: Approaches using nonparametric bootstrapping

The estimation of ever larger phylogenies requires consideration of alternative inference strategies, including divide-and-conquer approaches that decompose the global inference problem to a set of smaller, more manageable component problems. A prominent locus of research in this area is the development of supertree methods, which estimate a composite tree by combining a set of partially overlapping component topologies. Although promising, the use of component tree topologies as the primary data dissociates supertrees from complexities within the underling character data and complicates the evaluation of phylogenetic uncertainty. We address these issues by exploring three approaches that variously incorporate nonparametric bootstrapping into a common supertree estimation algorithm (matrix representation with parsimony, although any algorithm might be used), including bootstrap-weighting, source-tree bootstrapping, and hierarchical bootstrapping. We illustrate these procedures by means of hypothetical and empirical examples. Our preliminary experiments suggest that these methods have the potential to improve the correspondence of supertree estimates to those derived from simultaneous analysis of the combined data and to allow uncertainty in supertree topologies to be quantified. The ability to increase the transparency of supertrees to the underlying character data has several practical implications and sheds new light on an old debate. These methods have been implemented in the freely available program, tREeBOOT.