An optimal algorithm for computing all subtree repeats in trees

ArXiv, 2021

The problem of finding a common refinement of a set of rooted trees with common leaf set L appears naturally in mathematical phylogenetics whenever poorly resolved information on the same taxa from different sources is to be reconciled. This constitutes a special case of the wellstudied supertree problem, where the leaf sets of the input trees may differ. Algorithms that solve the rooted tree compatibility problem are of course applicable to this special case. However, they require sophisticated auxiliary data structures and have a running time of at least O(k|L| log(k|L|)) for k input trees. Here, we show that the problem can be solved in O(k|L|) time using a simple bottom-up algorithm called LinCR. An implementation of LinCR in Python is freely available at https://github.com/david-schaller/tralda.

Zeitschrift für Naturforschung C, 1979

An algorithm for phylogenetic trees’ construction is analyzed.

SIAM Journal on Discrete Mathematics, 2016

Manuscript distributed under the terms of the GNU Free Documentation License. 31 pp., 2005

1. Introduction 2. Implicit enumeration for nt terminals (nt >=2) 3. Find optimal binary trees using branch and bound, for nt terminals (nt >=2) 4. Build a tree by stepwise addition (n terminals, n >= 3) 5. Branch swapping 5.a. Introduction 5.b. A tree search strategy using SPR rearrangements of given trees 5.c. A tree search strategy using TBR rearrangements of given trees 6. Ratcheting 7. Tree drifting 8. Tree fusing 9. Static approximation 10. An integrated approach 11. Some quick comments on time complexity References

PLoS Computational Biology, 2013

Phylogenetic trees are used to analyze and visualize evolution. However, trees can be imperfect datatypes when summarizing multiple trees. This is especially problematic when accommodating for biological phenomena such as horizontal gene transfer, incomplete lineage sorting, and hybridization, as well as topological conflict between datasets. Additionally, researchers may want to combine information from sets of trees that have partially overlapping taxon sets. To address the problem of analyzing sets of trees with conflicting relationships and partially overlapping taxon sets, we introduce methods for aligning, synthesizing and analyzing rooted phylogenetic trees within a graph, called a tree alignment graph (TAG). The TAG can be queried and analyzed to explore uncertainty and conflict. It can also be synthesized to construct trees, presenting an alternative to supertrees approaches. We demonstrate these methods with two empirical datasets. In order to explore uncertainty, we constructed a TAG of the bootstrap trees from the Angiosperm Tree of Life project. Analysis of the resulting graph demonstrates that areas of the dataset that are unresolved in majority-rule consensus tree analyses can be understood in more detail within the context of a graph structure, using measures incorporating node degree and adjacency support. As an exercise in synthesis (i.e., summarization of a TAG constructed from the alignment trees), we also construct a TAG consisting of the taxonomy and source trees from a recent comprehensive bird study. We synthesized this graph into a tree that can be reconstructed in a repeatable fashion and where the underlying source information can be updated. The methods presented here are tractable for large scale analyses and serve as a basis for an alternative to consensus tree and supertree methods. Furthermore, the exploration of these graphs can expose structures and patterns within the dataset that are otherwise difficult to observe.

2004

The aim of the conference was to provide a common forum between academic and private research institutions to present and discuss their latest results and developments on Bioinformatics and Computational Biology. The scope of the conference covered nearly all aspects of basic and applied research on the field, such as functional and structural genomics and proteomics, comparative genomics and molecular evolution, algorithmic development and computational methods. The conference program included seven sessions of contributed papers, on Functional Analysis (chaired by Joaquín Dopazo), Comparative Genomics (chaired by Andrés Moya), Molecular Evolution (chaired by José Castresana), Structural Analysis and Modeling (chaired by Xavier Avilés), Biomedical Informatics (chaired by Ferran Sanz), Computational Methods (chaired by Gabriel Valiente), and Sequence Analysis (chaired by Roderic Guigó). The Proceedings of the 5th Annual Spanish Bioinformatics Conference consist of two parts. The first part comprises the 22 contributed papers, out of 45 submissions, that were alloted a 20-minute presentation at the conference. The second part comprises the remaining 23 contributed papers (in submission order) together with the 15 contributed posters (also in submission order) that were presented at the poster session. The acceptance ratio was 22/45 = 49%. We would like to thank the members of the program committee for their help in the selection process. Moreover, we would like to express our gratitude to the local committee members Rosa Badia, Marc Cid, Juan José Porta, and Romà Roset, as well as to the organizing committee members M. Mar Albà, Xavier Avilés, and Julio Rozas.

Journal of Computational Biology, 2006

A new problem in phylogenetic inference is presented, based on recent biological findings indicating a strong association between reversals (aka inversions) and repeats. These biological findings are formalized here in a new mathematical model, called repeatannotated phylogenetic trees (RAPT). We show that, under RAPT, the evolutionary process -including both the tree-topology as well as internal node genome orders -is uniquely determined, a property that is of major significance both in theory and in practice. Furthermore, the repeats are employed to provide linear-time algorithms for reconstructing both the genomic orders and the phylogeny, which are NP-hard problems under the classical model of sorting by reversals (SBR).

2006

Abstract: Phylogenetic trees are graph-like structures whose topology describes the inferred pattern of relationships among a set of biological entities, such as species or DNA sequences. Inference of these phylogenies typically involves evaluating large numbers of possible solutions and choosing the optimal topology, or set of topologies, from among all evaluated solutions. Such analyses are computationally intensive, especially when the pattern of relationships among a large number of entities is being sought.

1997

Abstract Phylogenetics is the study and identification of evolutionary patterns and structures in nature; this thesis explores the mathematics of these structures. The basic objects of study are the leaf labelled tree and its substructures: quartets, splits, clusters and rooted triples, among others. We present fundamental theorems and characterisations, as well as efficient algorithms for a range of phylogenetic problems. It is often possible to deduce phylogenetic information not in the original data.

Lecture Notes in Computer Science, 2009

Gene trees are leaf-labeled trees inferred from molecular sequences. Due to duplication events arising in genome evolution, gene trees usually have multiple copies of some labels, i.e. species. Inferring a species tree from a set of multi-labeled gene trees (MUL trees) is a wellknown problem in computational biology. We propose a novel approach to tackle this problem, mainly to transform a collection of MUL trees into a collection of evolutionary trees, each containing single copies of labels. To that aim, we provide several algorithmic building stones and describe how they fit within a general species tree inference process. Most algorithms have a linear-time complexity, except for an FPT algorithm proposed for a problem that we show to be intractable.

1989

ferring evolutionary trees from DNA sequence data was developed by Felsenstein (1 98 l). In evaluating the extent to which the maximum likelihood tree is a significantly better representation of the true tree, it is important to estimate the variance of the difference between log likelihood of different tree topologies. Bootstrap resampling can be used for this purpose (Hasegawaet al. 1 988; Hasegawa and Kishino 1989), but it imposes a great computation burden. To overcome this difficulty, we developed a new method for estimating the variance by expressing it explicitly. The method was applied to DNA sequence data from primates in order to evaluate the maximum likelihood branching order among Hominoidea. It was shown that, although the orangutan is convincingly placed as an outgroup of a human andAfrican apes clade, the branching order among human, chimpanzee, and gorilla cannot be determined confidently from the DNAsequence data presently available when the evolutionary rate constancy is not assumed.

bioRxiv (Cold Spring Harbor Laboratory), 2018

Over the last 20 years, TreeBASE has acquired a substantial body of phylogenetic data, including more than 20,000 published phylogenies. Given latency issues and limited options when it comes to querying the database remotely, a simplified and consolidated version of the database, here called TreeBASEdmp, is made available for download, allowing biologists to design custom analyses of the data on their local computers. The database is indexed to support searching for phylogenetic topologies using nested sets and closure tables. Here we propose a new approach to find broadly-defined phylogenetic patterns, a method we call Generic Topological Querying, which allows the user to find hypotheses of relationship without being constrained to use particular sets of specific taxa. Additionally, we normalize as many leaf nodes as possible to an equivalent species rank identifier to assist in supertree synthesis. Our example script rapidly assembles sets of trees and generates a matrix representation of them for subsequent supertree generation.

Lecture Notes in Computer Science, 2015

Tree alignment graphs (TAGs) provide an intuitive data structure for storing phylogenetic trees that exhibits the relationships of the individual input trees and can potentially account for nested taxonomic relationships. This paper provides a theoretical foundation for the use of TAGs in phylogenetics. We provide a formal definition of TAG that-unlike previous definition-does not depend on the order in which input trees are provided. In the consensus case, when all input trees have the same leaf labels, we describe algorithms for constructing majority-rule and strict consensus trees using the TAG. When the input trees do not have identical sets of leaf labels, we describe how to determine if the input trees are compatible and, if they are compatible, to construct a supertree that contains the input trees.

2009

Abstract-In the past research efforts on computational phylogenetic analysis were dedicated to the design of heuristics which can quickly find near-optimal trees under a specific optimization criterion. However, all criteria are over-simplified and cannot realistically model the real evolution process. Thus all existing algorithms for phylogenetic analysis have their limitations. It has become a serious issue for many important real-life applications which often demand accurate results from phylogenetic analysis.