Isomorphism and Symmetries in Random Phylogenetic Trees

The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic tree of large size obeys a limiting Gaussian distribution, in the sense of both central and local limits. The probability that two random phylogenetic trees have the same number of symmetries asymptotically obeys an inverse square-root law. Precise estimates for these problems are obtained by methods of analytic combinatorics, involving bivariate generating functions, singularity analysis, and quasi-powers approximations.

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Computing nearest neighbour interchange distances between ranked phylogenetic trees

Journal of Mathematical Biology ◽

10.1007/s00285-021-01567-5 ◽

2021 ◽

Vol 82 (1-2) ◽

Author(s):

Lena Collienne ◽

Alex Gavryushkin

Keyword(s):

Cancer Research ◽

Computational Complexity ◽

Phylogenetic Tree ◽

Shortest Path ◽

Phylogenetic Trees ◽

Shortest Paths ◽

Nearest Neighbour ◽

Tree Inference ◽

Subtree Prune And Regraft ◽

Comparison Algorithms

AbstractMany popular algorithms for searching the space of leaf-labelled (phylogenetic) trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are given by pairs of trees connected by one rearrangement operation (sometimes called a move). Most popular are the classical nearest neighbour interchange, subtree prune and regraft, and tree bisection and reconnection moves. The problem of computing distances, however, is $${\mathbf {N}}{\mathbf {P}}$$ N P -hard in each of these graphs, making tree inference and comparison algorithms challenging to design in practice. Although anked phylogenetic trees are one of the central objects of interest in applications such as cancer research, immunology, and epidemiology, the computational complexity of the shortest path problem for these trees remained unsolved for decades. In this paper, we settle this problem for the ranked nearest neighbour interchange operation by establishing that the complexity depends on the weight difference between the two types of tree rearrangements (rank moves and edge moves), and varies from quadratic, which is the lowest possible complexity for this problem, to $${\mathbf {N}}{\mathbf {P}}$$ N P -hard, which is the highest. In particular, our result provides the first example of a phylogenetic tree rearrangement operation for which shortest paths, and hence the distance, can be computed efficiently. Specifically, our algorithm scales to trees with tens of thousands of leaves (and likely hundreds of thousands if implemented efficiently).

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Techniques for the verification of minimal phylogenetic trees illustrated with ten mammalian haemoglobin sequences

Biochemical Journal ◽

10.1042/bj1870065 ◽

1980 ◽

Vol 187 (1) ◽

pp. 65-74 ◽

Cited By ~ 12

Author(s):

D Penny ◽

M D Hendy ◽

L R Foulds

Keyword(s):

Amino Acid ◽

Phylogenetic Tree ◽

Protein Sequence ◽

Phylogenetic Trees ◽

Sequence Data ◽

Protein Sequences ◽

Nucleotide Sequences ◽

Amino Acid Sequences ◽

Minimal Tree ◽

Protein Sequence Data

We have recently reported a method to identify the shortest possible phylogenetic tree for a set of protein sequences [Foulds Hendy & Penny (1979) J. Mol. Evol. 13. 127–150; Foulds, Penny & Hendy (1979) J. Mol. Evol. 13, 151–166]. The present paper discusses issues that arise during the construction of minimal phylogenetic trees from protein-sequence data. The conversion of the data from amino acid sequences into nucleotide sequences is shown to be advantageous. A new variation of a method for constructing a minimal tree is presented. Our previous methods have involved first constructing a tree and then either proving that it is minimal or transforming it into a minimal tree. The approach presented in the present paper progressively builds up a tree, taxon by taxon. We illustrate this approach by using it to construct a minimal tree for ten mammalian haemoglobin alpha-chain sequences. Finally we define a measure of the complexity of the data and illustrate a method to derive a directed phylogenetic tree from the minimal tree.

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Analysis of SARS-CoV-2 nucleocapsid protein sequence variations in ASEAN countries

Medical Journal of Indonesia ◽

10.13181/mji.oa.215304 ◽

2021 ◽

Author(s):

Mochammad Rajasa Mukti Negara ◽

Ita Krissanti ◽

Gita Widya Pradini

Keyword(s):

Phylogenetic Tree ◽

Phylogenetic Trees ◽

Protein Sequences ◽

Reference Sequence ◽

N Protein ◽

Asean Country ◽

Sequence Variations ◽

Complete Sequences ◽

Asean Countries ◽

Global Initiative

BACKGROUND Nucleocapsid (N) protein is one of four structural proteins of SARS-CoV-2 which is known to be more conserved than spike protein and is highly immunogenic. This study aimed to analyze the variation of the SARS-CoV-2 N protein sequences in ASEAN countries, including Indonesia. METHODS Complete sequences of SARS-CoV-2 N protein from each ASEAN country were obtained from Global Initiative on Sharing All Influenza Data (GISAID), while the reference sequence was obtained from GenBank. All sequences collected from December 2019 to March 2021 were grouped to the clade according to GISAID, and two representative isolates were chosen from each clade for the analysis. The sequences were aligned by MUSCLE, and phylogenetic trees were built using MEGA-X software based on the nucleotide and translated AA sequences. RESULTS 98 isolates of complete N protein genes from ASEAN countries were analyzed. The nucleotides of all isolates were 97.5% conserved. Of 31 nucleotide changes, 22 led to amino acid (AA) substitutions; thus, the AA sequences were 94.5% conserved. The phylogenetic tree of nucleotide and AA sequences shows similar branches. Nucleotide variations in clade O (C28311T); clade GR (28881–28883 GGG>AAC); and clade GRY (28881–28883 GGG>AAC and C28977T) lead to specific branches corresponding to the clade within both trees. CONCLUSIONS The N protein sequences of SARS-CoV-2 across ASEAN countries are highly conserved. Most isolates were closely related to the reference sequence originating from China, except the isolates representing clade O, GR, and GRY which formed specific branches in the phylogenetic tree.

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A General Asymptotic Scheme for the Analysis of Partition Statistics

Combinatorics Probability Computing ◽

10.1017/s0963548314000418 ◽

2014 ◽

Vol 23 (6) ◽

pp. 1057-1086 ◽

Cited By ~ 6

Author(s):

PETER J. GRABNER ◽

ARNOLD KNOPFMACHER ◽

STEPHAN WAGNER

Keyword(s):

Generating Function ◽

Asymptotic Expansions ◽

Generating Functions ◽

Singularity Analysis ◽

Higher Moments ◽

Integer Partitions ◽

Classical Singularity ◽

Random Integer ◽

Partition Statistics ◽

New Statistics

We consider statistical properties of random integer partitions. In order to compute means, variances and higher moments of various partition statistics, one often has to study generating functions of the form P(x)F(x), where P(x) is the generating function for the number of partitions. In this paper, we show how asymptotic expansions can be obtained in a quasi-automatic way from expansions of F(x) around x = 1, which parallels the classical singularity analysis of Flajolet and Odlyzko in many ways. Numerous examples from the literature, as well as some new statistics, are treated via this methodology. In addition, we show how to compute further terms in the asymptotic expansions of previously studied partition statistics.

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INFERRING PHYLOGENETIC RELATIONSHIPS AVOIDING FORBIDDEN ROOTED TRIPLETS

Journal of Bioinformatics and Computational Biology ◽

10.1142/s0219720006001709 ◽

2006 ◽

Vol 04 (01) ◽

pp. 59-74 ◽

Cited By ~ 20

Author(s):

YING-JUN HE ◽

TRINH N. D. HUYNH ◽

JESPER JANSSON ◽

WING-KIN SUNG

Keyword(s):

Approximation Algorithms ◽

Phylogenetic Tree ◽

Phylogenetic Trees ◽

Evolutionary History ◽

Phylogenetic Network ◽

Evolutionary Relationships ◽

Large Set ◽

Tree Network ◽

History Of ◽

Overlapping Sets

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 [Formula: see text] and none of the rooted triplets in another given set [Formula: see text]. 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.

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Visualizing Speciation in Artificial Cichlid Fish

Artificial Life ◽

10.1162/artl.2006.12.2.243 ◽

2006 ◽

Vol 12 (2) ◽

pp. 243-257 ◽

Cited By ~ 3

Author(s):

Ross Clement

Keyword(s):

Phylogenetic Tree ◽

Phylogenetic Trees ◽

Cichlid Fish ◽

Natural Consequence ◽

Open Problems ◽

Visualization System ◽

Low Level ◽

Wide Range ◽

Level Information ◽

History Of

The Cichlid Speciation Project (CSP) is an ALife simulation system for investigating open problems in the speciation of African cichlid fish. The CSP can be used to perform a wide range of experiments that show that speciation is a natural consequence of certain biological systems. A visualization system capable of extracting the history of speciation from low-level trace data and creating a phylogenetic tree has been implemented. Unlike previous approaches, this visualization system presents a concrete trace of speciation, rather than a summary of low-level information from which the viewer can make subjective decisions on how speciation progressed. The phylogenetic trees are a more objective visualization of speciation, and enable automated collection and summarization of the results of experiments. The visualization system is used to create a phylogenetic tree from an experiment that models sympatric speciation.

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Treeio: An R Package for Phylogenetic Tree Input and Output with Richly Annotated and Associated Data

Molecular Biology and Evolution ◽

10.1093/molbev/msz240 ◽

2019 ◽

Vol 37 (2) ◽

pp. 599-603 ◽

Cited By ~ 25

Author(s):

Li-Gen Wang ◽

Tommy Tsan-Yuk Lam ◽

Shuangbin Xu ◽

Zehan Dai ◽

Lang Zhou ◽

...

Keyword(s):

Phylogenetic Tree ◽

Phylogenetic Trees ◽

R Package ◽

External Data ◽

Input And Output ◽

Evolutionary Context ◽

Tree Data ◽

Downstream Analysis ◽

Different Sources ◽

Associated Data

Abstract Phylogenetic trees and data are often stored in incompatible and inconsistent formats. The outputs of software tools that contain trees with analysis findings are often not compatible with each other, making it hard to integrate the results of different analyses in a comparative study. The treeio package is designed to connect phylogenetic tree input and output. It supports extracting phylogenetic trees as well as the outputs of commonly used analytical software. It can link external data to phylogenies and merge tree data obtained from different sources, enabling analyses of phylogeny-associated data from different disciplines in an evolutionary context. Treeio also supports export of a phylogenetic tree with heterogeneous-associated data to a single tree file, including BEAST compatible NEXUS and jtree formats; these facilitate data sharing as well as file format conversion for downstream analysis. The treeio package is designed to work with the tidytree and ggtree packages. Tree data can be processed using the tidy interface with tidytree and visualized by ggtree. The treeio package is released within the Bioconductor and rOpenSci projects. It is available at https://www.bioconductor.org/packages/treeio/.

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Model checking software for phylogenetic trees using distribution and database methods

Journal of Integrative Bioinformatics ◽

10.1515/jib-2013-229 ◽

2013 ◽

Vol 10 (3) ◽

pp. 16-30 ◽

Cited By ~ 1

Author(s):

José Ignacio Requeno ◽

José Manuel Colom

Keyword(s):

Model Checking ◽

Phylogenetic Tree ◽

Dna Sequence ◽

Phylogenetic Trees ◽

Computation Time ◽

Biological Properties ◽

Traditional Model ◽

Temporal Logics ◽

Memory Consumption ◽

Speed Up

Summary Model checking, a generic and formal paradigm stemming from computer science based on temporal logics, has been proposed for the study of biological properties that emerge from the labeling of the states defined over the phylogenetic tree. This strategy allows us to use generic software tools already present in the industry. However, the performance of traditional model checking is penalized when scaling the system for large phylogenies. To this end, two strategies are presented here. The first one consists of partitioning the phylogenetic tree into a set of subgraphs each one representing a subproblem to be verified so as to speed up the computation time and distribute the memory consumption. The second strategy is based on uncoupling the information associated to each state of the phylogenetic tree (mainly, the DNA sequence) and exporting it to an external tool for the management of large information systems. The integration of all these approaches outperforms the results of monolithic model checking and helps us to execute the verification of properties in a real phylogenetic tree.

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Taxonomy of Anterastes and related genera: a new synonym and a new species of Anterastes

Zootaxa ◽

10.11646/zootaxa.2771.1.4 ◽

2011 ◽

Vol 2771 (1) ◽

pp. 41 ◽

Cited By ~ 2

Author(s):

SARP KAYA ◽

BATTAL CIPLAK

Keyword(s):

New Species ◽

Phylogenetic Tree ◽

Phylogenetic Trees ◽

Genetic Data ◽

New Combination ◽

New Synonym ◽

Male Calling ◽

Phylogenetic Hypotheses ◽

Distinct Features ◽

A New Species

Among the Anatolian Tettigoniinae (Orthoptera, Tettigoniidae) the genera Anterastes, Koroglus, Sureyaella and Rhacocleis are distinguishable from the others by presence of one pair of spurs on the apico-ventral end of hind tibiae. The last two can be easily distinguished from the others by several distinct features, but the separation of the first two from each other is problematic. A new species described here provided opportunity of re-evaluating their taxonomy. The new species Anterastes antecessor sp. n. is described based on morphology, male calling song and genetic data. The taxonomy of Anterastes and Koroglus is rectified based on phylogentic hypotheses obtained from representative 16S rDNA haplotypes. Sureyaella bella, Parapholidoptera signata and Bolua turkiyae are used as out groups in different combinations to obtain a more stable phylogeny. Although analyses with different outgroups suggested the same topology, the phylogenetic tree with outgroups Parapholidoptera signata and Bolua turkiyae resulted with the highest bootstrap supports to the branches. Phylogenetic trees suggested the following relationships for the ingroup species; (A. antecessor sp. n. + ((Koroglus disparalatus + A. uludaghensis) + (A. turcicus + (A. niger + (A. ucari + A. babadaghi))) + ((A. tolunayi + (A. serbicus + A. antitauricus + A. burri)))). Considering the phylogenetic hypotheses and characters used in previous publications, Koroglus is put in synonymy with Anterastes, and a new combination is suggested for the only species of the former Anterastes disparalatus comb. n. A short remark is given about the characters used in the generic taxonomy of the group.

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