scholarly journals Quartet Compatibility and the Quartet Graph

10.37236/827 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Stefan Grünewald ◽  
Peter J. Humphries ◽  
Charles Semple
Keyword(s):  
Phylogenetic Tree ◽  
Evolutionary Biology ◽  
Phylogenetic Trees ◽  
Chordal Graphs ◽  
Minimum Number ◽  
Edge Colourings ◽  
Computational Difficulty ◽  
Published Result

A collection ${\cal P}$ of phylogenetic trees is compatible if there exists a single phylogenetic tree that displays each of the trees in ${\cal P}$. Despite its computational difficulty, determining the compatibility of ${\cal P}$ is a fundamental task in evolutionary biology. Characterizations in terms of chordal graphs have been previously given for this problem as well as for the closely-related problems of (i) determining if ${\cal P}$ is definitive and (ii) determining if ${\cal P}$ identifies a phylogenetic tree. In this paper, we describe new characterizations of each of these problems in terms of edge colourings. Furthermore, making use of the tools that underlie these new characterizations, we also determine the minimum number of quartets required to identify an arbitrary phylogenetic tree, thus correcting a previously published result.

scholarly journals New substitution models for rooting phylogenetic trees

2015 ◽  
Vol 370 (1678) ◽  
pp. 20140336 ◽  
Author(s):  
Tom A. Williams ◽  
Sarah E. Heaps ◽  
Svetlana Cherlin ◽  
Tom M. W. Nye ◽  
Richard J. Boys ◽  
...  
Keyword(s):  
Phylogenetic Tree ◽  
Evolutionary Biology ◽  
Phylogenetic Trees ◽  
Deep Structure ◽  
Tree Of Life ◽  
Test Case ◽  
Phylogenetic Methods ◽  
New Models ◽  
Substitution Models ◽  
Biological Interpretation

The root of a phylogenetic tree is fundamental to its biological interpretation, but standard substitution models do not provide any information on its position. Here, we describe two recently developed models that relax the usual assumptions of stationarity and reversibility, thereby facilitating root inference without the need for an outgroup. We compare the performance of these models on a classic test case for phylogenetic methods, before considering two highly topical questions in evolutionary biology: the deep structure of the tree of life and the root of the archaeal radiation. We show that all three alignments contain meaningful rooting information that can be harnessed by these new models, thus complementing and extending previous work based on outgroup rooting. In particular, our analyses exclude the root of the tree of life from the eukaryotes or Archaea, placing it on the bacterial stem or within the Bacteria. They also exclude the root of the archaeal radiation from several major clades, consistent with analyses using other rooting methods. Overall, our results demonstrate the utility of non-reversible and non-stationary models for rooting phylogenetic trees, and identify areas where further progress can be made.

Darwin's two competing phylogenetic trees: marsupials as ancestors or sister taxa?

2012 ◽  
Vol 39 (2) ◽  
pp. 217-233 ◽  
Author(s):  
J. David Archibald
Keyword(s):  
Fossil Record ◽  
Evolutionary Biology ◽  
Phylogenetic Trees ◽  
Charles Darwin ◽  
The Other ◽  
Charles Lyell ◽  
Single Origin ◽  
Molecular Studies ◽  
Richard Owen ◽  
First Time

Studies of the origin and diversification of major groups of plants and animals are contentious topics in current evolutionary biology. This includes the study of the timing and relationships of the two major clades of extant mammals – marsupials and placentals. Molecular studies concerned with marsupial and placental origin and diversification can be at odds with the fossil record. Such studies are, however, not a recent phenomenon. Over 150 years ago Charles Darwin weighed two alternative views on the origin of marsupials and placentals. Less than a year after the publication of On the origin of species, Darwin outlined these in a letter to Charles Lyell dated 23 September 1860. The letter concluded with two competing phylogenetic diagrams. One showed marsupials as ancestral to both living marsupials and placentals, whereas the other showed a non-marsupial, non-placental as being ancestral to both living marsupials and placentals. These two diagrams are published here for the first time. These are the only such competing phylogenetic diagrams that Darwin is known to have produced. In addition to examining the question of mammalian origins in this letter and in other manuscript notes discussed here, Darwin confronted the broader issue as to whether major groups of animals had a single origin (monophyly) or were the result of “continuous creation” as advocated for some groups by Richard Owen. Charles Lyell had held similar views to those of Owen, but it is clear from correspondence with Darwin that he was beginning to accept the idea of monophyly of major groups.

scholarly journals Computing nearest neighbour interchange distances between ranked phylogenetic trees

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).

scholarly journals Minimum Number of Monotone Subsequences of Length 4 in Permutations

2014 ◽  
Vol 24 (4) ◽  
pp. 658-679 ◽  
Author(s):  
JÓZSEF BALOGH ◽  
PING HU ◽  
BERNARD LIDICKÝ ◽  
OLEG PIKHURKO ◽  
BALÁZS UDVARI ◽  
...  
Keyword(s):  
Lower Bound ◽  
Complete Graphs ◽  
Formula Group ◽  
Minimum Number ◽  
Additional Stability ◽  
Edge Colourings ◽  
Image Position

We show that for every sufficiently largen, the number of monotone subsequences of length four in a permutation onnpoints is at least\begin{equation*} \binom{\lfloor{n/3}\rfloor}{4} + \binom{\lfloor{(n+1)/3}\rfloor}{4} + \binom{\lfloor{(n+2)/3}\rfloor}{4}. \end{equation*}Furthermore, we characterize all permutations on [n] that attain this lower bound. The proof uses the flag algebra framework together with some additional stability arguments. This problem is equivalent to some specific type of edge colourings of complete graphs with two colours, where the number of monochromaticK4is minimized. We show that all the extremal colourings must contain monochromaticK4only in one of the two colours. This translates back to permutations, where all the monotone subsequences of length four are all either increasing, or decreasing only.

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

1980 ◽  
Vol 187 (1) ◽  
pp. 65-74 ◽  
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.

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

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.

Evolution: medicine’s most basic science

2010 ◽  
pp. 12-15 ◽  
Author(s):  
Randolph M. Nesse ◽  
Richard Dawkins
Keyword(s):  
Population Genetics ◽  
Basic Science ◽  
Evolutionary Biology ◽  
Phylogenetic Trees ◽  
Evolutionary Methods

The role of evolutionary biology as a basic science for medicine has been expanding rapidly. Some evolutionary methods are already widely applied in medicine, such as population genetics and methods for analysing phylogenetic trees. Newer applications come from seeking evolutionary as well as proximate explanations for disease. ...

Evolution: Medicine’s most basic science

2020 ◽  
pp. 39-42
Author(s):  
Randolph M. Nesse ◽  
Richard Dawkins
Keyword(s):  
Population Genetics ◽  
Natural Selection ◽  
Basic Science ◽  
Evolutionary Biology ◽  
Phylogenetic Trees ◽  
The Body ◽  
Clinical Implications ◽  
Trade Offs ◽  
The Cost

The role of evolutionary biology as a basic science for medicine is expanding rapidly. Some evolutionary methods are already widely applied in medicine, such as population genetics and methods for analysing phylogenetic trees. Newer applications come from seeking evolutionary as well as proximate explanations for disease. Traditional medical research is restricted to proximate studies of the body’s mechanism, but separate evolutionary explanations are needed for why natural selection has left many aspects of the body vulnerable to disease. There are six main possibilities: mismatch, infection, constraints, trade-offs, reproduction at the cost of health, and adaptive defences. Like other basic sciences, evolutionary biology has limited direct clinical implications, but it provides essential research methods, encourages asking new questions that foster a deeper understanding of disease, and provides a framework that organizes the facts of medicine.

INFERRING PHYLOGENETIC RELATIONSHIPS AVOIDING FORBIDDEN ROOTED TRIPLETS

2006 ◽  
Vol 04 (01) ◽  
pp. 59-74 ◽  
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.

Visualizing Speciation in Artificial Cichlid Fish

2006 ◽  
Vol 12 (2) ◽  
pp. 243-257 ◽  
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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