scholarly journals On Symmetries in Phylogenetic Trees

10.37236/5994 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Éric Fusy
Keyword(s):  
Simple Formula ◽  
Phylogenetic Trees ◽  
Binary Trees ◽  
Combinatorial Proof ◽  
Random Generation ◽  
Integer Partition ◽  
Binary Partition ◽  
Generation Procedure

Billey et al. [arXiv:1507.04976] have recently discovered a surprisingly simple formula for the number $a_n(\sigma)$ of leaf-labelled rooted non-embedded binary trees (also known as phylogenetic trees) with $n\geq 1$ leaves, fixed (for the relabelling action) by a given permutation $\sigma\in\frak{S}_n$. Denoting by $\lambda\vdash n$ the integer partition giving the sizes of the cycles of $\sigma$ in non-increasing order, they show by a guessing/checking approach that if $\lambda$ is a binary partition (it is known that $a_n(\sigma)=0$ otherwise), then$$a_n(\sigma)=\prod_{i=2}^{\ell(\lambda)}(2(\lambda_i+\cdots+\lambda_{\ell(\lambda)})-1),$$and they derive from it a formula and random generation procedure for tanglegrams (and more generally for tangled chains). Our main result is a combinatorial proof of the formula for $a_n(\sigma)$, which yields a simplification of the random sampler for tangled chains.

scholarly journals Visual Comparison of Phylogenetic Trees Through iPhyloC, a New Interactive Web-based Framework

2021 ◽  
Author(s):  
Muhsen Hammoud ◽  
Charles Morphy Santos ◽  
Joao Paulo Gois
Keyword(s):  
Phylogenetic Trees ◽  
Binary Trees ◽  
Automatic Identification ◽  
Structural Comparison ◽  
Web Based ◽  
Visual Comparison ◽  
Large Trees ◽  
Cross Platform ◽  
The Common ◽  
Intuitive Design

Current side-by-side phylogenetic trees comparison frameworks face two issues: (1) accepting binary trees as input, and (2) assuming input trees having identical or highly overlapping taxa. We present a task abstraction of the problem of side-by-side comparison of two phylogenetic trees and propose a set-based measure for detailed structural comparison between two phylogenetic trees, which can be non-binary and not highly overlapping. iPhyloC is an interactive web-based framework including automatic identification of the common taxa in both trees, comparing input trees in several modes, intuitive design, high usability, scalability to large trees, and cross-platform support. iPhyloC was tested in hypothetical and real biological examples.

scholarly journals A Combinatorial Proof of Postnikov's Identity and a Generalized Enumeration of Labeled Trees

10.37236/1890 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
Seunghyun Seo
Keyword(s):  
Rooted Trees ◽  
Binary Trees ◽  
Combinatorial Proof ◽  
Labeled Trees ◽  
Plane Trees

In this paper, we give a simple combinatorial explanation of a formula of A. Postnikov relating bicolored rooted trees to bicolored binary trees. We also present generalized formulas for the number of labeled $k$-ary trees, rooted labeled trees, and labeled plane trees.

scholarly journals Bruhat Order on Fixed-Point-Free Involutions in the Symmetric Group

10.37236/3861 ◽  
2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Matthew Watson
Keyword(s):  
Fixed Point ◽  
Symmetric Group ◽  
Bruhat Order ◽  
Binary Trees ◽  
Combinatorial Proof ◽  
Combinatorial Identity ◽  
Structural Description ◽  
Rook Placements ◽  
Dyck Paths ◽  
New Interpretation

We provide a structural description of Bruhat order on the set $F_{2n}$ of fixed-point-free involutions in the symetric group $S_{2n}$ which yields a combinatorial proof of a combinatorial identity that is an expansion of its rank-generating function. The decomposition is accomplished via a natural poset congruence, which yields a new interpretation and proof of a combinatorial identity that counts the number of rook placements on the Ferrers boards lying under all Dyck paths of a given length $2n$. Additionally, this result extends naturally to prove new combinatorial identities that sum over other Catalan objects: 312-avoiding permutations, plane forests, and binary trees.

scholarly journals Random Generation Using Binomial Approximations

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Dominique Gouyou-Beauchamps ◽  
Cyril Nicaud
Keyword(s):  
Binary Trees ◽  
Random Generation ◽  
Binomial Distributions ◽  
International Audience ◽  
Random Generators

International audience Generalizing an idea used by Alonso to generate uniformly at random Motzkin words, we outline an approach to build efficient random generators using binomial distributions and rejection algorithms. As an application of this method, we present random generators, both efficient and easy to implement, for partial injections and colored unary-binary trees.

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.

Analyzing the Phylogenetic Trees with Tree- building Methods

2011 ◽  
Vol 1 (7) ◽  
pp. 83-85
Author(s):  
Jasmine Jasmine ◽  
◽  
Pankaj Bhambri ◽  
Dr. O.P. Gupta Dr. O.P. Gupta
Keyword(s):  
Phylogenetic Trees ◽  
Tree Building ◽  
Building Methods

Gray-Code Ranking and Unranking on Left-Weight Sequences of Binary Trees

2016 ◽  
Vol E99.A (6) ◽  
pp. 1067-1074 ◽  
Author(s):  
Ro-Yu WU ◽  
Jou-Ming CHANG ◽  
Sheng-Lung PENG ◽  
Chun-Liang LIU
Keyword(s):  
Gray Code ◽  
Binary Trees

Application of DNA Barcoding in Taxonomy and Phylogeny: An Individual Case of COI Partial Gene Sequencing from Seven Animal Species

2019 ◽  
Vol 53 (5) ◽  
pp. 375-384
Author(s):  
M. Drohvalenko ◽  
A. Mykhailenko ◽  
M. Rekrotchuk ◽  
L. Shpak ◽  
V. Shuba ◽  
...  
Keyword(s):  
Phylogenetic Trees ◽  
Far East ◽  
Individual Case ◽  
Ambystoma Mexicanum ◽  
Leaf Miner ◽  
Horse Chestnut ◽  
Natural Reserve ◽  
Rock Lizard ◽  
Sand Lizard ◽  
Lacerta Agilis

Abstract A part of the COI mitochondrial barcoding gene was sequenced from seven species of different taxonomical groups: Ambystoma mexicanum (Amphibia, Ambystomatidae), Darevskia lindholmi, Lacerta agilis exigua (Reptilia, Lacertidae), Erinaceus roumanicus (Mammalia, Erinaceidae), Macrobiotus sp. 1 and 2 (Eutardigrada, Macrobiotidae) and Cameraria ohridella (Insecta, Gracillariidae). The sequences were compared with available sequences from databases and positioned on phylogenetic trees when the taxa had not yet been sequenced. The presence of Mexican axolotls in herpetoculture in Ukraine was confirmed. The partial COI genes of the Crimean rock lizard and an eastern sub-species of the sand lizard were sequenced. We demonstrated the presence of two tardigrade mitochondrial lineages of the Macrobiotus hufelandi group in the same sample from the Zeya Natural Reserve in the Far East: one was nearly identical to the Italian M. macrocalix, and the other one is similar to M. persimilis and M. vladimiri. We also confirmed the presence of the invasive haplotype “A” of the horse chestnut leaf miner in Ukraine, in line with the hypothesized route of invasion from Central Europe.

Sign in / Sign up

Export Citation Format

Share Document