scholarly journals A new balance index for phylogenetic trees

2013 ◽  
Vol 241 (1) ◽  
pp. 125-136 ◽  
Author(s):  
Arnau Mir ◽  
Francesc Rosselló ◽  
Lucı´a Rotger
Keyword(s):  
Phylogenetic Trees ◽  
Balance Index

scholarly journals On Sackin's original proposal: The variance of the leaves' depths as a phylogenetic balance index

2019 ◽  
Author(s):  
Tomás Martínez Coronado ◽  
Arnau Mir ◽  
Francesc Rossello ◽  
Lucía Rotger
Keyword(s):  
Phylogenetic Tree ◽  
Phylogenetic Trees ◽  
Rooted Tree ◽  
Rooted Trees ◽  
Closed Formula ◽  
Original Proposal ◽  
Yule Model ◽  
Uniform Model ◽  
Rooted Phylogenetic Tree ◽  
Balance Index

Abstract Background: The Sackin index S of a rooted phylogenetic tree, defined as the sum of its leaves' depths, is one of the most popular balance indices in phylogenetics, and Sackin's 1972 paper is usually cited as the source for this index. However, what Sackin actually proposed in his paper as a measure of the imbalance of a rooted tree was not the sum of its leaves' depths, but their "variation". This proposal was later implemented as the variance of the leaves' depths by Kirkpatrick and Slatkin, where moreover they posed the problem of finding a closed formula for its expected value under the Yule model. Nowadays, Sackin's original proposal seems to have passed into oblivion in the phylogenetics literature, replaced by the index bearing his name, which, in fact, was introduced a decade later by Sokal.Results: In this paper we study the properties of the variance of the leaves' depths, V, as a balance index. Firstly, we prove that the rooted trees with n leaves and maximum V value are exactly the combs with n leaves. But although V achieves its minimum value on every space BT_n of bifurcating rooted phylogenetic trees with n< 184 leaves at the so-called "maximally balanced trees" with n leaves, this property fails for almost every n>= 184. We provide then an algorithm that finds in O(n) time the trees in BT_n with minimum V value. Secondly, we obtain closed formulas for the expected V value of a bifurcating rooted tree with any number n of leaves under the Yule and the uniform models and, as a by-product of the computations leading to these formulas, we also obtain closed formulas for the variance of the Sackin index and the total cophenetic indexof a bifurcating rooted tree, as well as of their covariance, under the uniform model, thus filling this gap in the literature.Conclusions: The phylogenetics crowd has been wise in preferring as a balance index the sum S(T) of the leaves’ depths of a phylogenetic tree T over their variance V (T), because the latter does not seem to capture correctly the notion of balance of large bifurcating rooted trees. But for bifurcating trees up to 183 leaves, V is a valid and useful balance index.

scholarly journals A balance index for phylogenetic trees based on rooted quartets

2019 ◽  
Vol 79 (3) ◽  
pp. 1105-1148 ◽  
Author(s):  
Tomás M. Coronado ◽  
Arnau Mir ◽  
Francesc Rosselló ◽  
Gabriel Valiente
Keyword(s):  
Phylogenetic Trees ◽  
Balance Index

scholarly journals On Sackin's original proposal: The variance of the leaves' depths as a phylogenetic balance index

2020 ◽  
Author(s):  
Tomás Martínez Coronado ◽  
Arnau Mir ◽  
Francesc Rossello ◽  
Lucía Rotger
Keyword(s):  
Phylogenetic Tree ◽  
Phylogenetic Trees ◽  
Rooted Tree ◽  
Rooted Trees ◽  
Closed Formula ◽  
Original Proposal ◽  
Yule Model ◽  
Uniform Model ◽  
Rooted Phylogenetic Tree ◽  
Balance Index

Abstract Background. The Sackin index S of a rooted phylogenetic tree, defined as the sum of its leaves' depths, is one of the most popular balance indices in phylogenetics, and Sackin's 1972 paper is usually cited as the source for this index. However, what Sackin actually proposed in his paper as a measure of the imbalance of a rooted tree was not the sum of its leaves' depths, but their ``variation''. This proposal was later implemented as the variance of the leaves' depths by Kirkpatrick and Slatkin in 1993, where they also posed the problem of finding a closed formula for its expected value under the Yule model. Nowadays, Sackin's original proposal seems to have passed into oblivion in the phylogenetics literature, replaced by the index bearing his name, which, in fact, was introduced a decade later by Sokal. Results. In this paper we study the properties of the variance of the leaves' depths, V, as a balance index. Firstly, we prove that the rooted trees with $n$ leaves and maximum V value are exactly the combs with n leaves. But although V achieves its minimum value on every space of bifurcating rooted phylogenetic trees with at most 183 leaves at the so-called ``maximally balanced trees'' with n leaves, this property fails for almost every n larger than 184 We provide then an algorithm that finds the bifurcating rooted trees with n leaves and minimum V value in quasilinear time. Secondly, we obtain closed formulas for the expected V value of a bifurcating rooted tree with any number n of leaves under the Yule and the uniform models and, as a by-product of the computations leading to these formulas, we also obtain closed formulas for the variance under the uniform model of the Sackin index and the total cophenetic index of a bifurcating rooted tree, as well as of their covariance, thus filling this gap in the literature.

scholarly journals Limit distribution of the quartet balance index for Aldous’s β ≥ 0-model

2018 ◽  
Author(s):  
Krzysztof Bartoszek
Keyword(s):  
Fixed Point ◽  
Limit Distribution ◽  
Phylogenetic Trees ◽  
Contraction Operator ◽  
Balance Index

AbstractThis paper builds up on T. Martínez-Coronado, A. Mir, F. Rossello and G. Valiente’s work “A balance index for phylogenetic trees based on quartets”, introducing a new balance index for trees. We show here that this balance index, in the case of Aldous’s β ≥ 0-model, convergences weakly to a distribution that can be characterized as the fixed point of a contraction operator on a class of distributions.

scholarly journals On Sackin's original proposal: The variance of the leaves' depths as a phylogenetic balance index

2020 ◽  
Author(s):  
Tomás Martínez Coronado ◽  
Arnau Mir ◽  
Francesc Rossello ◽  
Lucía Rotger
Keyword(s):  
Phylogenetic Tree ◽  
Phylogenetic Trees ◽  
Rooted Tree ◽  
Rooted Trees ◽  
Closed Formula ◽  
Original Proposal ◽  
Yule Model ◽  
Uniform Model ◽  
Rooted Phylogenetic Tree ◽  
Balance Index

Abstract Background. The Sackin index S of a rooted phylogenetic tree, defined as the sum of its leaves' depths, is one of the most popular balance indices in phylogenetics, and Sackin's 1972 paper is usually cited as the source for this index. However, what Sackin actually proposed in his paper as a measure of the imbalance of a rooted tree was not the sum of its leaves' depths, but their ``variation''. This proposal was later implemented as the variance of the leaves' depths by Kirkpatrick and Slatkin in 1993, where they also posed the problem of finding a closed formula for its expected value under the Yule model. Nowadays, Sackin's original proposal seems to have passed into oblivion in the phylogenetics literature, replaced by the index bearing his name, which, in fact, was introduced a decade later by Sokal. Results. In this paper we study the properties of the variance of the leaves' depths, V, as a balance index. Firstly, we prove that the rooted trees with $n$ leaves and maximum V value are exactly the combs with n leaves. But although V achieves its minimum value on every space of bifurcating rooted phylogenetic trees with at most 183 leaves at the so-called ``maximally balanced trees'' with n leaves, this property fails for almost every n larger than 184 We provide then an algorithm that finds the bifurcating rooted trees with n leaves and minimum V value in quasilinear time. Secondly, we obtain closed formulas for the expected V value of a bifurcating rooted tree with any number n of leaves under the Yule and the uniform models and, as a by-product of the computations leading to these formulas, we also obtain closed formulas for the variance under the uniform model of the Sackin index and the total cophenetic index of a bifurcating rooted tree, as well as of their covariance, thus filling this gap in the literature.

scholarly journals A balance index for phylogenetic trees based on quartets

2018 ◽  
Author(s):  
Tomás M. Coronado ◽  
Arnau Mir ◽  
Francesc Rosselló ◽  
Gabriel Valiente
Keyword(s):  
Phylogenetic Trees ◽  
Expected Value ◽  
History Of ◽  
Number Of Leaves ◽  
Time Linear ◽  
Balance Index

AbstractWe define a new balance index for phylogenetic trees based on the symmetry of the evolutive history of every quartet of leaves. This index makes sense for polytomic trees and it can be computed in time linear in the number of leaves. We compute its maximum and minimum values for arbitrary and bifurcating trees, and we provide exact formulas for its expected value and variance for bifurcating trees under Ford’s α-model and Aldous’ β-model and for arbitrary trees under the α-γ-model.

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

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.

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