scholarly journals A Beta-splitting model for evolutionary trees

2016 ◽  
Vol 3 (5) ◽  
pp. 160016 ◽  
Author(s):  
Raazesh Sainudiin ◽  
Amandine Véber
Keyword(s):  
Continuous Time ◽  
Rooted Tree ◽  
Tree Topology ◽  
Sister Species ◽  
Evolutionary Trees ◽  
Diversification Rates ◽  
Branch Lengths ◽  
The Creation ◽  
Natural Way

In this article, we construct a generalization of the Blum–François Beta-splitting model for evolutionary trees, which was itself inspired by Aldous' Beta-splitting model on cladograms. The novelty of our approach allows for asymmetric shares of diversification rates (or diversification ‘potential’) between two sister species in an evolutionarily interpretable manner, as well as the addition of extinction to the model in a natural way. We describe the incremental evolutionary construction of a tree with n leaves by splitting or freezing extant lineages through the generating, organizing and deleting processes. We then give the probability of any (binary rooted) tree under this model with no extinction, at several resolutions: ranked planar trees giving asymmetric roles to the first and second offspring species of a given species and keeping track of the order of the speciation events occurring during the creation of the tree, unranked planar trees , ranked non-planar trees and finally ( unranked non-planar ) trees . We also describe a continuous-time equivalent of the generating, organizing and deleting processes where tree topology and branch lengths are jointly modelled and provide code in SageMath/Python for these algorithms.

Das Präphysiche Stadium und der Anfang der Welt

1998 ◽  
pp. 74-80
Author(s):  
Malgorzata Szczesniak
Keyword(s):  
Physical State ◽  
Big Bang ◽  
Evolution Of The Universe ◽  
Time Period ◽  
The Creation ◽  
The Absolute ◽  
The Big Bang ◽  
The Universe ◽  
Natural Way

This paper concerns the main physical, philosophical and existential aspects of the ‘pre-physical’ stage in the evolution of the universe. I will discuss the ways that contemporary cosmology tries to: (1) solve the problem about the time period of the ‘pre-physical’ state; (2) answer the question whether the beginning of time was at the same time as the beginning of the existence of the Universe; (3) answer another whether the Big Bang was an absolute beginning of the existence of the Universe or only a beginning of some stage of its evolution; (4) respond to another question whether the absolute beginning of the Universe inevitably implies its creation by God or whether it allows for the possibility of the creation of the Universe in a natural way; and (5) discuss the issue of the ‘singular’ moment. All of these questions, in particular the last one, will be discussed with reference to the latest achievements in the fields of physics and cosmology.

scholarly journals Markov Katana: a Novel Method for Bayesian Resampling of Parameter Space Applied to Phylogenetic Trees

2018 ◽  
Author(s):  
Stephen T. Pollard ◽  
Kenji Fukushima ◽  
Zhengyuan O. Wang ◽  
Todd A. Castoe ◽  
David D. Pollock
Keyword(s):  
Phylogenetic Tree ◽  
Phylogenetic Trees ◽  
Statistical Approach ◽  
Evolutionary Model ◽  
Complex Model ◽  
Tree Topology ◽  
Added Value ◽  
General Idea ◽  
Branch Lengths ◽  
Tree Space

ABSTRACTPhylogenetic inference requires a means to search phylogenetic tree space. This is usually achieved using progressive algorithms that propose and test small alterations in the current tree topology and branch lengths. Current programs search tree topology space using branch-swapping algorithms, but proposals do not discriminate well between swaps likely to succeed or fail. When applied to datasets with many taxa, the huge number of possible topologies slows these programs dramatically. To overcome this, we developed a statistical approach for proposal generation in Bayesian analysis, and evaluated its applicability for the problem of searching phylogenetic tree space. The general idea of the approach, which we call ‘Markov katana’, is to make proposals based on a heuristic algorithm using bootstrapped subsets of the data. Such proposals induce an unintended sampling distribution that must be determined and removed to generate posterior estimates, but the cost of this extra step can in principle be small compared to the added value of more efficient parameter exploration in Markov chain Monte Carlo analyses. Our prototype application uses the simple neighbor-joining distance heuristic on data subsets to propose new reasonably likely phylogenetic trees (including topologies and branch lengths). The evolutionary model used to generate distances in our prototype was far simpler than the more complex model used to evaluate the likelihood of phylogenies based on the full dataset. This prototype implementation indicates that the Markov katana approach could be easily incorporated into existing phylogenetic search programs and may prove a useful alternative in conjunction with existing methods. The general features of this statistical approach may also prove useful in disciplines other than phylogenetics. We demonstrate that this method can be used to efficiently estimate a Bayesian posterior.

scholarly journals Molecular identification of Rosa x damascena growing in Taif region (Saudi Arabia)

2016 ◽  
Vol 7 (1) ◽  
Author(s):  
Sayed Amer ◽  
Salih A. Basaid ◽  
Esmat Ali
Keyword(s):  
Saudi Arabia ◽  
Maximum Likelihood ◽  
Genetic Distance ◽  
Molecular Identification ◽  
Maximum Parsimony ◽  
Rooted Tree ◽  
Tree Topology ◽  
Neighbor Joining ◽  
Likelihood Methods ◽  
Maximum Likelihood Methods

A fragment of 772 bp of the chloroplast maturase K gene was amplified and sequenced for <em>Rosa x damascena trigintipetala</em> variety growing in Taif region of Saudi Arabia. The data were aligned with their counterparts of other varieties already found in the Genbank database and were analyzed by maximum-parsimony, neighbor-joining and maximum-likelihood methods and a single rooted tree was executed. <em>R. x damascena trigintipetala</em> was paraphyletic where one sample [A] clustered with all varieties while the second [B] was basal. <em>R. x damascena</em> was sister to <em>R. x chinensis semperflorens</em> with the later being basal. <em>R. x damascena gori</em> was basal for all taxa studied. <em>R. moschata</em> was inside the clade of <em>R. x damascena</em>. Hybridization could be possible among <em>R. damascena, R. chinensis</em> and <em>R. moschata</em>. The genetic distance and tree topology indicated that [A] variety could be originated from <em>R. moshata</em> while [B] could be originated from gori or <em>R. chinensis semperflorens</em>. We, therefore, may consider that <em>R. x damascena gori</em> or <em>R. chinensis</em> could be the origin of all nowadays <em>R. x damascena</em> varieties.

The probabilities of rooted tree-shapes generated by random bifurcation

1971 ◽  
Vol 3 (01) ◽  
pp. 44-77 ◽  
Author(s):  
E. F. Harding
Keyword(s):  
Probability Distribution ◽  
Statistical Approach ◽  
Rooted Tree ◽  
Difficult Problem ◽  
Numerical Results ◽  
Rooted Trees ◽  
Evolutionary Trees ◽  
Mathematical Problems ◽  
Labelled Trees ◽  
Random Bifurcation

The set of rooted trees, generated by random bifurcation at the terminal nodes, is considered with the aims of enumerating it and of determining its probability distribution. The account of enumeration collates much previous work and attempts a complete perspective of the problems and their solutions. Asymptotic and numerical results are given, and some unsolved problems are pointed out. The problem of ascertaining the probability distribution is solved by obtaining its governing recurrence equation, and numerical results are given. The difficult problem of determining the most probable tree-shape of given size is considered, and for labelled trees a conjecture at its solution is offered. For unlabelled shapes the problem remains open. These mathematical problems arise in attempting to reconstruct evolutionary trees by the statistical approach of Cavalli-Sforza and Edwards.

scholarly journals A metric on phylogenetic tree shapes

2016 ◽  
Author(s):  
C. Colijn ◽  
G. Plazzotta
Keyword(s):  
Phylogenetic Tree ◽  
Influenza A ◽  
Evolutionary Process ◽  
Evolutionary Trees ◽  
Full Characterization ◽  
Branch Lengths ◽  
Random Models ◽  
Branching Trees ◽  
Seasonal Flu

AbstractThe shapes of evolutionary trees are influenced by the nature of the evolutionary process, but comparisons of trees from different processes are hindered by the challenge of completely describing tree shape. We present a full characterization of the shapes of rooted branching trees in a form that lends itself to natural tree comparisons. The resulting metric distinguishes trees from random models known to produce different tree shapes. It separates trees derived from tropical vs USA influenza A sequences, which reflect the differing epidemiology of tropical and seasonal flu. We extend the shape metric to incorporate summary features such as asymmetry, or statistics on branch lengths. Our approach allows us to construct addition and multiplication on trees, and to create a convex metric on tree shapes which formally allows computation of average trees.

scholarly journals Creation of discontinuities in circle maps

2021 ◽  
Vol 477 (2251) ◽  
pp. 20200872
Author(s):  
G. Derks ◽  
P. A. Glendinning ◽  
A. C. Skeldon
Keyword(s):  
Cardiac Arrhythmias ◽  
Generic Properties ◽  
Circle Maps ◽  
Codimension Two ◽  
Integrate And Fire ◽  
Arnold Tongue ◽  
Saddle Node ◽  
The Creation ◽  
Natural Way ◽  
Codimension Two Bifurcation

Circle maps frequently arise in mathematical models of physical or biological systems. Motivated by Cherry flows and ‘threshold’ systems such as integrate and fire neuronal models, models of cardiac arrhythmias, and models of sleep/wake regulation, we consider how structural transitions in circle maps occur. In particular, we describe how maps evolve near the creation of a discontinuity. We show that the natural way to create discontinuities in the maps associated with both threshold systems and Cherry flows results in a singularity in the derivative of the map as the discontinuity is approached from either one or both sides. For the threshold systems, the associated maps have square root singularities and we analyse the generic properties of such maps with gaps, showing how border collisions and saddle-node bifurcations are interspersed. This highlights how the Arnold tongue picture for tongues bordered by saddle-node bifurcations is amended once gaps are present. We also show that a loss of injectivity naturally results in the creation of multiple gaps giving rise to a novel codimension two bifurcation.

scholarly journals OPERATORS OF GAMMA WHITE NOISE CALCULUS

2000 ◽  
Vol 03 (03) ◽  
pp. 303-335 ◽  
Author(s):  
YURI G. KONDRATIEV ◽  
EUGENE W. LYTVYNOV
Keyword(s):  
White Noise ◽  
Fock Space ◽  
Noise Analysis ◽  
Gamma Field ◽  
Chaos Decomposition ◽  
The Creation ◽  
The Fourier Transform ◽  
White Noise Calculus ◽  
Adjoint Operators ◽  
Natural Way

The paper is devoted to the study of Gamma white noise analysis. We define an extended Fock space ℱ ext (ℋ) over ℋ= L2(ℝd, dσ) and show how to include the usual Fock space ℱ(ℋ) in it as a subspace. We introduce in ℱ ext (ℋ) operators a(ξ)=∫ℝddxξ(x)a(x), ξ∈ S, with [Formula: see text], where [Formula: see text] and ∂x are the creation and annihilation operators at x. We show that (a(ξ))ξ∈S is a family of commuting self-adjoint operators in ℱ ext (ℋ) and construct the Fourier transform in generalized joint eigenvectors of this family. This transform is a unitary I between ℱ ext (ℋ) and the L2-space L2(S', dμ G ), where μ G is the measure of Gamma white noise with intensity σ. The image of a(ξ) under I is the operator of multiplication by <·,ξ>, so that a(ξ)'s are Gamma field operators. The Fock structure of the Gamma space determined by I coincides with that discovered in Ref. 22. We note that I extends in a natural way the multiple stochastic integral (chaos) decomposition of the "chaotic" subspace of the Gamma space. Next, we introduce and study spaces of test and generalized functions of Gamma white noise and derive explicit formulas for the action of the creation, neutral, and Gamma annihilation operators on these spaces.

scholarly journals Contingency Tests of Neutrality Using Intra/Interspecific Gene Trees: The Rejection of Neutrality for the Evolution of the Mitochondrial Cytochrome Oxidase II Gene in the Hominoid Primates

Genetics ◽  
1996 ◽  
Vol 144 (3) ◽  
pp. 1263-1270 ◽  
Author(s):  
Alan R Templeton
Keyword(s):  
Cytochrome Oxidase ◽  
Dna Sequences ◽  
Evolutionary Dynamics ◽  
Tree Topology ◽  
Mitochondrial Cytochrome ◽  
Gene Trees ◽  
Branch Lengths ◽  
Tests Of Neutrality ◽  
Cytochrome Oxidase Ii ◽  
Mitochondrial Cytochrome Oxidase

Abstract Contingency tests of neutrality are performed using mitochondrial cytochrome oxidase II (COII) DNA sequences from hominoid primates, including humans. An intra-/interspecific haplotype tree is estimated, including a statistical assessment of ambiguities in tree topology and branch lengths. Four functional mutational categories are considered: silent and replacement substitutions in the transmembrane portion of the COII molecule, and silent and replacement substitutions in the cytosolic portion. Three tree topological mutational categories are used: intraspecific tips, intraspecific interiors, and interspecific fixed mutations. A full contingency analysis is performed, followed by nested contingency analyses. The analyses indicate that replacement mutations in the cytosolic portion are deleterious, and replacement mutations in the transmembrane portion and silent mutations throughout tend to be neutral. These conclusions are robust to ambiguities in tree topology and branch lengths. These inferences would have been impossible with an analysis that only contrasts silent and replacement vs. polymorphic and fixed. Also, intraspecific interior mutations have similar evolutionary dynamics to fixed mutations, so pooling tip and interior mutations into a single “polymorphic” class reduces power. Finally, the detected deleterious selection causes lowered inbreeding effective sizes, so arguments for small effective sizes in recent human evolutionary history based upon mitochondrial DNA may be invalid.

scholarly journals Distance Measures for Tumor Evolutionary Trees

2019 ◽  
Author(s):  
Zach DiNardo ◽  
Kiran Tomlinson ◽  
Anna Ritz ◽  
Layla Oesper
Keyword(s):  
Breast Cancer ◽  
Tree Topology ◽  
Distance Measures ◽  
Evolutionary Trees ◽  
Complex Relationship ◽  
Developmental History ◽  
Inheritance Patterns ◽  
Tree Inference ◽  
Subclonal Mutation ◽  
Inference Methods

AbstractIn recent years, there has been increased interest in studying cancer by using algorithmic methods to infer the evolutionary tree underlying a tumor’s developmental history. Quantitative measures that compare such trees are then vital to benchmarking these algorithmic tree inference methods, understanding the structure of the space of possible trees for a given dataset, and clustering together similar trees in order to evaluate inheritance patterns. However, few appropriate distance measures exist, and those that do exist have low resolution for differentiating trees or do not fully account for the complex relationship between tree topology and how the mutations that label that topology are inherited. Here we present two novel distance measures,CommonAncestorSetdistance (CASet) andDistinctlyInheritedSetComparison distance (DISC), that are specifically designed to account for the subclonal mutation inheritance patterns characteristic of tumor evolutionary trees. We apply CASet and DISC to two simulated and two breast cancer datasets and show that our distance measures allow for more nuanced and accurate delineation between tumor evolutionary trees than existing distance measures. Implementations of CASet and DISC are available at:https://bitbucket.org/oesperlab/stereodist.

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