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11
Identifying evolutionary trees and substitution parameters for the general Markov model with invariable sites
, 2007
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Markov invariants, plethysms, and phylogenetics
, 2007
"... We explore model based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we establish a commonality in some special cases. We show that t ..."
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We explore model based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the LogDet distance measure. We take as our primary tool group representation theory, and show that it provides a general framework for analysing Markov processes on trees. From this algebraic perspective, the inherent symmetries of these processes become apparent, and focusing on plethysms, we are able to define Markov invariants and give existence proofs. We give an explicit technique for constructing the invariants, valid for any number of character states and taxa. For phylogenetic trees with three and four leaves, we demonstrate that the corresponding Markov invariants can be fruitfully exploited in applied phylogenetic studies.
RH: EVOLUTIONARY TIME IN NONSTATIONARY SYSTEMS Genetic Distance for a General NonStationary Markov Substitution Process
, 2014
"... Abstract. — The genetic distance between biological sequences is a fundamental quantity in molecular evolution. It pertains to questions of rates of evolution, existence of a molecular © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. This ..."
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Abstract. — The genetic distance between biological sequences is a fundamental quantity in molecular evolution. It pertains to questions of rates of evolution, existence of a molecular © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. This is an Open Access article distributed under the terms of the Creative Commons Attribution License
The Impact of Reticulate Evolution on
, 2008
"... To link to this Article: DOI: 10.1080/10635150802559265 ..."
TABLE OF CONTENTS
, 1969
"... Sulfoxides as solvent extraction reagents for the analytical separation of metal ions ..."
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Sulfoxides as solvent extraction reagents for the analytical separation of metal ions
A Nonstationary Markov Model Detects Directional Evolution in Hymenopteran Morphology
, 2015
"... Abstract.—Directional evolution has played an important role in shaping the morphological, ecological, and molecular diversity of life. However, standard substitution models assume stationarity of the evolutionary process over the time scale examined, thus impeding the study of directionality.Herewe ..."
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Abstract.—Directional evolution has played an important role in shaping the morphological, ecological, and molecular diversity of life. However, standard substitution models assume stationarity of the evolutionary process over the time scale examined, thus impeding the study of directionality.Herewe explore a simple, nonstationarymodel of evolution for discrete data, which assumes that the state frequencies at the root differ from the equilibrium frequencies of the homogeneous evolutionary process along the rest of the tree (i.e., the process is nonstationary, nonreversible, but homogeneous). Within this framework, we develop a Bayesian approach for testing directional versus stationary evolution using a reversiblejump algorithm. Simulations show that when only data from extant taxa are available, the success in inferring directionality is strongly dependent on the evolutionary rate, the shape of the tree, the relative branch lengths, and the number of taxa. Given suitable evolutionary rates (0.1–0.5 expected substitutions between root and tips), accounting for directionality improves
Lowparameter phylogenetic estimation under the general Markov model
, 2014
"... In their 2008 and 2009 papers, Sumner and colleagues introduced the “squangles ” – a small set of Markov invariants for phylogenetic quartets. The squangles are consistent with the general Markov model (GM) and can be used to infer quartets without the need to explicitly estimate all parameters. As ..."
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In their 2008 and 2009 papers, Sumner and colleagues introduced the “squangles ” – a small set of Markov invariants for phylogenetic quartets. The squangles are consistent with the general Markov model (GM) and can be used to infer quartets without the need to explicitly estimate all parameters. As GM is inhomogeneous and hence nonstationary, the squangles are expected to perform well compared to standard approaches when there are changes in basecomposition amongst species. However, GM includes the IID assumption, so the squangles should be confounded by data generated with invariant sites or with ratevariation across sites. Here we implement the squangles in a leastsquares setting that returns quartets weighted by either confidence or internal edge lengths; and use these as input into a variety of quartetbased supertree methods. For the first time, we quantitatively investigate the robustness of the squangles to the breaking of IID assumptions on both simulated and real data sets; and we suggest a modification that improves the performance of the squangles in the presence of invariant sites. Our conclusion is that the squangles provide a novel tool for phylogenetic estimation that is complementary to methods that explicitly account for ratevariation across sites, but rely on homogeneous – and hence stationary – models.
A BranchHeterogeneous Model of Protein Evolution for Efficient Inference of Ancestral Sequences
, 2013
"... Abstract.—Most models of nucleotide or amino acid substitution used in phylogenetic studies assume that the evolutionary process has been homogeneous across lineages and that composition of nucleotides or amino acids has remained the same throughout the tree. These oversimplified assumptions are ref ..."
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Abstract.—Most models of nucleotide or amino acid substitution used in phylogenetic studies assume that the evolutionary process has been homogeneous across lineages and that composition of nucleotides or amino acids has remained the same throughout the tree. These oversimplified assumptions are refuted by the observation that compositional variability characterizes extant biological sequences. Branchheterogeneousmodels of protein evolution that account for compositional variability have been developed, but are not yet in common use because of the large number of parameters required, leading to high computational costs and potential overparameterization. Here, we present a new branchnonhomogeneous and nonstationary model of protein evolution that captures more accurately the high complexity of sequence evolution. This model, henceforth called Correspondence and likelihood analysis (COaLA), makes use of a correspondence analysis to reduce the number of parameters to be optimized through maximum likelihood, focusing on most of the compositional variation observed in the data. The model was thoroughly tested on both simulated and biological data sets to show its high performance in terms of data fitting and CPU time. COaLA efficiently estimates ancestral amino acid frequencies
Genetic Distance for a General NonStationary Markov Substitution Process
, 2015
"... The genetic distance between biological sequences is a fundamental quantity in molecular evolution. It pertains to questions of rates of evolution, existence of a molecular clock, and phylogenetic inference.Under the class of continuoustime substitution models, the distance is commonly defined as ..."
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The genetic distance between biological sequences is a fundamental quantity in molecular evolution. It pertains to questions of rates of evolution, existence of a molecular clock, and phylogenetic inference.Under the class of continuoustime substitution models, the distance is commonly defined as the expected number of substitutions at any site in the sequence. We eschew the almost ubiquitous assumptions of evolution under stationarity and timereversible conditions and extend the concept of the expected number of substitutions to nonstationary Markov models where the only remaining constraint is of time homogeneity between nodes in the tree. Our measure of genetic distance reduces to the standard formulation if the data in question are consistent with the stationarity assumption. We apply this general model to samples from across the tree of life to compare distances so obtained with those from the general timereversible model,with and without rate heterogeneity across sites, and the paralinear distance, an empirical pairwise method explicitly designed to address nonstationarity. We discover that estimates from both variants of the general timereversible model and the paralinear distance systematically