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18
On qualitative research
 Library & Information Science Research
, 1990
"... New substitution models for rooting phylogenetic trees cell emerges from within the archaeal radiation, depends critically on a root for on September 17, ..."
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New substitution models for rooting phylogenetic trees cell emerges from within the archaeal radiation, depends critically on a root for on September 17,
Estimation of phylogeny and invariant sites under the general Markov model of nucleotide sequence evolution
 Systematic Biology
"... Abstract.—The models of nucleotide substitution used by most maximum likelihoodbased methods assume that the evolutionary process is stationary, reversible, and homogeneous. We present an extension of the Barry and Hartigan model, which can be used to estimate parameters by maximum likelihood (ML) ..."
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Abstract.—The models of nucleotide substitution used by most maximum likelihoodbased methods assume that the evolutionary process is stationary, reversible, and homogeneous. We present an extension of the Barry and Hartigan model, which can be used to estimate parameters by maximum likelihood (ML) when the data contain invariant sites and there are violations of the assumptions of stationarity, reversibility, and homogeneity. Unlike most ML methods for estimating invariant sites, we estimate the nucleotide composition of invariant sites separately from that of variable sites. We analyze a bacterial data set where problems due to lack of stationarity and homogeneity have been previously well noted and use the parametric bootstrap to show that the data are consistent with our general Markov model. We also show that estimates of invariant sites obtained using our method are fairly accurate when applied to data simulated under the general Markov model. [Invariant sites; maximum likelihood; nonhomogeneous process; nonstationary process; nucleotide substitution; phylogenetics.] Many maximumlikelihoodbased methods for phylogenetic inference rely on explicit models of nucleotide substitution, the common underlying assumption being that the process is Markovian (i.e., the conditional probability of change at a given site depends only on the
2005 SEQVIS: visualization of compositional heterogeneity in large alignments of nucleotides
 2007 Phylogeny of the snailfishes (Teleostei: Liparidae) based on molecular and morphological
, 1997
"... Summary: Most phylogenetic methods assume that the sequences evolved under homogeneous, stationary and reversible conditions. Compositional heterogeneity in data intended for studies of phylogeny suggests that the data did not evolve under these conditions. SeqVis, a Java application for analysis of ..."
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Summary: Most phylogenetic methods assume that the sequences evolved under homogeneous, stationary and reversible conditions. Compositional heterogeneity in data intended for studies of phylogeny suggests that the data did not evolve under these conditions. SeqVis, a Java application for analysis of nucleotide content, reads sequence alignments in several formats and plots the nucleotide content in a tetrahedron. Once plotted, outliers can be identified, thus allowing for decisions on the applicability of the data for phylogenetic analysis.
An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci
, 2010
"... A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction ..."
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A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface — a generalization of the hyperplane found by Zhivotovsky et al. (1994) for a multilocus recombination modifier. Increases in mutation rates at some loci may evolve if compensated for by decreases at other loci. The strength of selection on the modifier scales in proportion to the number of germline cell divisions, and increases with the number of loci affected. Loci that do not make a difference to marginal fitnesses at equilibrium are not subject to the reduction principle, and under fine tuning of mutation rates would be expected to have higher mutation rates than loci in mutationselection balance. Other results include the nonexistence of ‘viability analogous, HardyWeinberg ’ modifier polymorphisms under multiplicative mutation, and the sufficiency of average transmission rates to encapsulate the effect of modifier polymorphisms on the transmission of loci under selection. A conjecture is offered regarding situations, like recombination in the presence of mutation, that exhibit departures from the reduction principle. Constraints for tractability are: tight linkage of all loci, initial fixation at the modifier locus, and mutation distributions comprising transition probabilities of reversible Markov chains. 1
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.
Evolutionary Reduction of Mutation Rates in a Multivariate, Multilocus Model ∗
, 909
"... The evolution of genetic systems has been studied through the use of modifier gene models, in which a selectively neutral gene controls genetic transmission of other genes under selection. Analytical studies to obtain a general understanding of the dynamics have faced tradeoffs between different fea ..."
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The evolution of genetic systems has been studied through the use of modifier gene models, in which a selectively neutral gene controls genetic transmission of other genes under selection. Analytical studies to obtain a general understanding of the dynamics have faced tradeoffs between different features for tractability. No study has been able to obtain results for arbitrary selection on multiple loci undergoing multiple genetic transformation events. Here techniques from Karlin (1982) are applied to a multilocus model of mutation with multivariate control over mutation rates, and the reduction principle is found to operate. Constraining assumptions are that mutation distributions follow the transition probabilities of reversible Markov chains, and that all loci are tightly linked. The extension of the reduction principle is shown topologically to require a manifold of mutation rate alterations that are neutral for a new modifier allele, below which will cause a new modifier allele to increase when rare, and above which cause it to go extinct. This manifold is the same structure as found in a multivariate multilocus model of recombination modification by Zhivotovsky et al. (1994). A discussion of the nearequilibrium models that depart from the reduction principle concludes with a conjecture about the structural causes.
This work is licensed under a Creative Commons Attribution 4.0 International License
, 2015
"... © 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons ..."
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© 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons
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
ORIGINAL RESEARCH Topological Bias in DistanceBased Phylogenetic Methods: Problems with Over and Underestimated Genetic Distances
"... Abstract: I show several types of topological biases in distancebased methods that use the leastsquares method to evaluate branch lengths and the minimum evolution (ME) or the FitchMargoliash (FM) criterion to choose the best tree. For a 6species tree, there are two tree shapes, one with three c ..."
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Abstract: I show several types of topological biases in distancebased methods that use the leastsquares method to evaluate branch lengths and the minimum evolution (ME) or the FitchMargoliash (FM) criterion to choose the best tree. For a 6species tree, there are two tree shapes, one with three cherries (a cherry is a pair of adjacent leaves descending from the most recent common ancestor), and the other with two. When genetic distances are underestimated, the 3cherry tree shape is favored with either the ME or FM criterion. When the genetic distances are overestimated, the ME criterion favors the 2cherry tree, but the direction of bias with the FM criterion depends on whether negative branches are allowed, i.e. allowing negative branches favors the 3cherry tree shape but disallowing negative branches favors the 2cherry tree shape. The extent of the bias is explored by computer simulation of sequence evolution. Keywords: topological bias, minimum evolution, leastsquares method, FitchMargoliash.