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Lecture Notes: the Mathematics of Phylogenetics
Lecture Notes: The Mathematics of Phylogenetics Elizabeth S. Allman, John A. Rhodes IAS/Park City Mathematics Institute June-July, 2005 University of Alaska Fairbanks Spring 2009, 2012, 2016 c 2005, Elizabeth S. Allman and John A. Rhodes ii Contents 1 Sequences and Molecular Evolution 3 1.1 DNA structure . .4 1.2 Mutations . .5 1.3 Aligned Orthologous Sequences . .7 2 Combinatorics of Trees I 9 2.1 Graphs and Trees . .9 2.2 Counting Binary Trees . 14 2.3 Metric Trees . 15 2.4 Ultrametric Trees and Molecular Clocks . 17 2.5 Rooting Trees with Outgroups . 18 2.6 Newick Notation . 19 2.7 Exercises . 20 3 Parsimony 25 3.1 The Parsimony Criterion . 25 3.2 The Fitch-Hartigan Algorithm . 28 3.3 Informative Characters . 33 3.4 Complexity . 35 3.5 Weighted Parsimony . 36 3.6 Recovering Minimal Extensions . 38 3.7 Further Issues . 39 3.8 Exercises . 40 4 Combinatorics of Trees II 45 4.1 Splits and Clades . 45 4.2 Refinements and Consensus Trees . 49 4.3 Quartets . 52 4.4 Supertrees . 53 4.5 Final Comments . 54 4.6 Exercises . 55 iii iv CONTENTS 5 Distance Methods 57 5.1 Dissimilarity Measures . 57 5.2 An Algorithmic Construction: UPGMA . 60 5.3 Unequal Branch Lengths . 62 5.4 The Four-point Condition . 66 5.5 The Neighbor Joining Algorithm . 70 5.6 Additional Comments . 72 5.7 Exercises . 73 6 Probabilistic Models of DNA Mutation 81 6.1 A first example . 81 6.2 Markov Models on Trees . 87 6.3 Jukes-Cantor and Kimura Models . -
Phylogenetic Trees and Cladograms Are Graphical Representations (Models) of Evolutionary History That Can Be Tested
AP Biology Lab/Cladograms and Phylogenetic Trees Name _______________________________ Relationship to the AP Biology Curriculum Framework Big Idea 1: The process of evolution drives the diversity and unity of life. Essential knowledge 1.B.2: Phylogenetic trees and cladograms are graphical representations (models) of evolutionary history that can be tested. Learning Objectives: LO 1.17 The student is able to pose scientific questions about a group of organisms whose relatedness is described by a phylogenetic tree or cladogram in order to (1) identify shared characteristics, (2) make inferences about the evolutionary history of the group, and (3) identify character data that could extend or improve the phylogenetic tree. LO 1.18 The student is able to evaluate evidence provided by a data set in conjunction with a phylogenetic tree or a simple cladogram to determine evolutionary history and speciation. LO 1.19 The student is able create a phylogenetic tree or simple cladogram that correctly represents evolutionary history and speciation from a provided data set. [Introduction] Cladistics is the study of evolutionary classification. Cladograms show evolutionary relationships among organisms. Comparative morphology investigates characteristics for homology and analogy to determine which organisms share a recent common ancestor. A cladogram will begin by grouping organisms based on a characteristics displayed by ALL the members of the group. Subsequently, the larger group will contain increasingly smaller groups that share the traits of the groups before them. However, they also exhibit distinct changes as the new species evolve. Further, molecular evidence from genes which rarely mutate can provide molecular clocks that tell us how long ago organisms diverged, unlocking the secrets of organisms that may have similar convergent morphology but do not share a recent common ancestor. -
An Introduction to Phylogenetic Analysis
This article reprinted from: Kosinski, R.J. 2006. An introduction to phylogenetic analysis. Pages 57-106, in Tested Studies for Laboratory Teaching, Volume 27 (M.A. O'Donnell, Editor). Proceedings of the 27th Workshop/Conference of the Association for Biology Laboratory Education (ABLE), 383 pages. Compilation copyright © 2006 by the Association for Biology Laboratory Education (ABLE) ISBN 1-890444-09-X All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the copyright owner. Use solely at one’s own institution with no intent for profit is excluded from the preceding copyright restriction, unless otherwise noted on the copyright notice of the individual chapter in this volume. Proper credit to this publication must be included in your laboratory outline for each use; a sample citation is given above. Upon obtaining permission or with the “sole use at one’s own institution” exclusion, ABLE strongly encourages individuals to use the exercises in this proceedings volume in their teaching program. Although the laboratory exercises in this proceedings volume have been tested and due consideration has been given to safety, individuals performing these exercises must assume all responsibilities for risk. The Association for Biology Laboratory Education (ABLE) disclaims any liability with regards to safety in connection with the use of the exercises in this volume. The focus of ABLE is to improve the undergraduate biology laboratory experience by promoting the development and dissemination of interesting, innovative, and reliable laboratory exercises. -
Phylogenetic Definitions in the Pre-Phylocode Era; Implications for Naming Clades Under the Phylocode
PaleoBios 27(1):1–6, April 30, 2007 © 2006 University of California Museum of Paleontology Phylogenetic definitions in the pre-PhyloCode era; implications for naming clades under the PhyloCode MiChAel P. TAylor Palaeobiology research Group, School of earth and environmental Sciences, University of Portsmouth, Portsmouth Po1 3Ql, UK; [email protected] The last twenty years of work on phylogenetic nomenclature have given rise to many names and definitions that are now considered suboptimal. in formulating permanent definitions under the PhyloCode when it is implemented, it will be necessary to evaluate the corpus of existing names and make judgements about which to establish and which to discard. This is not straightforward, because early definitions are often inexplicit and ambiguous, generally do not meet the requirements of the PhyloCode, and in some cases may not be easily recognizable as phylogenetic definitions at all. recognition of synonyms is also complicated by the use of different kinds of specifiers (species, specimens, clades, genera, suprageneric rank-based names, and vernacular names) and by definitions whose content changes under different phylogenetic hypotheses. in light of these difficulties, five principles are suggested to guide the interpreta- tion of pre-PhyloCode clade-names and to inform the process of naming clades under the PhyloCode: (1) do not recognize “accidental” definitions; (2) malformed definitions should be interpreted according to the intention of the author when and where this is obvious; (3) apomorphy-based and other definitions must be recognized as well as node-based and stem-based definitions; (4) definitions using any kind of specifier taxon should be recognized; and (5) priority of synonyms and homonyms should guide but not prescribe. -
Phylogeny Codon Models • Last Lecture: Poor Man’S Way of Calculating Dn/Ds (Ka/Ks) • Tabulate Synonymous/Non-Synonymous Substitutions • Normalize by the Possibilities
Phylogeny Codon models • Last lecture: poor man’s way of calculating dN/dS (Ka/Ks) • Tabulate synonymous/non-synonymous substitutions • Normalize by the possibilities • Transform to genetic distance KJC or Kk2p • In reality we use codon model • Amino acid substitution rates meet nucleotide models • Codon(nucleotide triplet) Codon model parameterization Stop codons are not allowed, reducing the matrix from 64x64 to 61x61 The entire codon matrix can be parameterized using: κ kappa, the transition/transversionratio ω omega, the dN/dS ratio – optimizing this parameter gives the an estimate of selection force πj the equilibrium codon frequency of codon j (Goldman and Yang. MBE 1994) Empirical codon substitution matrix Observations: Instantaneous rates of double nucleotide changes seem to be non-zero There should be a mechanism for mutating 2 adjacent nucleotides at once! (Kosiol and Goldman) • • Phylogeny • • Last lecture: Inferring distance from Phylogenetic trees given an alignment How to infer trees and distance distance How do we infer trees given an alignment • • Branch length Topology d 6-p E 6'B o F P Edo 3 vvi"oH!.- !fi*+nYolF r66HiH- .) Od-:oXP m a^--'*A ]9; E F: i ts X o Q I E itl Fl xo_-+,<Po r! UoaQrj*l.AP-^PA NJ o - +p-5 H .lXei:i'tH 'i,x+<ox;+x"'o 4 + = '" I = 9o FF^' ^X i! .poxHo dF*x€;. lqEgrE x< f <QrDGYa u5l =.ID * c 3 < 6+6_ y+ltl+5<->-^Hry ni F.O+O* E 3E E-f e= FaFO;o E rH y hl o < H ! E Y P /-)^\-B 91 X-6p-a' 6J. -
Diversity-Dependent Cladogenesis Throughout Western Mexico: Evolutionary Biogeography of Rattlesnakes (Viperidae: Crotalinae: Crotalus and Sistrurus)
City University of New York (CUNY) CUNY Academic Works Publications and Research New York City College of Technology 2016 Diversity-dependent cladogenesis throughout western Mexico: Evolutionary biogeography of rattlesnakes (Viperidae: Crotalinae: Crotalus and Sistrurus) Christopher Blair CUNY New York City College of Technology Santiago Sánchez-Ramírez University of Toronto How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/ny_pubs/344 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] 1Blair, C., Sánchez-Ramírez, S., 2016. Diversity-dependent cladogenesis throughout 2 western Mexico: Evolutionary biogeography of rattlesnakes (Viperidae: Crotalinae: 3 Crotalus and Sistrurus ). Molecular Phylogenetics and Evolution 97, 145–154. 4 https://doi.org/10.1016/j.ympev.2015.12.020. © 2016. This manuscript version is made 5 available under the CC-BY-NC-ND 4.0 license. 6 7 8 Diversity-dependent cladogenesis throughout western Mexico: evolutionary 9 biogeography of rattlesnakes (Viperidae: Crotalinae: Crotalus and Sistrurus) 10 11 12 CHRISTOPHER BLAIR1*, SANTIAGO SÁNCHEZ-RAMÍREZ2,3,4 13 14 15 1Department of Biological Sciences, New York City College of Technology, Biology PhD 16 Program, Graduate Center, The City University of New York, 300 Jay Street, Brooklyn, 17 NY 11201, USA. 18 2Department of Ecology and Evolutionary Biology, University of Toronto, 25 Willcocks 19 Street, Toronto, ON, M5S 3B2, Canada. 20 3Department of Natural History, Royal Ontario Museum, 100 Queen’s Park, Toronto, 21 ON, M5S 2C6, Canada. 22 4Present address: Environmental Genomics Group, Max Planck Institute for 23 Evolutionary Biology, August-Thienemann-Str. -
A Phylogenetic Analysis of the Basal Ornithischia (Reptilia, Dinosauria)
A PHYLOGENETIC ANALYSIS OF THE BASAL ORNITHISCHIA (REPTILIA, DINOSAURIA) Marc Richard Spencer A Thesis Submitted to the Graduate College of Bowling Green State University in partial fulfillment of the requirements of the degree of MASTER OF SCIENCE December 2007 Committee: Margaret M. Yacobucci, Advisor Don C. Steinker Daniel M. Pavuk © 2007 Marc Richard Spencer All Rights Reserved iii ABSTRACT Margaret M. Yacobucci, Advisor The placement of Lesothosaurus diagnosticus and the Heterodontosauridae within the Ornithischia has been problematic. Historically, Lesothosaurus has been regarded as a basal ornithischian dinosaur, the sister taxon to the Genasauria. Recent phylogenetic analyses, however, have placed Lesothosaurus as a more derived ornithischian within the Genasauria. The Fabrosauridae, of which Lesothosaurus was considered a member, has never been phylogenetically corroborated and has been considered a paraphyletic assemblage. Prior to recent phylogenetic analyses, the problematic Heterodontosauridae was placed within the Ornithopoda as the sister taxon to the Euornithopoda. The heterodontosaurids have also been considered as the basal member of the Cerapoda (Ornithopoda + Marginocephalia), the sister taxon to the Marginocephalia, and as the sister taxon to the Genasauria. To reevaluate the placement of these taxa, along with other basal ornithischians and more derived subclades, a phylogenetic analysis of 19 taxonomic units, including two outgroup taxa, was performed. Analysis of 97 characters and their associated character states culled, modified, and/or rescored from published literature based on published descriptions, produced four most parsimonious trees. Consistency and retention indices were calculated and a bootstrap analysis was performed to determine the relative support for the resultant phylogeny. The Ornithischia was recovered with Pisanosaurus as its basalmost member. -
Is Ellipura Monophyletic? a Combined Analysis of Basal Hexapod
ARTICLE IN PRESS Organisms, Diversity & Evolution 4 (2004) 319–340 www.elsevier.de/ode Is Ellipura monophyletic? A combined analysis of basal hexapod relationships with emphasis on the origin of insects Gonzalo Giribeta,Ã, Gregory D.Edgecombe b, James M.Carpenter c, Cyrille A.D’Haese d, Ward C.Wheeler c aDepartment of Organismic and Evolutionary Biology, Museum of Comparative Zoology, Harvard University, 16 Divinity Avenue, Cambridge, MA 02138, USA bAustralian Museum, 6 College Street, Sydney, New South Wales 2010, Australia cDivision of Invertebrate Zoology, American Museum of Natural History, Central Park West at 79th Street, New York, NY 10024, USA dFRE 2695 CNRS, De´partement Syste´matique et Evolution, Muse´um National d’Histoire Naturelle, 45 rue Buffon, F-75005 Paris, France Received 27 February 2004; accepted 18 May 2004 Abstract Hexapoda includes 33 commonly recognized orders, most of them insects.Ongoing controversy concerns the grouping of Protura and Collembola as a taxon Ellipura, the monophyly of Diplura, a single or multiple origins of entognathy, and the monophyly or paraphyly of the silverfish (Lepidotrichidae and Zygentoma s.s.) with respect to other dicondylous insects.Here we analyze relationships among basal hexapod orders via a cladistic analysis of sequence data for five molecular markers and 189 morphological characters in a simultaneous analysis framework using myriapod and crustacean outgroups.Using a sensitivity analysis approach and testing for stability, the most congruent parameters resolve Tricholepidion as sister group to the remaining Dicondylia, whereas most suboptimal parameter sets group Tricholepidion with Zygentoma.Stable hypotheses include the monophyly of Diplura, and a sister group relationship between Diplura and Protura, contradicting the Ellipura hypothesis.Hexapod monophyly is contradicted by an alliance between Collembola, Crustacea and Ectognatha (i.e., exclusive of Diplura and Protura) in molecular and combined analyses. -
The Caper Package: Comparative Analysis of Phylogenetics and Evolution in R
The caper package: comparative analysis of phylogenetics and evolution in R David Orme April 16, 2018 This vignette documents the use of the caper package for R (R Development Core Team, 2011) in carrying out a range of comparative analysis methods for phylogenetic data. The caper package, and the code in this vignette, requires the ape package (Paradis et al., 2004) along with the packages mvtnorm and MASS. Contents 1 Background 2 2 Comparative datasets 3 2.1 The comparative.data class and objects. .3 2.1.1 na.omit ......................................3 2.1.2 subset ......................................5 2.1.3 [ ..........................................5 2.2 Example datasets . .6 3 Methods and functions provided by caper. 7 3.0.1 Phylogenetic linear models . .7 3.0.2 Fitting phylogenetic GLS models: pgls ....................8 3.1 Optimising branch length transformations: profile.pgls...............9 3.1.1 Criticism and simplification ofpgls models: plot, anova and AIC...... 11 3.2 Phylogenetic independent contrasts . 12 3.2.1 Variable names in contrast functions . 12 3.2.2 Continuous variables: crunch .......................... 13 3.2.3 Categorical variables: brunch .......................... 13 3.2.4 Species richness contrasts: macrocaic ..................... 14 3.2.5 Phylogenetic signal: phylo.d .......................... 15 3.3 Checking and comparing contrast models. 16 3.3.1 Testing evolutionary assumptions: caic.diagnostics............. 16 3.3.2 Robust contrasts: caic.robust ......................... 17 3.3.3 Model criticism: plot .............................. 19 3.3.4 Model comparison: anova & AIC ........................ 20 3.4 Other comparative functions . 21 3.4.1 Tree imbalance: fusco.test .......................... 21 3.5 Phylogenetic diversity: pd.calc, pd.bootstrap and ed.calc............ -
Interpreting Cladograms Notes
Interpreting Cladograms Notes INTERPRETING CLADOGRAMS BIG IDEA: PHYLOGENIES DEPICT ANCESTOR AND DESCENDENT RELATIONSHIPS AMONG ORGANISMS BASED ON HOMOLOGY THESE EVOLUTIONARY RELATIONSHIPS ARE REPRESENTED BY DIAGRAMS CALLED CLADOGRAMS (BRANCHING DIAGRAMS THAT ORGANIZE RELATIONSHIPS) What is a Cladogram ● A diagram which shows ● Is not an evolutionary ___________ among tree, ___________show organisms. how ancestors are related ● Lines branching off other to descendants or how lines. The lines can be much they have changed traced back to where they branch off. These branching off points represent a hypothetical ancestor. Parts of a Cladogram Reading Cladograms ● Read like a family tree: show ________of shared ancestry between lineages. • When an ancestral lineage______: speciation is indicated due to the “arrival” of some new trait. Each lineage has unique ____to itself alone and traits that are shared with other lineages. each lineage has _______that are unique to that lineage and ancestors that are shared with other lineages — common ancestors. Quick Question #1 ●What is a_________? ● A group that includes a common ancestor and all the descendants (living and extinct) of that ancestor. Reading Cladogram: Identifying Clades ● Using a cladogram, it is easy to tell if a group of lineages forms a clade. ● Imagine clipping a single branch off the phylogeny ● all of the organisms on that pruned branch make up a clade Quick Question #2 ● Looking at the image to the right: ● Is the green box a clade? ● The blue? ● The pink? ● The orange? Reading Cladograms: Clades ● Clades are nested within one another ● they form a nested hierarchy. ● A clade may include many thousands of species or just a few. -
Conceptual Issues in Phylogeny, Taxonomy, and Nomenclature
Contributions to Zoology, 66 (1) 3-41 (1996) SPB Academic Publishing bv, Amsterdam Conceptual issues in phylogeny, taxonomy, and nomenclature Alexandr P. Rasnitsyn Paleontological Institute, Russian Academy ofSciences, Profsoyuznaya Street 123, J17647 Moscow, Russia Keywords: Phylogeny, taxonomy, phenetics, cladistics, phylistics, principles of nomenclature, type concept, paleoentomology, Xyelidae (Vespida) Abstract On compare les trois approches taxonomiques principales développées jusqu’à présent, à savoir la phénétique, la cladis- tique et la phylistique (= systématique évolutionnaire). Ce Phylogenetic hypotheses are designed and tested (usually in dernier terme s’applique à une approche qui essaie de manière implicit form) on the basis ofa set ofpresumptions, that is, of à les traits fondamentaux de la taxonomic statements explicite représenter describing a certain order of things in nature. These traditionnelle en de leur et particulier son usage preuves ayant statements are to be accepted as such, no matter whatever source en même temps dans la similitude et dans les relations de evidence for them exists, but only in the absence ofreasonably parenté des taxons en question. L’approche phylistique pré- sound evidence pleading against them. A set ofthe most current sente certains avantages dans la recherche de réponses aux phylogenetic presumptions is discussed, and a factual example problèmes fondamentaux de la taxonomie. ofa practical realization of the approach is presented. L’auteur considère la nomenclature A is made of the three -
Probabilistic Methods Surpass Parsimony When Assessing Clade Support in Phylogenetic Analyses of Discrete Morphological Data
O'Reilly, J., Puttick, M., Pisani, D., & Donoghue, P. (2017). Probabilistic methods surpass parsimony when assessing clade support in phylogenetic analyses of discrete morphological data. Palaeontology. https://doi.org/10.1111/pala.12330 Publisher's PDF, also known as Version of record License (if available): CC BY Link to published version (if available): 10.1111/pala.12330 Link to publication record in Explore Bristol Research PDF-document This is the final published version of the article (version of record). It first appeared online via Wiley at http://onlinelibrary.wiley.com/doi/10.1111/pala.12330/abstract. Please refer to any applicable terms of use of the publisher. University of Bristol - Explore Bristol Research General rights This document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/red/research-policy/pure/user-guides/ebr-terms/ [Palaeontology, 2017, pp. 1–14] PROBABILISTIC METHODS SURPASS PARSIMONY WHEN ASSESSING CLADE SUPPORT IN PHYLOGENETIC ANALYSES OF DISCRETE MORPHOLOGICAL DATA by JOSEPH E. O’REILLY1 ,MARKN.PUTTICK1,2 , DAVIDE PISANI1,3 and PHILIP C. J. DONOGHUE1 1School of Earth Sciences, University of Bristol, Life Sciences Building, Tyndall Avenue, Bristol, BS8 1TQ, UK; [email protected]; [email protected]; [email protected]; [email protected] 2Department of Earth Sciences, The Natural History Museum, Cromwell Road, London, SW7 5BD, UK 3School of Biological Sciences, University of Bristol, Life Sciences Building, Tyndall Avenue, Bristol, BS8 1TQ, UK Typescript received 28 April 2017; accepted in revised form 13 September 2017 Abstract: Fossil taxa are critical to inferences of historical 50% support.