Biological Classification Cladistics Cladistics

Total Page:16

File Type:pdf, Size:1020Kb

Biological Classification Cladistics Cladistics Biological Classification Taxonomy & Linnaean Hierarchy Biological Classification • Levels called taxa (sing., taxon: “classification”) – The more similar two organisms are, the more levels “King Philip Came they have in common “Kings Play Chess On F • Taxonomy: naming & classifying a) Kingdom organisms b) Phylum (Division)* c) Class • Systematics: studying relationships Over F d) Order among taxonomic groups ine Gorreen Good Sand” Soup” e) Family* f) Genus g) Species *not in the original Linnaean hierarchy Carl Linné, 1737 IV. Phylogenetic Systems Problem: Divergence vs. Convergence • Classified based on presumed common ancestry — Homology vs. Analogy • Levels in common suggests a more recent divergence from a common ancestor. • But since we don’t actually know the ancestry above Similarity due to the level of genus or maybe family, dependent upon convergence is degrees of similarity. analogy. – Comparative morphology & anatomy – Comparative embryology (Similar – Comparative biochemistry — proteins & DNA adaptations to • Much disagreement may be debated regarding similar environments; which similarities and which differences are most not shared ancestry.) phylogenetically significant! Cladistics Cladistics More vocabulary: • Clade (“branch”) — replace traditional taxon • A true clade must be monophyletic – Groups of organisms presumed to be derived – must include an ancestor and all of the known from a common ancestor are organized by descendants of that ancestor. bifurcating (two-way splitting) of a branch • A grouping that only includes an ancestor and some of its descendants is paraphyletic. – Each bifurcation is based upon the acquisition • A grouping that includes organisms from different of a new, unique character (apomorphy). ancestries is polyphyletic. • Maximum parsimony: the branch pattern that • Derived apomorphic characters shared by can be created with the fewest required steps is members of a clade are synapomorphic. most likely the most correct. • Ancestral characteristics inherited prior to the branching of a clade are plesiomorphic. Heyer 1 Biological Classification For example: ©Pearson Education, Inc. Assuming this cladogram is correct: ©Pearson Education, Inc. • Retractable claws is a synapomorphic character for the Family Felidae. Hair, Carnivorous teeth, Retractable claws, & Ability to • Hair & Carnivorous teeth are plesiomorphic characters for the purr are all apomorphic characters in the presumed Family Felidae. ancestry of the domestic cat Assuming this cladogram is correct: ©Pearson Education, Inc. Assuming this cladogram is correct: ©Pearson Education, Inc. • Carnivorous teeth is a synapomorphic character for the • Hair is a synapomorphic character (synapomorphy) for the Order Carnivora. Class Mammalia. • Hair is a plesiomorphic character for the Order Carnivora. Tiger Shark Carnivorous (meat-eating) teeth Assuming this cladogram is correct: ©Pearson Education, Inc. ? ©Pearson Education, Inc. • The presence of carnivorous teeth in cats and wolves is a • The presence of carnivorous teeth in cats and sharks is an homology. analogy. • (in cladistics, also called a homoplasy). Heyer 2 Biological Classification Cladogram vs. Taxa Cladogram vs. Taxa Monophyletic Paraphyletic clades grouping Not a true clade! Cladogram vs. Taxa Building Cladograms Assemble a table of character states Polyphyletic grouping Not a true clade! Not phylogenetic! Building Cladograms Building Cladograms Major assumptions: Each bifurcation of the branch is based 1. The group of organisms is upon the state (presence/absence) of monophyletic an apomorphic character 2. The outgroup (used for comparison) is closely related to, but separate from your group 3. You can tell which character states are homologous or analogous. Heyer 3 Biological Classification Building Cladograms Cladograms Cladograms are 1. Arrange your ingroup species in order of 5 4 made by similarity to the outgroup. 3 2 hypothesizing 1 the sequence of evolution of 5 shared 2. Arrange apomorphic 4 derived characters in order of appearance in 3 (apomorphic) species most similar characters to the outgroup. 2 1 Building Cladograms Cladograms Rule of Parsimony: 5 5 4 5 4 3 The simplest explanation is 2 3 4 1 the most likely explanation. 2 3 1 2 1 5 4 3 2 Base change event 1 Cladograms Cladograms Rule of Parsimony: Rule of Parsimony: The simplest explanation is The simplest explanation is the most likely explanation. the most likely explanation. But not always! Heyer 4 .
Recommended publications
  • Ecological Correlates of Ghost Lineages in Ruminants
    Paleobiology, 38(1), 2012, pp. 101–111 Ecological correlates of ghost lineages in ruminants Juan L. Cantalapiedra, Manuel Herna´ndez Ferna´ndez, Gema M. Alcalde, Beatriz Azanza, Daniel DeMiguel, and Jorge Morales Abstract.—Integration between phylogenetic systematics and paleontological data has proved to be an effective method for identifying periods that lack fossil evidence in the evolutionary history of clades. In this study we aim to analyze whether there is any correlation between various ecomorphological variables and the duration of these underrepresented portions of lineages, which we call ghost lineages for simplicity, in ruminants. Analyses within phylogenetic (Generalized Estimating Equations) and non-phylogenetic (ANOVAs and Pearson correlations) frameworks were performed on the whole phylogeny of this suborder of Cetartiodactyla (Mammalia). This is the first time ghost lineages are focused in this way. To test the robustness of our data, we compared the magnitude of ghost lineages among different continents and among phylogenies pruned at different ages (4, 8, 12, 16, and 20 Ma). Differences in mean ghost lineage were not significantly related to either geographic or temporal factors. Our results indicate that the proportion of the known fossil record in ruminants appears to be influenced by the preservation potential of the bone remains in different environments. Furthermore, large geographical ranges of species increase the likelihood of preservation. Juan L. Cantalapiedra, Gema Alcalde, and Jorge Morales. Departamento de Paleobiologı´a, Museo Nacional de Ciencias Naturales, UCM-CSIC, Pinar 25, 28006 Madrid, Spain. E-mail: [email protected] Manuel Herna´ndez Ferna´ndez. Departamento de Paleontologı´a, Facultad de Ciencias Geolo´gicas, Universidad Complutense de Madrid y Departamento de Cambio Medioambiental, Instituto de Geociencias, Consejo Superior de Investigaciones Cientı´ficas, Jose´ Antonio Novais 2, 28040 Madrid, Spain Daniel DeMiguel.
    [Show full text]
  • 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 .
    [Show full text]
  • Phylogeny of a Rapidly Evolving Clade: the Cichlid Fishes of Lake Malawi
    Proc. Natl. Acad. Sci. USA Vol. 96, pp. 5107–5110, April 1999 Evolution Phylogeny of a rapidly evolving clade: The cichlid fishes of Lake Malawi, East Africa (adaptive radiationysexual selectionyspeciationyamplified fragment length polymorphismylineage sorting) R. C. ALBERTSON,J.A.MARKERT,P.D.DANLEY, AND T. D. KOCHER† Department of Zoology and Program in Genetics, University of New Hampshire, Durham, NH 03824 Communicated by John C. Avise, University of Georgia, Athens, GA, March 12, 1999 (received for review December 17, 1998) ABSTRACT Lake Malawi contains a flock of >500 spe- sponsible for speciation, then we expect that sister taxa will cies of cichlid fish that have evolved from a common ancestor frequently differ in color pattern but not morphology. within the last million years. The rapid diversification of this Most attempts to determine the relationships among cichlid group has been attributed to morphological adaptation and to species have used morphological characters, which may be sexual selection, but the relative timing and importance of prone to convergence (8). Molecular sequences normally these mechanisms is not known. A phylogeny of the group provide the independent estimate of phylogeny needed to infer would help identify the role each mechanism has played in the evolutionary mechanisms. The Lake Malawi cichlids, however, evolution of the flock. Previous attempts to reconstruct the are speciating faster than alleles can become fixed within a relationships among these taxa using molecular methods have species (9, 10). The coalescence of mtDNA haplotypes found been frustrated by the persistence of ancestral polymorphisms within populations predates the origin of many species (11). In within species.
    [Show full text]
  • Major Clades of Agaricales: a Multilocus Phylogenetic Overview
    Mycologia, 98(6), 2006, pp. 982–995. # 2006 by The Mycological Society of America, Lawrence, KS 66044-8897 Major clades of Agaricales: a multilocus phylogenetic overview P. Brandon Matheny1 Duur K. Aanen Judd M. Curtis Laboratory of Genetics, Arboretumlaan 4, 6703 BD, Biology Department, Clark University, 950 Main Street, Wageningen, The Netherlands Worcester, Massachusetts, 01610 Matthew DeNitis Vale´rie Hofstetter 127 Harrington Way, Worcester, Massachusetts 01604 Department of Biology, Box 90338, Duke University, Durham, North Carolina 27708 Graciela M. Daniele Instituto Multidisciplinario de Biologı´a Vegetal, M. Catherine Aime CONICET-Universidad Nacional de Co´rdoba, Casilla USDA-ARS, Systematic Botany and Mycology de Correo 495, 5000 Co´rdoba, Argentina Laboratory, Room 304, Building 011A, 10300 Baltimore Avenue, Beltsville, Maryland 20705-2350 Dennis E. Desjardin Department of Biology, San Francisco State University, Jean-Marc Moncalvo San Francisco, California 94132 Centre for Biodiversity and Conservation Biology, Royal Ontario Museum and Department of Botany, University Bradley R. Kropp of Toronto, Toronto, Ontario, M5S 2C6 Canada Department of Biology, Utah State University, Logan, Utah 84322 Zai-Wei Ge Zhu-Liang Yang Lorelei L. Norvell Kunming Institute of Botany, Chinese Academy of Pacific Northwest Mycology Service, 6720 NW Skyline Sciences, Kunming 650204, P.R. China Boulevard, Portland, Oregon 97229-1309 Jason C. Slot Andrew Parker Biology Department, Clark University, 950 Main Street, 127 Raven Way, Metaline Falls, Washington 99153- Worcester, Massachusetts, 01609 9720 Joseph F. Ammirati Else C. Vellinga University of Washington, Biology Department, Box Department of Plant and Microbial Biology, 111 355325, Seattle, Washington 98195 Koshland Hall, University of California, Berkeley, California 94720-3102 Timothy J.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • Understanding Cladistics
    Understanding Cladistics Activity for Grades 5–8 Introduction Objective At the American Museum of Natural History, In this activity, students will explore cladistics and scientists use a method called cladistics to group create a cladogram of their own. animals. They look for unique features, such as a hole in the hip socket, that the animals share. Materials Animals with like features are grouped together. A • Understanding Cladistics chart, called a cladogram, shows these relationships. • A penny, nickel, dime, and quarter for each pair Using cladistics, scientists can reconstruct genealogi- of students cal relationships and can show how animals are • 6-8 dinosaurs pictures duplicated for each group, linked to one another through a long and complex downloadable from history of evolutionary changes. amnh.org/resources/rfl/pdf/dino_16_illustrations.pdf Procedure 1. Write lion, elephant, zebra, kangaroo, koala, buffalo, raccoon, and alligator. Ask students how the animals are related and what might be a good way of grouping them into sets and subsets. Discuss students responses. Tyrannosaurus rex Apatosaurus excelsus 2. Explain to students that scientists use a method extinct extinct called cladistics to determine evolutionary relation- ships among animals. They look for features that animals share, such as four limbs, hooves, or a hole in the hip socket. Animals with like features are grouped together. Scientists make a chart called a cladogram to show these relationships. 3. Tell students that they will examine the features of various coins to determine how they are related. Remind students that cladistics is used to determine relationships among organisms, and Theropoda Sauropoda Foot with three main At least 11 or more not necessarily objects.
    [Show full text]
  • Phylogenetic Comparative Methods: a User's Guide for Paleontologists
    Phylogenetic Comparative Methods: A User’s Guide for Paleontologists Laura C. Soul - Department of Paleobiology, National Museum of Natural History, Smithsonian Institution, Washington, DC, USA David F. Wright - Division of Paleontology, American Museum of Natural History, Central Park West at 79th Street, New York, New York 10024, USA and Department of Paleobiology, National Museum of Natural History, Smithsonian Institution, Washington, DC, USA Abstract. Recent advances in statistical approaches called Phylogenetic Comparative Methods (PCMs) have provided paleontologists with a powerful set of analytical tools for investigating evolutionary tempo and mode in fossil lineages. However, attempts to integrate PCMs with fossil data often present workers with practical challenges or unfamiliar literature. In this paper, we present guides to the theory behind, and application of, PCMs with fossil taxa. Based on an empirical dataset of Paleozoic crinoids, we present example analyses to illustrate common applications of PCMs to fossil data, including investigating patterns of correlated trait evolution, and macroevolutionary models of morphological change. We emphasize the importance of accounting for sources of uncertainty, and discuss how to evaluate model fit and adequacy. Finally, we discuss several promising methods for modelling heterogenous evolutionary dynamics with fossil phylogenies. Integrating phylogeny-based approaches with the fossil record provides a rigorous, quantitative perspective to understanding key patterns in the history of life. 1. Introduction A fundamental prediction of biological evolution is that a species will most commonly share many characteristics with lineages from which it has recently diverged, and fewer characteristics with lineages from which it diverged further in the past. This principle, which results from descent with modification, is one of the most basic in biology (Darwin 1859).
    [Show full text]
  • 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.
    [Show full text]
  • Character Analysis in Cladistics: Abstraction, Reification, and the Search for Objectivity
    Acta Biotheor (2009) 57:129–162 DOI 10.1007/s10441-008-9064-7 REGULAR ARTICLE Character Analysis in Cladistics: Abstraction, Reification, and the Search for Objectivity Rasmus Grønfeldt Winther Received: 10 October 2008 / Accepted: 17 October 2008 / Published online: 7 January 2009 Ó Springer Science+Business Media B.V. 2009 Abstract The dangers of character reification for cladistic inference are explored. The identification and analysis of characters always involves theory-laden abstraction—there is no theory-free ‘‘view from nowhere.’’ Given theory-ladenness, and given a real world with actual objects and processes, how can we separate robustly real biological characters from uncritically reified characters? One way to avoid reification is through the employment of objectivity criteria that give us good methods for identifying robust primary homology statements. I identify six such criteria and explore each with examples. Ultimately, it is important to minimize character reification, because poor character analysis leads to dismal cladograms, even when proper phylogenetic analysis is employed. Given the deep and systemic problems associated with character reification, it is ironic that philosophers have focused almost entirely on phylogenetic analysis and neglected character analysis. Keywords Characters Á Cladistics Á Phylogenetics Á Morphology Á Abstraction Á Reification Á Biological theory Á Epistemology Á Causation How are we to recognize the ‘‘true’’ characters of organisms rather than imposing upon them arbitrary divisions that obscure the very processes that we seek to understand? …No issue is of greater importance in the study of biology. –Lewontin 2001, p. xvii Are characters natural units or artifacts of observation and description? In both systematics and ecology, there is often a considerable gulf between observables and the units that play causal roles in our models.
    [Show full text]
  • 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
    [Show full text]
  • Bioinfo 11 Phylogenetictree
    BIO 390/CSCI 390/MATH 390 Bioinformatics II Programming Lecture 11 Phylogenetic Tree Instructor: Lei Qian Fisk University Phylogenetic Tree Applications • Study ancestor-descendant relationships (Evolutionary biology, adaption, genetic drift, selection, speciation, etc.) • Paleogenomics: inferring ancestral genomic information from extinct species (Comparing Chimpanzee, Neanderthal and Human DNA) • Origins of epidemics (Comparing, at the molecular level, various virus strains) • Drug design: specially targeting groups of organisms (Efficient enumeration of phylogenetically informative substrings) • Forensic (Relationships among HIV strains) • Linguistics (Languages tree divergence times) Phylogenetic Tree Illustrating success stories in phylogenetics (I) For roughly 100 years (more exactly, 1870-1985), scientists were unable to figure out which family the giant panda belongs to. Giant pandas look like bears, but have features that are unusual for bears but typical to raccoons: they do not hibernate, they do not roar, their male genitalia are small and backward-pointing. Anatomical features were the dominant criteria used to derive evolutionary relationships between species since Darwin till early 1960s. The evolutionary relationships derived from these relatively subjective observations were often inconclusive. Some of them were later proved incorrect. In 1985, Steven O’Brien and colleagues solved the giant panda classification problem using DNA sequences and phylogenetic algorithms. Phylogenetic Tree Phylogenetic Tree Illustrating success stories in phylogenetics (II) In 1994, a woman from Lafayette, Louisiana (USA), clamed that her ex-lover (who was a physician) injected her with HIV+ blood. Records showed that the physician had drawn blood from a HIV+ patient that day. But how to prove that the blood from that HIV+ patient ended up in the woman? Phylogenetic Tree HIV has a high mutation rate, which can be used to trace paths of transmission.
    [Show full text]