DOCSLIB.ORG

The Probability of Monophyly of a Sample of Gene Lineages on a Species Tree

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Probability of Monophyly of a Sample of Gene Lineages on a Species Tree PAPER The probability of monophyly of a sample of gene COLLOQUIUM lineages on a species tree Rohan S. Mehtaa,1, David Bryantb, and Noah A. Rosenberga aDepartment of Biology, Stanford University, Stanford, CA 94305; and bDepartment of Mathematics and Statistics, University of Otago, Dunedin 9054, New Zealand Edited by John C. Avise, University of California, Irvine, CA, and approved April 18, 2016 (received for review February 5, 2016) Monophyletic groups—groups that consist of all of the descendants loci that are reciprocally monophyletic is informative about the of a most recent common ancestor—arise naturally as a conse- time since species divergence and can assist in representing the quence of descent processes that result in meaningful distinctions level of differentiation between groups (4, 18). between organisms. Aspects of monophyly are therefore central to Many empirical investigations of genealogical phenomena have fields that examine and use genealogical descent. In particular, stud- made use of conceptual and statistical properties of monophyly ies in conservation genetics, phylogeography, population genetics, (19). Comparisons of observed monophyly levels to model pre- species delimitation, and systematics can all make use of mathemat- dictions have been used to provide information about species di- ical predictions under evolutionary models about features of mono- vergence times (20, 21). Model-based monophyly computations phyly. One important calculation, the probability that a set of gene have been used alongside DNA sequence differences between and lineages is monophyletic under a two-species neutral coalescent within proposed clades to argue for the existence of the clades model, has been used in many studies. Here, we extend this calcu- (22), and tests involving reciprocal monophyly have been used to lation for a species tree model that contains arbitrarily many species. explain differing phylogeographic patterns across species (23). Comparisons of observed levels of monophyly with the level We study the effects of species tree topology and branch lengths on expected by chance alone (24) have assisted in establishing the the monophyly probability. These analyses reveal new behavior, distinctiveness of taxonomic groups (25, 26). Loci that conflict including the maintenance of nontrivial monophyly probabilities with expected monophyly levels have provided signatures of genic for gene lineage samples that span multiple species and even for roles in species divergences (27–29). EVOLUTION lineages that do not derive from a monophyletic species group. We For lineages from two species under a model of population illustrate the mathematical results using an example application to divergence, Rosenberg (4) computed probabilities of four differ- data from maize and teosinte. ent genealogical shapes: reciprocal monophyly of both species, monophyly of only one of the species, monophyly of only the other coalescent theory | monophyly | phylogeography species, and monophyly of neither species. The computation permitted arbitrary species divergence times and sample sizes— athematical computations under coalescent models have generalizing earlier small-sample computations (1–3, 30, 31)—and Mbeen central in developing a modern view of the descent of illustrated the transition from the species divergence, when mono- gene lineages along the branches of species phylogenies. Since phyly is unlikely for both species, to long after divergence, when early in the development of coalescent theory and phylogeography, reciprocal monophyly becomes extremely likely. Between these ex- coalescent formulas and related simulations have contributed to a tremes, the species can pass through a period during which mono- probabilistic understanding of the shapes of multispecies gene trees phyly of one species but not the other is the most probable state. (1–3), enabling novel predictions about gene tree shapes under Although this two-species computation has contributed to various insights about empirical monophyly patterns (21–23, 32–34), many evolutionary hypotheses (4, 5), new ways of testing hypotheses about scenarios deal with more than two species. Because multispecies gene tree discordances (6, 7), and new algorithms for problems of monophyly probability computations have been unavailable— species tree inference (8, 9) and species delimitation (10, 11). A – — “ ” except in limited cases with up to four species (4, 35 38) multispecies coalescent model, in which coalescent processes on multispecies studies have been forced to rely on two-species models, separate species tree branches merge back in time as species reach a restricting attention to species pairs (25, 34, 39) or pooling disparate common ancestor (12), has become a key tool for theoretical pre- lineages and disregarding their taxonomic distinctiveness (23, 26). dictions, simulation design, and evaluation of inference methods, Here, we derive an extension to the two-species monophyly and as a null model for data analysis. probability computation, examining arbitrarily many species re- A fundamental concept in genealogical studies is that of mono- lated by an evolutionary tree. Furthermore, we eliminate the past phyly. In a genealogy, a group that is monophyletic consists of all of restriction (4) that the lineages whose monophyly is examined all the descendants of its most recent common ancestor (MRCA): derive from the same population. This generalization is analo- every lineage in the group—andnolineageoutsideit—descends gous to the assumption that in computing the probability of a from this ancestor. Backward in time, a monophyletic group has all binary evolutionary character (40–42), one or both character of its lineages coalesce with each other before any coalesces with a states can appear in multiple species. Our approach uses a lineage from outside the group. The phylogenetic and phylogeographic importance of mono- phyly traces to the fact that monophyly enables a natural defini- This paper results from the Arthur M. Sackler Colloquium of the National Academy of Sci- tion of a genealogical unit. Such a unit can describe a distinctive ences, “In the Light of Evolution X: Comparative Phylogeography,” held January 8–9, 2016, at set of organisms that differs from other groups of organisms in the Arnold and Mabel Beckman Center of the National Academies of Sciences and Engineer- ways that are evolutionarily meaningful. Species can be delimited ing in Irvine, CA. The complete program and video recordings of most presentations are by characters present in every member of a species and absent available on the NAS website at www.nasonline.org/ILE_X_Comparative_Phylogeography. outside the species, and that therefore can reflect monophyly (13, Author contributions: R.S.M., D.B., and N.A.R. designed research; R.S.M. and N.A.R. performed 14). In conservation biology, monophyly can be used as a priori- research; R.S.M. analyzed data; and R.S.M., D.B., and N.A.R. wrote the paper. tization criterion because groups with many monophyletic loci are The authors declare no conflict of interest. likely to possess unique evolutionary features (15). Reciprocal This article is a PNAS Direct Submission. monophyly, in which a set of lineages is divided into two groups 1To whom correspondence should be addressed. Email: [email protected]. that are simultaneously monophyletic, is often used in a genea- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. logical approach to species divergence (16, 17). The proportion of 1073/pnas.1601074113/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1601074113 PNAS Early Edition | 1of8 Downloaded by guest on September 27, 2021 pruning algorithm, generalizing the two-species formula in a Table 2. Possible monophyly events for two disjoint lineage conceptually similar manner to other recursive coalescent com- classes, S and C – putations on arbitrary trees (9, 40 44). Monophyletic groups Description Notation Like the work of Degnan and Salter (5), which considered probability distributions for gene tree topologies under the S Monophyly of SES multispecies coalescent model, our work generalizes a coales- C Monophyly of CEC cent computation known only for small trees (4, 35) to arbitrary Only S Paraphyly of CESC′ species trees. We study the dependence of the monophyly proba- Only C Paraphyly of SES′C bility on the model parameters, providing an understanding of Both S and C Reciprocal monophyly ESC factors that contribute to monophyly in species trees of arbi- Neither S nor C Polyphyly ES′C′ trary size. Finally, we explore the utility of monophyly prob- abilities in an application to genomewide data from maize and teosinte. arbitrarily labeled diagram of species tree T . These labels are Results used only for bookkeeping; the labeling does not affect subse- quent calculations. Lineages entering from the left and right Model and Notation. branches are called “left inputs” and “right inputs,” respectively. T ℓ Overview. Consider a rooted binary species tree with leaves and Each node x of T is associated with exactly one branch, leading ℓ specified topology and branch lengths. For each of the species from node x to its immediate predecessor on T . We refer to this T represented by leaves of , a number of sampled lineages is branch with the shared label x. specified. Given a specified partition of the lineages into two For an internal branch x in T , the number of class-S left in- subsets, we consider a condition describing whether one, the other, L L L puts is sx (cx for class C, mx for class M); the number of class-S both, or neither of the two subsets of lineages is monophyletic. Our R R R right inputs is sx (cx for class C, mx for class M). The total goal is to provide a recursive computation of the probability that I = L + R I = L + R number of class-S inputs of x is sx sx sx (cx cx cx for class the condition is obtained under the multispecies coalescent model. I = L + R C, mx mx mx for class M). The number of lineages that exit Notation appears in Table S1. branch x, entering a branch farther up the species tree, is the set Lineage classes.
Load more

Recommended publications
  • Reticulate Evolution and Phylogenetic Networks 6
    CHAPTER Reticulate Evolution and Phylogenetic Networks 6 So far, we have modeled the evolutionary process as a bifurcating treelike process. The main feature of trees is that the flow of information in one lineage is independent of that in another lineage. In real life, however, many process- es—including recombination, hybridization, polyploidy, introgression, genome fusion, endosymbiosis, and horizontal gene transfer—do not abide by lineage independence and cannot be modeled by trees. Reticulate evolution refers to the origination of lineages through the com- plete or partial merging of two or more ancestor lineages. The nonvertical con- nections between lineages are referred to as reticulations. In this chapter, we introduce the language of networks and explain how networks can be used to study non-treelike phylogenetic processes. A substantial part of this chapter will be dedicated to the evolutionary relationships among prokaryotes and the very intriguing question of the origin of the eukaryotic cell. Networks Networks were briefly introduced in Chapter 4 in the context of protein-protein interactions. Here, we provide a more formal description of networks and their use in phylogenetics. As mentioned in Chapter 5, trees are connected graphs in which any two nodes are connected by a single path. In phylogenetics, a network is a connected graph in which at least two nodes are connected by two or more pathways. In other words, a network is a connected graph that is not a tree. All networks contain at least one cycle, i.e., a path of branches that can be followed in one direction from any starting point back to the starting point.
    [Show full text]
  • Splits and Phylogenetic Networks
    SplitsSplits andand PhylogeneticPhylogenetic NetworksNetworks DanielDaniel H.H. HusonHuson Paris, June 21, 2005 1 ContentsContents 1.1. PhylogeneticPhylogenetic treestrees 2.2. SplitsSplits networksnetworks 3.3. ConsensusConsensus networksnetworks 4.4. HybridizationHybridization andand reticulatereticulate networksnetworks 5.5. RecombinationRecombination networksnetworks 2 PhylogeneticPhylogenetic NetworksNetworks Bandelt (1991): Network displaying evolutionary relationships Other types of Splits Phylogenetic Reticulate phylogenetic networks trees networks networks Median Consensus Hybridization Recombination Augmented networks (super) networks networks trees networks Special case: “Galled trees” Any graph Ancestor Split decomposition, representing Split decomposition, recombination evolutionary Neighbor-net graphs data 3 PhylogeneticPhylogenetic NetworksNetworks 22 11 Other types of Splits Phylogenetic Reticulate phylogenetic networks trees networks networks 33 44 55 Median Consensus Hybridization Recombination Augmented networks (super) networks networks trees networks from sequences Special case: “Galled trees” from trees Any graph Ancestor Split decomposition, representing Split decomposition, recombination evolutionary Neighbor-net graphs data from distances 4 PhylogeneticPhylogenetic NetworksNetworksDan Gusfield: “Phylogenetic network” 22 11 “Generalized Other types of Splits Phylogenetic Reticulate phylogeneticphylogenetic networks trees networks network”networks 33 44 \ 55 Median Consensus Hybridization Recombination“More generalizedAugmented
    [Show full text]
  • 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.
    [Show full text]
  • Species Tree Likelihood Computation Given SNP Data Using Ancestral Configurations
    Species Tree Likelihood Computation Given SNP Data Using Ancestral Configurations DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Hang Fan, M.S. Graduate Program in Statistics The Ohio State University 2013 Dissertation Committee: Professor Laura Kubatko, Advisor Professor Bryan Carstens Professor Radu Herbei 1 Copyright by Hang Fan 2013 2 Abstract Inferring species trees given genetic data has been a challenge in the field of phylogenetics because of the high intensity during computation. In the coalescent framework, this dissertation proposes an innovative method of estimating the likelihood of a species tree directly from Single Nucleotide Polymorphism (SNP) data with a certain nucleotide substitution model. This method uses the idea of Ancestral Configurations (Wu, 2011) to avoid the computation burden brought by the enumeration of coalescent histories. Importance sampling is used to in Monte Carlo integration to approximate the expectations in the computation, where the accuracy of the approximation is tested in different tree models. The SNP data is processed beforehand which vastly boosts the efficiency of the method. Gene tree sampling given the species tree under the coalescent model is employed to make the computation feasible for large trees. Further, the branch lengths on the species tree are optimized according to the computed species tree likelihood, which provides the likelihood of the species tree topology given the SNP data. For inference, this likelihood computation method is implemented in the stepwise addition algorithm to infer the maximum likelihood species tree in the tree space given the SNP data, and simulations are conduced to test the performance.
    [Show full text]
  • EVOLUTIONARY INFERENCE: Some Basics of Phylogenetic Analyses
    EVOLUTIONARY INFERENCE: Some basics of phylogenetic analyses. Ana Rojas Mendoza CNIO-Madrid-Spain. Alfonso Valencia’s lab. Aims of this talk: • 1.To introduce relevant concepts of evolution to practice phylogenetic inference from molecular data. • 2.To introduce some of the most useful methods and computer programmes to practice phylogenetic inference. • • 3.To show some examples I’ve worked in. SOME BASICS 11--ConceptsConcepts ofof MolecularMolecular EvolutionEvolution • Homology vs Analogy. • Homology vs similarity. • Ortologous vs Paralogous genes. • Species tree vs genes tree. • Molecular clock. • Allele mutation vs allele substitution. • Rates of allele substitution. • Neutral theory of evolution. SOME BASICS Owen’s definition of homology Richard Owen, 1843 • Homologue: the same organ under every variety of form and function (true or essential correspondence). •Analogy: superficial or misleading similarity. SOME BASICS 1.Concepts1.Concepts ofof MolecularMolecular EvolutionEvolution • Homology vs Analogy. • Homology vs similarity. • Ortologous vs Paralogous genes. • Species tree vs genes tree. • Molecular clock. • Allele mutation vs allele substitution. • Rates of allele substitution. • Neutral theory of evolution. SOME BASICS Similarity ≠ Homology • Similarity: mathematical concept . Homology: biological concept Common Ancestry!!! SOME BASICS 1.Concepts1.Concepts ofof MolecularMolecular EvolutionEvolution • Homology vs Analogy. • Homology vs similarity. • Ortologous vs Paralogous genes. • Species tree vs genes tree. • Molecular clock.
    [Show full text]
  • Family Classification
    1.0 GENERAL INTRODUCTION 1.1 Henckelia sect. Loxocarpus Loxocarpus R.Br., a taxon characterised by flowers with two stamens and plagiocarpic (held at an angle of 90–135° with pedicel) capsular fruit that splits dorsally has been treated as a section within Henckelia Spreng. (Weber & Burtt, 1998 [1997]). Loxocarpus as a genus was established based on L. incanus (Brown, 1839). It is principally recognised by its conical, short capsule with a broader base often with a hump-like swelling at the upper side (Banka & Kiew, 2009). It was reduced to sectional level within the genus Didymocarpus (Bentham, 1876; Clarke, 1883; Ridley, 1896) but again raised to generic level several times by different authors (Ridley, 1905; Burtt, 1958). In 1998, Weber & Burtt (1998 ['1997']) re-modelled Didymocarpus. Didymocarpus s.s. was redefined to a natural group, while most of the rest Malesian Didymocarpus s.l. and a few others morphologically close genera including Loxocarpus were transferred to Henckelia within which it was recognised as a section within. See Section 4.1 for its full taxonomic history. Molecular data now suggests that Henckelia sect. Loxocarpus is nested within ‗Twisted-fruited Asian and Malesian genera‘ group and distinct from other didymocarpoid genera (Möller et al. 2009; 2011). 1.2 State of knowledge and problem statements Henckelia sect. Loxocarpus includes 10 species in Peninsular Malaysia (with one species extending into Peninsular Thailand), 12 in Borneo, two in Sumatra and one in Lingga (Banka & Kiew, 2009). The genus Loxocarpus has never been monographed. Peninsular Malaysian taxa are well studied (Ridley, 1923; Banka, 1996; Banka & Kiew, 2009) but the Bornean and Sumatran taxa are poorly known.
    [Show full text]
  • A Comparative Phenetic and Cladistic Analysis of the Genus Holcaspis Chaudoir (Coleoptera: .Carabidae)
    Lincoln University Digital Thesis Copyright Statement The digital copy of this thesis is protected by the Copyright Act 1994 (New Zealand). This thesis may be consulted by you, provided you comply with the provisions of the Act and the following conditions of use: you will use the copy only for the purposes of research or private study you will recognise the author's right to be identified as the author of the thesis and due acknowledgement will be made to the author where appropriate you will obtain the author's permission before publishing any material from the thesis. A COMPARATIVE PHENETIC AND CLADISTIC ANALYSIS OF THE GENUS HOLCASPIS CHAUDOIR (COLEOPTERA: CARABIDAE) ********* A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy at Lincoln University by Yupa Hanboonsong ********* Lincoln University 1994 Abstract of a thesis submitted in partial fulfilment of the requirements for the degree of Ph.D. A comparative phenetic and cladistic analysis of the genus Holcaspis Chaudoir (Coleoptera: .Carabidae) by Yupa Hanboonsong The systematics of the endemic New Zealand carabid genus Holcaspis are investigated, using phenetic and cladistic methods, to construct phenetic and phylogenetic relationships. Three different character data sets: morphological, allozyme and random amplified polymorphic DNA (RAPD) based on the polymerase chain reaction (PCR), are used to estimate the relationships. Cladistic and morphometric analyses are undertaken on adult morphological characters. Twenty six external morphological characters, including male and female genitalia, are used for cladistic analysis. The results from the cladistic analysis are strongly congruent with previous publications. The morphometric analysis uses multivariate discriminant functions, with 18 morphometric variables, to derive a phenogram by clustering from Mahalanobis distances (D2) of the discrimination analysis using the unweighted pair-group method with arithmetical averages (UPGMA).
    [Show full text]
  • Outer and Inner Indo-Aryan, and Northern India As an Ancient Linguistic Area
    Acta Orientalia 2016: 77, 71–132. Copyright © 2016 Printed in India – all rights reserved ACTA ORIENTALIA ISSN 0001-6483 Outer and Inner Indo-Aryan, and northern India as an ancient linguistic area Claus Peter Zoller University of Oslo Abstract The article presents a new approach to the old controversy concerning the veracity of a distinction between Outer and Inner Languages in Indo-Aryan. A number of arguments and data are presented which substantiate the reality of this distinction. This new approach combines this issue with a new interpretation of the history of Indo- Iranian and with the linguistic prehistory of northern India. Data are presented to show that prehistorical northern India was dominated by Munda/Austro-Asiatic languages. Keywords: Indo-Aryan, Indo-Iranian, Nuristani, Munda/Austro- Asiatic history and prehistory. Introduction This article gives a summary of the most important arguments contained in my forthcoming book on Outer and Inner languages before and after the arrival of Indo-Aryan in South Asia. The 72 Claus Peter Zoller traditional version of the hypothesis of Outer and Inner Indo-Aryan purports the idea that the Indo-Aryan Language immigration1 was not a singular event. Yet, even though it is known that the actual historical movements and processes in connection with this immigration were remarkably complex, the concerns of the hypothesis are not to reconstruct the details of these events but merely to show that the original non-singular immigrations have left revealing linguistic traces in the modern Indo-Aryan languages. Actually, this task is challenging enough, as the long-lasting controversy shows.2 Previous and present proponents of the hypothesis have tried to fix the difference between Outer and Inner Languages in terms of language geography (one graphical attempt as an example is shown below p.
    [Show full text]
  • Solution Sheet
    Solution sheet Sequence Alignments and Phylogeny Bioinformatics Leipzig WS 13/14 Solution sheet 1 Biological Background 1.1 Which of the following are pyrimidines? Cytosine and Thymine are pyrimidines (number 2) 1.2 Which of the following contain phosphorus atoms? DNA and RNA contain phosphorus atoms (number 2). 1.3 Which of the following contain sulfur atoms? Methionine contains sulfur atoms (number 3). 1.4 Which of the following is not a valid amino acid sequence? There is no amino acid with the one letter code 'O', such that there is no valid amino acid sequence 'WATSON' (number 4). 1.5 Which of the following 'one-letter' amino acid sequence corresponds to the se- quence Tyr-Phe-Lys-Thr-Glu-Gly? The amino acid sequence corresponds to the one letter code sequence YFKTEG (number 1). 1.6 Consider the following DNA oligomers. Which to are complementary to one an- other? All are written in the 5' to 3' direction (i.TTAGGC ii.CGGATT iii.AATCCG iv.CCGAAT) CGGATT (ii) and AATCCG (iii) are complementary (number 2). 2 Pairwise Alignments 2.1 Needleman-Wunsch Algorithm Given the alphabet B = fA; C; G; T g, the sequences s = ACGCA and p = ACCG and the following scoring matrix D: A C T G - A 3 -1 -1 -1 -2 C -1 3 -1 -1 -2 T -1 -1 3 -1 -2 G -1 -1 -1 3 -2 - -2 -2 -2 -2 0 1. What kind of scoring function is given by the matrix D, similarity or distance score? 2. Use the Needleman-Wunsch algorithm to compute the pairwise alignment of s and p.
    [Show full text]
  • A Fréchet Tree Distance Measure to Compare Phylogeographic Spread Paths Across Trees Received: 24 July 2018 Susanne Reimering1, Sebastian Muñoz1 & Alice C
    www.nature.com/scientificreports OPEN A Fréchet tree distance measure to compare phylogeographic spread paths across trees Received: 24 July 2018 Susanne Reimering1, Sebastian Muñoz1 & Alice C. McHardy 1,2 Accepted: 1 November 2018 Phylogeographic methods reconstruct the origin and spread of taxa by inferring locations for internal Published: xx xx xxxx nodes of the phylogenetic tree from sampling locations of genetic sequences. This is commonly applied to study pathogen outbreaks and spread. To evaluate such reconstructions, the inferred spread paths from root to leaf nodes should be compared to other methods or references. Usually, ancestral state reconstructions are evaluated by node-wise comparisons, therefore requiring the same tree topology, which is usually unknown. Here, we present a method for comparing phylogeographies across diferent trees inferred from the same taxa. We compare paths of locations by calculating discrete Fréchet distances. By correcting the distances by the number of paths going through a node, we defne the Fréchet tree distance as a distance measure between phylogeographies. As an application, we compare phylogeographic spread patterns on trees inferred with diferent methods from hemagglutinin sequences of H5N1 infuenza viruses, fnding that both tree inference and ancestral reconstruction cause variation in phylogeographic spread that is not directly refected by topological diferences. The method is suitable for comparing phylogeographies inferred with diferent tree or phylogeographic inference methods to each other or to a known ground truth, thus enabling a quality assessment of such techniques. Phylogeography combines phylogenetic information describing the evolutionary relationships among species or members of a population with geographic information to study migration patterns.
    [Show full text]
  • Stochastic Models in Phylogenetic Comparative Methods: Analytical Properties and Parameter Estimation
    Thesis for the Degree of Doctor of Philosophy Stochastic models in phylogenetic comparative methods: analytical properties and parameter estimation Krzysztof Bartoszek Division of Mathematical Statistics Department of Mathematical Sciences Chalmers University of Technology and University of Gothenburg G¨oteborg, Sweden 2013 Stochastic models in phylogenetic comparative methods: analytical properties and parameter estimation Krzysztof Bartoszek Copyright c Krzysztof Bartoszek, 2013. ISBN 978–91–628–8740–7 Department of Mathematical Sciences Division of Mathematical Statistics Chalmers University of Technology and University of Gothenburg SE-412 96 GOTEBORG,¨ Sweden Phone: +46 (0)31-772 10 00 Author e-mail: [email protected] Typeset with LATEX. Department of Mathematical Sciences Printed in G¨oteborg, Sweden 2013 Stochastic models in phylogenetic comparative methods: analytical properties and parameter estimation Krzysztof Bartoszek Abstract Phylogenetic comparative methods are well established tools for using inter–species variation to analyse phenotypic evolution and adaptation. They are generally hampered, however, by predominantly univariate ap- proaches and failure to include uncertainty and measurement error in the phylogeny as well as the measured traits. This thesis addresses all these three issues. First, by investigating the effects of correlated measurement errors on a phylogenetic regression. Second, by developing a multivariate Ornstein– Uhlenbeck model combined with a maximum–likelihood estimation pack- age in R. This model allows, uniquely, a direct way of testing adaptive coevolution. Third, accounting for the often substantial phylogenetic uncertainty in comparative studies requires an explicit model for the tree. Based on recently developed conditioned branching processes, with Brownian and Ornstein–Uhlenbeck evolution on top, expected species similarities are derived, together with phylogenetic confidence intervals for the optimal trait value.
    [Show full text]
  • The Shape of Phylogenetic Trees (Review Paper)
    REVIEW PAPER: THE SHAPE OF PHYLOGENETIC TREESPACE KATHERINE ST. JOHN Abstract: Trees are a canonical structure for representing evolutionary histories. Many popular criteria used to infer optimal trees are computationally hard, and the number of possible tree shapes grows super-exponentially in the number of taxa. The underlying structure of the spaces of trees yields rich insights that can improve the search for optimal trees, both in accuracy and running time, and the analysis and visualization of results. We review the past work on analyzing and comparing trees by their shape as well as recent work that incorporates trees with weighted branch lengths. Keywords: tree metrics, treespace, maximum parsimony, maximum likelihood. Tree structures have long been used to represent the evolutionary histories of sets of species. For example, the tips of the trees represent extant species and the internal nodes represent speciation events. Despite its simplicity, the tree model captures much of the complexity of the underlying phenomena. However, the sheer number of possibilities forces many simply presented operations on trees to be computationally hard. For example, the maximum parsimony criteria (Farris, 1970; Fitch, 1971) that seeks the tree with the minimal number of changes across the edges is compu- tationally hard to compute exactly (Foulds and Graham, 1982). The addition of weights on the branches, to denote quantities such as amount of evolutionary change, the time, or the confidence on the existence of the branch, adds complexity to the model (Felsenstein, 1973, 1978). A pop- ular corresponding optimality criteria for weighted trees, the maximum likelihood criteria, is also computationally hard (Roch, 2006).
    [Show full text]