Coalescent Theory and Yule Trees in Time and Space
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Coalescent Likelihood Methods
Coalescent Likelihood Methods Mary K. Kuhner Genome Sciences University of Washington Seattle WA Outline 1. Introduction to coalescent theory 2. Practical example 3. Genealogy samplers 4. Break 5. Survey of samplers 6. Evolutionary forces 7. Practical considerations Population genetics can help us to find answers We are interested in questions like { How big is this population? { Are these populations isolated? How common is migration? { How fast have they been growing or shrinking? { What is the recombination rate across this region? { Is this locus under selection? All of these questions require comparison of many individuals. Coalescent-based studies How many gray whales were there prior to whaling? When was the common ancestor of HIV lines in a Libyan hospital? Is the highland/lowland distinction in Andean ducks recent or ancient? Did humans wipe out the Beringian bison population? What proportion of HIV virions in a patient actually contribute to the breeding pool? What is the direction of gene flow between European rabbit populations? Basics: Wright-Fisher population model All individuals release many gametes and new individuals for the next generation are formed randomly from these. Wright-Fisher population model Population size N is constant through time. Each individual gets replaced every generation. Next generation is drawn randomly from a large gamete pool. Only genetic drift affects the allele frequencies. Other population models Other population models can often be equated to Wright-Fisher The N parameter becomes the effective -
Natural Selection and Coalescent Theory
Natural Selection and Coalescent Theory John Wakeley Harvard University INTRODUCTION The story of population genetics begins with the publication of Darwin’s Origin of Species and the tension which followed concerning the nature of inheritance. Today, workers in this field aim to understand the forces that produce and maintain genetic variation within and between species. For this we use the most direct kind of genetic data: DNA sequences, even entire genomes. Our “Great Obsession” with explaining genetic variation (Gillespie, 2004a) can be traced back to Darwin’s recognition that natural selection can occur only if individuals of a species vary, and this variation is heritable. Darwin might have been surprised that the importance of natural selection in shaping variation at the molecular level would be de-emphasized, beginning in the late 1960s, by scientists who readily accepted the fact and importance of his theory (Kimura, 1983). The motivation behind this chapter is the possible demise of this Neutral Theory of Molecular Evolution, which a growing number of population geneticists feel must follow recent observations of genetic variation within and between species. One hundred fifty years after the publication of the Origin, we are struggling to fully incorporate natural selection into the modern, genealogical models of population genetics. The main goal of this chapter is to present the mathematical models that have been used to describe the effects of positive selective sweeps on genetic variation, as mediated by gene genealogies, or coalescent trees. Background material, comprised of population genetic theory and simulation results, is provided in order to facilitate an understanding of these models. -
Population Genetics: Wright Fisher Model and Coalescent Process
POPULATION GENETICS: WRIGHT FISHER MODEL AND COALESCENT PROCESS by Hailong Cui and Wangshu Zhang Superviser: Prof. Quentin Berger A Final Project Report Presented In Partial Fulfillment of the Requirements for Math 505b April 2014 Acknowledgments We want to thank Prof. Quentin Berger for introducing to us the Wright Fisher model in the lecture, which inspired us to choose Population Genetics for our project topic. The resources Prof. Berger provided us have been excellent learning mate- rials and his feedback has helped us greatly to create this report. We also like to acknowledge that the research papers (in the reference) are integral parts of this process. They have motivated us to learn more about models beyond the class, and granted us confidence that these probabilistic models can actually be used for real applications. ii Contents Acknowledgments ii Abstract iv 1 Introduction to Population Genetics 1 2 Wright Fisher Model 2 2.1 Random drift . 2 2.2 Genealogy of the Wright Fisher model . 4 3 Coalescent Process 8 3.1 Kingman’s Approximation . 8 4 Applications 11 Reference List 12 iii Abstract In this project on Population Genetics, we aim to introduce models that lay the foundation to study more complicated models further. Specifically we will discuss Wright Fisher model as well as Coalescent process. The reason these are of our inter- est is not just the mathematical elegance of these models. With the availability of massive amount of sequencing data, we actually can use these models (or advanced models incorporating variable population size, mutation effect etc, which are how- ever out of the scope of this project) to solve and answer real questions in molecular biology. -
Science Fiction Stories with Good Astronomy & Physics
Science Fiction Stories with Good Astronomy & Physics: A Topical Index Compiled by Andrew Fraknoi (U. of San Francisco, Fromm Institute) Version 7 (2019) © copyright 2019 by Andrew Fraknoi. All rights reserved. Permission to use for any non-profit educational purpose, such as distribution in a classroom, is hereby granted. For any other use, please contact the author. (e-mail: fraknoi {at} fhda {dot} edu) This is a selective list of some short stories and novels that use reasonably accurate science and can be used for teaching or reinforcing astronomy or physics concepts. The titles of short stories are given in quotation marks; only short stories that have been published in book form or are available free on the Web are included. While one book source is given for each short story, note that some of the stories can be found in other collections as well. (See the Internet Speculative Fiction Database, cited at the end, for an easy way to find all the places a particular story has been published.) The author welcomes suggestions for additions to this list, especially if your favorite story with good science is left out. Gregory Benford Octavia Butler Geoff Landis J. Craig Wheeler TOPICS COVERED: Anti-matter Light & Radiation Solar System Archaeoastronomy Mars Space Flight Asteroids Mercury Space Travel Astronomers Meteorites Star Clusters Black Holes Moon Stars Comets Neptune Sun Cosmology Neutrinos Supernovae Dark Matter Neutron Stars Telescopes Exoplanets Physics, Particle Thermodynamics Galaxies Pluto Time Galaxy, The Quantum Mechanics Uranus Gravitational Lenses Quasars Venus Impacts Relativity, Special Interstellar Matter Saturn (and its Moons) Story Collections Jupiter (and its Moons) Science (in general) Life Elsewhere SETI Useful Websites 1 Anti-matter Davies, Paul Fireball. -
Harpercollins Books for the First-Year Student
S t u d e n t Featured Titles • American History and Society • Food, Health, and the Environment • World Issues • Memoir/World Views • Memoir/ American Voices • World Fiction • Fiction • Classic Fiction • Religion • Orientation Resources • Inspiration/Self-Help • Study Resources www.HarperAcademic.com Index View Print Exit Books for t H e f i r s t - Y e A r s t u d e n t • • 1 FEATURED TITLES The Boy Who Harnessed A Pearl In the Storm the Wind How i found My Heart in tHe Middle of tHe Ocean Creating Currents of eleCtriCity and Hope tori Murden McClure William kamkwamba & Bryan Mealer During June 1998, Tori Murden McClure set out to William Kamkwamba was born in Malawi, Africa, a row across the Atlantic Ocean by herself in a twenty- country plagued by AIDS and poverty. When, in three-foot plywood boat with no motor or sail. 2002, Malawi experienced their worst famine in 50 Within days she lost all communication with shore, years, fourteen-year-old William was forced to drop ultimately losing updates on the location of the Gulf out of school because his family could not afford the Stream and on the weather. In deep solitude and $80-a-year-tuition. However, he continued to think, perilous conditions, she was nonetheless learn, and dream. Armed with curiosity, determined to prove what one person with a mission determination, and a few old science textbooks he could do. When she was finally brought to her knees discovered in a nearby library, he embarked on a by a series of violent storms that nearly killed her, daring plan to build a windmill that could bring his she had to signal for help and go home in what felt family the electricity only two percent of Malawians like complete disgrace. -
The Drink Tank Sixth Annual Giant Sized [email protected]: James Bacon & Chris Garcia
The Drink Tank Sixth Annual Giant Sized Annual [email protected] Editors: James Bacon & Chris Garcia A Noise from the Wind Stephen Baxter had got me through the what he’ll be doing. I first heard of Stephen Baxter from Jay night. So, this is the least Giant Giant Sized Crasdan. It was a night like any other, sitting in I remember reading Ring that next Annual of The Drink Tank, but still, I love it! a room with a mostly naked former ballerina afternoon when I should have been at class. I Dedicated to Mr. Stephen Baxter. It won’t cover who was in the middle of what was probably finished it in less than 24 hours and it was such everything, but it’s a look at Baxter’s oevre and her fifth overdose in as many months. This was a blast. I wasn’t the big fan at that moment, the effect he’s had on his readers. I want to what we were dealing with on a daily basis back though I loved the novel. I had to reread it, thank Claire Brialey, M Crasdan, Jay Crasdan, then. SaBean had been at it again, and this time, and then grabbed a copy of Anti-Ice a couple Liam Proven, James Bacon, Rick and Elsa for it was up to me and Jay to clean up the mess. of days later. Perhaps difficult times made Ring everything! I had a blast with this one! Luckily, we were practiced by this point. Bottles into an excellent escape from the moment, and of water, damp washcloths, the 9 and the first something like a month later I got into it again, 1 dialed just in case things took a turn for the and then it hit. -
Frontiers in Coalescent Theory: Pedigrees, Identity-By-Descent, and Sequentially Markov Coalescent Models
Frontiers in Coalescent Theory: Pedigrees, Identity-by-Descent, and Sequentially Markov Coalescent Models The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Wilton, Peter R. 2016. Frontiers in Coalescent Theory: Pedigrees, Identity-by-Descent, and Sequentially Markov Coalescent Models. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493608 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Frontiers in Coalescent Theory: Pedigrees, Identity-by-descent, and Sequentially Markov Coalescent Models a dissertation presented by Peter Richard Wilton to The Department of Organismic and Evolutionary Biology in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Biology Harvard University Cambridge, Massachusetts May 2016 ©2016 – Peter Richard Wilton all rights reserved. Thesis advisor: Professor John Wakeley Peter Richard Wilton Frontiers in Coalescent Theory: Pedigrees, Identity-by-descent, and Sequentially Markov Coalescent Models Abstract The coalescent is a stochastic process that describes the genetic ancestry of individuals sampled from a population. It is one of the main tools of theoretical population genetics and has been used as the basis of many sophisticated methods of inferring the demo- graphic history of a population from a genetic sample. This dissertation is presented in four chapters, each developing coalescent theory to some degree. -
The Novel Map
The Novel Map The Novel Map Space and Subjectivity in Nineteenth-Century French Fiction Patrick M. Bray northwestern university press evanston, illinois Northwestern University Press www.nupress.northwestern.edu Copyright © 2013 by Northwestern University Press. Published 2013. All rights reserved. Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 Library of Congress Cataloging-in-Publication data are available from the Library of Congress. Except where otherwise noted, this book is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/. In all cases attribution should include the following information: Bray, Patrick M. The Novel Map: Space and Subjectivity in Nineteenth-Century French Fiction. Evanston, Ill.: Northwestern University Press, 2013. The following material is excluded from the license: Illustrations and the earlier version of chapter 4 as outlined in the Author’s Note For permissions beyond the scope of this license, visit www.nupress.northwestern.edu An electronic version of this book is freely available, thanks to the support of libraries working with Knowledge Unlatched. KU is a collaborative initiative designed to make high-quality books open access for the public good. More information about the initiative and links to the open-access version can be found at www.knowledgeunlatched.org. Contents List of Illustrations vii Acknowledgments ix Author’s Note xiii Introduction Here -
Variation in Meiosis, Across Genomes, and in Populations
REVIEW Identity by Descent: Variation in Meiosis, Across Genomes, and in Populations Elizabeth A. Thompson1 Department of Statistics, University of Washington, Seattle, Washington 98195-4322 ABSTRACT Gene identity by descent (IBD) is a fundamental concept that underlies genetically mediated similarities among relatives. Gene IBD is traced through ancestral meioses and is defined relative to founders of a pedigree, or to some time point or mutational origin in the coalescent of a set of extant genes in a population. The random process underlying changes in the patterns of IBD across the genome is recombination, so the natural context for defining IBD is the ancestral recombination graph (ARG), which specifies the complete ancestry of a collection of chromosomes. The ARG determines both the sequence of coalescent ancestries across the chromosome and the extant segments of DNA descending unbroken by recombination from their most recent common ancestor (MRCA). DNA segments IBD from a recent common ancestor have high probability of being of the same allelic type. Non-IBD DNA is modeled as of independent allelic type, but the population frame of reference for defining allelic independence can vary. Whether of IBD, allelic similarity, or phenotypic covariance, comparisons may be made to other genomic regions of the same gametes, or to the same genomic regions in other sets of gametes or diploid individuals. In this review, I present IBD as the framework connecting evolutionary and coalescent theory with the analysis of genetic data observed on individuals. I focus on the high variance of the processes that determine IBD, its changes across the genome, and its impact on observable data. -
The Ideologies of Lived Space in Literary Texts, Ancient and Modern
The Ideologies of Lived Space in Literary Texts, Ancient and Modern Jo Heirman & Jacqueline Klooster (eds.) ideologies.lived.spaces-00a.fm Page 1 Monday, August 19, 2013 9:03 AM THE IDEOLOGIES OF LIVED SPACE IN LITERARY TEXTS, ANCIENT AND MODERN ideologies.lived.spaces-00a.fm Page 2 Monday, August 19, 2013 9:03 AM ideologies.lived.spaces-00a.fm Page 3 Monday, August 19, 2013 9:03 AM THE IDEOLOGIES OF LIVED SPACE IN LITERARY TEXTS, ANCIENT AND MODERN Jacqueline Klooster and Jo Heirman (eds.) ideologies.lived.spaces-00a.fm Page 4 Monday, August 19, 2013 9:03 AM © Academia Press Eekhout 2 9000 Gent T. (+32) (0)9 233 80 88 F. (+32) (0)9 233 14 09 [email protected] www.academiapress.be The publications of Academia Press are distributed by: UPNE, Lebanon, New Hampshire, USA (www.upne.com) Jacqueline Klooster and Jo Heirman (eds.) The Ideologies of Lived Space in Literary Texts, Ancient and Modern Gent, Academia Press, 2013, 256 pp. Lay-out: proxessmaes.be Cover: Studio Eyal & Myrthe ISBN 978 90 382 2102 1 D/2013/4804/169 U 2068 No part of this publication may be reproduced in print, by photocopy, microfilm or any other means, without the prior written permission of the publisher. ideologies.lived.spaces.book Page 1 Saturday, August 17, 2013 11:47 AM 1 Contents INTRODUCTION . 3 The Ideologies of ‘Lived Space’, Ancient and Modern Part 1 LIVED SPACE AND SOCIETY CAVE AND COSMOS . 15 Sacred Caves in Greek Epic Poetry from Homer (eighth century BCE) to Nonnus (fifth century CE) Emilie van Opstall SPACE AND MYTH . -
Rapid Estimation of SNP Heritability Using Predictive Process Approximation in Large Scale Cohort Studies
bioRxiv preprint doi: https://doi.org/10.1101/2021.05.12.443931; this version posted May 14, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license. Rapid Estimation of SNP Heritability using Predictive Process approximation in Large scale Cohort Studies Souvik Seal1, Abhirup Datta2, and Saonli Basu3 1Department of Biostatistics and Informatics, University of Colorado Anschutz Medical Campus 2Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health 3Division of Biostatistics, University of Minnesota Twin Cities Abstract With the advent of high throughput genetic data, there have been attempts to estimate heritability from genome-wide SNP data on a cohort of distantly related individuals using linear mixed model (LMM). Fitting such an LMM in a large scale cohort study, however, is tremendously challenging due to its high dimensional linear algebraic operations. In this paper, we propose a new method named PredLMM approximating the aforementioned LMM moti- vated by the concepts of genetic coalescence and gaussian predictive process. PredLMM has substantially better computational complexity than most of the existing LMM based methods and thus, provides a fast alternative for estimating heritability in large scale cohort studies. Theoretically, we show that under a model of genetic coalescence, the limiting form of our approximation is the celebrated predictive process approximation of large gaussian process likelihoods that has well-established accuracy standards. We illustrate our approach with ex- tensive simulation studies and use it to estimate the heritability of multiple quantitative traits from the UK Biobank cohort. -
The Tajima Heterochronous N-Coalescent: Inference from Heterochronously Sampled Molecular Data
The Tajima heterochronous n-coalescent: inference from heterochronously sampled molecular data Lorenzo Cappello1,∗ Amandine Veber´ 2∗, Julia A. Palacios1;3∗ 1Department of Statistics, Stanford University 2CMAP, CNRS, Ecole´ Polytechnique, I.P. Paris 3Department of Biomedical Data Science, Stanford Medicine April 16, 2020 Abstract The observed sequence variation at a locus informs about the evolutionary history of the sample and past population size dynamics. The standard Kingman coalescent model on genealogies – timed trees that represent the ancestry of the sample – is used in a genera- tive model of molecular sequence variation to infer evolutionary parameters. However, the state space of Kingman’s genealogies grows superexponentially with sample size n, making inference computationally unfeasible already for small n. We introduce a new coalescent model called Tajima heterochronous n-coalescent with a substantially smaller cardinality of the genealogical space. This process allows to analyze samples collected at different times, a situation that in applications is both met (e.g. ancient DNA and RNA from rapidly evolving pathogens like viruses) and statistically desirable (variance reduction and parameter iden- tifiability). We propose an algorithm to calculate the likelihood efficiently and present a Bayesian nonparametric procedure to infer the population size trajectory. We provide a new MCMC sampler to explore the space of Tajima’s genealogies and model parameters. We compare our procedure with state-of-the-art methodologies in simulations and applications. We use our method to re-examine the scientific question of how Beringian bison went extinct analyzing modern and ancient molecular sequences of bison in North America, and to recon- arXiv:2004.06826v1 [q-bio.PE] 14 Apr 2020 struct population size trajectory of SARS-CoV-2 from viral sequences collected in France and Germany.