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Proquest Dissertations Host structuring of parasite populations: Some theoretical and computational studies Item Type text; Dissertation-Reproduction (electronic) Authors Taylor, Jesse Earl Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 03/10/2021 11:51:04 Link to Item http://hdl.handle.net/10150/289991 HOST STRUCTURING OF PARASITE POPULATIONS: SOME THEORETICAL AND COMPUTATIONAL STUDIES by Jesse Earl Taylor A Dissertation Submitted to the Faculty of the DEPARTMENT OF ECOLOGY AND EVOLUTIONARY BIOLOGY In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2 0 0 3 UMI Number: 3108960 INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. UMI UMI Microform 3108960 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 THE UNIVERSITY OF ARIZONA ® GRADUATE COLLEGE As members of the Final Examination Coininittee, we certify that we have read the dissertation prepared by entitled j-i 4- gtAi..',^ \4-^ 4-; a I i and recominend that it be accepted as fulfilling the dissertation requirement for the Degree of ph P to/a7(i)i Date ! 0 / -z-"? / o 3 Date n / ^ / "N. \if.I I r I \J ?-7/o3 Date \l y iO^ ( Date 7 \ /e5^2^-"^'' 3 Date Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requir^t^ent. / i /\ f /I / .^ « . f „ I „ wX' _L. Dis^er|ation\j)irector Date 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: 4 ACKNOWLEDGEMENTS Many persons have offered support and guidance during the not always straightfor­ ward transition from mathematics to biology. Foremost, I must thank my advisor, Bruce Walsh, whose facility and interest in both disciplines (and much else) is un- equaled in EEB. I am also indebted to the other members of my committee - much of what I know of probability and stochastic processes I have learned from numerous conversations and courses with Joe Watkins and Jan Wehr, and Michael Nachman and Mike Hammer have certainly broadened my understanding of population genet­ ics. Thanks are also due to several other current and former members of EEB and Applied Math, including John Jaenike, Mike Rosenzweig, Bill SchafFer, and Greg Eyink, all of whom have shared generously of their time and knowledge. In addition to introducing me to the curious world of mycophagous Drosophila, Kelly Dyer has been both a good friend and enthusiastic colleague. I have been very fortunate to spend several summers at Los Alamos National Labo­ ratory, where I had the privilege of working with Mac Hyman in the Mathematical Modeling and Analysis Group in 1999 and with Bette Korber in the Theoretical Bi­ ology and Biophysics Group in 2000-2003. Indeed, this dissertation would not have been possible without Bette's guidance and considerable insight into the biology of HIV. I have met few scientists who are as committed and as successful as Bette in using science to benefit the poorest and most oppressed inhabitants of our planet. I also wish to acknowledge my other colleagues in T-10, Brian Foley, Dorothy Lang, Karina Yusim, Una Smith, Carla Kuiken, Brian Gaschen, John Mokih, Lou Malchie, and Tanmoy Bhattacharya. Special thanks go to Tanmoy and to Daniel Steck in the Elementary Particles and Field Theory Group for computational resources and assistance. My interests in biology were and continue to be fueled by a fascination for birds and 1 have enjoyed the company of many fine birders and ornithologists while living in Tucson. Were it not for frequent excursions with Bill Flack, Andre Lehovich, Jay Withgott, Caleb Gordon, and Wade Leitner, this dissertation would probably have been completed a good bit earlier, but my stay in this desert would have been the much poorer for it. I am also deeply grateful to Torn Huels. curator of the UA bird collection, for his hospitality during my frequent visits to the collection. With much luck, I may yet turn out a skin decent enough to be added to the collection. Thanks are due to Wayne Hacker and Andre Lehovich for technical assistance with the typesetting of this document. 5 Finally, I would not be here today were it not for the constant support and un­ derstanding of my dearest friend and companion, Helen Herlocker. 6 TABLE OF CONTENTS LIST OF FIGURES 7 LIST OF TABLES 8 ABSTRACT 9 1. HOST STRUCTURE OF PARASITE POPULATIONS 11 1.1. Motivation 11 1.2. Model Formulation and Approximation 17 1.3. Invariant Measures and Equilibrium Jump Distributions .... 28 1.4. Examples 32 2. BIOLOGICAL INTERPRETATIONS 61 2.1. Sources of Transmission Bias 61 2.2. Additional Applications 67 3. TRANSMISSION BIAS AND HIV-1 VACCINE DESIGN 87 4. HOST STRUCTURE IN AN EXPANDING EPIDEMIC 101 4.1. Motivation 101 4.2. Branching Fisher-Wright Diffusions 104 4.3. Persistence and Absorption Probabilities 107 4.4. Extensions 118 5. HOST STRUCTURE, RECOMBINATION, AND HLV-1 SUPERINFECTION . 121 5.1. Background 121 5.2. Methods 127 5.3. Results 137 5.4. Discussion 141 REFERENCES 169 7 LIST OF FIGURES FIGURE 1.1. Invariant statistics for the finite infrapopulation model: ji •- 1.0 47 FIGURE 1.2. Invariant statistics for the finite infrapopulation model: /x = 0.1 48 FIGURE 1.3. Equilibrium metapopulation and jump frequencies for the infinite infrapopulation model 56 FIGURE 1.4. Metapopulation-jump frequency differences: influence of selec­ tion and transmission bias 57 FIGURE 1.5. Metapopulation-jump frequency differences: influence of trans­ mission rate 58 FIGURE 1.6. Equilibrium dispersion H for the infinite infrapopulation model 59 FIGURE 1.7. Metapopulation and jump frequencies for the finite infrapopula­ tion model: influence of genetic drift 60 FIGURE 2.1. Time series of the metapopulation allele frequency in a finite metapopulation: H = 10 74 FIGURE 2.2. Time series of the metapopulation allele frequency in a finite metapopulation: H = 100 75 FIGURE 2.3. Time series of the metapopulation allele frequency in a finite metapopulation: H --- 1000 76 8 LIST OF TABLES TABLE 5.1. Patient Data Sets 163 TABLE 5.2. Subtype Data Sets 163 TABLE 5.3. Simulated Data r = 5 164 TABLE 5.4. Simulated Data r = 10 165 TABLE 5.5. Superinfection Rate Estimates 166 TABLE 5.6. Distribution of p with Rare Superinfection 167 TABLE 5.7. Influence of Transmission Dose on p 168 9 ABSTRACT Because the ecological and the genetic interactions occurring between parasites be­ longing to different infections are constrained by the physical discreteness of the hosts, the host-parasite association imparts a spatial structure to the populations of parasitic microorganisms. Equating infections with demes or islands, the parasite population can be described by a variant of Wright's island model, in which recovery and in­ fection correspond to extinction and colonization and superinfection corresponds to migration. Here we investigate some of the population genetic consequences of host structure using a combination of theoretical and computational methods. In our first study, we introduce a measure-valued process as a model for the evo­ lution of an age-structured parasite metapopulation and show how to approximate this process using the measure flow generated by a jump-diffusion. We characterize the invariant measures and corresponding jump distributions for the approximation and apply these methods to an example involving a single locus subject to muta­ tion, selection, and genetic drift within hosts and to bottlenecks and bias during transmission. When intrahost selection and transmission bias act discordantly, it is shown that the invariant measure and the jump distribution can differ substan­ tially. We discuss the implications of such discordance for vaccine target selection and review the evidence for biased transmission of HIV-1. In our second study, we use a branching Fisher-Wright process to characterize diversity in an exponentially expanding epidemic. We derive a renewal equation for the persistence probability of the branching diffusion and show that with sufficiently rapid branching a set of k neutral alleles can persist indefinitely with positive probability.
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