A mutation-selection model with recombination for general genotypes / / Steven N. Evans, David Steinsaltz, Kenneth W. Wachter

• Record Nr.: UNINA9910828116803321
• Autore: Evans Steven N (Steven Neil)
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2012; ©2012
• ISBN: 0-8218-9511-7
• Descrizione fisica: 1 online resource (128 p.)
• Collana: Memoirs of the American Mathematical Society, , 1947-6221 ; ; Volume 222, Number 1044
• Disciplina: 572.8/38
• Soggetti: Evolutionary genetics; Mutation (Biology); Genetic recombination
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "March 2013, Volume 222, Number 1044 (third of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Contents -- Abstract -- Chapter 1. Introduction -- 1.1. Informal description of the limit model -- 1.2. Example I: Mutation counting -- 1.3. Example II: Polynomial selective costs -- 1.4. Example III: Demographic selective costs -- 1.5. Comments on the literature -- 1.6. Overview of the remainder of the work -- Chapter 2. Definition, Existence, and Uniqueness of the Dynamical System -- 2.1. Spaces of measures -- 2.2. Definition of the dynamical system -- 2.3. Existence and uniqueness of solutions -- 2.4. Lemmas used in the proof of existence and uniqueness -- Chapter 3. Equilibria -- 3.1. Introductory example: One-dimensional systems -- 3.2. Introductory example: Multiplicative selective costs -- 3.3. Frechet derivatives -- 3.4. Existence of equilibria via perturbation -- 3.5. Concave selective costs -- 3.6. Concave selective costs: Existence and stability of equilibria -- 3.7. Iterative computation of the minimal equilibrium -- 3.8. Stable equilibria in the concave setting via perturbation -- 3.9. Equilibria for demographic selective costs -- Chapter 4. Mutation, Selection, and Recombination in Discrete Time -- 4.1. Mutation and selection in discrete time -- 4.2. Recombination in discrete time -- 4.3. Recombination trees and annealed recombination -- 4.4. Vintages -- Chapter 5. Shattering and the Formulation of the Convergence ; Result -- 5.1. Shattering of random measures -- 5.2. Consequences of shattering -- 5.3. Convergence to Poisson of iterated recombination -- 5.4. Atoms in the initial intensity -- 5.5. Preview of the main convergence result -- Chapter 6. Convergence with Complete Poissonization -- Chapter 7. Supporting Lemmas for the Main Convergence Result -- 7.1. Estimates for Radon-Nikodym derivatives -- 7.2. Comparisons with complete Poissonization -- Chapter 8. Convergence of the Discrete Generation System -- 8.1. Outline of the proof -- 8.2. The convergence theorem -- Appendix A. Results Cited in the Text -- A.1. Gronwall's Inequality -- A.2. Two expectation approximations -- A.3. Identities for Poisson random measures -- A.4. Bounds for Poisson random measures -- A.5. Bounds for Radon-Nikodym derivatives -- Bibliography -- Index -- Glossary of Notation.