A mutation-selection model with recombination for general genotypes /

"We investigate a continuous time, probability measure-valued dynamical system that describes the process of mutation-selection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak assumptions on selective costs. Our model arises when we i...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Evans, Steven N. (Steven Neil) (Autor), Steinsaltz, David, 1966- (Autor), Wachter, Kenneth W. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, Rhode Island : American Mathematical Society, [2013]
Colección:Memoirs of the American Mathematical Society ; no. 1044.
Temas:
Evolutionary genetics.
Mutation (Biology)
Genetic recombination.
Génétique évolutive.
Mutation (Biologie)
Recombinaison génétique.
SCIENCE > Life Sciences > Biochemistry.
Evolutionary genetics
Genetic recombination
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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