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Mutation-Selection Model with Recombination for General Genotypes.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2013Copyright date: ©2012Edition: 1st edDescription: 1 online resource (142 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9780821895115
Subject(s): Genre/Form: Additional physical formats: Print version:: Mutation-Selection Model with Recombination for General GenotypesDDC classification:
  • 572.8/38
LOC classification:
  • QH390 -- .E936 2012eb
Online resources:
Contents:
Intro -- 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 -- 2.5. Density form of the dynamical system -- 2.6. Mutation measures with infinite total mass -- Chapter 3. Equilibria -- 3.1. Introductory example: One-dimensional systems -- 3.2. Introductory example: Multiplicative selective costs -- 3.3. Fréchet 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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Intro -- 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 -- 2.5. Density form of the dynamical system -- 2.6. Mutation measures with infinite total mass -- Chapter 3. Equilibria -- 3.1. Introductory example: One-dimensional systems -- 3.2. Introductory example: Multiplicative selective costs -- 3.3. Fréchet 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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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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