Electronic ISBN:  9780821895115 
Product Code:  MEMO/222/1044.E 
List Price:  $73.00 
MAA Member Price:  $65.70 
AMS Member Price:  $43.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 222; 2013; 128 ppMSC: Primary 60; 92; Secondary 37;
The authors investigate a continuous time, probability measurevalued dynamical system that describes the process of mutationselection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak assumptions on selective costs. Their model arises when they incorporate very general recombination mechanisms into an earlier model of mutation and selection presented by Steinsaltz, Evans and Wachter in 2005 and take the relative strength of mutation and selection to be sufficiently small. The resulting dynamical system is a flow of measures on the space of loci.
Each such measure is the intensity measure of a Poisson random measure on the space of loci: the points of a realization of the random measure record the set of loci at which the genotype of a uniformly chosen individual differs from a reference wild type due to an accumulation of ancestral mutations. The authors' motivation for working in such a general setting is to provide a basis for understanding mutationdriven changes in agespecific demographic schedules that arise from the complex interaction of many genes, and hence to develop a framework for understanding the evolution of aging. 
Table of Contents

Chapters

1. Introduction

2. Definition, Existence, and Uniqueness of the Dynamical System

3. Equilibria

4. Mutation, Selection, and Recombination in Discrete Time

5. Shattering and the Formulation of the Convergence Result

6. Convergence with Complete Poissonization

7. Supporting Lemmas for the Main Convergence Result

8. Convergence of the Discrete Generation System

A. Results Cited in the Text


RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
The authors investigate a continuous time, probability measurevalued dynamical system that describes the process of mutationselection balance in a context where the population is infinite, there may be infinitely many loci, and there are weak assumptions on selective costs. Their model arises when they incorporate very general recombination mechanisms into an earlier model of mutation and selection presented by Steinsaltz, Evans and Wachter in 2005 and take the relative strength of mutation and selection to be sufficiently small. The resulting dynamical system is a flow of measures on the space of loci.
Each such measure is the intensity measure of a Poisson random measure on the space of loci: the points of a realization of the random measure record the set of loci at which the genotype of a uniformly chosen individual differs from a reference wild type due to an accumulation of ancestral mutations. The authors' motivation for working in such a general setting is to provide a basis for understanding mutationdriven changes in agespecific demographic schedules that arise from the complex interaction of many genes, and hence to develop a framework for understanding the evolution of aging.

Chapters

1. Introduction

2. Definition, Existence, and Uniqueness of the Dynamical System

3. Equilibria

4. Mutation, Selection, and Recombination in Discrete Time

5. Shattering and the Formulation of the Convergence Result

6. Convergence with Complete Poissonization

7. Supporting Lemmas for the Main Convergence Result

8. Convergence of the Discrete Generation System

A. Results Cited in the Text