A mutation-selection model with recombination for general genotypes

by Evans, Steven N., (Steven Neil)

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Title Statements

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

Summary

"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 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 dynamical system 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: intensity measure 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. Our motivation for working in such a general setting is to provide a basis for understanding mutation-driven changes in age-specific demographic schedules that arise from the complex interaction of many genes, and hence to develop a framework for understanding the evolution of aging. We establish the existence and uniqueness of the dynamical system, provide conditions for the existence and stability of equilibrium states, and prove that our continuous-time dynamical system is the limit of a sequence of discrete-time infinite population mutation-selection-recombination models in the standard asymptotic regime where selection and mutation are weak relative to recombination and both scale at the same infinitesimal rate in the limit."

Edition Statements

Publication Date:©2012

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence, Rhode Island
Language:eng
Publication Date:©2012

Notes

"March 2013, Volume 222, Number 1044 (third of 5 numbers)."

The Physical Object

Description:1 online resource (viii, 128 pages) : : illustrations.

Edition Identifiers

ISBN:9780821895115, 0821895117
oclc:ocn828203660
LC Classification:QH390
Dewey Decimal:572.8/38

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 dis…

Subjects

Evolutionary genetics Genetic recombination Génétique évolutive Mutation (Biologie) Mutation (Biology) Recombinaison génétique SCIENCE -- Life Sciences