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A Mutation-Selection Model with Recombination for General Genotypes
Steven N. Evans, David Steinsaltz, and Kenneth W. Wachter, University of California, Berkeley, CA

Memoirs of the American Mathematical Society
2013; 128 pp; softcover
Volume: 222
ISBN-10: 0-8218-7569-8
ISBN-13: 978-0-8218-7569-8
List Price: US$73
Individual Members: US$43.80
Institutional Members: US$58.40
Order Code: MEMO/222/1044
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The authors 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. 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 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.

Table of Contents

  • Introduction
  • Definition, existence, and uniqueness of the dynamical system
  • Equilibria
  • Mutation, selection, and recombination in discrete time
  • Shattering and the formulation of the convergence result
  • Convergence with complete Poissonization
  • Supporting lemmas for the main convergence result
  • Convergence of the discrete generation system
  • Appendix A. Results cited in the text
  • Bibliography
  • Index
  • Glossary of notation
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