Memoirs of the American Mathematical Society 2013; 128 pp; softcover Volume: 222 ISBN10: 0821875698 ISBN13: 9780821875698 List Price: US$73 Individual Members: US$43.80 Institutional Members: US$58.40 Order Code: MEMO/222/1044
 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  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
