Title: Mutation-selection balance with recombination: convergence to equilibrium for polynomial selection costs
Author: Aubrey Clayton and Steven N. Evans
Abstract: We study a (possibly infinite-dimensional) dynamical system model for mutation and selection in the presence of recombination.  Some features of the model, such as existence and uniqueness of solutions and convergence to the dynamical system of an approximating sequence of discrete time models, were presented in earlier work by Evans, Steinsaltz, and Wachter for quite general selection costs.  Here we establish that the phenomenon of mutation-selection balance occurs in the special case of ``polynomial'' selection costs under mild conditions.  That is, we show that the dynamical system has a unique equilibrium and that it converges to this equilibrium from all initial conditions.
Date: September 2007