Labeled partitions in action: Recombination, selection, mutation and more

Abstract

In this paper, we consider the evolution of an (infinitely large) population under recombination and additional evolutionary forces, modeled by a measure-valued ordinary differential equation. We provide a stochastic representation for the solution of this model via duality to a new labeled partitioning process with Markovian labels. In the special case of single-crossover, this leads to a recursive solution formula. This extends (and unifies) previous results on the selection–recombination equation. As a concrete example, we consider the selection–mutation–recombination equation.