Labelled partitions in action: recombination, selection, mutation, and more
Probability
2024-10-03 v2 Populations and Evolution
Abstract
In this paper, we consider the evolution of an (infinitely large) population under recombination and additional evolutionary forces, modelled by a measure-valued ordinary differential equation. We provide a stochastic representation for the solution of this model via duality to a new labelled 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.
Cite
@article{arxiv.2203.10874,
title = {Labelled partitions in action: recombination, selection, mutation, and more},
author = {Frederic Alberti},
journal= {arXiv preprint arXiv:2203.10874},
year = {2024}
}