English

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.

Keywords

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}
}
R2 v1 2026-06-24T10:20:17.619Z