A probabilistic analysis of a discrete-time evolution in recombination

TL;DR

This paper provides a closed-form analysis of the discrete-time evolution in recombination processes in population genetics, introducing a Markov chain framework and examining convergence and quasi-stationary behavior.

Contribution

It offers a novel closed-form solution for the evolution of recombination transformations and characterizes the Markov chain dynamics and decay rates.

Findings

Derived a closed-form expression for the evolution of recombination.

Analyzed the geometric decay rate to the limit distribution.

Explored the quasi-stationary behavior conditioned on non-absorption.

Abstract

We give a closed form of the discrete-time evolution of a recombination transformation in population genetics. This decomposition allows to define a Markov chain in a natural way. We describe the geometric decay rate to the limit distribution, and the quasi-stationary behavior when conditioned to the event that the chain does not hit the limit distribution.