Muller's ratchet clicks in finite time

TL;DR

This paper proves that in a continuous time model of Muller's ratchet, the accumulation of deleterious mutations in an asexual population occurs almost surely in finite time, regardless of mutation rate, toxicity, or population size.

Contribution

It establishes that Muller's ratchet clicks in finite time for any parameters in the continuous time model, extending understanding of mutation accumulation dynamics.

Findings

Muller's ratchet clicks almost surely in finite time.

The result holds for all mutation rates, toxicity levels, and population sizes.

The minimum number of deleterious mutations diverges to infinity.

Abstract

We consider the accumulation of deleterious mutations in an asexual population, a phenomenon known as Muller's ratchet, using the continuous time model proposed in Etheridge et all. \cite{epw}. We show that for any parameter $\lambda>0$ (the rate at which mutations occur), for any $\alpha>0$ (the toxicity of the mutations) and for any size $N>0$ of the population, the ratchet clicks a.s. in finite time. That is to say the minimum number of deleterious mutations in the population goes to infinity a.s.