Estimation of Mutation Rates from Fluctuation Experiments via Probability Generating Functions

TL;DR

This paper introduces a generating function approach to model mutation rates in fluctuation experiments, simplifying calculations and applying them to yeast data, offering a new perspective on mutation rate estimation.

Contribution

It presents a novel generating function framework for calculating mutation distributions in fluctuation experiments, including a derivation of Haldane's distribution.

Findings

Derived a generating function for mutation distributions

Applied formulas to yeast mutation data

Simplified calculations of mutation probabilities

Abstract

This paper calculates probability distributions modeling the Luria-Delbr\"uck experiment. We show that by thinking purely in terms of generating functions, and using a 'backwards in time' paradigm, that formulas describing various situations can be easily obtained. This includes a generating function for Haldane's probability distribution due to Ycart. We apply our formulas to both simulated and real data created by looking at yeast cells acquiring an immunization to the antibiotic canavanine. This paper is somewhat incomplete, having been last significantly modified in March 29, 2014. However the first author feels that this paper has some worthwhile ideas, and so is going to make this paper publicly available.