Bootstrap estimation of confidence intervals on mutation rate ratios

New approaches to mutation rate fold change in Luria-Delbrück fluctuation experiments

For nearly eight decades the Luria-Delbrück protocol remains the preferred method for experimentally determining microbial mutation rates. However, earnest development and rigorous applications of statistical methods for mutation rate comparison using fluctuation assay data are a relatively recent phenomenon. While likelihood ratio tests tailored for the fluctuation protocol give investigators appropriate tools, researchers sometimes may prefer to view the comparison of two mutation rates through the lens of the ratio of the two mutation rates. The idea of using the bootstrap technique to construct intervals for mutation rate fold change was proposed nearly a decade ago, but it failed to gain traction partly due to a failure to incorporate likelihood-based estimation. In addition to extending the bootstrap method, this paper proposes two new methods of constructing intervals for mutation rate fold change: a profile likelihood method and a Bayesian method utilizing Monte Carlo Markov chain. All three methods are assessed by large-scale simulations.

A second look at the final number of cells in a fluctuation experiment

In a fluctuation experiment, the number of cells existing in a culture immediately before plating (commonly known as Nt) varies across the parallel cultures. However, most existing mathematical models for fluctuation assay data do not recognize the variation in Nt. Despite repeated attempts in the past to integrate this source of variability in the estimation of microbial mutation rates, several questions of practical importance remain unanswered. The present investigation finds that the variation needs accounting for only when the coefficient of variation for Nt is large, and experimental data suggest that the coefficient of variation is often moderate or small. Moreover, an increase in the inoculum size can reduce the coefficient of variation. Through extensive simulation, several existing methods that accommodate the variation in Nt are compared. It was found that a newly devised likelihood method based on the existing gamma mixture model outperforms other existing methods. The investigation focuses on the estimation of mutation rates using the Lea-Coulson model, under which mutation is selectively neutral; however, the paper also explores the major findings' implications for the comparison of mutation rates using the likelihood ratio test, and for the estimation of mutation rates using the Mandelbrot-Koch model that allows for non-neutral mutations.