New algorithms for Luria–Delbrück fluctuation analysis

Fluctuation analysis is the most widely used approach in estimating microbial mutation rates. Development of methods for point and interval estimation of mutation rates has long been hampered by lack of closed form expressions for the probability mass function of the number of mutants in a parallel culture. This paper uses sequence convolution to derive exact algorithms for computing the score function and observed Fisher information, leading to efficient computation of maximum likelihood estimates and profile likelihood based confidence intervals for the expected number of mutations occurring in a test tube. These algorithms and their implementation in SALVADOR 2.0 facilitate routine use of modern statistical techniques in fluctuation analysis by biologists engaged in mutation research.