Luria-Delbrück fluctuation analysis: Estimating the Poisson parameter in a compound Poisson distribution

Jones, Michael E.; Wheldrake, J.F.; Rogers, Alix

doi:10.1016/0010-4825(93)90099-m

Cited by 14 publications

(13 citation statements)

References 11 publications

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“…Estimating the two parameters of a classical Luria-Delbrück distribution by the method of maximum likelihood was proposed long ago [8], [12], [31], [32]. Using well known explicit formulas, the method has been implemented [11], [14], [33].…”

Section: Methodsmentioning

confidence: 99%

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Unbiased Estimation of Mutation Rates under Fluctuating Final Counts

Ycart

Véziris

2014

PLoS ONE

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Estimation methods for mutation rates (or probabilities) in Luria-Delbrück fluctuation analysis usually assume that the final number of cells remains constant from one culture to another. We show that this leads to systematically underestimate the mutation rate. Two levels of information on final numbers are considered: either the coefficient of variation has been independently estimated, or the final number of cells in each culture is known. In both cases, unbiased estimation methods are proposed. Their statistical properties are assessed both theoretically and through Monte-Carlo simulation. As an application, the data from two well known fluctuation analysis studies on Mycobacterium tuberculosis are reexamined.

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Section: Methodsmentioning

confidence: 99%

“…Classical methods : the estimate of the expected number of mutations was computed by two different methods: the -method [1], [5], [28], and the maximum likelihood (ML) method [12], [31], [32], both applied to the sample of mutant counts. Dividing by the expected final number , assumed to be known, leads to two estimates for .…”

Section: Methodsmentioning

confidence: 99%

Unbiased Estimation of Mutation Rates under Fluctuating Final Counts

Ycart

Véziris

2014

PLoS ONE

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“…The widely used estimators of mutation rates are: the P 0 estimator (Luria and Delbrück 1943), the median estimator (Lea and Coulson 1949), the Lea-Coulson estimator (1949), and the maximum likelihood estimator (MLE; Jones et al 1993;Zheng 2002) as well as Bayesian estimators (Asteris and Sarkar 2002), as reviewed by Foster (2006). However, most of these estimators, such as P 0 , mean and median, do not (and cannot) consider variations in population sizes of the parallel cultures, but assume the same population size for each parallel culture.…”

Section: Modified Median Estimator Of Mutation Ratesmentioning

confidence: 99%

“…The first explicit and practical algorithm for computing the MLE of m was published by Jones et al (1993). To evaluate the reliability of the MLE, Stewart then provided a systematic method for constructing CIs (Stewart 1994).…”

Section: Maximum Likelihood Estimatormentioning

confidence: 99%

Branching Processes in Biology

Kimmel

Axelrod

2015

Interdisciplinary Applied Mathematics

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Problems in engineering, computational science, and the physical and biological sciences are using increasingly sophisticated mathematical techniques. Thus, the bridge between the mathematical sciences and other disciplines is heavily traveled. The correspondingly increased dialog between the disciplines has led to the establishment of the series: Interdisciplinary Applied Mathematics.The purpose of this series is to meet the current and future needs for the interaction between various science and technology areas on the one hand and mathematics on the other. This is done, firstly, by encouraging the ways that mathematics may be applied in traditional areas, as well as point towards new and innovative areas of applications; and secondly, by encouraging other scientific disciplines to engage in a dialog with mathematicians outlining their problems to both access new methods as well as to suggest innovative developments within mathematics itself.The series will consist of monographs and high-level texts from researchers working on the interplay between mathematics and other fields of science and technology.More information about this series at

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“…Various mutation rate estimators have been developed based on the LD distribution, including the P 0 estimator (Luria and Delbrück, 1943), the mean estimator (Luria and Delbrück, 1943), the median estimator (Lea and Coulson, 1949;Drake, 1991;Jones et al, 1994) and the maximum likelihood estimator (MLE) Jones et al, 1993). Extensive simulations have shown that the MLE outperforms the other estimators in terms of bias and variance (Stewart, 1994;Rosche and Foster, 2000) since it incorporates all information from the mutant-count distribution (rather than just moments or quantiles).…”

Section: Introductionmentioning

confidence: 99%

Fast maximum likelihood estimation of mutation rates using a birth–death process

Zhu

2015

Journal of Theoretical Biology

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Luria-Delbrück fluctuation analysis: Estimating the Poisson parameter in a compound Poisson distribution

Cited by 14 publications

References 11 publications

Unbiased Estimation of Mutation Rates under Fluctuating Final Counts

Unbiased Estimation of Mutation Rates under Fluctuating Final Counts

Branching Processes in Biology

Fast maximum likelihood estimation of mutation rates using a birth–death process

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