Progress of a half century in the study of the Luria-Delbrück distribution
Abstract
The Luria-Delbrück mutation model has been mathematically formulated in a number of ways. This review article examines four most important formulations, focusing on important practical issues closely linked with the distribution of the number of mutants. These issues include the probability generating functions, moments (cumulants), computational methods and asymptotics. This review emphasizes basic principles which not only help to unify existing results but also allow for a few useful extensions. In addition, the review offers a historical perspective and some new explanations of divergent moments.
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Under a simple stochastic model, the chance of extinction as t→∞ of a population starting with N0 cells is d^N0.
“For example, under a simple stochastic model, the chance of extinction as t →∞ of a population starting with N 0 cells is d N 0 (see (8.59) in [12])”
From Efficient, robust, and versatile fluctuation data analysis using MLE MUtation Rate calculator (mlemur) (2023) · cites this paper as [12]
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“[14] does not hold in terms of the exact distribution.”
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Analysis of the Luria–Delbrück distribution using discrete convolution powers
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Theory of lethal mutagenesis for viruses
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Statistical and algorithmic methods for fluctuation analysis with SALVADOR as an implementation
Zheng, Q. (2002) · Mathematical Biosciences · doi:10.1016/s0025-5564(02)00087-1 · Cited by 70 · see citing works
Self-citationNew algorithms for Luria-Delbruck fluctuation analysis
Zheng, Q. (2005) · Mathematical Biosciences · doi:10.1016/j.mbs.2005.03.011 · Cited by 57 · see citing works
Self-citationOn Haldane’s formulation of Luria and Delbrück’s mutation model.
Zheng, Q. (2007) · Mathematical Biosciences · doi:10.1016/j.mbs.2007.03.003 · Cited by 19 · see citing works
Self-citationCarballo-Pacheco, M., Nicholson, M. D., Lilja, E. E., Allen, R. J., & Waclaw, B. (2020) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1007930 · Cited by 18 · see citing works
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Estimating mutation rates in low-replication experiments
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- Authors
- Zheng, Q.
- Affiliations
- National Center for Toxicological Research (US)
- Corresponding author
- Zheng, Qi
- ORCID
- Zheng, Qi
- Venue
- Mathematical Biosciences
- Publisher
- Elsevier BV
- Published
- 1999-11
- Volume
- 162
- Issue
- 1-2
- Pages
- 1-32
- ISSN
- 0025-5564 (ISSN-L)
- OpenAlex
- W2014268112
- Cited by
- 144
- References
- 3
- Citations by year
- 2026: 1 · 2025: 10 · 2024: 8 · 2023: 13 · 2022: 9 · 2021: 3 · 2020: 5 · 2019: 6 · 2018: 5 · 2017: 1 · 2016: 6 · 2015: 7 · 2014: 11 · 2013: 7 · 2012: 9
- FWCI
- 0.85
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Mathematical Biosciences (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Keywords
- mutation models, probability generating function, cumulants, asymptotic methods, computational methods
- MeSH terms
- Genetics, Models, Genetic, Mutation, Poisson Distribution, History, 20th Century
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