The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
Analysis of the Luria–Delbrück distribution using discrete convolution powers
Abstract
The Luria–Delbrück distribution arises in birth-and-mutation processes in population genetics that have been systematically studied for the last fifty years. The central result reported in this paper is a new recursion relation for computing this distribution which supersedes all past results in simplicity and computational efficiency: p0 = e^-m ; where m is the expected number of mutations. A new relation for the asymptotic behavior of pn (≈ c/n^2) is also derived. This corresponds to the probability of finding a very large number of mutants. A formula for the z-transform of the distribution is also reported.
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Cites
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Research works printed but not linked: 1
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Sorted by citations
Evolution of high mutation rates in experimental populations of E. coli
Sniegowski, P. D., Gerrish, P. J., & Lenski, R. E. (1997) · Nature · doi:10.1038/42701 · Cited by 879
Determining Mutation Rates in Bacterial Populations
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Branching Processes in Biology
Kimmel, M., & Axelrod, D. E. (2015) · Interdisciplinary applied mathematics · doi:10.1007/978-1-4939-1559-0 · Cited by 389
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Estimating the Per-Base-Pair Mutation Rate in the Yeast Saccharomyces cerevisiae
Lang, G. I., & Murray, A. W. (2008) · Genetics · doi:10.1534/genetics.107.071506 · Cited by 344
Metadata
- Authors
- Ma, W. T., Sandri, G. V., & Sarkar, S.
- Affiliations
- Boston University (US)
- Corresponding author
- Sarkar, S.
- ORCID
- Sarkar, S.
- Venue
- Journal of Applied Probability
- Publisher
- Cambridge University Press (CUP)
- Published
- 1992-06
- Volume
- 29
- Issue
- 2
- Pages
- 255-267
- ISSN
- 0021-9002 (ISSN-L)
- 1475-6072
- OpenAlex
- W2320526527
- Cited by
- 146
- References
- 10
- Citations by year
- 2026: 4 · 2025: 1 · 2024: 1 · 2023: 9 · 2022: 4 · 2021: 7 · 2020: 2 · 2019: 5 · 2018: 4 · 2017: 9 · 2016: 5 · 2015: 11 · 2014: 8 · 2013: 4 · 2012: 8
- FWCI
- 5.46
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Applied Probability (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- recurrence relations, population genetics, asymptotic behavior, z-transform
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- The paper
- Ma, W. T., Sandri, G. V., & Sarkar, S. (1992). Analysis of the Luria–Delbrück distribution using discrete convolution powers. Journal of Applied Probability. https://doi.org/10.1017/s0021900200043023
