The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
A Mathematical Theory for Single-Nutrient Competition in Continuous Cultures of Micro-Organisms
Abstract
The continuous culture of micro-organisms using the chemostat is an important research technique in microbiology and population biology. It offers advantages in the form of economical production of micro-organisms for the industrial microbiologist and is a laboratory idealization of nature for population studies. The paper studies a mathematical model, based on Michaelis-Menten kinetics, for one substrate and n competing species. Given the parameters of the system, we answer the basic question as to which species survive and which do not, and determine the limiting behaviors. The primary conclusion is that the species will survive whose Michaelis-Menten constant is smallest in comparison with its intrinsic rate of natural increase.
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Cites
Stability and Complexity in Model Ecosystems
May, R. M. (2001) · Princeton University Press eBooks · doi:10.1515/9780691206912 · Cited by 5,183
STABILITY AND COMPLEXITY IN MODEL ECOSYSTEMS
Schoener, T. W. (1974) · Evolution · doi:10.1111/j.1558-5646.1974.tb00784.x · Cited by 3,928
Hutchinson, E. G. (1957) · Medical Entomology and Zoology · Cited by 3,896
Qualitative Theory of Differential Equations
(1961) · Princeton University Press eBooks · doi:10.1515/9781400875955 · Cited by 1,480
The Continuous Culture of Bacteria; a Theoretical and Experimental Study
Herbert, D., Elsworth, R., & Telling, R. C. (1956) · Journal of General Microbiology · doi:10.1099/00221287-14-3-601 · Cited by 1,010
NUTRIENT LIMITATION IN THE SEA: DYNAMICS, IDENTIFICATION, AND SIGNIFICANCE1
Dugdale, R. C. (1967) · Limnology and Oceanography · doi:10.4319/lo.1967.12.4.0685 · Cited by 836
Novick, A., & Szilard, L. (1950) · Science · doi:10.1126/science.112.2920.715 · Cited by 765
Stewart, F. M., & Levin, B. R. (1973) · The American Naturalist · doi:10.1086/282825 · Cited by 439
A HYPOTHESIS CONCERNING SILICA AND THE FRESHWATER PLANKTONIC DIATOMS1
Kilham, P. (1971) · Limnology and Oceanography · doi:10.4319/lo.1971.16.1.0010 · Cited by 258
Introduction to research with continuous cultures
KUBITSCHEK, H. E. (1970) · Prentice Hall eBooks · Cited by 210
Cited by
Competition and Biodiversity in Spatially Structured Habitats
Tilman, D. (1994) · Ecology · doi:10.2307/1939377 · Cited by 2,780
Constraints and Tradeoffs: Toward a Predictive Theory of Competition and Succession
Tilman, D. (1990) · Oikos · doi:10.2307/3565355 · Cited by 750
Competitive exclusion and limiting similarity: A unified theory
Meszéna, G., Gyllenberg, M., Pásztor, L., & Metz, J. A. J. (2006) · Theoretical Population Biology · doi:10.1016/j.tpb.2005.07.001 · Cited by 298
Competitive Coexistence in an Oscillating Chemostat
Smith, H. L. (1981) · SIAM Journal on Applied Mathematics · doi:10.1137/0140042 · Cited by 166
Permanence via invasion graphs: incorporating community assembly into modern coexistence theory
Hofbauer, J., & Schreiber, S. J. (2022) · Journal of Mathematical Biology · doi:10.1007/s00285-022-01815-2 · Cited by 35
Metadata
- Authors
- Hsu, S. B., Hubbell, S., & Waltman, P.
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 1977-03
- Volume
- 32
- Issue
- 2
- Pages
- 366-383
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W1968201943
- Cited by
- 527
- References
- 15
- FWCI
- 5.77
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
