Rocky Mountain Journal of Mathematics

Interaction in a Chemostat: Introduction of a Competitor Can Promote Greater Diversity

Gail S.K. Wolkowicz, Mary M. Ballyk, and Spiro P. Daoussis

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 25, Number 1 (1995), 515-543.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181072300

Digital Object Identifier
doi:10.1216/rmjm/1181072300

Mathematical Reviews number (MathSciNet)
MR1340025

Zentralblatt MATH identifier
0824.92028

Keywords
Population dynamics ecology chemostat competition predation invasion paradox of enrichment

Citation

Wolkowicz, Gail S.K.; Ballyk, Mary M.; Daoussis, Spiro P. Interaction in a Chemostat: Introduction of a Competitor Can Promote Greater Diversity. Rocky Mountain J. Math. 25 (1995), no. 1, 515--543. doi:10.1216/rmjm/1181072300. https://projecteuclid.org/euclid.rmjm/1181072300


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References

  • R.A. Armstrong and R. McGehee, Competitive exclusion, Am. Nat. 115 (1980), 151-170.
  • M.M. Ballyk and G.S.K. Wolkowicz, Exploitative competition in the chemostat for two perfectly substitutable resources, Math. Biosci. 118 (1993), 127-180.
  • G.J. Butler, H.I. Freedman and P. Waltman, Uniformly persistent systems, Proc. Amer. Math. Soc. 96 (1986), 425-430.
  • G.J. Butler and G.S.K. Wolkowicz, A mathematical model of the chemostat with a general class of functions describing nutrient uptake, SIAM J. Appl. Math. 45 (1985), 138-151.
  • --------, Predator-mediated competition in the chemostat, J. Math. Biol. 24 (1986), 167-191.
  • --------, Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources, Math. Biosci. 83 (1987), 1-48.
  • S.P. Daoussis, Predator-mediated competition: Predator feeding on two different trophic levels, M.Sc. thesis, McMaster University, 1992.
  • H.I. Freedman and P. Waltman, Persistence in models of three interacting predator-prey populations, Math. Biosci. 68 (1984), 213-231.
  • S.B. Hsu, Limiting behaviour for competing species, SIAM J. Appl. Math. 34 (1978), 760-763.
  • S.B. Hsu, S.P. Hubbell and P. Waltman, A mathematical theory of single-nutrient competition in continuous cultures for microorganisms, SIAM J. Appl. Math. 32 (1987), 366-383.
  • J.A. León and D.B. Tumpson, Competition between two species for two complementary or substitutable resources, J. Theor. Biol. 50 (1975), 185-201.
  • R.T. Paine, Food web complexity and species diversity, Am. Nat. 100 (1966), 65-75.
  • D.J. Rapport, An optimization model of food selection, Am. Nat. 105 (1971), 575-587.
  • M.L. Rosenzweig, Paradox of enrichment: Destabilization of exploitation ecosystems in ecological time, Science 171 (1971), 385-387.
  • L.B. Slobodkin, Ecological populations of Hydrida., J. Anim. Ecology 33 (suppl) (1964), 131-148.
  • D. Tilman, Resource competition and community structure, Princeton University Press, Princeton, NJ, 1982.
  • P. Waltman, S.P. Hubbell and S.B. Hsu, Theoretical and experimental investigations of microbial competition in continuous culture, in Modelling and differential equations (T. Burton, ed.), Marcel Dekker, New York, 1980.
  • G.S.K. Wolkowicz, Successful invasion of a food web in a chemostat, Math. Biosci. 93 (1989), 249-268.
  • --------, Invasion of a persistent system, Rocky Mountain J. Math. 20 (1990), 1217-1234.
  • G.S.K. Wolkowicz and Z. Lu, Global dynamics of a mathematical model of competition in the chemostat: General response functions and differential death rates, SIAM J. Appl. Math. 52 (1992), 222-233.