Competition in the gradostat: the role of the communication rate

Hal Smith, Betty Tang

Research output: Contribution to journalArticle

18 Scopus citations

Abstract

In this paper we study a mathematical model of competition between two species of microorganisms for a single limiting nutrient in a laboratory device called a gradostat. A gradostat consists of several (we consider only two) chemostats (CSTR's) connected together so that material can flow between the vessels in such a way that a nutrient gradient is established. Our model is a slightly modified version of one considered recently by Jäger et al. [3], in that the rate of exchange of material between the two vessels (the communication rate) is allowed to differ from the dilution rate. The outcome of competition turns out to be surprisingly sensitive to variation of the communication rate. We identify several coexistence regimes in parameter space and describe a method for obtaining "operating diagrams" for given pairs of competing microorganisms.

Original languageEnglish (US)
Pages (from-to)139-165
Number of pages27
JournalJournal Of Mathematical Biology
Volume27
Issue number2
DOIs
StatePublished - Apr 1 1989

Keywords

  • Chemostat
  • Coexistence
  • Competition
  • Cooperative system
  • Gradostat
  • Monotone dynamical system

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

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