Competition and coexistence in flowing habitats with a hydraulic storage zone

James P. Grover*, Sze Bi Hsu, Feng Bin Wang

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

30 Scopus citations

Abstract

This paper examines a model of a flowing water habitat with a hydraulic storage zone in which no flow occurs. In this habitat, one or two microbial populations grow while consuming a single nutrient resource. Conditions for persistence of one population and coexistence of two competing populations are derived from eigenvalue problems, the theory of bifurcation and the theory of monotone dynamical systems. A single population persists if it can invade the trivial steady state of an empty habitat. Under some conditions, persistence occurs in the presence of a hydraulic storage zone when it would not in an otherwise equivalent flowing habitat without such a zone. Coexistence of two competing species occurs if each can invade the semi-trivial steady state established by the other species. Numerical work shows that both coexistence and enhanced persistence due to a storage zone occur for biologically reasonable parameters.

Original languageEnglish
Pages (from-to)42-52
Number of pages11
JournalMathematical Biosciences
Volume222
Issue number1
DOIs
StatePublished - 11 2009
Externally publishedYes

Keywords

  • Chemostat
  • Coexistence
  • Competition
  • Flow reactor
  • Flowing habitats
  • Global stability
  • Hydraulic storage zone
  • Lower solutions
  • Maximum principle
  • Monotone dynamical system
  • Theoretical ecology
  • Upper solutions

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