On the populations of competing species

Fred Brauer

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The population sizes of two species competing for the same food supply or living space are often modelled by a pair of ordinary differential equations. If the growth rates of the two population sizes are linear in the population sizes, then coexistence in stable equilibrium implies qualified competition at equilibrium, in the sense that the effect of the competition is to increase the total population. Since experiments indicate that a stable equilibrium with unqualified competition is possible, this suggests that non-linear growth rates would give a more accurate model. An example is given of a model with non-linear growth rates which exhibits a stable equilibrium with unqualified competition.

Original languageEnglish (US)
Pages (from-to)299-306
Number of pages8
JournalMathematical Biosciences
Issue number3-4
StatePublished - Apr 1974
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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