### Abstract

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 language | English (US) |
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Pages (from-to) | 299-306 |

Number of pages | 8 |

Journal | Mathematical Biosciences |

Volume | 19 |

Issue number | 3-4 |

DOIs | |

State | Published - Jan 1 1974 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Ecology, Evolution, Behavior and Systematics

### Cite this

*Mathematical Biosciences*,

*19*(3-4), 299-306. https://doi.org/10.1016/0025-5564(74)90045-5

**On the populations of competing species.** / Brauer, Fred.

Research output: Contribution to journal › Article

*Mathematical Biosciences*, vol. 19, no. 3-4, pp. 299-306. https://doi.org/10.1016/0025-5564(74)90045-5

}

TY - JOUR

T1 - On the populations of competing species

AU - Brauer, Fred

PY - 1974/1/1

Y1 - 1974/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0016184387&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016184387&partnerID=8YFLogxK

U2 - 10.1016/0025-5564(74)90045-5

DO - 10.1016/0025-5564(74)90045-5

M3 - Article

AN - SCOPUS:0016184387

VL - 19

SP - 299

EP - 306

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 3-4

ER -