Abstract
A three-species Lotka-Volterra competition community may exhibit population oscillations of a neutral or undamped nature. Nontransitive interference competition, in which 1 can exclude 2, 2 can exclude 3, but 3 can exclude 1, is the underlying mechanism. If immigration, incomplete spatial overlap, or any other mechanism prevents extinction, then such a three-species system must go into true limit cycles. For higher-dimension systems, limit cycles are more likely in communities with an odd number of species. Such limit cycles are most likely to be found in the tropics. A cautionary moral is given: simple competition systems that appear to be unstable and random may be stable and deterministic.
Keywords
Limit (mathematics)Competition (biology)Extinction (optical mineralogy)Storage effectCoexistence theoryPopulationMechanism (biology)Simple (philosophy)BiologyStatistical physicsEcologyEconomicsMathematicsPhysicsPaleontologyMathematical analysisQuantum mechanicsDemography
Related Publications
Nonlinear Aspects of Competition Between Three Species
It is shown that for three competitors, the classic Gause–Lotka–Volterra equations possess a special class of periodic limit cycle solutions, and a general class of solutions in...
The Roles of Harsh and Fluctuating Conditions in the Dynamics of Ecological Communities
Harsh conditions (e.g., mortality and stress) reduce population growth rates directly; secondarily, they may reduce the intensity of interactions between organisms. Near-exclusi...
Desert Rodent Community Structure: A Test of Four Mechanisms of Coexistence
Four mechanisms of coexistence are considered that may contribute to the diversity of desert granivorous rodent communities. In the first, bush/open microhabitat selection, coex...
The response of insect faunas to glacial-interglacial climatic fluctuations
The extinction of species of small invertebrates is difficult to recognize. However, in deposits that date from the past few million years, insect fossils are remarkably common ...
Predator-Mediated Coexistence: A Nonequilibrium Model
There is now convincing evidence, from a variety of ecological systems, that predation is capable of maintaining coexistence among a set of competing prey species, some of which...
Publication Info
- Year
- 1975
- Type
- article
- Volume
- 109
- Issue
- 965
- Pages
- 51-60
- Citations
- 257
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
257
OpenAlex
Cite This
Michael E. Gilpin
(1975).
Limit Cycles in Competition Communities.
The American Naturalist
, 109
(965)
, 51-60.
https://doi.org/10.1086/282973
Identifiers
- DOI
- 10.1086/282973