Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T14:32:16.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Multi-species population models and evolutionarily stable strategies

Published online by Cambridge University Press:  14 July 2016

W. G. S. Hines
W. G. S. Hines*
Affiliation:
University of Guelph
*
∗Postal address: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada, N1G 2W1.
Get access Rights & Permissions [Opens in a new window]

Abstract

The possibility that interspecific contest tactics might be able to stabilize two species predator-prey populations is investigated using a matrix model of the population. It is found that if the interspecific tactics have no influence on intraspecific encounters, the non-trivial equilibrium population composition is necessarily unstable. The result provides some insight into a reported instability of a predator-prey population with ‘stable' strategies.

Keywords

PREDATOR-PREY SYSTEMSEVOLUTIONARILY STABLE STRATEGIESINTERSPECIFIC CONFLICTSANIMAL CONFLICT MODELSDYNAMICAL POPULATION MODELSMULTI-SPECIES SYSTEMS
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 507 - 513
Copyright
Copyright © Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported by National Research Council Operating Grant A6187.

References

Auslander, D., Guckenheiner, J. and Oster, G. (1978) Random evolutionarily stable strategies. Theoret. Popn. Biol 13, 276–293.Google Scholar
Bishop, D. T. and Cannings, C. (1976) Models of animal conflict (abstract). Adv. Appl. Prob. 8, 616–621.Google Scholar
Dawkins, R. (1976) The Selfish Gene. Oxford University Press.Google Scholar
Friedman, A. (1971) Differential Games. Wiley-Interscience, New York.Google Scholar
Haigh, J. (1975) Game theory and evolution (abstract). Adv. Appl. Prob. 7, 8–11.Google Scholar
Hirsch, M. W. and Smale, S. (1974) Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, New York.Google Scholar
May, R. M. (1974) Stability and Complexity in Model Ecosystems. Princeton University Press.Google Scholar
Maynard Smith, J. (1974) The theory of games and the evolution of animal conflicts. J. Theoret. Biol. 47, 209–221.Google Scholar
Rao, C. R. (1973) Linear Statistical Inference and its Applications, 2nd edn. Wiley, New York.Google Scholar