Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T21:23:26.538Z Has data issue: false hasContentIssue false
  • English
  • Français

STOCHASTIC ANALYSIS FOR THE DESCRIPTION AND SYNTHESIS OF PREDATOR–PREY SYSTEMS*

Published online by Cambridge University Press:  31 May 2012

Guy L. Curry  and
Don W. DeMichele
Guy L. Curry
Affiliation:
Biosystems Research Group, Department of Industrial and Bioengineering, Texas A'M University
Don W. DeMichele
Affiliation:
Biosystems Research Group, Department of Industrial and Bioengineering, Texas A'M University
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, a stochastic analysis approach for predator–prey systems modeling is developed. The states of the system are assumed to have a natural probabilistic variation. Elements of queueing theory are used to describe these variations and to obtain both the transient and steady-state results for the system. The predator is considered analogous to a service facility and the prey as customers to be served. The Holling disk equation and mantid–fly experiments are analyzed by this approach. The method provides a framework for a straightforward synthesis of the system components and is readily generalized for multiple predator systems. Furthermore, hunger and other behavioral aspects can be easily incorporated into the mathematical analysis.

Type
Articles
Information
The Canadian Entomologist , Volume 109 , Issue 9 , September 1977 , pp. 1167 - 1174
Copyright
Copyright © Entomological Society of Canada 1977

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.)

References

Gause, G. F. 1934. The struggle for existence. Hafner, New York. Reference from Pielou, E. C.. 1969. An introduction to mathematical ecology, p. 21. Wiley-Interscience.Google Scholar
Hassell, M. P. 1966. Evaluation of parasite and predator responses. J. Animal Ecol. 35: 65–75.Google Scholar
Holling, C. S. 1959. Some characteristics of simple types of predation and parasitism. Can. Ent. 91: 385–398.Google Scholar
Holling, C. S. 1963. An experiment component analysis of population processes. Mem. ent. Soc. Can. 32. pp. 22–32.Google Scholar
Holling, C. S. 1966. The functional response of invertebrate predators to prey density. Mem. ent. Soc. Can. 48. 86 pp.Google Scholar
Huffaker, C. B. and Stinner, R.. 1971. The role of natural enemies in pest control programs, pp. 333–50. In Entomological essays to commemorate the retirement of Professor K. Yasumatsu. Hokuryukan, Tokyo.Google Scholar
Jaquette, D. L. 1970. A stochastic model for the optimal control of epidemics and pest populations. Mathematical Biosciences 8: 343–354.Google Scholar
Lotka, A. J. 1925. Elements of physical biology. Williams and Wilkins, Baltimore. Reference from Pielou, E. C.. 1969. An introduction to mathematical ecology, p. 21. Wiley-Interscience.Google Scholar
Nicholson, A. J. and Bailey, V. A.. 1935. The balance of animal populations, Part 1. Proc. zool. Soc. Lond.Google Scholar
Paloheimo, J. E. 1971 a. On the theory of search. Biometrics 58: 61–75.CrossRefGoogle Scholar
Paloheimo, J. E. 1971 b. A stochastic theory of search implications for predator-prey situations. Mathematical Biosciences 12: 105–132.Google Scholar
Royama, T. 1971. A comparative study of models for predation and parasitism. Researches Popul. Ecol. Kyoto Univ. 1 90 pp.Google Scholar
Saaty, T. 1961. Elements of queueing theory. McGraw-Hill, New York.Google Scholar
Solomon, M. E. 1949. The natural control of animal populations. J. Animal Ecol. 18: 1–35.CrossRefGoogle Scholar
Taha, A. 1971. Operations research: an introduction. Macmillan, New York.Google Scholar
Volterra, V. 1926. Discussion in Royama (1971).Google Scholar
Watt, K. E. F. 1959. A mathematical model for the effect of densities of attacked and attacking species on the number attacked. Can. Ent. 91: 129–144.Google Scholar