Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T09:21:25.358Z Has data issue: false hasContentIssue false
  • English
  • Français

A linear birth-and-death predator–prey process

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

John Coffey
John Coffey*
Affiliation:
Purdue University Calumet
*
∗Postal address: Department of Mathematics, Computer Science and Statistics, Purdue University Calumet, Hammond, IN 46323, USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ1X and death rate μ1X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ2Y and the death rate is . It is proven that and iff

Keywords

CONTINUOUS-TIME PROBABILISTIC PREDATOR-PREY PROCESSCONDITIONS FOR SURVIVAL

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 92D50: Animal behavior
Type
Short Communications
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 274 - 277
Copyright
Copyright © Applied Probability Trust 1995 

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 partially supported by LAS Scholarly Research Releases (Fall 1990 and Spring 1991), and by a Purdue Research Foundation Summer Faculty Grant (1991).

References

[1] Alsmeyer, G. (1993) On the Galton-Watson predator-prey process. Ann. Appl. Prob. 3, 198–211.Google Scholar
[2] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, New York.Google Scholar
[3] Coffey, J. and Bühler, W. J. (1991) The Galton-Watson predator-prey process. J. Appl. Prob. 28, 9–16.Google Scholar
[4] Freedman, D. (1971) Markov Chains. Holden-Day, San Francisco.Google Scholar
[5] Hutton, J. (1980) The recurrence and transience of two-dimensional linear birth and death processes. Adv. Appl. Prob. 12, 615–639.Google Scholar
[6] Kesten, H. (1976) Recurrence criteria for multidimensional Markov chains and multidimensional linear birth and death processes. Adv. Appl. Prob. 8, 58–87.CrossRefGoogle Scholar