David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Acta Biotheoretica 53 (4) (2005)
We study the effects of density dependent migrations on the stability of a predator-prey model in a patchy environment which is composed with two sites connected by migration. The two patches are different. On the first patch, preys can find resource but can be captured by predators. The second patch is a refuge for the prey and thus predators do not have access to this patch. We assume a repulsive effect of predator on prey on the resource patch. Therefore, when the predator density is large on that patch, preys are more likely to leave it to return to the refuge. We consider two models. In the first model, preys leave the refuge to go to the resource patch at constant migration rates. In the second model, preys are assumed to be in competition for the resource and leave the refuge to the resource patch according to the prey density. We assume two different time scales, a fast time scale for migration and a slow time scale for population growth, mortality and predation. We take advantage of the two time scales to apply aggregation of variables methods and to obtain a reduced model governing the total prey and predator densities. In the case of the first model, we show that the repulsive effect of predator on prey has a stabilizing effect on the predator-prey community. In the case of the second model, we show that there exists a window for the prey proportion on the resource patch to ensure stability.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Roman Frigg (2008). Models in Science. In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy.
Roman Frigg & Stephan Hartmann (2005). Scientific Models. In Sahotra Sarkar et al (ed.), The Philosophy of Science: An Encyclopedia, Vol. 2. Routledge.
Peter Antonelli & Pierre Auger (1995). Corals and Starfish Devastation of the Great Barrier Reef: Aggregation Methods. Acta Biotheoretica 43 (4).
Michael D. Intriligator & Dagobert L. Brito (1988). A Predator-Prey Model of Guerrilla Warfare. Synthese 76 (2):235 - 244.
Pierre M. Auger & Robert Roussarie (1994). Complex Ecological Models with Simple Dynamics: From Individuals to Populations. Acta Biotheoretica 42 (2-3).
Aaron Simmons (2009). Animals, Predators, the Right to Life, and the Duty to Save Lives. Ethics and the Environment 14 (1):pp. 15-27.
Etienne Kouokam, Pierre Auger, Hassan Hbid & Maurice Tchuente (forthcoming). Effect of the Number of Patches in a Multi-Patch SIRS Model with Fast Migration on the Basic Reproduction Rate. Acta Biotheoretica.
A. Tsoularis (2007). A Learning Strategy for Predator Preying on Edible and Inedible Prey. Acta Biotheoretica 55 (3).
Pierre M. Auger & Bruno Faivre (1993). Effects of Individual Activity Sequences on Prey-Predator Models. Acta Biotheoretica 41 (1-2).
Added to index2009-01-28
Total downloads12 ( #137,616 of 1,139,992 )
Recent downloads (6 months)2 ( #92,708 of 1,139,992 )
How can I increase my downloads?