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Effects of Density Dependent Migrations on the Dynamics of a Predator Prey Model

Effects of Density Dependent Migrations on the Dynamics of a Predator Prey Model 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Biotheoretica Springer Journals

Effects of Density Dependent Migrations on the Dynamics of a Predator Prey Model

Mchich, Rachid; Bergam, Amal; Raïssi, Nadia
Acta Biotheoretica , Volume 53 (4) – Jan 1, 2005
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References (22)

Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer Science + Business Media, Inc.
Subject
Philosophy; Philosophy of Biology; Evolutionary Biology
ISSN
0001-5342
eISSN
1572-8358
DOI
10.1007/s10441-005-4883-2
pmid
16583273
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Acta Biotheoretica – Springer Journals

Published: Jan 1, 2005

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