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Issue Math. Model. Nat. Phenom.
Volume 4, Number 6, 2009
Ecology (Part 1)
Page(s) 91 - 108
DOI 10.1051/mmnp/20094603
Published online 27 November 2009

Math. Model. Nat. Phenom. Vol. 4, No. 6, 2009, pp. 91-108
DOI: 10.1051/mmnp/20094603

Feeding Threshold for Predators Stabilizes Predator-Prey Systems

D. Bontje1, B.W. Kooi1, G.A.K. van Voorn2 and S.A.L.M Kooijman1

1  Department of Theoretical Biology, Vrije Universiteit, De Boelelaan 1085, 1081HV Amsterdam, The Netherlands
2  Biometris, Wageningen Universiteit & Research, 6708PB Wageningen, The Netherlands

daniel.bontje@falw.vu.nl

Published online: 27 November 2009

Abstract
Since Rosenzweig showed the destabilisation of exploited ecosystems, the so called Paradox of enrichment, several mechanisms have been proposed to resolve this paradox. In this paper we will show that a feeding threshold in the functional response for predators feeding on a prey population stabilizes the system and that there exists a minimum threshold value above which the predator-prey system is unconditionally stable with respect to enrichment. Two models are analysed, the first being the classical Rosenzweig-MacArthur (RM) model with an adapted Holling type-II functional response to include a feeding threshold. This mathematical model can be studied using analytical tools, which gives insight into the mathematical properties of the two dimensional ODE system and reveals underlying stabilisation mechanisms. The second model is a mass-balance (MB) model for a predator-prey-nutrient system with complete recycling of the nutrient in a closed environment. In this model a feeding threshold is also taken into account for the predator-prey trophic interaction. Numerical bifurcation analysis is performed on both models. Analysis results are compared between models and are discussed in relation to the analytical analysis of the classical RM model. Experimental data from the literature of a closed system with ciliates, algae and a limiting nutrient are used to estimate parameters for the MB model. This microbial system forms the bottom trophic levels of aquatic ecosystems and therefore a complete overview of its dynamics is essential for understanding aquatic ecosystem dynamics.


Mathematics Subject Classification. 2D40, 92B05, 34K18

Key words: algal-ciliate experiments -- feeding threshold -- mass-balance -- paradox of enrichment -- strong stability


© EDP Sciences 2009


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