Feeding Threshold for Predators Stabilizes Predator-Prey Systems

Abstract

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.

Evolutionary and plastic rescue in multitrophic model communities

“…Furthermore, we found that plasticity, but not genetic diversity, can lead to strong stabilization and therefore, plasticity can resolve the paradox of enrichment. Strong stabilization has been shown to occur in model food webs exhibiting ecological attributes such as inducible defences, inedible prey, predator feeding thresholds or predator interference (see van Voorn et al [47,48]). Predator interference works in a similar fashion to inducible defences; the transcritical bifurcation remains unaffected because at very low predator density there are not enough predators to induce prey to interfere with each other.…”

The AquaDEB project: Physiological flexibility of aquatic animals analysed with a generic dynamic energy budget model (phase II)

“…Where deterministic models can suddenly switch from a point attractor to a cyclic behaviour when the total nutrient load of a system is increased (the famous paradox of enrichment), stochastic variants show a smooth transition. Toxicants can modify the behaviour of integrated systems in complex ways and quite a bit of progress has been made to understand how (Kooi et al, 2008a,b;Liebig et al, 2008;Bontje et al, 2009Bontje et al, , 2010Bontje et al, , 2011. Ways have been explored to reduce the number of variables that has to be followed in ecosystem model by focussing on trait-based approaches and refrain from following species individually.…”