Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Fox-Voles Interactions: Selection and Dynamical Properties of a Multi-Species Functional Response.
Virgile Baudrot

Last modified: 2014-03-28


In ecosystems, predator-prey interactions exhibit complex patterns and are the vehicle of energy and material through the food web. Predator-prey dynamics are commonly analyzed through differential equations, since they give a suitable framework to handle properties such as persistence, stability and bifurcation. The functional response, defined as the rate of exploitation/consumption of preys by predators, is nonlinear whenever there are satiation conditions and sizable handling time (capturing and eating) [1]. Moreover, in a real food web, including generalist predators, functional responses depend on all prey densities leading to the use of multi-species functional responses (MSFR).

In eastern France, the red fox (Vulpes vulpes) is a generalist predator with two rodents as main preys: the water vole (Arvicola terrestris) and the common vole (Microtus arvalis). The ecological niches of both preys may partially overlap while their density dynamics respond differently according to landscape patterns. As foxes are opportunistic and omnivorous predators, we hypothesized that they exhibit intense switching behavior. Many MSFR have been proposed with different assumptions such as (i) the presence of switching [2], (ii) optimal and complementary feeding [3], and (iii) dietary history [4]. We aim at studying several hypothesis underlying MSFR formulations in the fox-voles system of central Europe.

Using a Bayesian approach, several theoretical functional responses built on different combinations of predation strategies were fitted to data previously collected [5]. We showed that the best MSFR models (according to DIC and WAIC) matched with previous estimations showing a preference for Microtus sp. over A. terrestris when both preys are at low densities followed by a switch to A. terrestris preference when both abundances are high. We also suggested that a synergism occurs (i.e.: over constant total biomass, the total ingestion is greater when prey densities are evenly distributed).

Then, through mathematical models built on logistic growth functions and MSFR, we investigated the stabilizing effect of the best MSFR on voles populations. Simulations showed that switching and synergistic effects of predation may accentuate an observed phenomenon of decorrelation of voles populations [5]. This work has a direct application in the building of trophic transfer models able to accommodate parasite and pollutant transmissions between small-mammals and foxes.

[1] Jeschke, J.M., Kopp, M. and Tollrian, R., 2004. Consumer-food systems: why type I functional responses are exclusive to filter feeders. Biological Reviews 79, 337–349.

[2] Murdoch, W.W., 1969. Switching in general predators: experiments on predator specificity and stability of prey populations. Ecological Monographs 39, 335–354.

[3] Gentleman, W., Leising, A., Frost, B., Strom, S., Murray, J., 2003. Functional responses for zooplankton feeding on multiple resources: a review of assumptions and biological dynamics. Deep-Sea Research II 50, 2847–2875.

[4] van Leeuwen, E., Jansen, V.A.A., Bright, P.W., 2007. How population dynamics shape the functional response in a one-predator-two-prey system. Ecology 88, 1571–1581.

[5] Raoul, F., Deplazes, P., Rieffel, D., Lambert, J.-C. and Giraudoux, P., 2010. Predator dietary response to prey density variation and consequences for cestode transmission. Oecologia 164,129–139.


Multi-Species Functional Response ; Vulpes vulpes ; Micro-mammals ; Ordinary differential equations