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Functional responses and how they evolve by natural selection

Oct 6, 2014  ·  3:00 p.m. 4:00 p.m.  ·  209 Eno Hall

Mats Gyllenberg - Department of Mathematics and Statistics,
University of Helsinki, Finland.

The functional response is a fundamental concept in theoretical biology. By definition, it is the number of prey eaten by a predator per unit of time. Most often, as in the pioneering work by Holling  and co-workers in the 1950s, the functional response is a function of prey density, but in the mid 1970s DeAngelis and Beddington et al. independently put forward the idea that it could depend on the predator density as well.

The purpose of this talk is twofold: Firstly, I present a mechanistic derivation, based on assumptions concerning individual behaviour of predator and prey, of the DeAngelis-Beddington functional response.  Surprisingly, it turns out that the dependence on the predator density in the DeAngelis-Beddington functional response is a consequence of prey behaviour and not of predator behaviour. Proponents of the functional response has previously argued that competition between predators should be reflected in the functional response.

A great advantage of the mechanistic derivation is that all parameters in the functional response reflect individual traits that are subject to natural selection. In the second part of my talk I use adaptive dynamics to investigate possible evolutionary outcomes of natural selection on one of the parameters, viz. “timidity” of the prey, that is, its readiness to seek refuge. It turns out that the results depend on whether the predator-prey system remains at equilibrium or whether it exhibits cycles. As a matter of fact, typical predator-prey cycles that can be observed in nature could be the result of natural selection.

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