How Population Dynamics Shape the Functional Response in a One-Predator–two-Prey System

Abstract

The type III functional response has historically been associated with switching predators; when there is a choice of prey the predator favors the more abundant prey type. Although this functional response has been found in experiments where both prey densities are manipulated, in real world studies the type II functional response is more commonly found. In modeling, the type III functional response is often used in systems where the second prey type is, implicitly, assumed to be constant. Here we define a functional response that takes into account both prey densities. This causes the functional response to show both type II and type III behavior, dependent on the interaction between the two prey densities. If we take into account population dynamics, we find a type II functional response in most cases, because predation regulates the relative prey densities. This explains why type III functional responses are found in experiments where both prey densities are manipulated, but type II functional responses occur when the feedback of population dynamics on the functional response is important. Furthermore, the results show that switching can have a stabilizing or destabilizing effect and can even lead to predator extinction.

A generalized functional response for predators that switch between multiple prey species

“…To construct a functional response that incorporates switching between multiple prey species, we follow Oaten and Murdoch (27) and Van Leeuwen et al (7) in modelling a predator's diet such that it incorporates the order in which it encounters and successfully attacks prey. As a simplifying assumption required for analytical tractability, only the last consumed prey is taken into account.…”

“…Through such extensions, our model can be used to study optimal foraging while relaxing the, often implicit, assumption that predators have perfect knowledge of prey densities (34). Instead predators obtain knowledge about prey densities through their foraging activity (7,30,34).…”

Evolutionary consequences of a search image

“…If we make the reasonable assumption that a search image would be formed for the more abundant prey type, this leads to a disproportionally high predation rate on the more abundant prey type and, thus, to prey switching (Murdoch, 1969;Oaten and Murdoch, 1975;Van Leeuwen et al, 2007). Search images cause prey switching by a predator, which leads to coexistence between prey species even if the prey species are in direct competition (Murdoch, 1969), such behaviour could also lead to polymorphism in prey species (Allen et al, 1998;Bond and Kamil, 2006).…”

“…In this paper we try to answer this question with a theoretical model. For this we use a one predator-two prey model based on a previously developed functional response in which attack rates depend on the last encountered prey (Oaten and Murdoch, 1975;Van Leeuwen et al, 2007) and include the aforementioned trade off. We then use this model for the evolution of search images for two prey species.…”

“…For this we use the functional response first described by Oaten and Murdoch (1975) and extended by Van Leeuwen et al (2007) that incorporates dietary history in the functional response.…”