## The type 2 functional response

The most frequently observed functional response is the 'type 2' response, in which consumption rate rises with prey density, but gradually decelerates until a plateau is reached at which consumption rate remains constant irrespective of prey density. (Realistically, even a type 1 response must have a plateau, as in the example above. The distinction is between the deceleration of a type 2 response and the linearity of the type 1 response.) Type 2 responses are shown for a carnivore, a herbivore and a parasitoid in Figure 10.9.

how important is mutual interference in practice?

Figure 10.9 Type 2 functional responses. (a) Tenth-instar damselfly nymphs (Ishnura elegans) eating Daphnia of approximately constant size. (After Thompson, 1975.) (b) Wood bison (Bison bison) feeding on the sedge Carex atherodes presented at a range of sedge biomass densities. (After Bergman et al., 2000.) (c) The parasitoid Microplitis croceipes attacking the tobacco budworm Heliothis virescens. (After Tillman, 1996.)

Figure 10.9 Type 2 functional responses. (a) Tenth-instar damselfly nymphs (Ishnura elegans) eating Daphnia of approximately constant size. (After Thompson, 1975.) (b) Wood bison (Bison bison) feeding on the sedge Carex atherodes presented at a range of sedge biomass densities. (After Bergman et al., 2000.) (c) The parasitoid Microplitis croceipes attacking the tobacco budworm Heliothis virescens. (After Tillman, 1996.)

the type 2 response and handling time

The type 2 response can be explained by noting that a predator has to devote a certain handling time to each prey item it consumes (i.e. pursuing, subduing and consuming the prey item, and then preparing itself for further search). As prey density increases, finding prey becomes increasingly easy. Handling a prey item, however, still takes the same length of time, and handling overall therefore takes up an increasing proportion of the predator's time - until at high prey densities the predator is effectively spending all of its time handling prey. The consumption rate therefore approaches and then reaches a maximum (the plateau), determined by the maximum number of handling times that can be fitted into the total time available.

We can derive a relationship between Pe (the number of prey items eaten by a predator during a period of searching time, Ts) and N, the density of those prey items (Holling, 1959). Pe increases with the time available for searching, it increases with prey density, and it increases with the searching efficiency or attack rate of the predator, a. Thus:

Holling's type 2 response equation

However, the time available for searching will be less than the total time, T, because of time spent handling prey. Hence, if Th is the handling time of each prey item, then ThPe is the total time spent handling prey, and:

Substituting this into Equation 1G.16 we have:

or, rearranging:

Note that the equation describes the amount eaten during a specified period of time, T, and that the density of prey, N, is assumed to remain constant throughout that period. In experiments, this can sometimes be guaranteed by replacing any prey that are eaten, but more sophisticated models are required if prey density is depleted by the predator. Such models are described by Hassell (1978), who also discusses methods of estimating attack rates and handling times from a set of data. (Trexler et al., 1988, discuss the general problem of fitting functional response curves to sets of data.)

It would be wrong, however, to imagine that the existence of a handling time is the only or the complete explanation for all type 2 functional responses. For instance, if the prey are of variable profitability, then at high densities the diet may tend towards a decelerating number of highly profitable items (Krebs et al., 1983); or a predator may become confused and less efficient at high prey densities.

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