Na=aTsN (10.4)Substituting eqns 10.1 and 10.2 into 10.4 we get:Na=a(Tt−hNa)N (10.5)or:Na=(aTtN)/(1 +ahN) (10.6)This is Holling’s (1959) “disc equation” which describes a Type IIfunctional
response, where Naincreases to an asymptote as prey density increases (Fig. 10.2a).
When there are several prey types (species, sex or age classes), the multispecies
disc equation for prey type ieaten per predator is then:Nai=(aiTtNi)/(1 +∑jajhjNj) (10.7)where the sum is across all prey types eaten.
The Type II functional response can be constructed from the parameters of the
disc equation estimated from observations. Searching efficiency is the product of pc
and a′. The probability of capture is usually low, about 0.1–0.3 in most wildlife cases
(Walters 1986). The area of search, a′, can be approximated from (distance moved)
×(width of reaction field or detection distance). Handling time per prey item, h,
can be obtained from direct observation or from maximum feeding rates because the
maximum rate is 1/h. Examples of such calculations are given in Clark et al. (1979)
and Walters (1986).
The important effect of the Type II response is seen when numbers eaten per preda-
tor are re-expressed as a proportion of the living prey population alive (Fig. 10.2b).
The Type II curve shows a decreasing proportion of prey eaten as prey density rises.
Figure 10.4a illustrates the Type II response of European kestrels (Falco tinnunculus)
feeding on voles (Microtus species) in Finland (Korpimäki and Norrdahl 1991).
The functional responses of herbivores are not as well known as those of carnivores
but where measured they appear to be Type II as in Fig. 10.4b for bank voles
(Clethrionomys glareolus) feeding on willow shoots (Lundberg 1988). Deer and elk
show Type II functional responses to their food supply. Dale et al. (1994) report Type
II responses of wolves preying on caribou.
Holling found a third type of functional response (Type III; Fig. 10.2). The num-
ber of prey caught per predator per unit time increases slowly at low prey densities,
but fast at intermediate densities before leveling off at high densities, producing an
S-shaped curve. When those eaten are expressed as a proportion of the live popula-
tion, the proportion consumed increases first, then declines. Hen harriers (Circus cya-
neus) in the UK show a Type III functional response (Fig. 10.5) to changes in red
grouse (Lagopus l.scoticus) populations (Redpath and Thirgood 1999).
The S shape of this curve is attributed to a behavioral characteristic of predators
called switching. If there are two prey types, A being rare and B being common, the
predators will concentrate on B and ignore A. Predators may switch their search from
B to A, thus producing an upswing in the number of A killed when A becomes more
common. There is often a sudden switch at a characteristic density of A. Birds have