untitled

has been observed in northern Canada when numbers of their primary prey, snow-

shoe hares, collapse.

The initial increase in numerical response may or may not be density dependent.

However, because of the asymptote, the numerical response at higher prey densities

can only be depensatory (inversely density dependent). This means it has a destabil-

izing effect on the prey population, by either driving the prey to extinction or

allowing it to erupt. This is an important characteristic of populations and it is

illustrated in Buckner and Turnock’s (1965) study: the proportion of sawfly eaten by

birds in the area of high prey density was lower than that in the low-density area

(i.e. predation was depensatory and, therefore, could not keep the sawfly popula-

tion down). The conditions when regulation can or cannot occur are discussed in

Section 10.7.

We can now multiply the number of prey eaten by one predator (Na, the functional

response) with the number of predators (P, numerical response) to give a total mor-

tality, M, where:

M=NaP (10.8)

The instantaneous change in prey numbers is:

dN/dt=−NaP (10.9)

and an approximation for changes in prey number, over short intervals when prey

populations do not change too much (<50%), is given by:

Nt+ 1 =Nt+Nte−NaP/ Nt (10.10)

where Nt=Nin eqn. 10.6 (Walters 1986).

If we express this total mortality, M, as a proportion of the living prey population,

N, we can get a family of curves, as shown in Fig. 10.7, which depend on whether

or not there is density dependence in the functional and numerical responses. If there

is density dependence (for example from a Type III functional response) then we

have a curve with an increasing (regulatory) part followed by a decreasing (depen-

satory) part. These are called the total response curves, and examples are shown for

170 Chapter 10

Prey density

Predator density

Fig. 10.6The numerical
response may be
depicted as the trend of
predator numbers
against prey density.

10.7 The total response