ANALYSIS O F PROCESSES I N CONTROL OF INSECTS
47
3. Density Relations of the Responses of SawJEy Predators
A point worth examining is the density-dependence or otherwise of
the separate functional and combined responses. When a functional
response is graphed as predation rate per individual predatoq per day
against prey density, as in Fig. 1 8 ~ ,
whether the response is densitydependent or inversely density related depends on whether the rising
curve is concave or convex. Only if the increase in individual predation
rate is proportionately greater than the increase in prey density is the
effect density-dependent ; for density-dependence is measured as an
effect per individual of the prey population, such as percentage mortality. The rising curves drawn to the data by Holling (Fig. 1 8 ~ )
show
slight density-dependence in the responses of Blarina and Sorex, and a
more marked density-dependence in that of Peromyscus. Holling wrote :
“Unfortunately the data for any one functional response curve are not
complete enough to establish a sigmoid relation, but the six curves
presented thus far and the several curves to be presented in the following section all suggest a point of inflection.” The numerical responses, as
graphedin Fig. 1 8 ~ ,
can be tested for density-dependence in the same way.
There is a suggestion’ of some density-dependence in the rising curve for
Sorex, but the curve for Peromyscus indicates an inverse density relationship throughout (I differ from Holling’s statement on this point), and
this is the general tenor also of the roughly horizontal curve for Blarina.
I n the graph of combined responses (Fig. 18c) where the ordinate
is in proportionate terms (percent predation), the criterion of densitydependence is simply a rising curve, which each of the three species
achieves up to a certain level of prey density.
It is appropriate here to make the general point that when both
functional and numerical responses are involved, the combined response
may be density-dependent even when the separate components are
not. For example, if prey density rises from 1 000 to 3 000 the functional
response of a predator may be an increase in the daily individual
predation rate from 2 to 4, and its numerical response an increase in
density from 10 to 20. Each of these responses amounts only to an
inverse density relationship. Yet their combined effect, which is what
matters most in practice, is an increase from 2 x 10 to 4 x 20, that is
a-fold, compared with the %fold increase in prey density - a clearly
density-dependent relationship.
E. FUNCTIONAL RESPONSES O F OTHER VERTEBRATE
PREDATORS O F INSECTS
As we have seen (Fig. 18), the functional responses of the mammalian
predators of the pine sawfly were not quite of the simple type of the
47
3. Density Relations of the Responses of SawJEy Predators
A point worth examining is the density-dependence or otherwise of
the separate functional and combined responses. When a functional
response is graphed as predation rate per individual predatoq per day
against prey density, as in Fig. 1 8 ~ ,
whether the response is densitydependent or inversely density related depends on whether the rising
curve is concave or convex. Only if the increase in individual predation
rate is proportionately greater than the increase in prey density is the
effect density-dependent ; for density-dependence is measured as an
effect per individual of the prey population, such as percentage mortality. The rising curves drawn to the data by Holling (Fig. 1 8 ~ )
show
slight density-dependence in the responses of Blarina and Sorex, and a
more marked density-dependence in that of Peromyscus. Holling wrote :
“Unfortunately the data for any one functional response curve are not
complete enough to establish a sigmoid relation, but the six curves
presented thus far and the several curves to be presented in the following section all suggest a point of inflection.” The numerical responses, as
graphedin Fig. 1 8 ~ ,
can be tested for density-dependence in the same way.
There is a suggestion’ of some density-dependence in the rising curve for
Sorex, but the curve for Peromyscus indicates an inverse density relationship throughout (I differ from Holling’s statement on this point), and
this is the general tenor also of the roughly horizontal curve for Blarina.
I n the graph of combined responses (Fig. 18c) where the ordinate
is in proportionate terms (percent predation), the criterion of densitydependence is simply a rising curve, which each of the three species
achieves up to a certain level of prey density.
It is appropriate here to make the general point that when both
functional and numerical responses are involved, the combined response
may be density-dependent even when the separate components are
not. For example, if prey density rises from 1 000 to 3 000 the functional
response of a predator may be an increase in the daily individual
predation rate from 2 to 4, and its numerical response an increase in
density from 10 to 20. Each of these responses amounts only to an
inverse density relationship. Yet their combined effect, which is what
matters most in practice, is an increase from 2 x 10 to 4 x 20, that is
a-fold, compared with the %fold increase in prey density - a clearly
density-dependent relationship.
E. FUNCTIONAL RESPONSES O F OTHER VERTEBRATE
PREDATORS O F INSECTS
As we have seen (Fig. 18), the functional responses of the mammalian
predators of the pine sawfly were not quite of the simple type of the