A comparative study of models for predation and parasitism

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and t2 hours were required to consume WI and Wz, respectively, after the flies were
offered. Then the rates of consumption W~/t~ and W2/t~ could be considered as
instantaneous rates if tl and t2 were not too large. It might be technically difficult to
keep tPs sufficiently small, for otherwise W's could not be measured. If t's are long,
then digestion may take place during those hours, and this must influence the value
of W. Then what is required is the measurement of the relationship between W and
t for various Tts, from which the instantaneous rate, d W/dt, may be obtained. And,
of course, it is d W/dt which should be incorporated in the synthesized instantaneous
hunting equation.
Although HOLLING'S approach, which he called an 'experimental component analy-
sis', is no doubt important, some technical difficulties are expected, namely how to
design experiments to meet theoretically required conditions; the example cited above
clearly illustrates these difficulties. This is why I proposed a simpler approach in w 3,
which can tentatively be used for calculating a predator-prey interaction without going
through the details of physiological studies of hunger.
In passing, HULLING tOO used differential equations, which could yield curves
resembling observed ones, without attaching any significance to the equations as the
means of inference. I must again suggest avoiding this unjustifiable operation.
5. DISCUSSION AND CONCLUSIONS
In this section, I shall deal with problems that are more methodological than
technical. Before doing so, however, what was dealt with in w 4 will be summarized
in the following diagram (Fig. 13).
It is a flow diagram of reasoning leading to
each model reviewed, and shows the scope that is covered by that model. The dia-
gram is based on my own study and not necessarily identical to what the authors
claimed in their original papers, as their verbal statements were often wrong.
The reasoning starts from (A), a generalized instantaneous hunting equation.
This generalization is obvious from eq. (3. 18), in which H(x, Y, t)f(x) can be written
as f(X, Y, t) if x is fixed at X. From (A) there are two main streams, dealing with
parasitism and predation.
The predation flow is further divided into subflows 1 and 2.
Subflow 2 goes
directly to the determination of specific forms of (A) to evaluate n, the number of
prey taken per unit area in time interval t when the prey density is kept constant.
All the models after 1955 (except mine) belong to this flow. Since (A) is an instan-
taneous equation, it cannot be used for comparison with observation except for cases
in which reduction in the prey density can be neglected. Also (A) does not give any
means of estimating the final density of the prey or host population at the end of
each generation.
Hence, these equations in the category of (A) cannot be used, as
they stand, for the study of prey-predator or host-parasite interaction systems.
Subflow 1, however, incorporates the effects upon the number of prey taken per
unit area (i. e. z) of (a) diminishing returns, (b) changes in the number in the prey