A comparative study of models for predation and parasitism

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The structure of predation is considered first. Suppose that there are x prey and
y predator individuals per unit area, and that each individual predator consumes, on
the average, f(x) prey individuals per unit time. For the moment, the analytic form
of f(x) is not specified, but it is an assumed, increasing function of x.
It is also
assumed for the moment that the prey and predator numbers are fixed at X and Y
respectively throughout one observation period t, i.e. that during t the prey population
is replenished as fast as it is reduced by predation, and no increase or decrease
occurs among the predators. Under these assumptions, the following will hold :
n-~f(X) Yt (3.1)
where n is the total number of prey killed by predators per unit area during t.
capital letters for x and y indicate that these values are fixed during an observation
period t.) At this stage, neither the effect of changes in the predator's psycho-physio-
logical state nor the effect of social interaction is considered.
(The
Equation (3.1) is shown graphically in Fig. 1 where hypothetical values of n are
plotted against X; note that Y and t are both fixed for all X's. The evaluation of n is
nl when X is X~ and n2 when X is Xz. Of course, the measurements of n~ and n~
must be made in two separate observations to meet the condition under which eq.
(3.1) holds. It should also be noticed that eq. (3.1) does not provide any means of
evaluating the effect of predation upon the prey density because the latter is fixed in
each observation period.
rl
n~
N
y
X2
Fig. 1. A hypothetical example of curves for eq. (3. 1) The prey density,
fixed at X during time-interval t, is plotted on the horizontal axis,
and the total number (n) preyed upon for t, when the predator density
y is fixed at Y, is plotted on the vertical axis.
Now, suppose a new situation in which the prey population is not replenished so
that the prey density is gradually depleted while the predators are hunting in one
observation period, i.e.t.
Xl
As the prey density decreases during the period, the number
that the predators can kill per unit time per unit area must also decrease. This
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