A comparative study of models for predation and parasitism

18
these circumstances, the effective instantaneous hunting function is Hf(x) instead of
f(x), so that we have, from eq. (3.4),
dx/dt =--Hf(x) Y (3.17).
Naturally, H is dependent on the net food intake into the stomach and the speed
of digestion. No doubt, the net food intake depends on the density of food, the density
of predators, and the time spent in hunting; 3nd the speed of digestion is also a
function of time, at least. Therefore, an argument similar to that in social interaction
applies here too. One essential difference between the effect of social interaction and
hunger is that the latter involves the effect of initial state ; i. e. the factor H is
influenced by the level of satiation or hunger just before the start of the observation.
So if this initial state is denoted by the symbol I0, we can write the factor H as
H(x, Y, t]I0), and so the instantaneous hunting equation will be of the form
dx/dt=-H(x, Y, t! Io)f(x) Y (3.18).
Both functions S and H in the above examples are indices of the partial realization
of the potential performance that an individual predator could exert if the influence
of social interaction or hunger did not exist. Of course, this index method of building
a model may not toke account of the actual and detailed processes of such psycho-
logical and physiological states, although these states must actually have influences on
particular components of the hunting activity ; e.g. the threshold at which searching
or catching action is triggered must be reflected in, say, the effective speed of search-
ing or the distance at which a predator reacts to a prey. Nevertheless, the index
method has the advantage of illustrating some basic properties that a model must
have, without going into too minute and unnecessary details of the structure, and
provides a criterion for evaluating some of the models reviewed in later sections.
For instance, it shows that all the components that one wants to incorporate into a
model have to be considered in the form of an instantaneous hunting equation from
which the overall equation will be derived. To incorporate new components directly
into the overall function that had been derived before these components were dis-
covered is not valid, unless the new components are known to have no influence on the
effect of diminishing returns.
treatment will be reviewed later.
Some examples of models containing such erroneous
A model for parasitism has a different structure than that for predation, and a
brief account of it will be given below.
In predation, prey individuals normally disappear from the hunting area one after
another as they ~re preyed upon, and so these "already eaten" prey are no longer
available to the predators. This process is described by a differential equation, e.g.
eq. (3. 4), which is the basis of a predation model. In parasitism, however, host
individuals do not necessarily disappear and are still available to parasites during the
course of hunting. Under these circumstances, the approach based on a differential
equation loses its logical basis. Also, the availability of already parasitized hosts has
different influences on those parasites that do not discriminate between parasitized