A comparative study of models for predation and parasitism

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of Hierodula crassa GIGLIO-TOs., approached the problem from a different direction.
A female mantid, H. crassa, had been deprived of food for various lengths of time
before flies (as prey) were offered, and then the weight of flies eaten by the mantid
was measured for each length-class of deprivation time. It was found that the weight
of flies eaten increased as the deprivation time increased (and hence the mantid was
hungrier), gradually leading to a plateau.
The effect of hunger revealed itself not only in the mantid's increased demand
for food to the level of satiation, but also in other components, e.g. the size of the
area of reaction to the prey, speed of reaction, capture success, time spent in pursuing
and in eating prey, and in the digestive pause. The influence of the deprivation time
on each of these components was expressed by separate descriptive equations which
were then synthesized to describe the relationship between the number of prey killed,
the density of prey, and the time involved; the relationship thus obtained was illustrated
by HOLLING (1966) in his figure 29.
It is not my intention here to review critically every detail of HOLLING'S mathematical
treatment, as the study of the effect of hunger is still in its infancy, and also
because I have not had sufficient experience with the problem myself. There are,
however, a few things to be pointed out which HOLLINC seems to have missed.
First, in this study again HOLLING did not recognize the effect of diminishing
returns. It is not certain whether, in the observation that appeared in his figure 29,
the prey density was kept constant during each set of observations. If so, the figure
represents an instantaneous hunting surface equivalent to eq. (3. 18) in which dx/dt
is written simply as n. If, however, the prey density was depleted during the course
of observation, the figure represents a particular one of the overall hunting surfaces
which is specific only to the mantid density used in this particular experiment. In
this case, the density of predators should have been stated (the number of mantids
used might have been just one, but as the fly density was expressed per square centimetre,
the mantid density could not be unity). Also, the theoretical curve fitted to
the data in the same figure is in fact an instantaneous rate, and so if the density was
depleted, the comparison is not justifiable.
Secondly, if our aim is to obtain an overall hunting equation, which is no doubt
needed in population dynamics, an appropriate instantaneous hunting equation is
required, the reason for this being explicit in earlier sections of the present paper.
To obtain an instantaneous hunting equation, from which the final synthesis is made,
the experimental analysis of the elemental components should have been designed
accordingly. However, the observed relationship, for instance, between the amount of
prey eaten and the deprivation time in HOLLING'S original paper (1966, figures 4 and
5) is not appropriately tailored for the above purpose. This is because the time
involved in consuming a given amount of prey was not explicitly considered by the
author. Suppose the amount eaten up to the state of satiation (see HOLLING'S definition,
1966 p. 16) was W~ and W2, when the deprivation time was 7", and 2"2, and tl