A comparative study of models for predation and parasitism

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However, the similarity in their shapes can be compared, if desired, by parallel
translation of the relative position of the coordinate systems between the observed
and hypothetical relationships, since the curves are drawn on the ln-ln scale. Then,
the shapes of curves (a) and (a') in Fig. lla are comparable to a certain part of
curve (1) in Fig. 12b. The scattergram (e) in Fig. llb resembles curve (3) in Fig.
12a, and so on. A strict comparison will not be attempted here for the above reason,
however.
It should be mentioned finally that fitting a straight line to these observed relationships
may be justified only for the purpose of showing the declining tendency of
the value of ~ with increasing parasite density. In other words, the only conclusion
that one can draw from such linear regression analysis is restricted to the suggestion
that social interference is involved among parasites. However, there is no justified
basis for adopting the hypothesis that the relationship is linear. Also, the assumption
of the 'quest constant' by HASSELL and VARLEY (1969) (see w 4h) is justified only in
the linear regression analysis of those data in which host density is known to be
constant: the assumption is, however, hardly justified for speculating about the stability
of host-parasite oscillations in which host density is changing all the time. The
possibility of stable oscillations induced by social interference among parasites is yet
to be demonstrated on a more reasonable basis; until it is, the suggestion by HASSELL
and VARLEY is only a possibility.
Appendix to w 4i. Is the concept of 'area of discovery' useful in studies
of predation and parasitism ?
It has been shown in this paper that the concept of 'area of discovery', originally
introduced by NICHOLSON (1933), cannot be used as a geometric attribute of the
hunting process, since this simple, but highly hypothetical, concept involves a contradiction
from the energetics point of view. But the concept has been shifted, as one
way of expressing the hunting efficiency of predators or parasites, and has been widely
used in the literature of population dynamics. The shifted concept is now defined as
d in eq. (4b. 7) for predation and in eq. (4b. 8) for parasitism. The definition, however,
is not a straightforward expression of hunting efficiency, as it is the logarithm
of the reciprocal value of the survival rate, for a specified value of the initial density
of the hunted species per hunter.
My question here is whether this concept of 'area of discovery' is altogether
useful in the study of predation and parasitism. Of course, the concept has played a
significant role in its original context as a species specific constant under a given
condition. But, once the original meaning of this index as a species specific constant
is lost, what does the shifted concept signify ? Is there any particular advantage in
using this index in shifted, and more general, situations ? In order to answer these
questions, the index d will be evaluated in various models reviewed in this paper
and will be compared with the instantaneous hunting function on which each model