A comparative study of models for predation and parasitism

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effect of local depletion of prey upon the hunting efficiency will be less at higher
values of x0. If a cross-section parallel to the z-xo
circumstances, it should again be wavy.
plane is observed under these
A similar tendency to periodic deviation from a random distribution in accordance
with changes in the host density was shown by SIMMONDS (1943, see also citation by
WILLIAMS 1964). SIMMONDS, and
odic deviation in relation to the
SIMMONDS' experiments, however,
WILLIAMS as well, presented and analysed the peri-
parasite/host ratio, rather than to the density. In
parasite density was kept constant and host density
changed for ratios between 1/200 and 1/25, but for those between 2/25 and 10/25 the
parasite density was changed and the host density kept constant.
Therefore, the
former corresponds to a cross-section parallel to the z-xo plane in the hunting surface,
but the latter is a cross-section parallel to the z-Yt
parable even if the ratio declines continually.
plane, and so they are not com-
Keeping this point in mind, one can
compare my simulation model and SIMMONDS' observation, and find again a close simi-
larity between them. It should be borne in mind that from the standpoint of my
simulation model, it is not the parasite/host ratio which is essential: it is the geo-
metric properties of parasites' searching activity, changing as the densities change,
that results in the pattern described above.
Now, a question is posed as to whether the wavy trend in the hunting surface is
inherent in predation and parasitism. As already shown, a hunting curve comes closer
to the one expected in the random encounters between prey and predators, and
between hosts and parasites, when the predators, or parasites, shift their hunting area
frequently.
Of course, an approach to the curve expected in random encounters
suggests a rise in the average hunting efficiency. This is, however, just an apparent
relationship, because the time needed to handle a victim has been excluded in the
above models. If, in reality, a hunter shifts its hunting area much too often, the time
involved in travelling from place to place will also increase. Consequently, the advan-
tage of shifting will eventually be cancelled by the disadvantage.
Hence, there must
be an optimal frequency of shifts and an optimal distance (average) of travel that
result in the highest hunting efficiency. Therefore, a perfectly smooth hunting surface
would not at any rate be expected.
If, however, the prey or host individuals also
move around independently of each other and of the predators or parasites, then
random encounters might again be expected.
It should be mentioned that the wavy pattern of a hunting curve (i. e. z plotted
against n) is caused entirely by uninterrupted searching in the first simulation experi-
ment, i.e. the predator's path is continuously increased with time. If the experi-
ment was designed, however, so that the paths of some predators consisted of a
number of short ones, as in the second simulation experiment, the wavy trend will
be less pronounced. If the predator's path was completely discontinuous, that is, if n
was varied entirely by Y, and t was extremely short, the waves would eventually
disappear. However, as long as the path of each predator is allowed to be continuous