A comparative study of models for predation and parasitism

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1954; MILNE 1957) who thought that the premise and the structure of the classical
models were far too simple to be realistic.
It should be pointed out, however, that
those who proposed what was claimed to be more realistic, taking so many conceiv-
able factors into account, have never been able to formalize the ideas that they stated
only verbally, or have not even tried to do so.
From such verbal statements, one
cannot draw a quantitatively expressed conclusion that can be compared with ob-
served quantities for testing.
Now it is clear that the criticism of the classical models was due to insufficient
understanding of the nature of inferences.
As pointed out in w 4f, although WATT
claimed that the assumption of the coefficient A as it appeared in eq. (4f. 5) was
based on an empirical fact, it was in fact an illusion, since the assumption proved to
be nothing but dogmatic and even impossible a priori. Obviously, the author did not
test his hypothesis (i, e. eq.
(4f. 5)) by any means and this positively violates, con-
trary to what was claimed, the code of rules for inferences by induction. The same
criticism applies to the HASSELL-VARLEY model in w 4h.
The above discussion suggests that the stage we are in is still very primitive,
with an evident lack of rigor in methodology. This, however, may well be because
the nature of the objects we are studying have influenced the development of ideas
in this field. My point may be illustrated by contrast with the development of the
physical sciences.
In physics, some properties of certain objects were, very fortunately, describable
deterministically (sensu BORN 1964--predictable without the causal relationships being
known; a timeless and spaceless link between the events, e.g. a railway time-table).
The arithmetic prediction of the stars' motion by the Babylonians or, more recently,
KEPLER'S Law, are perhaps typical examples. As modern physicists went into the
more minute details of atoms, and as the required measurements became finer and
finer, they eventually reached a stage where the classical method of induction was no
longer applicable. A positive barrier was encountered when HEISENBERG enunciated
his Uncertainty Principle in 1927; this predicts that some physical attributes of the
object being measured are influenced by interaction between the object and the meas-
uring system. However, before this stage was reached, there were enough examples
of success in macrophysics, i.e. in NEWTONIAN physics, which encouraged the phys-
icists to explore thoroughly the method of induction.
In the field of population dynamics, however, difficulties similar to those that
modern physics is currently facing have been a major problem from the beginning.
Some may be only technical difficulties in obtaining accurate measurements.
example, the concept of the handling time (h), originally suggested by HOLLING
(1956), was found to be highly idealized in my study of the great tit, Parus major
L. (ROYAMA 1970). I tried to time the tit as it searched for food and as it handled
each item.
The information was used to calculate a theoretical value for the amount
of food that the tit could collect per day using HOLLING'S disc equation (for the
For