A comparative study of models for predation and parasitism

paratively high. However, the more axiomatic K~ is, the lower Pr {cn} will be, and
so the less likely is event (E=O) to occur.
For the above reason, a simple, deductive model often fails to agree with obser-
vation. But such failures in deductive models are more likely to be caused either
by c~2 or c~3 than by c2z. If so, there is no reason to reject the hypothesis ; it only
needs further elaboration. The only case in which at least a part of the components
or the structure should be rejected, is C~. Here, a careful observation of the disagree-
ment is of paramount importance.
There are, broadly speaking, two possible kinds of alterations when a disagree-
ment is observed. A method frequently seen in the literature is to adjust the structure
of the model or to add some more components to obtain E=O. Here, Pr{E=O}
certainly increases, but at the same time there is a risk of getting a high Pr{C2},
and hence Prl(E=O)[c21}. The risk is greater if the added components are those
whose trend is not fully understood. The estimation of coefficients involved in the
empirical equation could amount to this kind of adjustment, as the coefficients often
have to be estimated by comparing E with O. The recent predation models in fact
involve such a risk, as will be shown later. The worst thing is to obtain E=O by
adjustment when the first disagreement was in fact caused by c22 ; it only increases
Prl(E=O)]c21} and has no meaning at all.
The second type of improvement is to look for more of the axiomatic components,
or of those which are known to be true for any reason, without making a particular
effort to obtain E=O. This keeps Pr {C2} to a low level, and therefore the improve-
ment, if any, increases, though only gradually, Pr {c1~}.
Although the second method will provide a steady approach to the goal, a question
arises whether a collection of axiomatic assumptions can eventually produce a suffi-
cient model. WALKER (1963) argued that "it is a common misconception that new
models are constructed by strict logical deduction from observed facts and from
previous models". Certainly, nothing new will come from mere accumulations of
known concepts. However, a model is not a mere collection of already known com-
ponents but involves a positive recombination of them which is applied to a new
situation. And the role of the model is to produce a useful recombination by analogy.
The efficiency of finding a useful model depends on the efficiency in selecting
axiomatic components and recombining them. A model is therefore required to have
room for accommodating added components and recombining them. This calls for
a general and idealized model to start with: too specific a model has to be rejected
upon finding a disagreement because of its limited capacity for modification, or it
could involve a high value of Pr{(E=O)Ic2~}, particularly when some coefficients
involved have to be estimated rather than determined by independent and direct
observations of what these coefficients' represent.
The role of idealization is again seen in the history of the physical sciences,
which should be understood in the context of fact-observation relationships and of