A comparative study of models for predation and parasitism

etween the assumption (CHAPMAN's (1931) concept of 'environmental resistance')
and the attributes of the subject (population growth), so the latter remain unknown.
The logistic equation was derived through metaphoric inferences rather than through
comparisons between the attributes of the subject and those of a model in which
factors involved are known.
Thus, we can see that differences between (a) a deductive model (deduced only
by reasoning) and (b) a descriptive equation like that of the logistic law, lie in
differences between (a) a comparison of components in the subject with equivalent
parts of the model and (b) a metaphoric juxtaposition of the observed trend of the
subject with that of some known concepts.
While the importance of metaphor, as SCHON (1967) emphasized, is appreciated,
it should be borne in mind that metaphor alone does not necessarily lead to explanations
and understandings. Quoting one of SCHON'S examples, the original concept of
'foot', restricted to an animal's foot, can be shifted to a much broader concept including
'the foot of a mountain'. Although this example certainly shows the importance
of metaphor in, say, the evolution of languages, such juxtaposition does not immediately
imply the understanding of the structure of the foot of mountains. In other words,
metaphor, playing its important role in one situation, or in a certain part of the process
in the formation of ideas, can be too vague to be useful in another. In the
example of the logistic law, metaphor led to the formulation of the equation that can
often describe observed relationships satisfactorily, but such success often depends
on how the observed relationships are described deterministically.
Normally, in the field of population ecology, a deterministic description of phenomena
is often so difficult that a descriptive, empirical equation can be adopted only
casually. Such casual equations often involve some coefficients whose nature is not
known. The equation is then hard to rationalize as there can be some other forms
of equations which fit the same observation equally well. Also, the coefficients must
be estimated from a limited set of observed data (our observations are, at any rate,
limited), and the more limited the number of observations, the less generalized the
estimate will be. Further, the more coefficients that are involved and that need to be
estimated, the more flexible the equation becomes since the degrees of freedom for
fitting increase. The above statement simply suggests that a good fit does not imply
that the equation concerned explains the mechanism.
Conversely, if an equation, derived from metaphoric inference, did not fit observed
relationships, it would have to be rejected. The rejection, however, involves a risk
of rejecting a correct assemblage of right components. This is because the disagreement
could be due to some other components or conditions which were missed, and
not due to inappropriate metaphor; if this is so, the equation need not be rejected
but only improved by further search for these overlooked factors. The difficulty is,
however, that there is no systematic way to know whether the disagreement is due
to the inadequate assemblage of factors or to inappropriate metaphor.