WHAT IS A MODEL?
Biologists, like other scientists, use the notion of
model in a host of
ways. At one extreme they may
mean a scaled-up, three-dimensional wire and
plastic
representation of a cell. At the other, they may mean
an
abstract structure such as a “mathematical model”
of
evolution which may consist only of a set of differ-
ential equations. In what sense can the wire and
plastic
cell be said to be the same kind of structure as a set
of
differential equations? And in what sense are they
like a mouse, which is
said to be a “model organism”
for the study of
certain physiological or genetical
problems?
The similarities of these models can best be under-
stood by beginning with the most abstract. The basic
theory of
evolutionary genetics is well worked out,
based on a detailed knowledge of
the mechanics of
inheritance and certain empirical information about
the biology of reproduction and survival of a variety
of organisms. This
theoretical superstructure is suffi-
ciently complex that quantitative predictions of the
outcome of
evolutionary changes cannot be made by
inspection. In order to find out
what is entailed by the
theory in any particular case, a model is built.
First,
the theory is abstracted and is framed in terms of a
logical
flow diagram involving dummy variables and
logical relations among these
variables. Then this logi-
cal structure is
realized by a program for a computer,
or a set of matrices and matrix
operators, or a system
of difference or differential equations. All these
real-
izations are isomorphic with each
other and with the
original logical structure.
A second possibility is that a series of resistors, ca-
pacitors, and other electric and electronic devices is
used to make a physical model such that these electri-
cal elements produce a set of electrical
quantities
(current, voltages) that behave isomorphically with the
dummy variables of the abstract system. Alternatively,
a “model
organism” may be employed, like the fruit
fly, Drosophila, which is thought to be a specific real-
ization of the same general principles as are
expressed
in the abstract representation of the original theory.
In
fact, with a physical analogue as complex as a
“model
organism,” the explicit construction of the
abstract system that
served as the pattern for the
mathematical realizations may never be made.
Rather,
the model organism is assumed to embody the general
properties
of the system being modelled and, in fact,
the general theory of
evolutionary genetics supposes
that all organisms embody certain general relations
which are
the subject of investigation. A model orga-
nism can then be used, and often is, in the absence
of a well
worked-out theory of a biological process
on the assumption that general
biological similarities
between the systems will guarantee isomorphism
with
respect to the specific aspects under investigation.
The differences between the mathematical model,
the electronic model, and
the model organism as real-
izations of the
underlying abstractions, are of great
importance. The physical entities in
the latter two
kinds of models carry with them certain intrinsic prop-
erties that are different from those in
the original being
modelled. That is, these physical realizations are
meta-
phorical
and their iconic elements can be a source of
serious difficulty. The
physical realizations were chosen
because some set of their properties was
isomorphic
with some set of properties of the original system or
theory. In the case of the electronic analogue, the
theory of capacitors,
resistors, and vacuum tubes is so
well understood and the empirical
properties of these
objects are so different from the system being
modelled
that there is no danger of confusion from the meta-
phorical elements. That vacuum tubes
glow, get hot,
break when jarred, make a tinkling sound when
knocked
together, will in no way confound the biolo-
gist since he is unlikely to confuse these properties with
the
properties of evolving organisms. In the case of
model organisms, however,
the danger is very great,
because the metaphorical elements introduced by
these
organisms are in some cases so subtly different from
the
properties being modelled, that they cannot be
distinguished, yet they
produce great distortions.
Moreover, since such metaphors are often introduced
without an explicit
laying out of the abstract system
of which the model should be a
realization, there is
no clear way of differentiating relevant from
irrelevant
from obfuscating properties of the model. For example,
Drosophila was used for a long time as the model for
the genetic mechanism of sex determination in man,
because of a general
similarity of genetic mechanisms
between flies and man. But this has turned
out to be
completely wrong, and the conclusions that arose from
this
model were erroneous. This danger does not arise
only from using complex
organisms as realizations. The
“digital computer”
model of the central nervous system
has been one of the most misleading and
possibly
harmful examples of allowing metaphorical properties
to
intrude. In this case such properties as redundancy
checks, topological
relationship between physical ele-
ments and
conceptual elements, and the bit structure
of information characteristic of
electronic digital com-
puters, although all
metaphorical, were taken to be
isomorphic with the elements of the central nervous
system,
whereas they certainly are not. It is for this
reason that an explicit
abstraction of the original sys-
tem, followed by
a realization of that abstraction in
either an abstract or physical form is
much preferable
to modelling by generalized and
“felt” analogy.
There is some confusion in biology between “models
of”
and “models for.” The isomorphisms with particu-
lar biological systems are
“models of.” But models in
the sense of ideals or
patterns, like the “model of a
modern major general,”
are also found in the biological
literature. The essential difference is in
their epistemo-
logical status.
“Models of” are not intended, especially
when they
are abstract, as contingent. They are ana-
lytic isomorphs of some phenomenon or system. They
may be good or
bad models as they are perfect or
imperfectly isomorphic, but they cannot
be said to be
true or false. On the other hand, “models
for” like the
logistic model of population growth or the Lotka-
Volterra model of species
competition, or the gradient
model of development, are taken as statements
about
the real world, as contingent, and are in fact assertions
about
the way organisms really behave. Sometimes
such models (patterns) are
introduced as examples of
how nature might be, but
they very soon become reified
by biologists. Such
“models” are most common in those
branches of biology
where there is little or no theoret-
ical
basis. In these cases it is quite proper to speak
of “testing
the model” since it is not really a model
but a hypothesis.
Unfortunately, confusion between
these two senses of
“model” sometimes results in an
attempt to test a
“model of” which always results in
a vacuous
“confirmation” of the model. Since the
model is
analytic, it must be, and always is, confirmed.
Some such
“tests” of analytic models go on in popula-
tion biology, where a model organism is placed
under
extremely well controlled experimental conditions so
that it
realizes a mathematical structure that has been
solved. If the mathematics
has been done competently,
the model, which is a living computer, confirms
it. But,
of course, no “test” (except of the
competence of the
investigator) has been performed.