FUNCTIONS OF MODELS
Model-making in biology serves much the same set
of functions as in any
science. The special complexity
of many biological systems and the apparent
diversity
of biological phenomena place a rather different
weight on
various functions of modelling in biology
than in the physical or social
sciences.
1.
Models have an experimental convenience. Fruit
flies are easier to breed than man, and the giant axon
of the squid is easy
to manipulate in neurophysiological
experiments. The very great delicacy of
many biologi
cal materials and especially the idiosyncrasies of each
species,
make the search for “model organisms” in
which
particular features are convenient for investi-
gation one of the outstanding features of research
strategy.
Most important advances in biology depend
upon finding just the right
“model organism” or “model
system” for investigation. The best known example is
the
dependence on the use of bacteriophage for the
development of molecular
genetics (Cairns, Stent, and
Watson, 1966). This case also shows how unique
aspects
of the model system itself, its metaphorical content,
can
distract attention from the central features of the
realization. A great
deal of the research on bacte-
riophage is
now concerned with the peculiar properties
of this parasite interacting
with its host, properties that
are irrelevant or even misleading for
general genetical
problems. At the present time a determined search is
under way for a model organism for the study of the
molecular and
micro-anatomical basis of central nerv-
ous
system function, based on an explicit list of desira-
ble model properties.
2.
Second in importance for models in biology is
the function of computation. An increasing number of
biological
theories are framed in terms of numerically
quantified variables. Even when
the variables are
themselves qualitative (“on” vs.
“off” in nerve firings,
“male”
vs. “female,” “gene A” vs.
“gene a”), many
theories are probabilistic and
provide only probability
distributions for the states, even for fixed
inputs. The
computation of such probability distributions cannot
be
carried out by observing nature since only single
realizations of
particular input sets exist. It is not pos-
sible, for example, to build and check a quantitative
theory of
population extinction by observing actual
populations becoming extinct.
Extinction is reasonably
rare in nature and no two populations have the
same
starting conditions or environments. A theory of extinc-
tion is expressed in terms of a very
large number of
variables including certain stochastic inputs from the
physical environment. Such theories are modelled by
analogue or digital
computer programs in which there
is no metaphorical element and the model
is isomor-
phic, with stochastic variables
introduced to provide
an empirical probability distribution of results.
An
alternative has been to create large numbers of con-
trolled populations in the laboratory or on islands.
3.
Of lesser importance to biology is the function
of reification. In physics, inferred entities like electrons
and
constructs like the photon are reified in macro-
scopic models, presumably because one cannot “un-
derstand” or
“comprehend” them otherwise. Most of
the entities of
biology are either macroscopic or can
be visualized with optical devices.
As molecular biol-
ogy has grown, however, with
its concept of gene as
molecule and with its preoccupation with the mechan-
ical interactions between molecules, there has been
an
increase in macroscopic modelling. Molecular models
of metal or
rubber in which atoms and chemical bonds
are represented by
three-dimensional objects with ex-
actly cut
angles and shapes are now common in biol-
ogy.
Most of these models are built in order to “have
a look
at” a complex biological molecule because it
is felt that
somehow its three-dimensional structure will
provide some intuition about
its function. Closely re-
lated to this kind of
comprehension is a form of weak
hypotheses testing that accompanies
reification. When
J. D. Watson and F. H. C. Crick were investigating
the molecular structure of DNA, they built metal real-
izations of their hypothetical structures, based on nu-
merical information from X-ray
crystallography. A
number of those did not fit together too well (one
is
described as a “particularly repulsive back-bone
model”) while the final, correct solution looked right
(“Maurice [Wilkins] needed but a minute's look at the
model to
like it”). The fact that many of the structures
seemed strained
and tortured while the one model had
an elegant and easy-fitting look was
important in
reaching the final conclusion about the correct molec-
ular configuration (Watson, 1968).
4.
Slowly, biological model-making is coming to
serve as a function of
unification. Biology has been
marked in the past
by particularism, by the notion that
most generalizations are only
trivially true, and that
what is truly interesting and unique about
biological
systems is their variety and uniqueness, arising from
their
complexity. Even a great generalization like
Darwinism allows for such a
vast variety of forms of
natural selection and variation, that
evolutionists for
many years concentrated on individual patterns of
evolutionary change. This has been even truer of ecol-
ogy, which has remained anecdotal and particularist
in the
extreme. Abstract models usually framed in
logical and mathematical terms
with little or no iconic
element, have come into use in an attempt to
unify
large areas of biological investigation. Computer simu-
lations especially have shown that a
model involving
only a few genes and a fairly simple set of
assumptions
about the environment will predict a great variety of
possible evolutionary outcomes depending upon the
initial state of the
population that is evolving. Models
of coupled harmonic oscillators appear
to be predictive
of events in the central nervous system, embryonic
development, and physiological rhythms, and may in-
dicate an underlying general mechanism for all these
diverse
phenomena.
5.
Unification of diverse phenomena can be accom-
plished by increasing complications of models. A suffi-
ciently complex model will be
homomorphic with
(structurally similar to) a vast variety of phenomena,
but
trivially so. But models in biology are increasingly
being used for simplification as well. A new technique
in the
investigation of problems in community ecology
is to make a series of
models with fewer and fewer
entities, variables, and syntactical rules in
an attempt
to find the “simplest” model that will
give a satisfactory
account of the observations. While this seems a com-
monplace description of how science in
general is done,
it has not been true of community ecology in the
past.
The explicit program of R. MacArthur and R. Levins
(1967) to
express the ecological niche in terms of a
very small number of abstract
dimensions sufficient to
explain the numbers of organisms of different
species
coexisting, is a radical departure in ecology and one
not
universally approved. The opposite approach, that
of “systems
analysis” (Watt, 1968) is to build a model
so complex that it
approaches as closely as possible
an isomorphism (one to one
correspondence) with the
natural systems. In part, this difference in
approach
reflects a difference in intent. The systems analytic
model
is designed for the control of particular pest
organisms, or the management
of wildlife. As such it
is concerned with a particular organism in a
particular
circumstance. The minimal model is esteemed chiefly
for its
elegance and is viewed as a part of the general
program of natural
science—to explain as much as
possible by as little as possible.
