120 CATALYZING INQUIRY
more compelling and more accessible interpretations of what the models predict.^3 This has made it
easier to earn the recognition of biologists.
On the other hand, modeling—especially computational modeling—should not be regarded as an
intellectual panacea, and models may prove more hindrance than help under certain circumstances. In
models with many parameters, the state space to be explored may grow combinatorially fast so that no
amount of data and brute force computation can yield much of value (although it may be the case that
some algorithm or problem-related insight can reduce the volume of state space that must be explored
to a reasonable size). In addition, the behavior of interest in many biological systems is not characterized
as equilibrium or quasi-steady-state behavior, and thus convergence of a putative solution may never
be reached. Finally, modeling presumes that the researcher can both identify the important state vari-
ables and obtain the quantitative data relevant to those variables.^4
Computational models apply to specific biological phenomena (e.g., organisms, processes) and are
used for a number of purposes as described below.
5.2.1 Models Provide a Coherent Framework for Interpreting Data,
A biologist surveys the number of birds nesting on offshore islands and notices that the number
depends on the size (e.g., diameter) of the island: the larger the diameter d, the greater is the number of
nests N. A graph of this relationship for islands of various sizes reveals a trend. Here the mathematically
informed and uninformed part ways: simple linear least-squares fit of the data misses a central point.
A trivial “null model” based on an equal subdivision of area between nesting individuals predicts that
N~ d^2 , (i.e., the number of nests should be roughly proportional to the square of island area). This simple
geometric property relating area to population size gives a strong indication of the trend researchers
should expect to see. Departures from this trend would indicate that something else may be important.
(For example, different parts of islands are uninhabitable, predators prefer some islands to others, and
so forth.)
Although the above example is elementary, it illustrates the idea that data are best interpreted
within a context that shapes one’s expectations regarding what the data “ought” to look like; often a
mathematical (or geometric) model helps to create that context.
5.2.2 Models Highlight Basic Concepts of Wide Applicability,
Among the earliest applications of mathematical ideas to biology are those in which population
levels were tracked over time and attempts were made to understand the observed trends. Malthus
proposed in 1798 the fitting of population data to exponential growth curves following his simple
model for geometric growth of a population.^5 The idea that simple reproductive processes produce
(^3) As one example, Ramon Felciano studied the use of “domain graphics” by biologists. Felciano argued that certain visual
representations (known as domain graphics) become so ingrained in the discourse of certain subdisciplines of biology that they
become good targets for user interfaces to biological data resources. Based on this notion, Felciano constructed a reusable
interface based on the standard two-dimensional layout of RNA secondary structure. See R. Felciano, R. Chen, and R. Altman,
“RNA Secondary Structure as a Reusable Interface to Biological Information Resources,” Gene 190:59-70, 1997.
(^4) In some cases, obtaining the quantitative data is a matter of better instrumentation and higher accuracy. In other cases, the
data are not available in any meaningful sense of practice. For example, Richard Lewontin notes that the probability of survival
Ps of a particular genotype is an ensemble property, rather than the property of a single individual who either will or will not
survive. But if what is of interest is Ps as a function of the alternative genotypes deriving from a single locus, the effects of the
impacts deriving from other loci must be randomized. However, in sexually reproducing organisms, there is no way known to
produce an ensemble of individuals that are all identical with respect to a single locus but randomized over other loci. Thus, a
quantitative characterization of Ps is in practice not possible, and no alternative measurement technologies will be of much value
in solving this problem. See R. Lewontin, The Genetic Basis of Evolutionary Change, Columbia University Press, New York, 1974.
(^5) T.R. Malthus, An Essay on the Principle of Population, First Edition, E.A. Wrigley and D. Souden, eds., Penguin Books,
Harmondsworth, England, 1798.