122 CATALYZING INQUIRY
resource limitations on stabilizing a population that would otherwise grow explosively. All of these
concepts arose from mathematical models that highlighted and explained dynamic behavior within the
context of simple models. Indeed, such models are useful for helping scientists to recognize patterns
and predict system behavior, at least in gross terms and sometimes in detail.
5.2.5 Models Can Link Levels of Detail (Individual to Population),
Biological observations are made at many distinct hierarchies and levels of detail. However, the
links between such levels are notoriously difficult to understand. For example, the behavior of single
neurons and their response to inputs and signaling from synaptic connections might be well known.
The behavior of a large assembly of such neurons in some part of the central nervous system can be
observed macroscopically by imaging or electrode recording techniques. However, how the two levels
are interconnected remains a massive challenge to scientific understanding. Similar examples occur in
countless settings in the life sciences: due to the complexity of nonlinear interactions, it is nearly impos-
sible to grasp intuitively how collections of individuals behave, what emergent properties of these
groups arise, or the significance of any sensitivity to initial conditions that might be magnified at higher
levels of abstraction. Some mathematical techniques (averaging methods, homogenization, stochastic
methods) allow the derivation of macroscopic statements based on assumptions at the microscopic, or
individual, level. Both modeling and simulation are important tools for bridging this gap.
5.2.6 Models Enable the Formalization of Intuitive Understandings,
Models are useful for formalizing intuitive understandings, even if those understandings are partial
and incomplete. What appears to be a solid verbal argument about cause and effect can be clarified and
put to a rigorous test as soon as an attempt is made to formulate the verbal arguments into a mathemati-
cal model. This process forces a clarity of expression and consistency (of units, dimensions, force
balance, or other guiding principles) that is not available in natural language. As importantly, it can
generate predictions against which intuition can be tested.
Because they run on a computer, simulation models force the researcher to represent explicitly
important components and connections in a system. Thus, simulations can only complement, but never
replace, the underlying formulation of a model in terms of biological, physical, and mathematical
principles. That said, a simulation model often can be used to indicate gaps in one’s knowledge of some
phenomenon, at which point substantial intellectual work involving these principles is needed to fill the
gaps in the simulation.
5.2.7 Models Can Be Used as a Tool for Helping to Screen Unpromising Hypotheses,
In a given setting, quantitative or descriptive hypotheses can be tested by exploring the predictions
of models that specify precisely what is to be expected given one or another hypothesis. In some cases,
although it may be impossible to observe a sequence of biological events (e.g., how a receptor-ligand
complex undergoes sequential modification before internalization by the cell), downstream effects may
be observable. A model can explore the consequences of each of a variety of possible sequences can and
help scientists to identify the most likely candidate for the correct sequence. Further experimental
observations can then refine one’s understanding.
5.2.8 Models Inform Experimental Design,
Modeling properly applied can accelerate experimental efforts at understanding. Theory embedded
in the model is an enabler for focused experimentation. Specifically, models can be used alongside
experiments to help optimize experimental design, thereby saving time and resources. Simple models