202 CATALYZING INQUIRY
dispersal declines with distance. Mortality risk is also stochastic and has two elements: random mortal-
ity and mortality associated with suppressed growth.
Because SORTIE is intended to aggregate statistical properties of forests, an ensemble of simulation runs
is necessary, in which different degrees of smoothing and aggregation are used to determine how much
information is lost by averaging and to find out where error is compressed and where it is enlarged in the
course of this process. SORTIE is a computation-intensive simulation even for individual simulations, be-
cause multiple runs are needed to generate the necessary ensembles for statistical analysis. In addition,
simulations carried out for heterogeneous environments require an interface between large dynamic simula-
tions and geographic information systems, providing real-time feedbacks between the two.
5.5 TECHNICAL CHALLENGES RELATED TO MODELING
A number of obstacles and difficulties must be overcome if modeling is to be made useful to life
scientists more broadly than is the case today. The development of a sophisticated computational model
requires both a conceptual foundation and implementation. Challenges related to conceptual founda-
tions can be regarded as mathematical and analytical; challenges related to implementation can be
regarded as computational or, more precisely, as related to computer science (Box 5.24).
Today’s mathematical tools for modeling are limited. Nonlinear dynamics and bifurcation theory
provide some of the most well-developed applied mathematical techniques and offer great successes in
illuminating simple nonlinear systems of differential equations. But they are inadequate in many situa-
tions, as illustrated by the fact that understanding global stability in systems larger than four equations
is prohibitively hard, if not unrealistic. Visualization of high-dimensional dynamics is still problematic
in computational as well as analytical frameworks; the question remains as to how to represent such
complex dynamics in the best, most easily understood ways. Moreover, many high-dimensional sys-
tems have effectively low-dimensional dynamics. A challenge is to extract the dynamical behavior from
the equations without first knowing what the low-dimensional subspace is. Box 5.25 describes one new
and promising approach to dealing with high-dimensional multiscale problems.
Other mathematical methods and new theory will be needed to find solutions that apply not only to
biological problems, but to other scientific and engineering applications as well. These include methods
for global optimization and for reverse engineering of structure (of any “black box,” be it a network of
genes, a signal transduction pathway, or a neuronal system) based on data elicited in response to
stimuli and perturbations.
Identification of model structure and parameters in nonlinear systems is also nontrivial. This is
especially true in biological systems due to incomplete knowledge and essentially limitless types of
interactions. Decomposition of complex systems into simpler subsystems (“modules”) is an important
challenge to our ability to analyze and understand such systems (a point discussed in Chapter 6).
Development of frameworks to incorporate moving boundaries and changing geometries or shapes is
essential to describing biological systems. This is traditionally a difficult area. Ideally, it would be
desirable to be able to synthesize and analyze models that have nonlinear deterministic as well as
stochastic elements, and continuous as well as discrete, algebraic constraints, with other more tradi-
tional nonlinear dynamics. (See Section 5.3.2 for greater detail.) All of these can be viewed as challenges
in nonlinear dynamics aspects of modeling.
Further developing both computational (numerical simulation) methods and analytical methods
(bifurcation, perturbation methods, asymptotic analysis) for large nonlinear systems will invariably
mean great progress in the ability to build more elaborate and detailed models. However, with these
large models come large challenges. One is how to find methodical ways of organizing parameter space
exploration for systems that have numerous parameters. Another is the development of ways to codify
and track assumptions that have gone into the construction of a model. Understanding these assump-
tions (or simplifications) is essential to understanding the limitations of a model and when its predic-
tions are no longer biologically relevant.