Environmental Engineering Reference
In-Depth Information
plausible parameters within a certain range often leads to reasonable results without
elaborated fine-tuning. A reason for this is that, on the level of the single organisms,
processes operate with a certain robustness, as depending on constricting extreme
precisions would frequently conflict with the sustainability of the general condi-
tions for existence. On the other hand, the occurrence of extreme sensitivities
frequently indicates that highly aggregated process descriptions were used. Ratz
(1995) illustrates in a forest fire model that model assumptions are likely to be
unrealistic if the result depends on extremely fine-tuned parameter (in this case
within a linear model), whereas other assumptions (here, the introduction of a
nonlinearity) makes the model considerably less sensitive to changes in parameter-
ization. Hence, we can state that beyond limits of plausibility for biological para-
meters the results frequently turn unrealistic.
23.4.2 Result-Probability Distributions, Parameter Ranges
and Phase Transitions
Often, not just one specific simulation result is of interest, but instead we have to
deal with a whole class of simulation output resulting from systematic tests of
varied initial conditions, parameter ranges or external influences. Such an approach
is frequently used for dynamic systems in all fields of application. When for a given
system the outcome cannot be predicted with a high precision, frequently it is
possible to specify a probability range which can be derived through a large number
of model re-runs with varied parameters or initial conditions.
Frequently, an unevenly distributed probability density structure can be found
and characteristic spatio-temporal probability structures emerge. Structures can
comprise heterogeneous output densities, phase transitions between different
dynamic or structural regimes and gaps in which it is improbable to find the model's
state. Without specific reference to this concept, it has been used in a previous
chapter (see Fig. 1.4). It shows the result of re-iterations of a small equation-based
system with a successively changed input parameter and shows the response space
which exhibits a complex fractal structure.
23.5 Model Documentation and Communication
Modelling involves complex interaction networks (Reuter et al. 2008). While a short
formula can be relatively easily surveyed, it is a challenge of its own for most of the
practically relevant ecological applications to bring them in a form that conforms to
scientific standards, including an independent confirmation of the results. This
marks the difference between art and science: while an artist is happy with a unique
