Environmental Engineering Reference
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contain theoretical or empirical elements or assumptions, which are brought together
for making final statements that deal with cause and effect. In the following, we will
refer to this abstract representation by using the term model . A model can be a
conceptual setting, a verbal description, a simplified physical representation, and
of course also a description in quantitative mathematical relations. While mathe-
matical representations and verbal descriptions sometimes are seen as something
entirely different, we would like to emphasize that there are usually transitions and
translations between both. This is meant as an invitation to all ecologists not only to
observe organisms and patterns in the field but equally to think how observations can
be captured in formal settings and thereby used to investigate the underlying
processes and mechanisms. When we arrive at such a turning point between empirical
investigations and their transformation in mathematical forms, we are able to look
at our observations from another angle. Taking a modelling perspective, we will
discover new implications which were not entirely obvious at first glance and lead to
new insights. The ecological complexity we observe is not always and necessarily
complicated: There are surprisingly simple avenues to complexity, which are starting
directly in the heart of simplicity.
1.2 Simplicity and Formal Representations: Appetisers
to Model Complex Ecological Dynamics
Models need to be simpler than the original. A model representation as complex as
the relations it represents would not really be enlightening and helpful. A model
should aid in the understanding by allowing an overview and focusing on certain
important aspects. The challenge is to make a simplification to capture the essence
of a specific focus of interest. In fact, this is one of the most important challenges in
modelling and a source of lasting controversies (DeAngelis and Gross 1992).
Now, let us see how complex the relations will be that can result from very
simple approaches. The black box approach is perhaps the most radical simplifica-
tion that made many phenomena accessible for modelling. In this approach, theo-
retically, in the considered context, everything is put into a box. It is assumed that
the internal dynamics in the box are irrelevant as long as they do not greatly change
the amount of the relevant content. Only an accounting for the input and output
of the desired variables is done. In principle, this is what Alfred Lotka and Vito
Volterra (Lotka 1925; Volterra 1926) did in their famous model approach on the
relation of a predator and a prey population that they tackled with a simple
differential equation model (see Chap. 6).
But how can such an approach help to understand complexity? Some empirical
ecologists used to critisize (specifically mathematical) models as being too theoret-
ical because the simplifications, manifested in the black-box approach, seemed to
ignore what is biologically interesting to them: the diversity, variability and hetero-
geneity of ecological entities.
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