The Lake as a System of Differential Equations – A Paradigm for the Aquatic

In the course of the 20th century limnology and oceanography have been transformed from purely descriptive disciplines to sciences that champion quantitative approaches and aim to reveal mechanistic relationships. In particular, the increasing use of mathematical formulations and models to understand lakes, streams and oceans as dynamical systems can be viewed as a paradigm shift. The mathematicaldynamical approach is irreversibly integrated into this field and has revolutionized aquatic ecology, although its gradual and on-going adoption is best characterized as an evolutionary process and, therefore, does not meet the criteria of the KUHNIAN concept of a paradigm shift. I here show how this new approach historically emerged from the understanding of lakes and oceans as complex yet decomposable systems and describe the development of the new paradigm into the 21st century. I explain methods of validation and give examples of successful applications of the mathematical-dynamical approach. I end with an outlook on some current, promising research directions that may influence the future path of this “ever-evolving paradigm shift.” Seltsam ist Propheten Lied, doppelt seltsam, was geschieht1 J. W. VON GOETHE, Weissagungen des Bakis 1. Mathematical Dynamic Models in Aquatic Ecology – an Incomplete Paradigm Shift The face of aquatic ecology has changed significantly over the course of the 20th century. Limnology and oceanography have shifted from largely descriptive disciplines to sciences that embrace a dynamical ecosystem concept and attempt to understand the processes that generate the observed patterns. In particular, the use of mathematical formulations and models has emerged as a means to better describe, understand and predict the dynamical properties in lakes, streams and oceans. This new approach, bolstered by the microelectronic revolution and rapid increase in computing power, has drastically changed the way aquatic ecologists do their science; it could therefore be perceived as a paradigm shift as described by KUHN (1962). In this article, I have chosen to describe the integration of mathematical modelling approaches as an influential and promising development in aquatic ecology. However, it will become clear that the establishment of this new view does not fit particularly 1 Loose translation from German: “Strange is the prophet’s song, twice as strange is what really