Environmental Engineering Reference
In-Depth Information
Fig. 3.2 Pierre Francois
Verhulst
source
: wikimedia commons
a well established mathematical underpinning and to the discovery of more and
more quantitative relations. Ecology - terminologically existing as a sub-discipline
of biology - was still largely dominated by qualitative assessment.
3.3 Founders of Ecological Modelling
In the first half of the twentieth century, Einstein's relativity theory of 1905 had
been successively accepted in physics. Quantum theory was on the way, and David
Hilbert discussed infinite dimensional vectors as mathematical objects. With some
lag, the relevance of quantitative relations received attention in ecology as well.
This started with quite elementary and simple contexts, which did not require
elaborated mathematical forms. Differential equations, which describe the change
of particular variables over time, played the leading role.
Lotka and Volterra: Setting the Stage for Network
Approaches
Independent from each other, Alfred Lotka (1880-1949) and Vito Volterra
(1860-1940) developed the same simplistic form to describe the interaction of a
predator population and a prey population (Lotka 1925; Volterra 1926). The
equations are explained in detail in Chap. 6. In the subsequent time, this model
inspired innumerable variations, modifications, and adaptations to specific con-
texts. To this day, the original works of Lotka and Volterra are among the most
frequently cited papers in ecological modelling. The Verhulst-equation, re-dis-
covered by Pearl around the same time, helped to extend the functional repertoire
usable in the equations. The Lotka-Volterra (LV) model describes the interaction
