Environmental Engineering Reference
In-Depth Information
Fig. 3.1 Robert Malthus
source
: wikimedia commons
over time. On the other hand, Malthus argued, resource development would not
proceed exponentially but follow a linear dynamic. Malthus saw the discrepancy
between these two growth forms of arithmetic versus geometric growth as an
inevitable source of tension and instability. This controversy substantially
inspired the following scientific debate on well reasoned, quantitative considera-
tions on the human use of natural resources. At that time, Malthus' major impact
was not in the field of ecology as he worked in the newly developing field of
political economics. Here, in the era of European imperialism, his ideas played an
important role in the discussion about how to deal with scarce and limited
resources (Claeys 2000).
Verhulst: Early Functional Generalizations
It did not take long until other, successively more elaborated functional forms to
describe growth were provided. Pierre Francois Verhulst (1804-1849) (Fig.
3.2
)
was a Belgian mathematician, who sought a way to describe the modification
of growth intensity under the conditions of limited resources. He found a
rather simplistic form in 1838. His function is still widely used in ecological
modelling under the name of logistic growth (see Chap. 6: Differential Equa-
tions (6.7)).
The growth process that this equation describes always tends towards an equi-
librium. Interestingly, for quite a long time logistic growth was far less considered,
compared to Malthus. It was largely forgotten until Raymond Pearl (1879-1940)
rediscovered it when ecological modelling had made its first steps in the 1920s
(Pearl 1925). This was when the relevance of quantitative considerations as a
foundation of ecology became more and more potent (see Lotka and Volterra,
below). In physics, chemistry and other fields of science, advancement had led to
