Hamilton's variational principle and ecological models

Abstract

In physics, dynamical equations are often derived from a quantity known as the “action” using Hamilton's variational principle. In effect, the action provides a convenient and elegant summary of the properties of a system. In this paper the use of Hamilton's variational principle to derive ecological models is discussed, using the logistic equation as a simple example. A second model which displays contrasting dynamical behaviour is also considered. The action is interpreted as the sum of a term describing the intrinsic dynamical behaviour of the population (e.g. exponential growth) and a term describing environmental factors. This approach shifts the emphasis away from system behaviour as a basis for modelling. Instead the emphasis is on factors affecting the system, which consequently determine its behaviour. Models based on second-order differential equations arise naturally in this approach.