The Analysis of Complex Population Processes

Abstract

Population ecology requires realistic and precise analyses of whole systems, or processes, and not just fragments of them. This poses some difficult problems because of the distinctive complexity of these processes. Recent studies of predation have shown, however, that it is possible to achieve great analytical depth and to simulate whole systems in the form of realistic and precise mathematical models. This is accomplished by ignoring the degree of simplicity traditionally required of population models and by emphasizing the need for reality. Extensive experimentation is required to suggest and test possible explanations for the action of each component of the process so that the explanation evolves in gradual steps to include one component after another. The form of the explanation and the resulting equations is hence dictated by the process itself and not by the need for mathematical neatness. The considerable complexity of the predation model arose from features common to many biological processes i.e. the prevalence of limits and thresholds, the presence of important discontinuities and the historical character of biological events. These features can be analyzed effectively only by establishing an intimate feed-back between experiment and theory. Mathematical models incorporating these features are admirably solved using digital computers. Computers, and the languages used to program them, seem to be ideally suited to handle the distinctive type of complexity shown by population processes.