Continuous Population Models for Single Species

Abstract

The increasing study of realistic mathematical models in ecology (basically the study of the relation between species and their environment) is a reflection of their use in helping to understand the dynamic processes involved in such areas as predator-prey and competition interactions, renewable resource management, evolution of pesticide resistant strains, ecological control of pests, multi-species societies, plant-herbivore systems and so on. The continually expanding list of applications is extensive. There are also interesting and useful applications of single species models in the biomedical sciences: in Section 1.5 we discuss two practical examples of these which arise in physiology. Here, and in the following three chapters, we shall consider some deterministic models. The book edited by May (1981) gives an overview of theoretical ecology from a variety of different aspects; experts in diverse fields review their areas. The book by Nisbet and Gurney (1982) is a comprehensive account of mathematical modelling in population dynamics: a good elementary introduction is given in the textbook by Edelstein-Keshet (1988).