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1IntroductionAn increasing amount of study is being devoted to mathematical models which seek to capture some of the essential dynamical features of plant and animal populations. Some of these models describe specific systems in a very detailed way, and others deal with general questions in a relatively abstract fashion: all share the common purpose of helping to construct a broad theoretical framework within which to assemble an otherwise indigestible mass of field and laboratory observations.The present book aims to review and to draw together some of these theoretical insights, to show how they can shed light on empirical observations, and to examine some of the practical implications. In so doing, the book seeks to occupy a useful niche intermediate between the .^oiM^-^ compendious and general text (of which there are an increasing number of excellent examples) and the often highly technical journal and monograph literature on theoretical ecology (which many people will find impenetrable). The book is directed to an audience of upper level undergraduates, graduate students, or general readers with an educated interest in the discipline of ecology.Attention is focussed on the biological assumptions which underlie the various models, and on the way the consequent mathematical behaviour of the models explains aspects of the dynamics of populations or of entire communities. That is, the approach is descriptive, with emphasis on the biological inputs in construpting thg models, and on the emergent biological understanding. The in'terveriing mathematical details are, by and large, glossed over; this is a book for people who did not get beyond a freshman course or A levels in calculus. Those readers who dislike ex cathedra pronouncements, or who wish to savour the detailed mathematical development, will find signposts to guide them to the more technical literature. Other people may be content to follow the advice given by St Thomas Aquinas (concerning technical details of proofs of the existence of God): 'Truths which can be proved