Introduction

Abstract

AbstractChapter 1 presents a brief history of mathematical theory in ecology dealing with interspecific competition. It argues that competition is a key process in the dynamics of all ecological systems. The chapter then presents the original 2-species model of competition developed independently by Lotka and Volterra. The lack of resources in this model is argued to be a major shortcoming. The definition of a single resource is treated briefly. The more recent history of competition theory is outlined, beginning with a brief discussion of Robert MacArthur’s consumer–resource model. Following a hiatus of research on competition in the last two decades of the twentieth century, theoretical work has increased. However, much of this work has focused on classifying mechanisms of coexistence, rather than developing models that could help predict or understand changes in abundances. While some recent authors have explored models with resources, many have continued to explore models in which competition is modelled as a direct effect. Those who have included resources have most often assumed linear relationships for all of the component functions, such as resource per capita growth rate and consumer functional response. The chapter discusses reasons for this very narrow range of models, and some of its adverse effects on our current understanding. The final section classifies the chapters, and discusses the mathematical background required to understand them.