Necessary background and a look ahead
This book does not attempt to cover a large fraction of the mathematical models and methods that have been used to study competition. Rather it is an attempt to find ways to restructure the theoretical work being done on competition so that it is more likely to produce an empirically useful body of predictions and explanations.
This involves mathematics, but all of the arguments are illustrated using the mathematically simple framework of ordinary differential equation models of homogeneous populations, and the examples all involve six or fewer species. (Models that include space are considered, but, in these cases, the dynamics within a patch are based on homogeneous populations that are well-mixed within the patch.)While the book does not employ any advanced mathematics, some familiarity with differential equation models in ecology is assumed. Case (2000) or Otto and Day (2007) would provide more than enough background. The recent article by Grainger et al. (2022) describes most of the techniques used here. Some of the chapters focus more on history and philosophy than on specific models (Chapters 2, 3, 4, and 12). Others present fairly detailed analyses of simple models with resources, most of which were initially explored prior to this century (Chapters 5 and 6). Chapter 7 contains the main treatment of empirical work (and one model). Chapters 8 and 9 describe new analyses of models with seasonal variation in conditions, and they contain a large amount of numerical results. Chapters 9, 10, and 11 are broad reviews of subfields within competition theory, and Chapter 12 provides an overview.