The Geometry of Ecological Interactions
Simplifying Spatial Complexity

Provides introduction to exciting new areas of spatial ecological theory, simplifying spatial complexity.

Ulf Dieckmann (Edited by), Richard Law (Edited by), Johan A. J. Metz (Edited by)

9780521022095, Cambridge University Press

Paperback / softback, published 3 November 2005

580 pages, 148 b/w illus. 13 tables
23 x 15.3 x 3.4 cm, 0.871 kg

'… a valuable text for graduate students and researchers in ecology …'. Monatshefte für Mathematik

The field of theoretical ecology has expanded dramatically in the last few years. This volume gives detailed coverage of the main developing areas in spatial ecological theory, and is written by world experts in the field. Integrating the perspective from field ecology with novel methods for simplifying spatial complexity, it offers a didactical treatment with a gradual increase in mathematical sophistication from beginning to end. In addition, the volume features introductions to those fundamental phenomena in spatial ecology where emerging spatial patterns influence ecological outcomes quantitatively. An appreciation of the consequences of this is required if ecological theory is to move on in the 21st century. Written for reseachers and graduate students in theoretical, evolutionary and spatial ecology, applied mathematics and spatial statistics, it will be seen as a ground breaking treatment of modern spatial ecological theory.

1. Introduction Richard Law, Ulf Dieckmann and J. A. J. Metz
Part I. Empirical and Statistical Background: 2. A neighbourhood view of interactions among individual plants Peter Stoll and Jacob Weiner
3. Spatial interactions among grassland plant populations Jonathan Silvertown and Bastow Wilson
4. Spatio-temporal patterns in grassland communities Tomás Herben, Heinjo During and Richard Law
5. Statistical modelling and analysis of spatial patterns David Cox, Valerie Isham and Paul Northrop
Part II. When the Mean-Field Approximation Breaks Down: 6. Grid-based models as tools for ecological research Christian Wissel
7. Coexistence of replicators in prebiotic evolution Tamas Czárán and Eörs Szathmáry
8. Games on grids Martin Nowak and Karl Sigmund
9. The interplay between reaction and diffusion Mikael Cronhjort
10. Spirals and spots: novel evolutionary phenomena through spatial self-structuring Maarten Boerlijst
11. The role of space in reducing predator-prey cycles Vincent Jansen and André de Roos
Part III. Simplifying Spatial Complexity: Examples: 12. Spatial scales and low-dimensional deterministic dynamics Howard Wilson and Matthew Keeling
13. Lattice models and pair-approximation in ecology Yoh Iwasa
14. Moment approximations of individual-based models Richard Law and Ulf Dieckmann
15. Evolutionary dynamics in spatial host-pathogen systems Matthew Keeling
16. Foci, small and large: a specific class of biological invasion Jan-Carel Zadoks
17. Wave patterns in spatial games and the evolution of cooperation Régis Ferriere and Rick Michod
Part IV. Simplifying Spatial Complexity: Techniques: 18. Pair approximations for lattice-based ecological models Kazunori Sato and Yoh Iwasa
19. Pair approximations for different spatial geometries Minus van Baalen
20. Moment methods for ecological processes in continuous space Benjamin Bolker, Steven Pacala and Simon Levin
21. Relaxation projections and the method of moments Ulf Dieckmann
22. Methods for reaction-diffusion models Vivian Hutson and Glen Vickers
23. The dynamics of invasion waves Johan A. J. Metz, Denis Mollison and Frank van den Bosch
24 Epilogue Johan A. J. Metz, Ulf Dieckmann and Richard Law
References
Index.

Subject Areas: Animal behaviour [PSVP], Ecological science, the Biosphere [PSAF], Mathematical modelling [PBWH]