The Geometry of Ecological Interactions: Simplifying Spatial Complexity

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

• ISBN13: 9780521022095
• ISBN10: 0521022096
• Format: Paperback
• Copyright: 2005-11-03
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

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 Tomá

s 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 Czá

rá

n and Eö

rs Szathmá

ry

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 Ré

gis 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.