The Geometry of Ecological Interactions: Simplifying Spatial Complexity

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

• ISBN13: 9780521642941
• ISBN10: 0521642949
• Edition: 1st
• Format: Hardcover
• Copyright: 2000-07-03
• 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

Contributing Authors	xiii
Introduction	1	(6)
Richard Law
Ulf Dieckmann
Johan A.J. Metz
A Empirical and Statistical Background: A Plant Ecological Perspective	7	(82)
A Neighborhood View of Interactions among Individual Plants	11	(17)
Peter Stoll
Jacob Weiner
Introduction	11	(1)
Competition Mechanisms	12	(6)
Moving from the Population to the Individual Level	18	(1)
What is a Plant's Neighborhood?	19	(5)
Challenges for a Neighborhood Perspective of Plant Interactions	24	(2)
Suggestions for Modelers	26	(2)
Spatial Interactions among Grassland Plant Populations	28	(20)
Jonathan Silvertown
J. Bastow Wilson
Introduction	28	(1)
Methods of Measuring Competition in the Field	29	(3)
Results of Field Experiments	32	(6)
Competition Matrices	38	(4)
Community Consequences of Spatial Interactions	42	(4)
Concluding Comments	46	(2)
Spatio-temporal Patterns in Grassland Communities	48	(17)
Tomas Herben
Heinjo J. During
Richard Law
Introduction	48	(1)
Spatio-temporal Patterns in Plant Communities	48	(4)
Externally versus Internally Generated Spatial Patterns	52	(2)
Concepts in Spatio-temporal Processes in Plant Communities	54	(6)
Ergodic and Non-ergodic Communities	60	(4)
Concluding Comments	64	(1)
Statistical Modeling and Analysis of Spatial Patterns	65	(24)
David R. Cox
Valerie Isham
Paul Northrop
Introduction	65	(1)
Descriptive Analysis	66	(4)
Stochastic Models	70	(10)
Model Fitting	80	(8)
Concluding Comments	88	(1)
B When the Mean-field Approximation Breaks Down	89	(114)
Grid-based Models as Tools for Ecological Research	94	(22)
Christian Wissel
Introduction	94	(1)
Grid-based Simulation Models	95	(2)
Spread and Control of Rabies	97	(7)
Dynamics of a Dwarf Shrub Community	104	(5)
A Generic Forest Fire Model	109	(5)
Concluding Comments	114	(2)
Coexistence of Replicators in Prebiotic Evolution	116	(19)
Tamas Czaran
Eors Szathmary
Introduction	116	(3)
Metabolic Replication: A Cellular Automaton Model	119	(4)
The Phenomenology of Coexistence	123	(4)
Spatial Pattern and the ``Advantage of the Rare'' Effect	127	(2)
Resistance to Parasites and the Evolution of Community Size	129	(4)
Toward a Dynamical Theory of Surface Metabolism	133	(2)
Games on Grids	135	(16)
Martin A. Nowak
Karl Sigmund
Introduction	135	(2)
One-round Games	137	(8)
Repeated Games	145	(4)
Extensions and Related Work	149	(1)
Concluding Comments	150	(1)
The Interplay between Reaction and Diffusion	151	(20)
Mikael B. Cronhjort
Introduction	151	(2)
The Models: Cellular Automata Versus Partial Differential Equations	153	(6)
Spiral and Scroll Ring Patterns	159	(4)
Cluster Dynamics	163	(6)
Concluding Comments	169	(2)
Spirals and Spots: Novel Evolutionary Phenomena through Spatial Self-structuring	171	(12)
Maarten C. Boerlijst
Introduction	171	(2)
A Spatial Hypercycle Model	173	(1)
Spirals and Spots	174	(1)
Local Versus Global Extinction	175	(3)
Resistance to Parasites	178	(2)
Concluding Comments	180	(3)
The Role of Space in Reducing Predator-Prey Cycles	183	(20)
Vincent A. A. Jansen
Andre M. de Roos
Introduction	183	(1)
Individual-based Predator-Prey Models	184	(3)
A Deterministic Model of Two Coupled Local Populations	187	(6)
Larger Spatial Domains	193	(3)
The Spatial Rosenzweig-Mac Arthur Model	196	(3)
Concluding Comments	199	(1)
Stability Analysis of a Multi-patch System	200	(3)
C Simplifying Spatial Complexity: Examples	203	(134)
Spatial Scales and Low-dimensional Deterministic Dynamics	209	(18)
Howard B. Wilson
Matthew J. Keeling
Introduction	209	(1)
Two Models from Evolutionary Ecology	210	(3)
Identifying Spatial Scales	213	(6)
Dynamics, Determinism, and Dimensionality	219	(6)
Concluding Comments	225	(1)
Singular Value Decomposition	225	(2)
Lattice Models and Pair Approximation in Ecology	227	(25)
Yoh Iwasa
Introduction	227	(1)
Plants Reproducing by Seed and Clonal Growth	228	(8)
Forest Gaps	236	(7)
Colicin-producing and Colicin-sensitive Bacteria	243	(4)
Limitations, Extensions, and Further Applications	247	(5)
Moment Approximations of Individual-based Models	252	(19)
Richard Law
Ulf Dieckmann
Introduction	252	(1)
Spatial Patterns and Spatial Moments	253	(3)
Extracting the Ecological Signal from Stochastic Realizations	256	(5)
Qualitative Dependencies in a Spatial Logistic Equation	261	(6)
Exploration of Parameter Space	267	(2)
Concluding Comments	269	(2)
Evolutionary Dynamics in Spatial Host-Parasite Systems	271	(21)
Matthew J. Keeling
Introduction	271	(1)
Dynamics of the Spatial Host-Parasite Model	272	(7)
A Difference Equation for the Dynamics of Local Configurations	279	(3)
Evolution to Critical Transmissibility	282	(6)
Concluding Comments	288	(1)
Mathematical Specification of the PATCH Model	289	(3)
Foci, Small and Large: A Specific Class of Biological Invasion	292	(26)
Jan-Carel Zadoks
Introduction	292	(1)
Epidemic Orders	293	(5)
A Theory of Foci	298	(14)
Generalizations	312	(3)
Concluding Comments	315	(1)
Quantitative Applications of Models for Spatial Population Expansion	315	(3)
Johan A. J. Metz)
Wave Patterns in Spatial Games and the Evolution of Cooperation	318	(19)
Regis Ferriere
Richard E. Michod
Introduction	318	(1)
Invasion in Time-and Space-continuous Games	319	(4)
Invasion of Tit For Tat in Games with Time-limited Memory	323	(6)
Invasion of Tit For Tat in Games with Space-limited Memory	329	(3)
Concluding Comments	332	(5)
D Simplifying Spatial Complexity: Techniques	337	(180)
Pair Approximations for Lattice-based Ecological Models	341	(18)
Kazunori Sato
Yoh Iwasa
Introduction	341	(3)
Pair Approximation	344	(5)
Improved Pair Approximation	349	(6)
Improved Pair Approximation with Variable Discounting	355	(2)
Concluding Comments	357	(2)
Pair Approximations for Different Spatial Geometries	359	(29)
Minus van Baalen
Introduction	359	(5)
The Dynamics of Pair Events	364	(4)
Average Event Rates	368	(4)
Pair Approximations for Special Geometries	372	(7)
Pair Approximations versus Explicit Simulations	379	(3)
Invasion Dynamics	382	(3)
Concluding Comments	385	(3)
Moment Methods for Ecological Processes in Continuous Space	388	(24)
Benjamin M. Bolker
Stephen W. Pacala
Simon A. Levin
Introduction	388	(1)
Moment Methods	389	(2)
A Spatial Logistic Model	391	(9)
A Spatial Competition Model	400	(3)
Extensions and Related Work	403	(2)
Concluding Comments	405	(1)
Mean Equation	406	(2)
Covariance Equation	408	(1)
Analyzing the One-species System	409	(1)
Analyzing the Two-species System	410	(2)
Relaxation Projections and the Method of Moments	412	(44)
Ulf Dieckmann
Richard Law
Introduction	412	(6)
Individual-based Dynamics in Continuous Space	418	(7)
Dynamics of Correlation Densities	425	(13)
Moment Closures and their Performance	438	(9)
Further Developments and Extensions	447	(5)
Derivation of Pair Dynamics	452	(4)
Methods for Reaction-Diffusion Models	456	(26)
Vivian Hutson
Glenn T. Vickers
Introduction	456	(3)
Continuous Models	459	(7)
Linearized Stability and the Turing Bifurcation	466	(5)
Comparison Methods	471	(4)
Traveling Waves	475	(4)
The Evolution of Diffusion	479	(2)
Concluding Comments	481	(1)
The Dynamics of Invasion Waves	482	(31)
Johan A. J. Metz
Denis Mollison
Frank van den Bosch
Introduction	482	(1)
Relative Scales of the Process Components	483	(2)
Independent Spread in Homogeneous Space: A Natural Gauging Point	485	(12)
Complications	497	(7)
The Link with Reaction-Diffusion Models	504	(3)
Dispersal on Different Scales	507	(5)
Concluding Comments	512	(1)
Epilogue	513	(4)
Johan A. J. Metz
Ulf Dieckmann
Richard Law
References	517	(36)
Index	553