
Niche Hierarchy: Structure, Organization, and Assembly in Natural Systems
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Content
- Front Cover
- Title Page
- Copyright
- Contents
- Foreward by Lord May
- Foreward by Jordi Bascompte, Ph.D
- Abstract
- Preface
- Acknowledgments
- Chapter 1: The Beginning
- 1.1 Introduction
- 1.2 Menu
- Chapter 2: Characterizing the Niche
- 2.1 A Problem of Incompatible Dimensions
- 2.2 Handling the Dimensionality Problem
- 2.2.1 The Consumer Overlap Graph
- 2.2.2 The Resource Graph: A Tinker Toy Model
- 2.2.3 Species as Convex Polyhedra
- 2.3 Trophic Equivalence
- Summary
- Chapter 3: Holes in Niche Space
- 3.1 The Mathematical Structure of Holes
- 3.1.1 Standard Homology for KC(R
- ?-1)
- 3.1.2 Computing ß1(K) from Gc(R
- ?-1)
- 3.2 Homology of Real Food Webs
- 3.2.1 Results
- 3.2.2 Statistical Significance of Results
- 3.2.3 Interpretation of Results
- 3.3 Robustness: Do Holes Appear Across Variable Thresholds?
- 3.3.1 Cody's Community Matrices
- 3.3.2 Quasiconvexity in the Niche
- Summary
- Chapter 4: Intervality: Tip of an Iceberg
- 4.1 Necessary and Sufficient Conditions for Intervality
- 4.2 Rigid Circuits: A Robust Property of Real Communities
- 4.3 Holes, Rigidity, and Intervality
- 4.4 Assembly Rules Implied by the Rigid Circuit Property in GR(C
- ?)
- 4.5 Assembly and Holes in KC(R
- ?-1)
- 4.6 Assembly and Intervality
- Summary
- Chapter 5: Hierarchical Organization in the Niche
- 5.1 Structural Hierarchy
- 5.1.1 Trees: A Characterization of Rigid Circuit Graphs
- 5.2 Hierarchy in Real Communities
- 5.3 Functional Hierarchy
- 5.3.1 Compatibility Between Structural and Functional Portraits
- Summary
- Chapter 6: Dynamic Linkages and Topological Patterns
- 6.1 Triangulation and Stability: A Simple Example
- 6.2 Triangulation and Stability: Dynamic Selection
- 6.3 Hierarchy and Stability
- 6.3.1 Structural Hierarchy
- 6.3.2 Functional Hierarchy
- Summary
- Chapter 7: Hierarchies of Abundance
- 7.1 The Niche Hierarchy Model
- 7.2 Supporting Evidence for Niche Hierarchy
- 7.2.1 The Geometric Series and Broken Stick Patterns as Special Cases
- 7.2.2 A Deductive Approach
- 7.2.3 A Direct Approach
- 7.2.4 Implications of a Correspondence Between Organization and Abundance
- 7.3 Related Results
- 7.3.1 Moments of Species Abundance Distributions
- 7.3.2 Abundance Patterns Implied by Dynamic Models
- Summary
- Appendix A
- Appendix B
- Appendix C
- Appendix D
- References
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