Niche Hierarchy. Structure, Organization and Assembly in Natural Systems

Contents......Page 3
Foreword......Page 5
Foreword......Page 7
Abstract......Page 11
Preface......Page 10
1.1 Introduction......Page 13
1.2 Menu......Page 14
2.1 A Problem of Incompatible Dimensions......Page 18
2.2 Handling the Dimensionality Problem......Page 19
2.2.1 The Consumer Overlap Graph......Page 20
2.2.2 The Resource Graph: A Tinker Toy Model......Page 23
2.2.3 Species as Convex Polyhedra......Page 25
2.3 Trophic Equivalence......Page 28
Summary......Page 29
3 Holes in Niche Space......Page 31
3.1.1 Standard Homology for KC(R; λ−1)......Page 34
3.1.2 Computing β1(K) from Gc(R; λ−1)......Page 40
3.2.1 Results......Page 43
3.2.2 Statistical Significance of Results......Page 48
3.2.3 Interpretation of Results......Page 51
3.3 Robustness: Do Holes Appear Across Variable Thresholds?......Page 56
3.3.1 Cody’s Community Matrices......Page 57
3.3.2 Quasiconvexity in the Niche......Page 62
Summary......Page 64
4 Intervality - Tip of an Iceberg......Page 66
4.1 Necessary and Sufficient Conditions for Intervality......Page 67
4.2 Rigid Circuits: A Robust Property of Real Communities......Page 70
4.3 Holes, Rigidity, and Intervality......Page 73
4.4 Assembly Rules Implied by the Rigid Circuit Property in GR(C; λ)......Page 79
4.5 Assembly and Holes in KC(R; λ−1)......Page 84
4.6 Assembly and Intervality......Page 85
Summary......Page 86
5 Hierarchical Organization in the Niche......Page 87
5.1.1 Trees: A Characterization of Rigid Circuit Graphs......Page 88
5.2 Hierarchy in Real Communities......Page 91
5.3 Functional Hierarchy......Page 95
5.3.1 Compatibility Between Structural and Functional Portraits......Page 96
Summary......Page 99
6 Dynamic Linkages & Topological Patterns......Page 100
6.1 Triangulation and Stability: A Simple Example......Page 102
6.2 Triangulation and Stability: Dynamic Selection......Page 105
6.3.1 Structural Hierarchy......Page 111
6.3.2 Functional Hierarchy......Page 114
Summary......Page 115
7 Hierarchies of Abundance......Page 116
7.1 The Niche Hierarchy Model......Page 117
7.2.2 A Deductive Approach......Page 122
7.2.3 A Direct Approach......Page 126
7.2.4 Implications of a Correspondence Between Organization and Abundance......Page 128
7.3.1 Moments of Species Abundance Distributions......Page 131
7.3.2 Abundance Patterns Implied by Dynamic Models......Page 132
Summary......Page 133
Summary of Corrections for Briand (1982) Webs......Page 134
Niche Overlap Graph Gr(C; λ), Resource Graph Gc(R; λ-1) & Food Web Matrix for Corrected Briand Communities......Page 135
Niche Overlap Graphs at various Thresholds for Cody’s (1972) Bird Communities......Page 178
Moments of Particle Size Distributions under Sequential Breakage......Page 187
Refs......Page 192