Niche Hierarchy: Structure, Organization, and Assembly in Natural Systems

by George Sugihara, Jordi Bascompte (Preface by), Robert G. May (Foreword by)

Overview

Written by Dr. George Sugihara, this pioneering work represents a unifying synthesis to tie together four disparate areas of ecology: 1) topological structure of food webs; 2) ecosystem dynamics; 3) ecosystem/food web assembly; and 4) universal patterns of species abundance. Based on the premise that deep general principles are likely to be associated with widely observed empirical regularities, it is organized around uncovering and explaining such patterns for each of the four research areas, and then showing how they interrelate. While this book has historic interest, it is even more relevant today in its findings and overall scope.

Product Details

ISBN-13:	9781604271287
Publisher:	Ross, J. Publishing, Incorporated
Publication date:	12/01/2016
Pages:	208
Product dimensions:	6.00(w) x 9.00(h) x 0.70(d)

About the Author

George Sugihara is a professor of biological oceanography and a member of the Physical Oceanography Research Division at Scripps Institution of Oceanography, UC San Diego, where he is currently the inaugural holder of the McQuown Chair in Natural Science. Dr. Sugihara's research into complex systems and nonlinear forecasting has led to diverse collaborations across academic disciplines as well as with governmental and industrial partners. Part of his current research at Scripps seeks solutions to environmental problems through a combination of scientific and financial market innovations, two areas that reflect his background as a scientist and Managing Director for Deutsche Bank. Sugihara conducts fundamental research on a variety of natural science areas including ecology, neuroscience, gene expression, atmospheric and climate science, and is currently championing a method for addressing Berkeley's age-old dilemma of detecting causation (versus correlation) in time-series data. Prior to joining Scripps, Sugihara was concurrently the Wigner Prize Fellow at Oak Ridge National Laboratory and associate professor of Mathematics at the University of Tennessee. He has been a visiting professor at Cornell University, Imperial College London, Kyoto University, and the Tokyo Institute of Technology. He held the UC San Diego John Dove Isaacs Chair at Scripps Oceanography, and was a visiting fellow at Merton College, Oxford University. He is the recipient of several national and international awards, and was a member of the National Academy of Sciences Board on Mathematical Sciences and its Applications, a National Research Council advisory board that advises government agencies, and guides the nation's mathematics agenda to better serve national needs. Sugihara received an M.S. in biology and a Ph.D. in mathematical biology, both from Princeton University, where he received the Ogden Porter Jabocbus Prize, Princeton's highest academic award given by the Graduate School.

Table of Contents

Foreward Lord May v

Foreward Jordi Bascompte, Ph.D vii

Abstract xi

Preface x

Acknowledgments xiii

Chapter 1 The Beginning 1

1.1 Introduction 1

1.2 Menu 2

Chapter 2 Characterizing the Niche 7

2.1 A Problem of Incompatible Dimensions 7

2.2 Handling the Dimensionality Problem 8

2.2.1 The Consumer Overlap Graph 9

2.2.2 The Resource Graph: A Tinker Toy Model 12

2.2.3 Species as Convex Polyhedra 14

2.3 Trophic Equivalence 17

Summary 18

Chapter 3 Holes in Niche Space 21

3.1 The Mathematical Structure of Holes 24

3.1.1 Standard Homology for K_c(R;λ^-1) 24

3.1.2 Computing β₁(K) from G_c(R;λ^-1) 30

3.2 Homology of Real Food Webs 33

3.2.1 Results 33

3.2.2 Statistical Significance of Results 38

3.2.3 Interpretation of Results 41

3.3 Robustness: Do Holes Appear Across Variable Thresholds? 46

3.3.1 Cody's Community Matrices 47

3.3.2 Quasiconvexity in the Niche 52

Summary 54

Chapter 4 Intervality: Tip of an Iceberg 57

4.1 Necessary and Sufficient Conditions for Intervality 58

4.2 Rigid Circuits: A Robust Property of Real Communities 61

4.3 Holes, Rigidity, and Intervality 64

4.4 Assembly Rules Implied by the Rigid Circuit Property in G_R(C;λ) 70

4.5 Assembly and Holes in K_C(R;λ^-1) 75

4.6 Assembly and Intervality 76

Summary 77

Chapter 5 Hierarchical Organization in the Niche 79

5.1 Structural Hierarchy 80

5.1.1 Trees: A Characterization of Rigid Circuit Graphs 80

5.2 Hierarchy in Real Communities 83

5.3 Functional Hierarchy 87

5.3.1 Compatibility Between Structural and Functional Portraits 88

Summary 91

Chapter 6 Dynamic Linkages and Topological Patterns 93

6.1 Triangulation and Stability: A Simple Example 95

6.2 Triangulation and Stability: Dynamic Selection 98

6.3 Hierarchy and Stability 104

6.3.1 Structural Hierarchy 104

6.3.2 Functional Hierarchy 107

Summary 108

Chapter 7 Hierarchies of Abundance 109

7.1 The Niche Hierarchy Model 110

7.2 Supporting Evidence for Niche Hierarchy 115

7.2.1 The Geometric Series and Broken Stick Patterns as Special Cases 115

7.2.2 A Deductive Approach 115

7.2.3 A Direct Approach 119

7.2.4 Implications of a Correspondence Between Organization and Abundance 123

7.3 Related Results 124

7.3.1 Moments of Species Abundance Distributions 124

7.3.2 Abundance Patterns Implied by Dynamic Models 125

Summary 126

Appendix A 127

Appendix B 129

Appendix C 173

Appendix D 183

References 189