Understanding Complex Ecosystem Dynamics

Description

Understanding Complex Ecosystem Dynamics: A Systems and Engineering Perspective takes a fresh, interdisciplinary perspective on complex system dynamics, beginning with a discussion of relevant systems and engineering skills and practices, including an explanation of the systems approach and its major elements. From this perspective, the author formulates an ecosystem dynamics functionality-based framework to guide ecological investigations.

Next, because complex system theory (across many subject matter areas) is crucial to the work of this book, relevant network theory, nonlinear dynamics theory, cellular automata theory, and roughness (fractal) theory is covered in some detail. This material serves as an important resource as the book proceeds. In the context of all of the foregoing discussion and investigation, a view of the characteristics of ecological network dynamics is constructed. This view, in turn, is the basis for the central hypothesis of the book, i.e., ecological networks are ever-changing networks with propagation dynamics that are punctuated, local-to-global, and perhaps most importantly fractal. To analyze and fully test this hypothesis, an innovative ecological network dynamics model is defined, designed, and developed. The modeling approach, which seeks to emulate features of real-world ecological networks, does not make a priori assumptions about ecological network dynamics, but rather lets the dynamics develop as the model simulation runs. Model analysis results corroborate the central hypothesis. Additional important insights and principles are suggested by the model analysis results and by the other supporting investigations of this book – and can serve as a basis for going-forward complex system dynamics research, not only for ecological systems but for complex systems in general.

Provides a fresh interdisciplinary perspective, offers a broad integrated development, and contains many new ideas
Clearly explains the elements of the systems approach and applies them throughout the book
Takes on the challenging and open issues of complex system network dynamics
Develops and utilizes a new, innovative ecosystem dynamics modeling approach
Contains over 135 graphic illustrations to help the reader visualize and understand important concepts

Front Cover 2
Understanding Complex Ecosystem Dynamics: A Systems and Engineering Perspective 5
Copyright 6
Contents 7
Preface 11
Introduction 15
- ``Map´´ of the Book 15
  - Part I. The Systems and Engineering Perspective 15
  - Part II. A Function-Structure-Process Framework for Ecological System Dynamics 16
  - Part III. Complex Systems Theory: Networks, Nonlinear Dynamics, Cellular Automata, and Fractals (Roughness) 16
  - Part V. Modeling Ecological Network Dynamics and the Generation and Analysis of Results 17
  - Part IV. A View of the Characteristics of Ecological Network Dynamics 17
  - Part VI. Pulling It All Together 18
  - Appendix 18
- A ``Fresh´´ Look at Complex System Dynamics 18

Front Cover 2
Understanding Complex Ecosystem Dynamics: A Systems and Engineering Perspective 5
Copyright 6
Contents 7
Preface 11
Introduction 15
- ``Map´´ of the Book 15
  - Part I. The Systems and Engineering Perspective 15
  - Part II. A Function-Structure-Process Framework for Ecological System Dynamics 16
  - Part III. Complex Systems Theory: Networks, Nonlinear Dynamics, Cellular Automata, and Fractals (Roughness) 16
  - Part V. Modeling Ecological Network Dynamics and the Generation and Analysis of Results 17
  - Part IV. A View of the Characteristics of Ecological Network Dynamics 17
  - Part VI. Pulling It All Together 18
  - Appendix 18
- A ``Fresh´´ Look at Complex System Dynamics 18
Part I: The Systems and Engineering Perspective 21
- Chapter 1: A Systems Engineers Perspective 23
  - 1.1. Introduction 23
  - 1.2. Definitions 24
  - 1.3. Systems Engineering Skills Framework 24
    - 1.3.1. Systems Engineering Domain 26
    - 1.3.2. Engineering Technical Methods 27
      - 1.3.2.1. Mathematical Methods 28
      - 1.3.2.2. Empirical Methods 31
    - 1.3.3. System Development Skills 32
      - 1.3.3.1. System Design 32
      - 1.3.3.2. System Modeling 34
      - 1.3.3.3. System Architecting 35
    - 1.3.4. Systems Thinking 35
    - 1.3.5. Communication Skills 36
  - 1.4. Technical Rationality and Reflective Rationality 37
- Chapter 2: More Views on Systems Thinking 41
  - 2.1. Origin and Evolution of Systems Thinking Movements 41
    - 2.1.1. Cybernetics 41
    - 2.1.2. General Systems Theory 42
    - 2.1.3. Related Efforts 44
      - 2.1.3.1. Isomorphies 44
      - 2.1.3.2. Systems Repertoire 45
      - 2.1.3.3. Patterns 45
    - 2.1.4. Assessment 46
  - 2.2. Weavers Ranges of System Complexity 47
  - 2.3. The Many Ways of Knowing 50
    - 2.3.1. Ancient and Contemporary Views 51
      - 2.3.1.1. Aristotelian View 51
      - 2.3.1.2. Contemporary Views 52
    - 2.3.2. A Synthesis 52
    - 2.3.3. The Ways of Knowing Are Complementary 54
    - 2.3.4. Additional Properties of the Ways of Knowing 60
      - 2.3.4.1. Objectivity and Subjectivity 60
      - 2.3.4.2. Evidence Requirement 61
    - 2.3.5. Integrating the Ways of Knowing 61
  - 2.4. A Debate on the Integration of the Sciences and the Humanities 62
    - 2.4.1. Discussion of Wilson's Position 64
    - 2.4.2. Discussion of Gould's Position 65
  - Chapter 3: The Major Elements of the Systems Approach 67
    - 3.1. A Blend of Synthesis and Analysis 67
      - 3.1.1. An Incremental, Cyclical, and Iterative Process 67
      - 3.1.2. Potential Problems with the Reductionist Approach 69
      - 3.1.3. More Views on Synthesis and Analysis 71
    - 3.2. Network Thinking 73
      - 3.2.1. West and East 73
      - 3.2.2. Network Thinking Trumps Node Thinking 74
      - 3.2.3. The Importance of Network Dynamics 75
        
        3.2.3.1. The Human Genome 75
        
        3.2.3.2. Node Replacement 76
      - 3.3. The Systems Triad 77
        
        3.3.1. Definition of Terms 77
        
        3.3.2. Function and Form 78
        
        3.3.3. Process-Over-Structure Flow 80
        
        3.3.4. New Perspective on Statics and Dynamics 82
      - Chapter 4: Reductionism and Information Loss 85
        
        4.1. Introduction 85
        
        4.2. Networks and Connections 87
        
        4.3. Short Paths and Power-Law Distributions 88
        
        4.3.1. Lévy Flights 88
        
        4.3.2. Foraging Ant Colonies 89
        
        4.4. Information Theory 90
        
        4.4.1. Conditional Entropy 92
        
        4.4.2. Joint Entropy 93
        
        4.4.3. Entropy ``Chain Rule´´ 93
        
        4.5. Information Loss from Broken Connections 93
      - Part II: A Function-Structure-Process Framework for Ecological System Dynamics 101
        
        Chapter 5: Overview of an Ecological System Dynamics Framework 103
        
        5.1. Two Essential Questions 103
        
        5.2. Developing the Framework 105
        
        5.3. The Three Core Functions of the Framework 107
        
        5.3.1. Self-organization 107
        
        5.3.2. Regulation/Adaptation and Propagation 109
        
        5.4. Self-organization and Thermodynamic Entropy in Ecological Systems 109
        
        5.4.1. The ``Revised´´ Second Law of Thermodynamics 110
        
        Chapter 6: Regulation/Adaptation: Control Aspects of Ecological Systems 113
        
        6.1. Introduction 113
        
        6.2. General Principles and Control of Human-Made Systems 114
        
        6.3. Control of Biological/Ecological Systems 115
        
        6.3.1. Biological Systems 117
        
        6.3.2. Ecological Systems 117
        
        6.4. Core Function Relationships and the Nature of the Resulting Dynamics 119
        
        6.4.1. The Regulation/Adaptation-to-Propagation Relationship 119
        
        6.4.1.1. Life as a Relaxation Phenomenon 119
        
        6.4.1.2. Local-to-Global Dynamics 120
        
        6.4.2. Fluctuating Dynamics 120
        
        Chapter 7: Evolution and Universal Development Concepts 123
        
        7.1. Evolution: Spatial and Temporal Perspectives 123
        
        7.2. Formulating an Evolution Process Model 124
        
        7.3. The Evolution Model as a Universal Development Model 128
        
        7.3.1. Human-Made System Design 129
        
        7.3.2. Social System Development 131
        
        7.3.3. Evolutionary Engineering 133
        
        7.3.4. The Evolution Model, the Scientific Method, and General Problem Solving 134
        
        7.3.5. Development of a Scientific Field 137
        
        7.4. Summary Observations and the Path Forward 140
        
        Part III: Complex Systems Theory: Networks, Nonlinear Dynamics, Cellular Automata, and Fractals (Roughness) 143
        
        Chapter 8: Network Theory: The Structure of Complex Networks 145
        
        8.1. Network Structure Concepts, Properties, and Characteristics 145
        
        8.1.1. Random and Nonrandom Networks 146
        
        8.1.2. Some Important Network Properties 148
        
        8.1.2.1. Path Length 149
        
        8.1.2.2. Clustering 150
        
        8.1.2.3. Node Degree 152
        
        8.1.3. Small-World Characteristics 154
        
        8.1.3.1. Commentary 156
        
        8.1.4. Scale-Free Characteristics 156
        
        8.2. Empirical View of Real-World Networks 159
        
        8.3. Theoretical View of Model Networks 164
        
        8.3.1. Poisson Random Graphs 165
        
        8.3.1.1. Poisson Degree Distribution 165
        
        8.3.1.2. Other Random Graph Properties 165
        
        8.3.2. Generalized Random Graphs and Scale-Free Networks 166
        
        8.3.3. The Small-World Network Model 168
        
        Chapter 9: Network Theory: The Dynamics of Complex Networks 171
        
        9.1. Introduction 171
        
        9.2. Scaling, Power Laws, and Fractals 172
        
        9.2.1. Relationships 172
        
        9.2.2. Fractals in Space and Time 173
        
        9.3. The Dynamics of Network Phase Transitions 174
        
        9.3.1. Network Transition from Unconnected to Connected 174
        
        9.3.2. Percolation in Networks 178
        
        9.3.3. The Self-Organized Criticality Hypothesis 181
        
        9.3.4. Other Topological Phase Transitions in Networks 182
        
        9.4. Network Dynamics: Processes Taking Place on Networks 185
        
        9.4.1. Epidemic Processes on Networks 185
        
        9.4.2. Network Failure Processes 186
        
        9.4.3. Macroevolution Processes 189
        
        9.4.3.2. Macroevolution Matrix Modeling 190
        
        9.4.3.1. Macroevolution as a Network Phenomenon 190
        
        9.4.4. Network Growth via Preferential Attachment 194
        
        9.5. Concluding Remarks 196
        
        Chapter 10: Fundamentals of Nonlinear Dynamics 197
        
        10.1. Introduction 197
        
        10.2. Fundamental Concepts 198
        
        10.2.1. Rate Equations 198
        
        10.2.3. Attractors 199
        
        10.2.2. State Space 199
        
        10.3. Starting Simple 200
        
        10.4. Types of Attractors 201
        
        10.5. Bifurcation and Complex Nonlinear Behavior 205
        
        10.5.1. Comments 207
        
        10.6. Unpredictability 208
        
        10.7. Universality 210
        
        Chapter 11: Cellular Automata Investigations and Emerging Complex System Principles 213
        
        11.1. Introduction 213
        
        11.2. Some Cellular Automata History 214
        
        11.3. Explicit Experimentation via Cellular Automata 215
        
        11.4. Simple Programs/Simple Rules and Highly Complex Behavior 216
        
        11.5. Cellular Automata Classes 218
        
        11.5.1. Information Handling and Communication 219
        
        11.5.2. Complexity and Simplicity 220
        
        11.5.3. Correspondence with Nonlinear Dynamics Attractors 220
        
        11.6. All Kinds of Systems 221
        
        11.6.1. Beyond Cellular Automata 221
        
        11.6.2. Natural Systems 222
        
        11.7. A Computational View of Systems 223
        
        11.7.2. The Concept of Computational Universality 224
        
        11.7.1. Computational Framework for System Principles 224
        
        11.7.3. Computational Universality and Cellular Automata 225
        
        11.7.4. Additional Implications of Computational Universality 226
        
        11.8. The Principle of Computational Equivalence 227
        
        11.8.1. Computational Properties of Complex Systems 228
        
        11.9. Summary of My Perspectives on these Complex System Principles 230
        
        11.9.1. The Principle of Computational Equivalence and the Mind/Brain System 231
        
        11.9.2. Wolfram's insights 232
        
        Chapter 12: Fractals: The Theory of Roughness 233
        
        12.1. Introduction 233
        
        12.2. Fractals and Roughness 234
        
        12.3. Fractal Geometry 235
        
        12.3.1. Fractal Dimension 235
        
        12.3.2. Human-Generated and Natural Fractal Objects 237
        
        12.3.2.1. Human-Generated Fractal Objects 237
        
        12.3.2.3. Natural Fractal Objects 239
        
        12.3.2.2. Iterated Function Systems 239
        
        12.3.2.4. Fractal Objects and Power Laws 242
        
        12.3.3. Fractal Geometry of Networks 243
        
        12.3.3.1. Description of the Box Covering Method 245
        
        12.4. The Mandelbrot Set 247
        
        12.5. My Perspectives 250
        
        12.5.1. Simple Rules, Complexity, and Fractals 250
        
        12.5.2. On to Ecological Network Dynamics 251
        
        Part IV: A View of the Characteristics of Ecological Network Dynamics Based 253
        
        Chapter 13: Issues of Human Perception 255
        
        13.1. Introduction 255
        
        13.2. Is Reality Knowable? 256
        
        13.3. Limitations of Human Perception 258
        
        13.4. Roughness versus Smoothness 261
        
        13.4.1. The Typical Human Perceptual Domain 262
        
        13.4.2. Analysis of the Relationships Between Scale and Perception 263
        
        13.4.2.1. Perceptual Effects in Natural System Hierarchical Architecture 263
        
        13.4.2.2. Perceived Complexity versus Spatial Scale for Three Important System Categories 264
        
        13.5. Modeling and Human Perception 265
        
        13.5.1. Models are Simplifications 266
        
        13.5.2. Differential Equation Models and Steady State Behavior 268
        
        Chapter 14: The Nature of Order and Complexity in Ecological Systems 273
        
        14.1. Introduction 273
        
        14.2. Thinking about Order, Complexity, and Systems 274
        
        14.2.1. Nonlinear Dynamics Attractor Types 274
        
        14.2.2. Order, Complexity, and Weaver's Ranges 274
        
        14.2.3. Maximal Complexity and the Edge-of-Order Domain 277
        
        14.3. The Myth of Persistence 278
        
        14.4. Chance and Change: Probabilistic Aspects of Natural Systems 280
        
        14.5. Optimal or Good Enough? 282
        
        Chapter 15: Characteristics of Ecological Network Dynamics 285
        
        15.1. Introduction 285
        
        15.2. Flickering Networks 286
        
        15.3. Punctuated Dynamics 287
        
        15.3.1. Black Swans 289
        
        15.4. Fractal Behavior 291
        
        15.4.1. Two Types of Fractals 292
        
        15.4.2. Mathematical Representations of Process Fractals: Event Time Series and Event Distribution 293
        
        15.4.3. Mathematical Representations of Process Fractals: Frequency Spectrum 296
        
        15.4.4. Heart Rate Dynamics 300
        
        15.4.5. Cross-similarity 301
        
        15.4.6. Commentary 303
        
        15.5. Local-to-Global Interaction 305
        
        15.5.1. An Operational View 305
        
        15.5.2. Facilitators of Local-to-Global Interaction 306
        
        15.5.2.1. The Small-World Network Property 306
        
        15.5.2.2. The Network Critical Connectivity Property 308
        
        15.5.2.2.1. Random Network Unconnected-to-Connected Transition 308
        
        15.5.2.2.2. Lattice Network Percolation 310
        
        15.5.2.2.3. Boolean Network Investigations 311
        
        15.6. Indirect Effects 312
        
        15.6.1. Indirect Effects: Prominence or Dominance? 313
        
        15.7. The Characteristics Hypothesis 316
        
        Part V: Modeling Ecological Network Dynamics and the Generation and Analysis of Results 319
        
        Chapter 16: A New Approach to Modeling Ecological Network Dynamics 321
        
        16.1. Introduction 321
        
        16.2. Overview of Model Features 322
        
        Model feature summary list: 322
        
        Discussion of features: 322
        
        16.3. Cellular Automata Based Model 323
        
        16.4. Propagation Neighborhoods and Preferences 326
        
        16.5. Underlying Ecological Network Compartment Model 329
        
        16.5.1. Compartment-to-Node Transition 331
        
        16.5.2. Candidate and Operational Adjacency Matrices 332
        
        16.6. Simple Rules 332
        
        16.7. Summary of Analysis Requirements 333
        
        16.8. Comment on Intention 334
        
        Chapter 17: Model Software Design and Development 335
        
        17.1. Introduction 335
        
        17.2. Model Network Structure, Parameters, and Relationships 336
        
        17.3. Ecological Network Propagation Process 337
        
        17.3.1. Propagation Process Flow 337
        
        17.3.2. Implementing the Propagation Process 338
        
        17.3.2.3. Node Propagation Event Loop 339
        
        17.3.2.1. Time Step Loop 339
        
        17.3.2.2. Stage Loop 339
        
        17.4. Analysis Activities 341
        
        17.4.1. Network Operational Propagation Flow Analysis 341
        
        17.4.2. Network Propagation Event Analysis 342
        
        17.4.3. Path Length Analysis 343
        
        17.4.3.1. Path Length Calculations 343
        
        17.4.3.2. Integration Over Space and Time 345
        
        17.4.4. Indirect Effects Analysis 346
        
        17.4.4.1. Indirect Effects and Direct Effects Indicator Analysis 346
        
        17.4.4.2. Additional Analysis 349
        
        17.4.5. Network Connectivity Analysis 349
        
        17.4.5.1. Node Degree Analysis 349
        
        17.4.5.1.2. Per-Time-Step and Over-Time Cumulative Node Degree Distributions 350
        
        17.4.5.1.1. Integration over Space and Time 350
        
        17.4.5.2. Other Connectivity Considerations 351
        
        17.5. Graphics Generation 352
        
        17.6. A Note about Results 354
        
        Chapter 18: Ecological Network Dynamics Results 355
        
        18.1. Introduction 355
        
        18.2. Operational Propagation Flow Results 356
        
        18.2.1. Network Node-and-Link Propagation Flow Results 356
        
        18.2.2. Input/Output/Stock Histories 365
        
        18.3. Network Propagation Event Results 368
        
        18.4. Path Length Results 372
        
        18.5. Indirect Effects Results 377
        
        18.6. Network Connectivity Results 382
        
        Part VI: Pulling It All Together 391
        
        Chapter 19: An Increased Understanding of Complex System Dynamics 393
        
        19.1. Summary of the Work 393
        
        19.2. An Advantageous Perspective 395
        
        19.3. The Mechanism of Complexity 396
        
        19.3.2. Optimal vs. Adequate 397
        
        19.3.1. Probabilistic Context 397
        
        19.4. The Characteristics of Complex Ecosystem Dynamics 398
        
        19.4.1. Model Robustness 400
        
        19.4.2. Descriptive vs. Predictive Results 400
        
        19.5. Complex System Universal Behavior 401
        
        19.6. A Going-Forward Integrated View of Complex System Dynamics 403
        
        Appendix: Selections from the Dynamics Model Programming Code 407

Author's affiliation

William S. Yackinous: Retired Systems Engineer, Bell Labs, US

A Systems and Engineering Perspective

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