Theoretical Systems Ecology

Advances and Case Studies

1st Edition - January 28, 1979
Author: Efraim Halfon
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 4 6 9 2 - 0

Theoretical Systems Ecology: Advances and Case Studies aims to relate systems ecology theory to theoretical systems ecologists and other theoreticians in systems science. The main… Read more

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Theoretical Systems Ecology: Advances and Case Studies aims to relate systems ecology theory to theoretical systems ecologists and other theoreticians in systems science. The main language of systems theory is mathematics. This book somewhat simplifies concepts, advances, and developments of the field to non-mathematicians who lack background in some aspects of systems ecology. It presents examples after every chapter that shows the application of theory to the development and analysis of models. This book generally focuses on three problems. The first problem is the selection of components found in the system model. The definition of the relationships and interactions between the system variables is another concern of this book. It also looks into the model analysis. These problems are thoroughly discussed in each section of the book. The theory of modeling, formalisms, classes, and properties of models are covered in the first two sections of this book. A whole section in this book is dedicated to Systems Identification and deals mostly with the problem of extracting information from data. Other sections cover model analysis with focus on trends in some aspects, such as stability and control theory.

List of Contributors

Preface

Preview: Theory in Ecosystem Analysis

1. Introduction

2. Aggregation and Organization

3. Model Structures, Formalisms, and Theory of Modeling

4. System Identification

5. Model Analysis, Control Theory, and Stability

6. Outlook

References

Part I Aggregation and Organization

Chapter 1 Multilevel Multiformalism Modeling: An Ecosystem Example

1. Introduction

2. The Ecosystem: Questions of Interest and Models

3. Organization of Questions and Models

4. Experimental Frames

5. Constructed Models

6. Organization of Models

7. Applicability of Frames to Models

8. Summary

9. Discussion

Appendix: Some Results on Estimated Parameters and Model Cross Comparison

References

Chapter 2 Concerning Aggregation in Ecosystem Modeling

1. Introduction

2. Modeling: General

3. Modeling: Specific

4. The Aggregation Model

5. Concluding Remarks

Appendix

References

Chapter 3 Use of First-Order Analysis in Estimating Mass Balance Errors and Planning

Sampling Activities

1. Introduction

2. First-Order Analysis

3. Results

4. Applications to Experimental Design

5. Summary

Appendix: Notation

References

Part II Model Structures, Formalisms, and Theory of Modeling

Chapter 4 Prediction, Chaos, and Ecological Perspective

1. Introduction

2. Determinism and Chaos

3. Ecological Perspective

4. Summary

References

Chapter 5 Hierarchical Organization of Ecosystems

1. Introduction

2. Definition of Hierarchy

3. The Hierarchical Organization of Nature

4. Hierarchical Levels of Ecological Interest

5. Application of Hierarchy Theory to Ecosystems

References

Chapter 6 Hierarchical Adaptability Theory and Its Cross-Correlation with Dynamical Ecological Models

1. Introduction

2. Review of Adaptability Theory

3. Hierarchical Adaptability Theory

4. Cross-Correlation with Dynamical Ecological Models

5. Conclusion

References

Chapter 7 Structure and Stability of Model Ecosystems

1. Introduction

2. System Structure

3. Partitions and Condensations

4. Vulnerability of Structure

5. Vulnerability of Stability

6. Conclusion

References

Chapter 8 Systems Approach to Continental Shelf Ecosystems

1. Introduction

2. Causal Theory of Environment

3. Causal Analysis of Ecosystems

4. Flow Analysis of the Ross Sea Pelagic Ecosystem

5. Summary

References

Chapter 9 A Framework for Dynamical System Models: Cause-Effect Relationships and State Representations

1. Introduction

2. Input-Output System

3. Causality

4. State

5. Discussion of Ecological Examples

References

Part III System Identification

Chapter 10 Structural Identifiability of Linear Compartmental Models

1. Introduction

2. Linear Time-Invariant Compartmental Models

3. The Problem of Structural Identifiability

4. Structural Properties Related to Identifiability

5. The Analysis of Structural Identifiability

6. Examples and Conclusions

References

Chapter 11 Model Structure Identification from Experimental Data

1. Introduction

2. System Identification: A Brief Review

3. Model Structure Identification: Black Box Models

4. Model Structure Identification: Internally Descriptive Models

5. Conclusions

References

Chapter 12 Computer-Aided Systems Modeling

1. Introduction

2. Relevant Concepts

3. Systems Modeling

4. Examples of Systems Modeling in Ecology

5. Conclusions

References

Chapter 13 Identification of the Mathematical Model of a Complex System by the Self-Organization Method

1. Introduction

2. Present State of the Theory of Computer-Aided Self-Organization of Mathematical Models

3. Computer-Aided Self-Organization of Models

4. Discovery of Laws with the Aid of GMDH

5. Application of GMDH to Environmental Problems

6. Conclusions

References

Part IV Model Analysis, Control Theory, and Stability

Chapter 14 An Analysis of Turnover Times in a Lake Ecosystem and Some Implications for System Properties

1. Introduction

2. Methods

3. Results

4. Discussion

5. Summary and Conclusions

References

Chapter 15 The Usefulness of Optimal Control Theory to Ecological Problem

1. Introduction

2. Discrete-Time Optimal Control

3. Continuous-Time Optimal Control

4. Conclusions

References

Chapter 16 Toward Optimal Impulsive Control of Agroecosystems

1. Introduction

2. Optimal Single-Impulse Control of S-Shaped Growth

3. Numerical Experiments

4. Comments on the Optimal Impulse Control of J-Shaped Growth

5. Concluding Remarks

References

Chapter 17 Hierarchical Methods in River Pollution Control

1. Introduction

2. Problem Formulation

3. The Three-Level Method of Tamura

4. The Time Delay Algorithm of Tamura

5. The Interaction Prediction Approach

6. River Pollution Control

7. Hierarchical Feedback Control for Linear Quadratic Problems

8. Extension to the Servomechanism Case

9. Conclusions

References

Chapter 18 Ecosystem Stability and the Distribution of Community Matrix Eigenvalues

1. Introduction

2. A Practical Measure of Stability

3. Analysis of the Stability Measure

4. Discussion

Appendix

References

Chapter 19 Robust Stability Concepts for Ecosystems Models

1. Introduction

2. Global and Finite Stability

3. Nonvulnerability

4. Sector Stability

5. Conclusion

References

Chapter 20 Stability of Holistic Ecosystem Models

1. Introduction

2. Holistic Ecosystem Modeling

3. Discussion

4. Conclusion

Appendix

References

Index