J. J. Kay, Ph.D Thesis

REFERENCE:

Kay, J, 1984, Self-Organization In Living Systems, Ph.D. Thesis, Deparment of Systems Design Engineering, University of Waterloo, Waterloo, Ontario, Canada

by: James J. Kay

"Let me state the lesson first... It is simply this: You cannot base a general mathematical theory on imprecisely defined concepts. You can make some progress that way; but sooner or later the theory is bound to dissolve in ambiguities which prevent you from extending it further. Failure to recognize this fact has another unfortunate consequence which is, in a practical sense, even more disastrous: Unless the conceptual problems of a field have been clearly resolved, you cannot say which mathematical problems are the relevant ones worth working on; and your efforts are more likely to be wasted. I believe that, in this century, thousands of man-years of our finest mathematical talent have been lost through failure to understand this simple principle of methodolgy;..."
E. T. Jaynes, 1967.

ABSTRACT A paradigm, based on far from equilibrium thermodynamics, is proposed for discussing self-organization in ecosystems. Central to this paradigm is the idea of an optimum operating point, the endpoint of succession and the furthest from equilibrium state which an ecosystem can reach in its environment. Ecosystem succession and stress response can be discussed in terms of the ability of the system to attain and maintain its optimum operating point. Some hypotheses concerning ecosystem development are presented.

Using the paradigm, information-theoretic measures of ecosystem structural self-organization are identified. Hypotheses concerning changes in these measures with succession are put forward. A number of examples of the use of these measures and tests of the hypotheses are discussed.

Some tentative discussion of the development of measures of functional self-organization using Prigogine's non-equilibrium thermodynamics and Jaynes' generalization of statistical mechanics is presented.

Chapters are being added as time permits. Chapters which are full of equations are being added last.

1. MOTIVATION AND INTRODUCTION                           1
(PDF file  54K)

2. SELF-ORGANIZATION AND THE THERMODYNAMICS OF LIVING SYSTEMS: A PARADIGM 11

2-1 Introduction, 11
2-2 Some Definitions, Concepts and Guiding Principles, 19
	2.2.1 The System Definition, 19
	2.2.2 Some Guiding Principles, 27
2-3 Current Investigations of Self-organization, 29
	2.3.1 Emergence of Stable Complex Organized Molecular structures, 30
	2.3.2 Neo-Darwinism, 48
	2.3.3 Definitions of Complexity, Organization, Order, Etc., 52
2-4 A Paradigm for Discussing Self-organization and Stress-response of Living Systems, 57
	2.4.1 Complexity, Order and Organization, 57
	2.4.2 The Forces Acting on Living Systems and their Implications, 65
	2.4.3 The Paradigm: Life as a Solution to aThermodynamic and Systems Problem, 79
	2.4.4 Toward a Scientific Theory of Self-organizaiton, 81
	2.4.5 Self-organization and Health, 88
2-5 Summary of the Paradigm, 100
2-6 What is to follow?, 105

3. INFORMATION THEORY MEASURES OF STRUCTURAL SELF-ORGANIZATION (PDF file 216K)

3-1 Introduction, 112
3-2 Review of Information Theory, 113
3-3 Examples: Application to Population Diversity Measures, 122
3-4 Measures of Food Web Structures, 131
	3.4.1 The Probability Distributions, 132
	3.4.2 The Measures, 143
	3.4.3 Comparison of the Measures and Hypotheses, 152
3-5 Structural Self-organization, 158
3-6 Measures of Resource Niche, 161
3-7 The Advantages of Using S and D, 172
Appendix 3-1  A Hypothetical Food Web, 184

4.HYPOTHESES CONCERNING STRUCTURAL SELF-    189
 ORGANIZATION
4-1 Self-organization and Stress-response Revisited, 189
4-2 Discussion of Rutledge, Atlan and Ulanowicz's Hypotheses, 193
4-3 Succession and S and D, 199
4-4 Movement to a New Optimum Operating Point and S and D, 202
4-5 Rutledge, Atlan, Ulanowicz Revisited, 203
4-6 Classifications of Stress and Avoidance of Catastrophes, 208
Appendix: Generation of Table 2, 217

5. THE USE OF S AND D: SOME EXAMPLES                   220
5-1 Static Examples, 221
	5.1.1 Odum (1981), 222
	5.1.2 Walsh (1981), 232
	5.1.3 Walter (1979), 241
	5.1.4 Wiegert and Wetzel (1979), 249
	5.1.5 Sorokin (1981), 251
	5.1.6 Browder (1981), 251
5-2 Some concluding remarks on the Static Models, 275
5-3 Comparing Different Values of S and D, 278
	5.3.1 Pelagic Ecosystem, Peruvian Upwelling. Sorokin (1981), 278
	5.3.2 A Salt Marsh-Tidal Creek Stressed by Hot Water Discharge
	from a Nuclear Power Plant 
	(Ulanowicz, 1983, 1980, Homer and Kemp, 1975), 295
	5.3.3 Some Observations, 303
5-4 Rutledge (1974), 317
	5.4.1 Simulation results, 317
	5.4.2 A Critique of Rutledge's Interpretation
of the Results, 327
	5.4.3 A Different Interpretation of the Results, 331
5-5 Concluding Comments, 335


6. TOWARDS MEASURES OF FUNCTIONAL ORGANIZATION        340
(PDF file 84K)  
6-1 The Issues, 340
6-2  Thermodynamics a la Jaynes, Tribus and Evans, 351
6-3 Statistical vs Physical laws of Thermodynamics, 358

7. CONCLUDING COMMENTS                                366

APPENDICES:

1: The Maximum Entropy and Minimum                      378
     Cross-Entropy Principles. (PDF file 80K)
2: Ecological Stability                                 401
3: Data Sources for Testing Structural Measures         416
4: Organization, System's Goals, and                    424
Driving Forces
5: Program to Calculate Information Measures            427

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