Positive Feedback in Natural Systems

Cybernetics, a science concerned with understanding how systems are regulated, has reflected the preoccupations of the century in which it was born. Regulation is important in twentieth century society, where both machines and social organizations are complex. Cybernetics focused on and became primarily associated with the homeostasis or stability of system behavior and with the negative feedbacks that stabilize systems. It paid less attention to the processes opposite to negative feedback, the positive feedback processes that act to change systems. We attempt to redress the balance here by illustrating the enormous importance of positive feedbacks in natural systems. In an article in the American Scientist in 1963, Maruyama called for increased attention to this topic, noting that processes of change could occur when a "deviation in anyone component of the system caused deviations in other components that acted back on the first component to reinforce of amplify the initial deviation." The deviation amplification is the result of positive feedback among system components. Maruyama demonstrated by numerous examples that the neglect of such processes was unjustified and suggested that a new branch of cybernetics, "the second cybernetics," be devoted to their study.

1. Introduction.- 1.1 Homeostasis.- 1.2 Positive Feedback.- 1.3 Ecological Systems with Positive Feedback.- 1.4 Generalization 1: Increasing Complexity.- 1.5 Generalization 2: Accelerating Change.- 1.6 Generalization 3: Threshold Effects.- 1.7 Generalization 4: Fragility of Complex Systems.- 1.8 Summary and Conclusions.- 2. The Mathematics of Positive Feedback.- 2.1 Graphical Analysis of a Simple Dynamic Positive Feedback System.- 2.2 A System of Two Mutualists.- 2.3 A System of Two Competitors.- 2.4 Mathematical Analysis of Positive Feedback.- 2.5 Summary and Conclusions.- 3. Physical Systems.- 3.1 The Life History of a Star.- 3.2 Geophysical Systems.- 3.3 Autocatalysis in Chemical Systems.- 3.4 Summary and Conclusions.- 4. Evolutionary Processes.- 4.1 Early Evolution of Life.- 4.2 Evolution at the Species Level.- 4.3 Coevolution.- 4.4 Summary and Conclusions.- 5. Organisms Physiology and Behaviour.- 5.1 Destructive Positive Feedback.- 5.2 Biochemical Processes in Cells and Organisms.- 5.3 Feeding and Drinking Behavior.- 5.4 Sleep.- 5.5 Movement and Motor-Sensory Relationships.- 5.6 Mind-Body Relationship.- 5.7 Summary and Conclusions.- 6. Resource Utilization by Organisms.- 6.1 Energy Allocation Tactics.- 6.2 Territorial Defense Strategies.- 6.3 Chemical Defense Strategies.- 6.4 Growth Rate Strategy.- 6.5 Summary and Conclusions.- 7. Social Behavior.- 7.1 Evolution of r- and K-strategies.- 7.2 Development of Social Strategies.- 7.3 Mating and Reproduction.- 7.4 Population Models Incorporating Sexual Reproduction.- 7.5 Small Group Dynamics.- 7.6 Castes In Insect Societies.- 7.7 Dominance Within Groups.- 7.8 Models of Group Formation and Size.- 7.9 The Schooling of Fish.- 7.10 Social Interactions and Game Theory.- 7.11 Summary and Conclusions.- 8. Mutualistic and Competitive Systems.- 8.1 Dynamics of Mutualistic Communities.- 8.2 Limits to Mutual Benefaction.- 8.3 Multi-Species Mutualism.- 8.4 Models of the Evolution of Mutualism.- 8.5 Isolation and Obligate Mutualism.- 8.6 Limited Competition.- 8.7 Summary and Conclusions.- 9. Age-Structured Populations.- 9.1 Age Structure.- 9.2 Leslie Matrices.- 9.3 Compensatory Leslie Matrices.- 9.4 Interacting Populations.- 9.5 Coexistence of Two Interacting Populations.- 9.6 Other Compensatory Models.- 9.7 Life-History Strategies.- 9.8 Intrinsic Rate of Increase.- 9.9 Reproductive Strategies.- 9.10 Summary and Conclusions.- 10. Spatially Heterogeneous Systems: Islands and Patchy Regions.- 10.1 Classical Theory of Island Biogeography.- 10.2 Island Clusters.- 10.3 Insular Reserves.- 10.4 Modeling the Patchy System.- 10.5 A Single Species in a Patchy Region.- 10.6 Time to Extinction on a Patch.- 10.7 Persistence of a Species in a Two-Patch Environment.- 10.8 Stability of a Single-Species, Two-Patch System.- 10.9 Persistence of a Species in an N-Patch Environment.- 10.10 Multi-Species, Multi-patch Systems with Competition and Mutalism.- 10.11 Persistence of a Species in a Two-Species, Two-Patch Environment.- 10.12 Persistence of a Species in an L-Species, iV-Patch Environment.- 10.13 Stability of a Two-Species, Two-Patch Model.- 10.14 Stability of an L-Species, iV-Patch Model.- 10.15 Relationship Between Reserve Design and Species Persistence.- 10.16 Summary and Conclusions.- 11. Spatially Heterogeneous Ecosystems: Pattern Formation.- 11.1 Spontaneous Emergence of Spatial Patterns.- 11.2 Diffusion Model.- 11.3 Pattern Formation Through Instability.- 11.4 Congregation of Colonial Organisms.- 11.5 Boundary Formation by Competition.- 11.6 Summary and Conclusions.- 12. Disease and Pest Outbreaks.- 12.1 Physiological Effects in the Host Species.- 12.2 Mutualistic Interactions of more than one Pathogenic Agent.- 12.3 Models of a Directly Communicated Disease or Parasite.- 12.4 Effects of Spatial Heterogeneity on Disease Outbreak Threshold Conditions.- 12.5 Design of Immunization Programs.- 12.6 Shape of the Contagion Rate Function.- 12.7 Comparison with other Spatially Heterogeneous Models.- 12.8 Host-Vector Models.- 12.9 Summary and Conclusions.- 13. The Ecosystem and Succession.- 13.1 The Ecosystem.- 13.2 Succession as a Positive Feedback Process.- 13.3 A Clementsian Model.- 13.4 Markov Chain Models.- 13.5 A Model of a Fire-Dependent System.- 13.6 Positive Feedback Loops in Ecosystems.- 13.7 Nutrient Cycling.- 13.8 Selection on the Community or Ecosystem Level.- 13.9 Summary and Conclusions.- Appendices.- Appendix A: Positive Linear Systems.- Appendix B: Stability of Positive Feedback Systems.- Appendix C: Stability of Discrete-Time Systems.- Appendix D: Positive Equilibria and Stability.- Appendix E: Comparative Statics of Positive Feedback Systems.- Appendix F: Similarity Transforms.- Appendix G: Bounds on the Roots of a Positive Linear System.- Appendix H: Relationship Between Positive Linear System Stability Criteria and the Routh-Hurwitz Criteria.- References.- Author Index.