1. Introduction to and Measurement of Complexity FRST 532C – Complex Adaptive Systems Lorea Coronado-Garcia

2. Readings Levin, S (2005) Self-organization and the emergence of complexity in ecological systems. BioScience 55: 1075-1079. Levin, S (2005) Self-organization and the emergence of complexity in ecological systems. BioScience 55: 1075-1079. Parrot L (2010) Measuring ecological complexity. Ecological Indicators 4: 85-92. Parrot L (2010) Measuring ecological complexity. Ecological Indicators 4: 85-92.

3. Self-organization and the emergence of complexity in ecological systems Described by physical and biological mechanisms that are well understood Described by physical and biological mechanisms that are well understood Given an initial soup on which these mechanisms can act Given an initial soup on which these mechanisms can act No invocation of ecosystem-level selection or intelligent design is needed or justified No invocation of ecosystem-level selection or intelligent design is needed or justified

4. Gaia Proposed by James Lovelock Proposed by James Lovelock Postulates that biota self regulate conditions for levels it needs for survival system, species and environment co-evolve, the two are inseperable Postulates that biota self regulate conditions for levels it needs for survival system, species and environment co-evolve, the two are inseperable

5. Extreme: Teleological Gaia Biosphere is a superorganism selected for its macroscopic properties in order to serve the biota Biosphere is a superorganism selected for its macroscopic properties in order to serve the biota Problem: macroscopic regularities in the biosphere in terms of selection acting upon the whole system Problem: macroscopic regularities in the biosphere in terms of selection acting upon the whole system Lovelocks imposes optimization argumets. E.g., puddle in a hole. Lovelocks imposes optimization argumets. E.g., puddle in a hole. Not useful for repairing the damage we cause Not useful for repairing the damage we cause

6. Self-organized Criticality (SOC)

7. Question How do modularity and heterogeneity arise in this context, how are they maintained, and what are the implications for maintaining the robustness of ecosystems and the biosphere? How do modularity and heterogeneity arise in this context, how are they maintained, and what are the implications for maintaining the robustness of ecosystems and the biosphere?

8. Biosphere and ecosystem as compex adaptive systems Pattern emerges from individual agents Pattern emerges from individual agents Feed back to affect individual agents Feed back to affect individual agents Develop cycle to provide the regulation of local environments Develop cycle to provide the regulation of local environments

9. Truth between extremes Move towards From models that recognize the heterogeneity of systems Move towards From models that recognize the heterogeneity of systems Intermediate levels: forging mutualisms, coalitions, and even multicellular assemblages Intermediate levels: forging mutualisms, coalitions, and even multicellular assemblages The domain of science to explain how such complexity can arise from local interactions The domain of science to explain how such complexity can arise from local interactions

10. Self Organization Autocatalytic networks Autocatalytic networks Agent-based approaches to understanding all aspects of biospheric organization Agent-based approaches to understanding all aspects of biospheric organization Tinkerer rather than master craftsman Tinkerer rather than master craftsman

11. Measuring Ecological Complexity Differentiate simple from complex system Differentiate simple from complex system Lies at the edge of chaos Lies at the edge of chaos Linked to concept of ecosystem diversity, resilience, integrity Linked to concept of ecosystem diversity, resilience, integrity

12. Two Types Type 1 Type 1 Increases linearly with increasing disorder in the system Increases linearly with increasing disorder in the system Type 2 Type 2 Convex function Convex function

13. Measures Temporal Temporal Spatial Spatial Spatiotemporal Spatiotemporal Structural Structural

14. Temporal Measures Use symbols Use symbols Assigned probability Assigned probability +founded in tradition of information-based measures +founded in tradition of information-based measures - loss of information pre-treatment of the series - loss of information pre-treatment of the series Type 1: Mean Information Gain, Recurrence Quantification Analysis Type 1: Mean Information Gain, Recurrence Quantification Analysis Type 2: Fluctuation Complexity Type 2: Fluctuation Complexity

15. Spatial Measures Characterize, ordered, random and complex two- dimensional patterns Characterize, ordered, random and complex two- dimensional patterns Type 1: Fractal Dimensions Type 1: Fractal Dimensions Type 2: Number of points required to trace boundaries Type 2: Number of points required to trace boundaries

16. Spatiotemporal Measures Typically used in 2D Typically used in 2D 3D: Blobs in space-time 3D: Blobs in space-time

17. Structural Measures Describes organization and relationships between components of a system Describes organization and relationships between components of a system Represented with nodes and connecting edges Represented with nodes and connecting edges Non-random, irregular structure: characterized by short diameters Non-random, irregular structure: characterized by short diameters Implication: robust to random loss of nodes, but highly vulnerable to the loss of hubs (possible keystone). Implication: robust to random loss of nodes, but highly vulnerable to the loss of hubs (possible keystone).

18. Ecological Complexity as an Ecological Orientor Few examples Few examples Can use to identify priority areas for conservation (by degree of maturity of complexity) Can use to identify priority areas for conservation (by degree of maturity of complexity) Apply to remote sensing and flux tower data Apply to remote sensing and flux tower data Type 2: Contribute to the idea of a local optimum Type 2: Contribute to the idea of a local optimum Work should focus on distinguishing subtle differences between similar ecosystems in different stages of development Work should focus on distinguishing subtle differences between similar ecosystems in different stages of development

19. Questions What makes a system complex? What distinguishes a complex adaptive system from a complex one? What makes a system complex? What distinguishes a complex adaptive system from a complex one? What is the atmosphere (just complex, or complex adaptive)? The biosphere? What is the atmosphere (just complex, or complex adaptive)? The biosphere? How specific should we aim to be with our measurements? How specific should we aim to be with our measurements? Can you imagine additional applications from the development of measurements other than what was suggested in the readings? Can you imagine additional applications from the development of measurements other than what was suggested in the readings?