A Swarm-Based Approach to Integrating Multiple Temporal and Spatial Scales

1. A Swarm-Based Approach to Integrating Multiple Temporal and Spatial Scales Shrimp, Humans, and Hydrology in the Luquillo Forest, Puerto Rico Jorge Ramirez1, Paul Box2, Todd Crowl3, John Loomis1 Funding provided by NSF CHN Systems BioComplexity Grant 1: Colorado State University 2: CSIRO Sustainable Ecosystems 3: Utah State University

2. Research Question • The Project • Multiple users of tropical rainforest watershed • Shrimp, people • Connected via landscape and hydrology • While landscape and ecology are well studied, interactions are not well known or clear • Modeling challenge • integrate processes at multiple temporal and spatial scales into one framework

3. Research Question • The Project • Multiple users of tropical rainforest watershed • Shrimp, people • Connected via landscape and hydrology • While landscape and ecology are well studied, interactions are not well known or clear • Modeling challenge • Find integrate processes at multiple temporal and spatial scales into one framework Funded by National Science Foundation Biocomplexity Grant #0308414, studying coupled human and social interactions Collaborative project between Colorado State University, University of Puerto Rico, Utah State University, University of Georgia, University of Pennsylvania, US Forest Service, and CSIRO Australia http://biocomplexity.warnercnr.colostate.edu/

4. Systemic representation • Conceive of entire system as an interconnected set of discrete subsystems • Climate, landscape, ecosystem, social system, etc. • Definition of each component done through multiple representations, • verbal, mathematical, and statistical descriptions • Choice of best representation is dependent on discipline

5. Representation of subsystem (your wolrd as it matters) • Any mathematical or conceptual description needs to define boundaries, scales, and units of analysis • Landscape processes operate in kilometers and years • Human recreators operate in days and sites (tens of meters) • Migrating shrimp operate in pools (a few meters) and hours

6. Representation of subsystem (your wolrd as it matters) • Any mathematical or conceptual description needs to define boundaries, scales, and ultimately units • Units that are good and appropriate for one thing are too coarse or too fine (computational overkill) for another thing • When one wishes to integrate components of one part of the system with another system, the differing units of analysis are simply not compatible with each other • Simply taking numbers from one model and entering them as parameters in another model is wrong in many ways

7. Swarm models • A swarm is one more way to describe or represent a system • Swarms are an extension of agent-based models (individual based models) • Representing world as a bunch of autonomous entities with their own rules • Swarms are useful for modeling decentralized systems • Everyone is participating, but nobody is in control • A swarm is a collection of agents with their own schedule of actions that tell the agents when and how to act • A swarm may itself become an object or agent in a greater swarm • Example: stomach is collection of microbes that digest food • Stomach becomes component of grazing animal, who is in turn a member of a herd of grazing animals • Note: Swarm model vs. Swarm software….

8. Swarm models vs statistical models • Summary description form multiple observations • Representative model is specified before hand • Assumed structure of model (e.g., statistical distributions) • Calculation based • Computationally simple, solvable by numeric methods • Model that describes the most variation with the fewest parameters wins • Grows model from a few representative rules • Representative model emerges from interactions and agent behavior • Much structure is unknown when model is constructed • Algorithm or rule based • Computationally intensive, many parts not solvable by numerical methods • Model that captures most system behavior with the fewest and simplest rules wins These are simply different ways to describe a system, and the output of one should be used to better understand the other Researchers should rely on multiple representations of their systems to better understand them One model should be able to replicate the results of the other model

9. Structure of Luquillo forest watershed models • Starting idea: • Each component of the model is an autonomous, independent entity, that interacts with other components in known ways By specifying the starting parameters and rules of interaction for all of those entities, they should be able to replicate behaviors of other (better studied) models of the same system If all entities are successfully represented in swarm formulation, then they can be coupled without violating fundamentals of the model structure

10. Structure of Luquillo forest watershed models: entities • Pool (world where shrimp lives and recreators swim)

11. Structure of Luquillo forest watershed models: entities • A stream is an interconnected series of pools

12. Structure of Luquillo forest watershed models: entities • Cell is an arbitrary patch of land • Analogous to a pixel or cell in raster GIS

13. Structure of Luquillo forest watershed models: entities • A Landscape or Watershed is a collection of cells who know their relationships to each other • Shrimp can migrate up from one pool to another • Landscape can control runoff, which affects pool depth and other characteristics

14. Structure of Luquillo forest watershed models: entities • A road is represented via vector-based (arc-node) topology

15. Structure of Luquillo forest watershed models: entities • A watershed is a collection of cells and streams • Our watersheds have roads and free-roaming agents in them as well (shrimp and recreators)

16. Model representation Mameyes Watershed

17. Mameyes Watershed

18. Mameyes Watershed

19. Mameyes Watershed

20. Mameyes Watershed

21. Verification: shrimp migration • Start with field-based measurement of shrimp distribution in a series of pools • Implement alternate sets of rules for shrimp to move between pools • Compare outcome of model to field observation • Result: a few simple rules better reproduces shrimp distribution than statistical model

22. Verification: hydrology and surface flow Translate differential equations for each cell to simple rules of receiving and sending runoff to neighbors Resulting hydrographic curves are similar to diffusion wave model

23. Conclusions • Rule-based model allows for concurrent representation of processes at multiple temporal and spatial scales • Reproduces results of other modeling techniques, and can reproduce real-world observations • Method is computationally intensive and not (yet) practical for large cases • Requires significant modeling expertise to do correctly • Expertise can be difficult to communicate (i.e., present for genuine peer review) • Future seems bright!!!!

24. http://biocomplexity.warnercnr.colostate.edu/