Monte Carlo-Markov Chain

1. Monte Carlo-Markov Chain • Markov Chain: • A series of states of being that have probabilities associated with transitions (i.e. the state is not deterministic but has some stochastic component).

2. Caribou – Wolf Interactions • http://www.youtube.com/watch?v=nK1JOmMQ5Fc

3. Issues with Simulations • Realistic Movement • Moving toward desired areas • Keep animals from getting “stuck” • Validation • Boundary conditions • What happens at the edges? • Disappear/die (need immigration as well) • Reverse direction • Wrap to the other side (not realistic) • Model stability • Model complexity/Performance

4. Moving Toward Desired Areas • Use Distance Raster • Desired area: • Spawning ground, feeding grounds • Destination is desired area • Pixels with lower cost are closer to desired area • Animals move to adjacent pixels with lower cost

5. Moving Through Networks • Use polylines with network nodes • Move in direction (or against) of polylines • Need to make decisions at nodes

6. Getting “Stuck” • Certain conditions arise and animals can become stuck and just move back and forth • Add additional randomness • Examine environmental layers for unrealistic values • Streams not flowing perfectly down hill • Bays not connected with the ocean

7. Validation • Run models over and over again • Record locations, births, deaths, feeding • Create probability surfaces • Validate against existing datasets • Are observations/measurements within the predicted areas? • Could use likelihood/AIC…

8. Model Stability • Density dependence • Most species struggle more when crowded • Reduces food availability, increases disease • Places a control the number of individuals • Balancing birth rates and death rates • Realistic lifecycles, predation rates

9. Model Complexity • Typically there are lots of agents • Need to keep the behaviors and attributes simple • The group behaviors are typically more complex than expected from the individuals • Model a population • Convert “groups” of individuals to populations when they cluster

10. Performance • Select the right resolution for rasters • High enough to be realistic • Low enough for speed • May have to just simulate a smaller area than desired.

11. 3D and Temporal • Simulations are almost always temporally based • 3D is common but requires more hardware/time • Also requires special software and 3D data

12. Ecological Modeling • Water, carbon, nutrient cycling • Trophic models • Population models • Predator/Prey • Disease wsu.edu

13. Sustainable Fisheries www.niwa.co.nz

14. Can operating rooms in Second Life teach real doctors? - Discover Sims World of Warcraft

15. Tools • NetLogo • HexSim • MASON Multi-Agent Simulation Toolkit • Repast • Programming! • Python • Java • Books: “Agent-Based Models of Geographical Systems”

16. Possible Simple Models • Fire w/fire fighters • Zombies and humans • Reef fish • Wolves and elk • Invasive species (w/managers)

17. Envision – Policy Simulation

18. Simulations • Parameterization • Based on mechanisms/theories • Typically include random effects • “Tweeked” to fit reality • Validation • Run over observed space and time • Do simulated measures match observed? • Run it over and over • Observed fit into “Confidence interval”?

19. Simulations • Startup: • Either simulate a known situation • Or, run until reaches an expected state • Stability • Populations tend to breed out of control or die out over time • Build in realistic limitations

20. Python SEIBM • Very simple model • Includes 3 classes: • Animal, Predator, Prey

21. SEIBM – Main Script • Imports: Tkinter, time, Predator, Prey, Animal • Setup the GUI • Initialize animal objects in an array • Loop forever: • Update each object • Redraw the window • Let Python process events (mouse clicks) • Sleep for a bit

22. Animals • Initializatoin: • Create our oval on the canvas • Update: • Find a random direction to move • If moving off the canvas, reverse direction • Do the move

23. Prey • Initialization: • Call the Animal class to create a green oval • Set the time until birth • Update: • Call the Animal to update movement • Decrement the time until birth • If it’s time for birth: • Create a new object at the current coordinate • Add the object to the array

24. Predator • Initialization • Call the Animal class to create a red oval • Set the time to birth • Update: • All the Animal to do movement • Decrement time to birth • If it’s time to birth: • Create a new Predator • Add it to the array and reset the time to birth • If any prey are close by • Delete them

25. HexSim • Visit Hexsim.net to download • Decompress the folder • Can run “Hexsim.exe” from within the folder without other installation • See the “Examples” on the HexSim website to get started • The User’s Guide has good information on how HexSim works

26. HexSim Basics • Set the workspace: • HexSim -> Set Workspace • Select a “*.grid” file • Double click on a scenario to “open” • Adds a tab for that scenario • “Scenario” menu items work on the currently selected tab • View spatial data: • In the “Spatial Data” panel, open items • Double-click on “-> 1” to show the data

27. HexSim Basics • Select “Scenario -> Run Simulation” • Save an XML file for the run • Click “Start” in the window that is displayed • These examples are not yet parameterized so you may need to modify them to do something interesting

28. Comparison of Software • http://en.wikipedia.org/wiki/Comparison_of_agent-based_modeling_software

29. Simulation Modeling • Climate: • http://climate.nasa.gov/meteorologists • Tsunamis: • http://www.youtube.com/watch?v=_bCTa5su8II • http://www.youtube.com/watch?v=WgpXzwLuGDo • Plate tectonics: • http://www.youtube.com/watch?v=ryrXAGY1dmE