Dynamic Modeling in Object-Oriented GIS Fundamentals of object-oriented models Spatio-temporal simulation of geographic phenomena Application examples: tiger modeling

Agents and movement in Space and Time: Tiger Modeling (TIGMOD) 1 Dr. Sean C. Ahearn, and Ms. Ji Ding Dr. James D. Smith and Mr. Anup Josi CARSI, Hunter College University of Minnesota Background –human-tiger interaction –OOGIS Methodology –data model –dynamic simulation Results –tiger survivability wild prey wild and domestic prey –model validity 1 Ahearn, S. J.L.D. Smith, A. Joshi, J. Ding, “TIGMOD: an individual-based spatially explicit model for simulating Tiger/human interaction in multiple use forests”. Ecological Modeling 140 (2001)

Objects not the geometric components of layers are the “units” for modeling and interaction –Implications object can have multiple geometries (e.g. a tiger can have both a location and a home range) simpler less constrained interface between objects encapsulation creates autonomous entities Spatial Models in TIGMOD

Goal of Simulation Model Accurately model tiger populations through time to determine their survivability given changes in the environment (e.g. forest degradation, habitat fragmentation, poisoning of tigers, reduction of prey, habitat improvement). Find the right balance of different uses for land in multiple-use management. Simulate tiger behavior using an spatial individual-based model not an aggregate statistical models.

Study Area 5 Kilometers Rapti River Narayani River Siwalik Hills

Inheritance structure for TIGMOD

Object model

Time The simulation menu keeps the time field of each object current and sets the relationships between real world time and simulation time A change in the time triggers all activities of the tiger and prey –aging –hunter –thirst –matting

Event Scheduling Events are scheduled to occur at a specific time ( e.g. a female becomes fertile at “fixed” intervals and gives birth with x months of fertilization) These events are stochastically determined (e.g. time of birth number of cubs,.. Etc.)

Figure 7: diagram of dynamic activity Changeobjectstate change behavior female tiger gets older gets hungry get stressed? gets pregnant? time to be fertile/not ? Time to give birth? Domestic prey Wild prey male tiger gets older gets hungry gets stressed? time to visit next female? Hunting f(hunger) turns red, search for prey, kill prey Mating f(event) move toward female, make female pregnant Feeding f(kill) stay near prey, reduce hunger Hunting f(hunger) search for prey, kill prey, turn red Fertile f(schedule) change movement rate, turn cyan Feeding f(kill) stay near prey, reduce hunger Pregnant f(male prox.) change movement rate, turn blue With cubs change movement rate, increase rate of hunger Dead f(poison/stress) fire kill cubs trigger, turn black Dead f(killed) turn black, fire poison trigger Poison f(dead cattle turn red within 1 KM radius) Dead f(killed) turn black Dead f(poison/stress) turn black Stress f(hunger level) increase movement, die

Movement pattern of Tiger Distance is state-based and is modeled as a Chi-Squared Random Variable with mean and variance functionally dependent on the tiger’s state Direction is shown as the length of the vector. Movement is biased toward a direction as selected from a normal random variable with  = a direction and  = x degrees. Tiger distance P r o b. direction

Model input 400 m/day

Versions for testing prey composition and density

Validity of Model Model results show survivability at a prey density of 4 per km 2 This is consistent with field observations. Model results show lack of survivability below 3 per km 2. This is consistent with field observations. Prey were killed on average one every 7 days for normal prey densities. This is consistent with field studies. Validity of movement pattern tested using the distribution of prey kills as a proxy. Prey was initially distributed randomly throughout the region. A nearest neighbor analysis confirms that the distribution of prey is also random. Four breeding females gave birth to an average of 5.5 cubs over a 265 day period. This is consistent with field observations.

Tiger survivability with different densities of wild prey

Tiger survivability with different wild and domestic prey densities

Sensitivity to time villagers remain angry after a cattle kill

Sensitivity to villager tolerance

Reduction of probability of killing success of domestic prey due to guarding

Why put GPS on Tiger? We need detailed behavioral information on tigers to set management prescriptions to ensure: That habitat connectivity is increased To reduce potential human-tiger conflict To determine how the behavior of resident tigers living outside of PAs differs from those living in reserves To calibrate our model on tiger use of the human dominated landscape

Management questions about tigers living outside of reserves –How often do tigers kill domestic & natural prey? –How do tigers respond to humans? –Does high domestic prey abundance induce tigers to remain in an area?

1 Kilometers Home Range

April 17, hr April 8, hr 19 to April 11, hr 02 April 14, hr April 30, hr 6-22 April 26, hr 14 April 27, hr 18 April 1, hr 14 April 2, hr 14 April 22, hr 2-10 Hypothesized kills Rest Area

Results of tiger GPS research TM1 –Frequency of observation:1 every hour –Number of observations: 546 –GPS data period: 5.5 months TF4 –Frequency of observations:1 every 2 hours –Number of observations:469 –GPS data period: 4.5 months TF 5 –Frequency of observation:1 every 2 hours –Number of observations:529 –GPS data period: 5.4 months TF 5 and TM1 re-collared 2 weeks ago with PTTEP satellite collars

Patterns of Tiger Movement for three tigers during a 17 day period TMale1TFem 4TFem 5 (with 4 mo old cubs) 16.0 KM 10.6 KM 10.1 KM 124 observations 59 observations 45 observations

Movement of TF5 as cubs mature Cubs 4-5 months Cubs 6-7 months Cubs 8-9 months 8.7 KM9.1 KM12.4 KM Each 17 day period

Home range shifts by TM1 and TF5

Model Calibration What is the relationship between state (as manifested in behavior) of the tiger and movement? Rephrased: how can we impute states and their duration from a series of GPS points collected at fixed temporal intervals? A signal processing problem