1. Animal Movement in Home Ranges By Steven and Paul

2. Home ranges are often determined by: Proximity to den & resting areas Territorial markers (scents, calls, etc) Familiarity with region Prey density

3. We did this: 1.Used one-dimensional random walk functions to model animal roaming. 2.Added various biases to 1-D random functions to keep animal from roaming too far (Holgate Models). 3.Expanded den-biased walk functions to 2-D. 4.Included scent marking and sensing with biases. Ran a two-animal scenario to test competitive home range formation.

4. One-Dimensional Random Walks Began with basic function from Maple worksheets. Then implemented two bias types proposed by Holgate as well as one other.

5. Den Bias Functions: Case I: Familiarity Attraction. Animal is less familiar with surroundings further from den, thus less likely to know which way is towards the den. Consequently, the pro-den bias term from epsilon drops linearly with distance. All three have a bias toward the den site. But each case varies this bias differently.

6. Case II: Den attraction due to range limit: The animal is increasingly attracted to the den the further it moves away. This is accomplished by subtracting an inverse function of the distance limit from the probability to move away from the den.

7. Case III: The third case was a simple constant bias towards the den. The bias sign would change with orientation to the den, while the strength remained constant.

8. MAPLE

9. Multiple Animals and Scent: Multiple animals simulated simultaneously to allow for interactions Animals randomly lay scents Scents are detected by other animals Animals react to scents by avoiding those of others, while being drawn one’s own scent Animals more likely to drop scent when another’s scent is detected

10. In the end: Built random walk models in one and two dimensions that appear to yield results similar to theory. We were not able to work with the multiple animals/scents model enough to extract meaningful results.

11. Problems: Poor data transport between programs C++ is not ideal for math

12. IMPROVEMENTS: Allow for resting and various movement speeds Make location grids continuous Make scent influence on probability more complex More comparisons to theoretical results Faster computers/programs More data runs (POSSIBLE)