1. The Wolves and Moose on Isle Royal

3. Isle Royale images from: http://www.kgcphoto.com/isle_royale_national_park.htm

6. Wolf and moose images from http://blog.kingsoutdoorworld.com/2007/02/

9. alright – back to work…

10. Largest island in lake Superior Isolated from mainland most of the time Home to moose and wolves For now: concentrate on actions between wolves and moose herd ignore other influences on moose population (such as ?) rather limited “systems” approach (see additional reading on web page)

11. How to describe feedback: size of moose herdsize of wolf pack size of moose herd positive feedback negative feedback more food on four legs more hungry mouths to feed

12. Example of a Feedback Loop Size of moose herd More food for wolves Appetite for mooseSize of wolf pack

13. Note: A feedback loop needs to be closed ! Therefore it needs at least two components two connections between these components

14. Or Somewhat Simplified: size of moose herdsize of wolf pack positive negative

15. How to analyze a feedback loop: Need to disturb the system Doesn’t matter where you start Analyze how disturbance moves through the system How does wolf – moose system behave ? size of moose herdsize of wolf pack

16. Sign of Feedback Loop number of negative couplings determines sign of feedback loop even number of negative couplings: positive feedback loop odd number of negative couplings: negative feedback loop

17. Effects of Negative of Positive Feedbacks

18. positive feedback: input signal will be amplified negative feedback: input signal will be damped

19. Size of wolf and deer herds From Science Times (3/19/1996) (http://www.admin.mtu.edu/urel/PressReleases/feature/wolves/wolf.html)