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The Wolf population vs. Farm Profits.

The Wolf population vs. Farm Profits. Scientific Computing Spring 2003 Avani Gadani. Problem. In 1914, Congress passed a resolution to eradicate Gray wolves ( Canis lupus ). They have since have become endangered in the US, and efforts have been made to reintroduce them.

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The Wolf population vs. Farm Profits.

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  1. The Wolf population vs. Farm Profits. Scientific Computing Spring 2003 Avani Gadani

  2. Problem • In 1914, Congress passed a resolution to eradicate Gray wolves (Canis lupus). They have since have become endangered in the US, and efforts have been made to reintroduce them. • Ranchers are against this because wolves kill livestock.

  3. Yellowstone

  4. Qualitative: • Should ranchers be allowed to shoot Yellowstone’s wolves? • Can wolves and livestock co-exist?

  5. Quantitative • What is the difference in a farmer’s profits if he hunts wolves? • How long will wolves survive being hunted?

  6. Food chain

  7. Wolf/Sheep

  8. Modified Holling-Tanner Model with Hunting

  9. Bad news…

  10. Fewer Deer and Wolf Hunting

  11. No Wolf Hunting

  12. Wolf Population

  13. What about the wolves? • Hunting: Wolves go extinct in 38 years • No Hunting: Wolf population doubles in 20 years!

  14. No Deer or Hunting

  15. …And what about the farmers? • If the farmer had a secondary crop that deer ate, profits increase with wolf population (though decrease overall). • Even without, the birthrate of wolves and the amount they kill is small enough that they don’t impact the system.

  16. Conclusions • Qualitative: • Ranchers should not be allowed to shoot the wolves. • Currently, the model seems to indicate livestock thrives if wolves are the only problem.

  17. Conclusions • Quantitative • A farmer is making profit regardless of the wolves. The profit levels faster without the wolves, but in either case carrying capacity is reached in 40 years. If he has other crops that deer eat, his profits decrease because wolves can’t kill enough of the deer. • Wolves lived 38 years with ranchers picking 10% off per year.

  18. Future Work • Model bursts in wolf activity, and their effect on the system. • Incorporate other factors that kill livestock. • Use real data.

  19. References • Dai, Guoren and Moxun Tang. “Coexistence Region and Global Dynamics of a Harvested Predator-Prey System.” SIAM Journal on Applied Mathematics. Volume 58, No. 1 (1998). • Duke University-CCP Predator-Prey Modelshttp://www.math.duke.edu/education/ccp/materials/diffeq/predprey/pred5.html • Hsu, Sze-Bi and Tzy-Wei Huang. “Global Stability for a Class of Predator-Prey Systems.” SIAM Journal on Applied Mathematics. Volume 55, No. 3 (1995). • http://www.yellowstone-natl-park.com/wolf.htm

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