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Lotka-Volterra Modifications for Endangered Species

Lotka-Volterra Modifications for Endangered Species. Stephanie Constantino Scott McCalla Kalab Yohannes. Topic Overview. The kiwi bird is an endangered species indigenous to New Zealand We used a modified Lotka-Voltera model to show the decrease in population of the kiwi bird

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Lotka-Volterra Modifications for Endangered Species

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  1. Lotka-Volterra Modifications for Endangered Species Stephanie Constantino Scott McCalla Kalab Yohannes

  2. Topic Overview • The kiwi bird is an endangered species indigenous to New Zealand • We used a modified Lotka-Voltera model to show the decrease in population of the kiwi bird • Using differential equations, the graphs show that the kiwi is going extinct in the wild • There are a few ways in which humans are attempting to help the kiwi bird

  3. The Kiwi • Size of a chicken • Lays about 2 eggs, 2 to 3 times a year • Can live for up to 40 years in wild

  4. The Problem • Europeans introduced dogs and other predators into New Zealand • Only about 5% of kiwi chicks survive to be one year old • Kiwis are going extinct

  5. Logistic Model

  6. Our Model

  7. Coefficients • α=4 • β=1/5 • γ=24 • δ=0 • M=500 000 • N=12 000 000

  8. Our Model

  9. Linearization . (0,0), (12 000 000,0), (0,500 000), and ( -1.8 x 1014,500 000)

  10. Equilibrium Points • equilibrium point (0,0) - source

  11. Equilibrium Points • equilibrium point (0, 500 000) - sink

  12. Equilibrium Points • equilibrium point – (12 000 000,0) -saddle

  13. Equilibrium Points • equilibrium point (-1.8x10^14, 500 000) – saddle

  14. Saving the Kiwi • Remove dogs from New Zealand • Remove them from designated area where kiwis are • Move equilibrium point to positive quadrant ( ) ,

  15. Need to make K coordinate positive • Occurs when > 0, aka when • Increase the reproductive rate of the kiwi, α, which is currently 4, α >

  16. Lower the loss to the kiwi population per • encounter with a dog, γ, currently 24, • Lower threshold number of dogs, M, currently 500,000,

  17. Conclusion • Our model agrees with the situation that kiwis will be extinct unless humans make more of an effort to conserve them, and validates the existence of Kiwi Preserves in New Zealand.

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