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

7. Our Model

8. Coefficients
α=4
β=1/5
γ=24
δ=0 M= N=

9. Our Model

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

13. Equilibrium Points
equilibrium point (0,0) - source

14. Equilibrium Points
equilibrium point (0, ) - sink

15. Equilibrium Points
equilibrium point – ( ,0) -saddle

16. Equilibrium Points
equilibrium point (-1.8x10^14, ) – saddle

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

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

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

20. 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.