LotkaVolterra Modifications for Endangered Species Stephanie Constantino Scott

Topic Overview The kiwi bird is an endangered species indigenous to New Zealand We

The Kiwi Size of a chicken Lays about 2 eggs, 2 to 3 times

The Problem Europeans introduced dogs and other predators into New Zealand Only about 5%

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

. Linearization (0, 0), (12 000, 0), (0, 500 000), and ( -1. 8

Equilibrium Points equilibrium point (0, 0) - source

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

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

Equilibrium Points equilibrium point (-1. 8 x 10^14, 500 000) – saddle

Saving the Kiwi Remove dogs from New Zealand Remove them from designated area where

• Need to make K coordinate positive • Occurs when > 0, aka

• Lower the loss to the kiwi population per encounter with a dog,

Conclusion Our model agrees with the situation that kiwis will be extinct unless humans

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Lotka-Volterra Modifications for Endangered Species Stephanie Constantino Scott Mc. Calla 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 Using differential equations, the graphs show that the kiwi is going extinct in the wild There a few ways in which humans are attempting to help the kiwi bird

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

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

Logistic Model

Our Model

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

Our Model

. Linearization (0, 0), (12 000, 0), (0, 500 000), and ( -1. 8 x 1014, 500 000)

Equilibrium Points equilibrium point (0, 0) - source

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

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

Equilibrium Points equilibrium point (-1. 8 x 10^14, 500 000) – saddle

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

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

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

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.