Clone of Final Midterm Student version of A More Realistic Model of Isle Royale: Predator Prey Interactions
Allison Zembrodt's Model

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

We incorporate logistic growth into the moose dynamics, and we replace the death flow of the moose with a kill rate modeled from the kill rate data found on the Isle Royale website.

I start with these parameters:
Wolf Death Rate = 0.15
Wolf Birth Rate = 0.0187963
Moose Birth Rate = 0.4
Carrying Capacity = 2000
Initial Moose: 563
Initial Wolves: 20

I used RK-4 with step-size 0.1, from 1959 for 60 years.

The moose birth flow is logistic, MBR*M*(1-M/K)
Moose death flow is Kill Rate (in Moose/Year)
Wolf birth flow is WBR*Kill Rate (in Wolves/Year)
Wolf death flow is WDR*W

equations I used in kill rate :

power model - 12*0.1251361120909615*([Moose]/[Wolves])^.44491970277839954*[Wolves]


Kill rate sqrt = 12*(0.0933207+.0873463*([Moose]/[Wolves])^.5)*[Wolves]


Holling Type III - ((0.986198*([Moose]/[Wolves])^2)/ (601.468 +([Moose]/[Wolves])^2))*[Wolves]*12


linear - 12*[Wolves]*(.400271+.00560299([Moose]/[Wolves]))



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