A More Realistic Model of Isle Royale: Predator Prey Interactions
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.
A decent match to the data is made with
Wolf Death Rate = 0.15
Wolf Birth Rate Factor = 0.0203
Moose Death Rate Factor = 1.08
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 MBR*M*(1-M/K)
Moose death flow is MDRF*Sqrt(M*W)
Wolf birth flow is WBRF*Sqrt(M*W)
Wolf death flow is WDR*W