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Isle Royale: Predator/Prey Model for Moose and Wolves

Andrew E Long
This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale. It was "cloned" from a model that InsightMaker provides to its users, at
Thanks Scott Fortmann-Roe.

I've created a Mathematica file that replicates the model, at

It allows one to experiment with adjusting the initial number of moose and wolves on the island.

I used steepest descent in Mathematica to optimize the parameters, with my objective data being the ratio of wolves to moose. You can try my (admittedly) kludgy code, at

woStart} =

Environment Ecology Populations Math Modeling Mat375

  • 1 year 9 months ago

S-Curve + Delay for Bell Curve by Guy Lakeman

Guy Lakeman
​S-Curve + Delay for Bell Curve Showing Erlang Distribution
Generation of Bell Curve from Initial Market through Delay in Pickup of Customers
This provides the beginning of an Erlang distribution model

The Erlang distribution is a two parameter family of continuous probability distributions with support . The two parameters are:

  • a positive integer 'shape' 
  • a positive real 'rate' ; sometimes the scale , the inverse of the rate is used.

MATHS Statistics Physics Science Ecology Climate Weather Intelligence Education Probability Density Function Normal Bell Curve Gaussian Distribution Democracy Voting Politics Policy Erlang

  • 3 years 11 months ago

Vegetation interspecific competition

Andrew Hofmeister
Common Timothy is an invasive grass species.  Alpine Timothy is the native grass species in Yellowstone.  I calculated the carrying capacity of the grasses by converting acres, square feet, pounds per square feet and seeds per pound.  There is a higher birth rate and lower death rate for the common timothy because the grass is taking over the area due to a lack of wildlife predators.


  • 4 years 4 weeks ago

Sharks, Turtles, and Sea Grasses Population Dynamics

Tesslyn Knapp
This insight models the intertwining relationships of sea grass, Chelonia mydas (green sea turtles), and Galeocerdo cuvier (tiger sharks). Each of these populations are connected to one another through a food chain interaction, making all of the populations dependent upon each other.


  • 8 months 2 weeks ago

Final Midterm Student version of A More Realistic Model of Isle Royale: Predator Prey Interactions

Andrew E Long
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

Environment Ecology Populations Midterm

  • 1 year 8 months ago