This is a basic BIDE (birth, immigration, death, emigration) model.  Not all parts are implemented, however Birth and Death are.

This is a basic BIDE (birth, immigration, death, emigration) model.  Not all parts are implemented, however Birth and Death are.

This is a basic model for use with our lab section.  The full BIDE options.

B

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

This model has two main components. First is modelling the change in population composition as non-First Nations immigration increases with the opening of new mines in the region. The second is modelling the increasing income disparity between First Nations and non-First Nations as mining jobs are disproportionately gained by non-First Nations workers.

This is a basic BIDE (birth, immigration, death, emigration) model.  Not all parts are implemented, however Birth and Death are.

This is a demonstration of how logistic growth can be modeled with either one or two stocks. However, the two-stock case shows how the implementation of the carrying capacity is somehow less arbitrary than in the one-stock case.

This model explains the difference between Mountain bikes riding compared to logging in the Tasmanian forests.

This is a basic BIDE (birth, immigration, death, emigration) model.  Not all parts are implemented, however Birth and Death are.

A simulation illustrating simple predator prey dynamics. You have two populations.

This model is to be used with Mr. Roderick's AP biology activity on population growth. See steveroderick.net for a copy of the activity worksheet.

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
https://insightmaker.com/insight/2068/Isle-Royale-Predator-Prey-Interactions
Thanks Scott Fortmann-Roe.

I've created a Mathematica file that replicates the model, at
http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker.nb

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
http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker-BestFit.nb

{WolfBirthRateFactorStart,
WolfDeathRateStart,
MooseBirthRateStart,
MooseDeathRateFactorStart,
moStart,
woStart} =
{0.000267409,
0.239821,
0.269755,
0.0113679,
591,
23.};

Cloned from Ash Moran's Insight 1256 Systems and Models (Hartmut Bossel) Figure 2.16. Notation matches the Appendix of Marten Scheffer's 2009 Book Critical Transitions in Nature and Society p329 

Modeling forest succession in a northeast deciduous forest.

A simulation illustrating simple predator prey dynamics. You have two populations.

​Climate Sector Boundary Diagram By Guy Lakeman

This very simple model generates a tidal curve and a light climate at the sea surface to illustrate the non-linearity of the diel and tidal cycles. This has repercussions on benthic primary (and therefore also secondary) production.