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 websi
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 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.
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.
There is a concern that Logging has an adverse effect on the experience of tourist mountain bikers looking for nature experiences in Derby, Tasmaina.    This model helps give more insight on the relationship between the forest industry and mountain tourism, showing that despite the changes and incre
There is a concern that Logging has an adverse effect on the experience of tourist mountain bikers looking for nature experiences in Derby, Tasmaina.

This model helps give more insight on the relationship between the forest industry and mountain tourism, showing that despite the changes and increase in logging activities with the aim of generating more income from timber, there can be a balance between mountain tourism and the forest industry.
Interactions between wolves and livestock depending on abundance
Interactions between wolves and livestock depending on abundance
A simple and easy to follow model of how fertility and mortality affect a population, using ferns as an example.
A simple and easy to follow model of how fertility and mortality affect a population, using ferns as an example.
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.
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.};

 Overview:   This simulation will show the relationship between tree logging forestry and how this can affect mountain biking tourism in Derby Park Tasmania. The main goal of this simulation is to show these two industries can co-exist in the same environment, or increase in demand or production in
Overview: 
This simulation will show the relationship between tree logging forestry and how this can affect mountain biking tourism in Derby Park Tasmania. The main goal of this simulation is to show these two industries can co-exist in the same environment, or increase in demand or production in one sector will affect the result of another.  

Function of the model:
In comparison there are both pros and cons for both sectors working correspondently. Demand for derby park is caused by individual past experience when visiting the park or friends recommendation which increase in the number of demands. Increase in demands will increase in the number of visitors. When visitors visits the park they require make a purchase a bike and pay the park for using the park facilities. All this will adds up to bikers total spending when visiting Derby. When consumer spend it is booting the economy especially in the tourism sector. Similarly tree logging will also contribute financially towards the Tasmania economy. The regeneration stage is relatively low compare to the logging rate. The growth will not cover the loss which can cause some level of damage in the scenery of the park, affecting tourist to view when mountain biking. Visitors overall experience will have the impact towards the demand for mountain biking in derby park, if visitors experience is satisfied they will come back to visit again or visit with group of friends, even words of mouth recommendation will also increase the level of demand of visiting Derby. 

Some key insights base on the simulation:
Based on the simulation of the two models we can see there are some key changes.
Tree logging increase will cause the disturbance of the natural scenery, thus change the overall experience of the visitors, decrease in the level of demand. Tree logging will also have negative impact towards the overall tourist experience thus affect the park facility and track. The natural scenery and the overall experience can affect their experience and if they would continue to recommend this area to friends to increase the demand. 

  ​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 dis
​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.

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 websi
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

 Overview:   The model shows the industry competition and relationship between Forrestry and Mountain Bike Trip in Derby, Tasmania. The aim of the simulation is to find a balance between the co-existence of these two industry.      How Does the Model Work?       Both industries will generate incomes
Overview: 
The model shows the industry competition and relationship between Forrestry and Mountain Bike Trip in Derby, Tasmania. The aim of the simulation is to find a balance between the co-existence of these two industry.

How Does the Model Work?

Both industries will generate incomes. Firstly, income is generated from the sale of timber through logging. In addition, income is also generated from the consumption of mountain bike riders. Regarding to the Forrestry industry, people cut down trees because there is a market demand for timber. The timber is sold for profits. However, the experience of mountain biking tourism is largely affected by the low regeneration rate of trees and the degradation of the environment and landscape due to tree felling. People have better riding experiences when trees are abundant and the scenery is beautiful. People's satisfaction and expectations depend on the scenery and experience. Recommendations of past riders will also impact the tourists amount.

Interesting Insights

The income generated by logging can provide a significant economic contribution to Tasmania, but excessive logging can lead to environmental problems and a reduction in visitors. Excessive logging can lead to a decline in tourism in the mountains, which will affect tourism. Despite the importance of forestry, tourism can also provide a significant economic contribution to Tasmania. The government should find a balance between the two industries while maintaining the number of tourists. 



Dynamic system modelling the effect of pest population reductions in transport vectors hubs (e.g. marina or port), by means of a biocontrol agent (e.g. gastropod snail), on the spread of marine pests into new areas.
Dynamic system modelling the effect of pest population reductions in transport vectors hubs (e.g. marina or port), by means of a biocontrol agent (e.g. gastropod snail), on the spread of marine pests into new areas.
 The purpose of this deer management model is to explore the capacity of wildlife management actions to help us adapt to the effects of climate change.

The purpose of this deer management model is to explore the capacity of wildlife management actions to help us adapt to the effects of climate change.

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 websi
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 illustrates predator prey interactions using real-life data of fox and rabbit populations.
This model illustrates predator prey interactions using real-life data of fox and rabbit populations.
A collaborative class project with each participant creating an animal/plant sub-model​ to explore the greater population/community dynamics of the Yellowstone ecosystem.
A collaborative class project with each participant creating an animal/plant sub-model​ to explore the greater population/community dynamics of the Yellowstone ecosystem.
Modeling forest succession in a northeast deciduous forest.
Modeling forest succession in a northeast deciduous forest.