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.
This non-dimensionalized, sleekest most neatest model illustrates predator prey interactions using logistic growth for the moose population, for the wolf and moose populations on Isle Royale.   Thanks Scott Fortmann-Roe for the original model.  I've added in an adjustment to handle population sizes,
This non-dimensionalized, sleekest most neatest model illustrates predator prey interactions using logistic growth for the moose population, for the wolf and moose populations on Isle Royale.

Thanks Scott Fortmann-Roe for the original model.

I've added in an adjustment to handle population sizes, by dividing by moose carrying capacity.

Time is scaled by the moose birth parameter:
tau=bm*t

There are therefore only three parameters left to account for any dynamics:

beta = bw/bm (relative wolf to moose births)
delta = dm/bm (relative death to birth ratio for moose)
gamma = dw/bm (wolf deaths to moose births)

The equations are thus

dM/dtau = M [ (1-M) - delta W ]
dW/dtau = W [beta M - gamma ]

There is a stable equilibrium pair of population values, relative to the carrying capacity:

M^* = gamma / beta
W^* = (1-gamma / beta) / delta

I have a sleek version with a logistical growth term for the moose, at

http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker-sleek.nb
This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.
This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.
 A simulation illustrating simple predator prey dynamics. You have two populations.

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

Westley, F. R., O. Tjornbo, L. Schultz, P. Olsson, C. Folke, B. Crona and Ö. Bodin. 2013. A theory of transformative agency in linked social-ecological systems.  Ecology and Society   18 (3): 27.  link
Westley, F. R., O. Tjornbo, L. Schultz, P. Olsson, C. Folke, B. Crona and Ö. Bodin. 2013. A theory of transformative agency in linked social-ecological systems. Ecology and Society 18(3): 27. link

  Overview     This model simulates logging and mountain biking competition in Derby, Tasmania. The Simulation is referenced to simulate Derby mountain biking with logging.      Model   W  ork     The tourism industry is represented on the model's left side, and the logging industry is on the right

Overview

This model simulates logging and mountain biking competition in Derby, Tasmania. The Simulation is referenced to simulate Derby mountain biking with logging.

 

Model Work

The tourism industry is represented on the model's left side, and the logging industry is on the right side. Interactions between these two industries generate tax revenues. Logging and tourism have different growth rates regarding people working/consuming. The initial values of these two industries in the model are not fixed but increase yearly due to inflation or economic growth.

 

Detail Insights

From the perspective of tourism, as the number of tourists keeps growing, the number of people who choose to ride in Derby City also gradually increases. And the people who ride rate the ride. The negative feedback feeds back into the cycling population. Similarly, positive cycling reviews lead to more customer visits. And all the customers will create a revenue through tourism, and a certain proportion of the income will become tourism tax.

From a logging perspective, it is very similar to the tourism industry. As the number of people working in the industry is forecast to increase, the industry's overall size is predicted to grow. And as the industry's size continues to rise, the taxes on the logging industry will also continue to rise. Since logging is an industry, the tax contribution will be more significant than the tourism excise tax.

 

This model assumption is illustrated below:

1. The amount of tax reflects the level of industrial development.

2. The goal of reducing carbon emissions lets us always pay attention to the environmental damage caused by the logging industry.

3. The government's regulatory goal is to increase overall income while ensuring the environment.

4. Logging will lead to environmental damage, which will decrease the number of tourists.

 

This model is based on tourism tax revenue versus logging tax revenue. Tourism tax revenue is more incredible than logging tax revenue, indicating a better environment. As a result of government policy, the logging industry will be heavily developed in the short term. Growth in the logging industry will increase by 40%. A growth rate of 0.8 and 0.6 of the original is obtained when logging taxes are 2 and 4 times higher than tourism taxes.

 

Furthermore, tourism tax and logging tax also act on the positive rate, which is the probability that customers give a positive evaluation. The over-development of the logging industry will lead to the destruction of environmental resources and further affect the tourism industry. The logging tax will also affect the tourism Ride Rate, which is the probability that all tourism customers will choose Derby city.

 

This model more accurately reflects logging and tourism's natural growth and ties the two industries together environmentally. Two ways of development are evident in the two industries. Compared to tourism, logging shows an upward spiral influenced by government policies. Government attitudes also affect tourism revenue, but more by the logging industry. 

This is my first Insight from the BIDE model of environmental science for BIO 190
This is my first Insight from the BIDE model of environmental science for BIO 190
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

 The body of research and studies generated on the Fryingpan River between the 1940s and the present supports the development of a conceptual model of ecosystem responses to hydrological regime behavior and streamflow management activities. This conceptual model should encourage conversations about

The body of research and studies generated on the Fryingpan River between the 1940s and the present supports the development of a conceptual model of ecosystem responses to hydrological regime behavior and streamflow management activities. This conceptual model should encourage conversations about system behavior and collective understanding among stakeholders regarding connections between specific hydrological regime characteristics affected by management of Ruedi Reservoir and the ecological or biological variables important to local communities. For the sake of simplicity, the model includes mostly unidirectional relationships—feedback loops are exploded to reveal intermediate connections between variables. This approach increases the number of variables represented in the system, perhaps increasing its complexity at first glance. However, the primary benefit to the end user is that the model becomes more readable and explicit in its representation of system behavior. 

 

The conceptual model presented here likely differs by degrees from those held by the various investigators who considered Fryingpan River processes over the previous 80 years. However, it affectively aggregates the ideas main presented by each of those individuals. This model focuses on hydrological and biological variables and does not incorporate the entire diversity of human uses and needs for water from the Fryingpan River (e.g. hydropower production for the City of Aspen, revenue generated in the Town of Basalt by angling activities, etc.).  Rather it attempts to illustrate how the conditional state of important ecosystem characteristics might respond to reservoir management activities that impact typical spring flows, peak flow timing and magnitude, summer flows, fall flows, and winter flows. 

Simple dynamic model of species gain and loss from individual trees as patches in the landscape, including removal of surrounding trees and changes in climatic stressors.
Simple dynamic model of species gain and loss from individual trees as patches in the landscape, including removal of surrounding trees and changes in climatic stressors.
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 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.};

A flow based recreation of the base model presented in Munz et al 2009 using zombies to teach basic SIR epidemiology models
A flow based recreation of the base model presented in Munz et al 2009 using zombies to teach basic SIR epidemiology models
This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.  Experiment with adjusting the initial number of moose and wolves on the island.
This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

Experiment with adjusting the initial number of moose and wolves on the island.
 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 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.
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.