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 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.
 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 an implementation of the 'Very Simple Ecosystem Model' (VSEM) from R package BayesianTools (Hartig et al. 2019). It consists of three stocks: aboveground carbon in plant biomass, belowground carbon in plant biomass and carbon in soil organic matter.     Reference:  Florian Hartig, Francesco
This is an implementation of the 'Very Simple Ecosystem Model' (VSEM) from R package BayesianTools (Hartig et al. 2019). It consists of three stocks: aboveground carbon in plant biomass, belowground carbon in plant biomass and carbon in soil organic matter. 

Reference:
Florian Hartig, Francesco Minunno and Stefan Paul (2019). BayesianTools: General-Purpose MCMC and SMC Samplers and Tools for Bayesian Statistics. R package version 0.1.7. https://CRAN.R-project.org/package=BayesianTools
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

Clone of:  'Sucesion Forestal' (by Denny S. Fernandez del Viso) for subtropical forest, which in turn is a modification of 'Modeling forest succession in a northeast deciduous forest' (by Owen Stuart).   Translated to English (by Lisa Belyea)
Clone of: 
'Sucesion Forestal' (by Denny S. Fernandez del Viso) for subtropical forest, which in turn is a modification of 'Modeling forest succession in a northeast deciduous forest' (by Owen Stuart).
Translated to English (by Lisa Belyea)
    Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system.  For some time modelers have been particularly int

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system.  For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system.  The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926).  Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them.  Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined.  Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed.  Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey.  It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature.  And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.
2. The food supply of the predator population depends entirely on the size of the prey population.
3. The rate of change of population is proportional to its size.
4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.
5. Predators have limitless appetite.
As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey
When multiplied out, the prey equation becomes
dx/dtαx - βxy
 The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.


 This model is a modified version of the 'Very Simple Ecosystem Model' (VSEM; Hartig et al. 2019). Controls have been added to gross primary productivity (GPP) and heterotrophic respiration (Rhetero) based on evapotranspiration rates.    Reference:  Hartig, F., Minunno, F., and Paul, S. (2019). Baye
This model is a modified version of the 'Very Simple Ecosystem Model' (VSEM; Hartig et al. 2019). Controls have been added to gross primary productivity (GPP) and heterotrophic respiration (Rhetero) based on evapotranspiration rates.

Reference:
Hartig, F., Minunno, F., and Paul, S. (2019). BayesianTools: General-Purpose MCMC and SMC Samplers and Tools for Bayesian Statistics. R package version 0.1.7. https://CRAN.R-project.org/package=BayesianTools
241 12 months ago
  Overview  A model which simulates the competition between logging versus adventure tourism (mountain bike ridding) in Derby Tasmania.  Simulation borrowed from the Easter Island simulation.     How the model works.   Trees grow, we cut them down because of demand for Timber amd sell the logs.  Wit
Overview
A model which simulates the competition between logging versus adventure tourism (mountain bike ridding) in Derby Tasmania.  Simulation borrowed from the Easter Island simulation.

How the model works.
Trees grow, we cut them down because of demand for Timber amd sell the logs.
With mountain bkie visits.  This depends on past experience and recommendations.  Past experience and recommendations depends on Scenery number of trees compared to visitor and Adventure number of trees and users.  Park capacity limits the number of users.  
Interesting insights
It seems that high logging does not deter mountain biking.  By reducing park capacity, visitor experience and numbers are improved.  A major problem is that any success with the mountain bike park leads to an explosion in visitor numbers.  Also a high price of timber is needed to balance popularity of the park. It seems also that only a narrow corridor is needed for mountain biking
 ​Physical meaning of the equations  The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:        1. The prey population finds ample food at all times.    2. The food supply of the predator population depends entirely on the
​Physical meaning of the equations
The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.
2. The food supply of the predator population depends entirely on the size of the prey population.
3. The rate of change of population is proportional to its size.
4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.
5. Predators have limitless appetite.
As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey
When multiplied out, the prey equation becomes
dx/dtαx - βxy
 The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.


This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.
This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.


  Overview  A model which simulates the competition between logging versus adventure tourism (mountain bike ridding) in Derby Tasmania.  Simulation borrowed from the Easter Island simulation.     How the model works.   Trees grow, we cut them down because of demand for Timber amd sell the logs.  Wit
Overview
A model which simulates the competition between logging versus adventure tourism (mountain bike ridding) in Derby Tasmania.  Simulation borrowed from the Easter Island simulation.

How the model works.
Trees grow, we cut them down because of demand for Timber amd sell the logs.
With mountain bkie visits.  This depends on past experience and recommendations.  Past experience and recommendations depends on Scenery number of trees compared to visitor and Adventure number of trees and users.  Park capacity limits the number of users.  
Interesting insights
It seems that high logging does not deter mountain biking.  By reducing park capacity, visitor experience and numbers are improved.  A major problem is that any success with the mountain bike park leads to an explosion in visitor numbers.  Also a high price of timber is needed to balance popularity of the park. It seems also that only a narrow corridor is needed for mountain biking
 Introduction  Simple model of the spring bloom in coastal temperate coastal waters. Nitrogen is assumed to be the limiting nutrient, so the model is based on N only. The model represents one liter of water. Dissolved inorganic nitrogen (DIN) accumulates in the water column during winter and has rea
Introduction
Simple model of the spring bloom in coastal temperate coastal waters. Nitrogen is assumed to be the limiting nutrient, so the model is based on N only. The model represents one liter of water. Dissolved inorganic nitrogen (DIN) accumulates in the water column during winter and has reached 250 µmol/L on March 1st where the model starts. At this time the light intensity have just reached the level necessary to initiate the bloom.

Model setup
N uptake: Michaelis Menten kinetics with a maximum growth rate that doubles the population each day. Km=5µM.

Grazing: Michaelis Menten kinetics with a maximum daily uptake equal to the N in the population. Km=50µM.

Sloppy eating: 60% of the grazing is wasted to PON

Death: 5% of the zooplankton dies each day

Mineralization: 1% of the PON is mineralized to DIN each day

Results
For the first 6 days the phytoplankton grows exponentially and depletes the DIN pool. The peak in phytoplankton is followed by a delayed peak in zooplankton due to its slower growth rate. Slowly the zooplankton graze down the spring bloom and the nitrogen is transformed to the pool of particulate dead organic nitrogen (PON). While this happens the phytoplankton is kept low by the still high zooplankton which allow the DIN pool to increase from day 25 to day 55. Eventually the phytoplankton escapes the top down control and we see a secondary bloom based on regenerated DIN.
 A simulation illustrating simple predator prey dynamics. You have two populations.

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

This model explains the difference between Mountain bikes riding compared to logging in the Tasmanian forests. Logging allows the activity in the forest with a negative demand for timber providing an income (with the price variable). The deforestation variable shows us that over time, the forest wil
This model explains the difference between Mountain bikes riding compared to logging in the Tasmanian forests.
Logging allows the activity in the forest with a negative demand for timber providing an income (with the price variable). The deforestation variable shows us that over time, the forest will run out if the logging keeps going on this way.
Alternatively, mountain biking allows a demand of visitors who want to see the scenary. They increase the regional tourism which is good for the community as it involves other businesses around too. The charges paid by visitors and tourists allow an income for the activity which makes it productive over time and great for TAS.
As we stimulate the model, we can see that it is better to have more visitors and more tourists rather than more logging as it will be better over time.
This model describes how costs, income and ecosystem services change with stocking rate.
This model describes how costs, income and ecosystem services change with stocking rate.
  Overview  

 It is a model simulating
logging and adventure tourism (mountain bike riding) competition in Derby,
Tasmania. It is a chance for northeast Tasmania to become an exciting, new, world-class
product for the mountain bike tourism industry, which drives local economic
development. 

 Simul

Overview

It is a model simulating logging and adventure tourism (mountain bike riding) competition in Derby, Tasmania. It is a chance for northeast Tasmania to become an exciting, new, world-class product for the mountain bike tourism industry, which drives local economic development.

Simulation borrowed from the Easter Island simulation.

How the model works

l  Trees grow; we cut them down because of demand for Timber and sell the logs.

l  The mountain bike visits depend on previous experience and suggestions.

l  Previous experience and suggestions depend on the number of trees compared to visitors and adventure number of trees and users. Park capacity limits the number of mountain bike trail users.

l  The employment opportunity depends on the mountain bike demand and demand for Timber.

Interesting Insights

Mountain biking appears to be unaffected by heavy logging. The visitor experience and numbers are improved by reducing park capacity. The main issue is that any success with the mountain bike park increases visitor numbers. A high timber price is also required to balance the park's popularity. Mountain biking appears to require only a narrow corridor; that is, single-track mountain bike trails are enough. The employment is a measure of the economic acting, a recession or growth trends.

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.
This model illustrates predator prey interactions using real-life data of bison and wolf populations at Yellowstone National Park.
This model illustrates predator prey interactions using real-life data of bison and wolf populations at Yellowstone National Park.


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.};

    Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system.  For some time modelers have been particularly int

Dynamic simulation modelers are particularly interested in understanding and being able to distinguish between the behavior of stocks and flows that result from internal interactions and those that result from external forces acting on a system.  For some time modelers have been particularly interested in internal interactions that result in stable oscillations in the absence of any external forces acting on a system.  The model in this last scenario was independently developed by Alfred Lotka (1924) and Vito Volterra (1926).  Lotka was interested in understanding internal dynamics that might explain oscillations in moth and butterfly populations and the parasitoids that attack them.  Volterra was interested in explaining an increase in coastal populations of predatory fish and a decrease in their prey that was observed during World War I when human fishing pressures on the predator species declined.  Both discovered that a relatively simple model is capable of producing the cyclical behaviors they observed.  Since that time, several researchers have been able to reproduce the modeling dynamics in simple experimental systems consisting of only predators and prey.  It is now generally recognized that the model world that Lotka and Volterra produced is too simple to explain the complexity of most and predator-prey dynamics in nature.  And yet, the model significantly advanced our understanding of the critical role of feedback in predator-prey interactions and in feeding relationships that result in community dynamics.The Lotka–Volterra model makes a number of assumptions about the environment and evolution of the predator and prey populations:

1. The prey population finds ample food at all times.
2. The food supply of the predator population depends entirely on the size of the prey population.
3. The rate of change of population is proportional to its size.
4. During the process, the environment does not change in favour of one species and genetic adaptation is inconsequential.
5. Predators have limitless appetite.
As differential equations are used, the solution is deterministic and continuous. This, in turn, implies that the generations of both the predator and prey are continually overlapping.[23]

Prey
When multiplied out, the prey equation becomes
dx/dtαx - βxy
 The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in the equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by βxy. If either x or y is zero then there can be no predation.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

Predators

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.


 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.