Ecology | Insight Maker

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/dt = αx - 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.

Clone of Prey&Predator

Anthony Tan

This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.

Clone of Plant, Deer and Wolf Population Dynamics

Hans Niedderer

wolf ~ delayed logistic growth

K Phu

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.

Clone of Clone of Isle Royale: Predator Prey Interactions

Yan

Implications of spraying pesticides to control insects. http://bit.ly/diYPED

Clone of Insect Pest Control

Sam Russell

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.

Senina

Senina Anastassiya

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.

Clone of Isle Royale: Predator Prey Interactions

franzol

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

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

Connor Edwards

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

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

Sally Dufek

Modelo retirado do link

https://insightmaker.com/insight/71649/Fern-Population-Model

Clone of Modelo da populacao de samambaias

joD. Roger

Basic idea is to model demand with endogenous growth (but "satiation" becomes possible - eventually - at some notional "sufficiency" level); and supply then tracks demand with some time lag (~5-50 years - characteristic of commissioning/decommissioning large scale energy infrastructure). Then add cumulative pollution, with a hard constraint/limit which trumps demand and forces supply (of any non-zero polluting source) to zero. In the first instance we'll only have one source, and it will be polluting: so expect to see supply crash. Of course, "demand" will still carry merrily on its way up anyway, but the interpretation of the consequently growing supply shortfall will be left to the eye of the beholder...

Clone of Dystopia: simple energy system model

Paul Price

This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.

Clone of Plant, Deer and Wolf Population Dynamics

Scott Guthrie

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.

Thanks to Jacob Englert for the model if-then-else structure.

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

Clone of MAT 375 Midterm file: Model of Isle Royale: Predator Prey Interactions

Terra Ficke

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.};

Clone of Isle Royale: Predator/Prey Model for Moose and Wolves

Benjamin Nguyen

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

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

Donna Odhiambo

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/dt = αx - 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.

Clone of Predator-Prey Model ("Lotka'Volterra")

Sebastian Mora

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

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

Joey Stevens

This simulation shows how plant, deer and wolf populations impact each other in a deciduous forest ecosystem.

Clone of Plant, Deer and Wolf Population Dynamics

Isaiah Ritzmann

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.

Monday Clone of Isle Royale: Predator Prey Interactions

Andrew E Long

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.

Assignment 3 Derby mountain biking and the effect of logging - 586984

Kelly

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

Clone of Bio 190: BIDE Model With Carrying Capacity

Setya Uswatun Hasanah

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

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

Lizzy Compton

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

Clone of Very Simple Ecosystem Model with Evapotranspiration (VSEM-ET)

beth spilling

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.

Simulation of Derby Mountain bikes versus logging

nicole

Ecology Models