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This tutorial describes how to construct a model of the interactions betweenThis tutorial describes how to construct a model of the interactions between

a predator species (wolves) and a prey species (moose). Before starting thea predator species (wolves) and a prey species (moose). Before starting the

tutorial, make sure you have familiarized yourself with how to tutorial, make sure you have familiarized yourself with how to createcreate

primitivesprimitives and and run modelsrun models..

First, let's create the structure to model a small population ofFirst, let's create the structure to model a small population of

moose.moose.

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Predator-Prey Interactions (SD)

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Predator-Prey Interactions (SD)

Create a new Create a new StockStock named named MooseMoose ..11

Create a new Create a new FlowFlow going from empty space to the primitive going from empty space to the primitive MooseMoose . Name that flow. Name that flow

Moose BirthsMoose Births ..

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Create a new Create a new FlowFlow going from the primitive going from the primitive MooseMoose to empty space. Name that flow to empty space. Name that flow

Moose DeathsMoose Deaths ..

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The model diagram should now look something like this:The model diagram should now look something like this:

Now that the structure has been defined, let's enter theNow that the structure has been defined, let's enter the

equations to define how our moose population behaves.equations to define how our moose population behaves.

We'll assume 150 moose to start and constant birth- andWe'll assume 150 moose to start and constant birth- and

death-rates.death-rates.

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Change the Change the Initial ValueInitial Value property of the primitive property of the primitive MooseMoose to to 150150 ..55

Change the Change the Flow RateFlow Rate property of the primitive property of the primitive Moose BirthsMoose Births to to 0.16*[Moose]0.16*[Moose] ..66

Change the Change the Flow RateFlow Rate property of the primitive property of the primitive Moose DeathsMoose Deaths to to 0.10*[Moose]0.10*[Moose] ..77

Run the model. Here are sample results:Run the model. Here are sample results:

We see an exponential growth pattern to this model. ThatWe see an exponential growth pattern to this model. That

because the birth-rate is higher than the death-rate. If thebecause the birth-rate is higher than the death-rate. If the

reverse had been true, we would have seen a populationreverse had been true, we would have seen a population

decline over time.decline over time.

Now let's create a population of wolves.Now let's create a population of wolves.

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Create a new Create a new StockStock named named WolvesWolves ..99

Create a new Create a new FlowFlow going from empty space to the primitive going from empty space to the primitive WolvesWolves . Name that flow. Name that flow

Wolf BirthsWolf Births ..

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Create a new Create a new FlowFlow going from the primitive going from the primitive WolvesWolves to empty space. Name that flow to empty space. Name that flow

Wolf DeathsWolf Deaths ..

1111

The model diagram should now look something like this:The model diagram should now look something like this:1212

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Now we can enter equations to define the behavior of theNow we can enter equations to define the behavior of the

wolf population.wolf population.

Change the Change the Initial ValueInitial Value property of the primitive property of the primitive WolvesWolves to to 100100 ..1313

Change the Change the Flow RateFlow Rate property of the primitive property of the primitive Wolf BirthsWolf Births to to 0.2*[Wolves]0.2*[Wolves] ..1414

Change the Change the Flow RateFlow Rate property of the primitive property of the primitive Wolf DeathsWolf Deaths to to 0.12*[Wolves]0.12*[Wolves] ..1515

Run the model. Here are sample results:Run the model. Here are sample results:

So far, so good.So far, so good.

Before we have the two populations interact, let's makeBefore we have the two populations interact, let's make

our model more modular by putting all the rate constantsour model more modular by putting all the rate constants

into separate variable primitives. This will make the modelinto separate variable primitives. This will make the model

easier to mantain.easier to mantain.

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Create a new Create a new VariableVariable named named Moose Birth RateMoose Birth Rate ..1717

Create a new Create a new VariableVariable named named Wolf Birth RateWolf Birth Rate ..1818

Create a new Create a new VariableVariable named named Moose Death RateMoose Death Rate ..1919

Create a new Create a new VariableVariable named named Wolf Death RateWolf Death Rate ..2020

The model diagram should now look something like this:The model diagram should now look something like this:2121

Create a new Create a new LinkLink going from the primitive going from the primitive Moose Birth RateMoose Birth Rate to the primitive to the primitive

Moose BirthsMoose Births ..

2222

Create a new Create a new LinkLink going from the primitive going from the primitive Wolf Birth RateWolf Birth Rate to the primitive to the primitive

Wolf BirthsWolf Births ..

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Create a new Create a new LinkLink going from the primitive going from the primitive Moose Death RateMoose Death Rate to the primitive to the primitive

Moose DeathsMoose Deaths ..

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Create a new Create a new LinkLink going from the primitive going from the primitive Wolf Death RateWolf Death Rate to the primitive to the primitive

Wolf DeathsWolf Deaths ..

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The model diagram should now look something like this:The model diagram should now look something like this:2626

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Let's add the equations for the new cariables to completeLet's add the equations for the new cariables to complete

this modularization.this modularization.

Change the Change the Flow RateFlow Rate property of the primitive property of the primitive Moose BirthsMoose Births to to

[Moose Birth Rate]*[Moose][Moose Birth Rate]*[Moose] ..

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Change the Change the EquationEquation property of the primitive property of the primitive Moose Birth RateMoose Birth Rate to to 0.160.16 ..2828

Change the Change the Flow RateFlow Rate property of the primitive property of the primitive Moose DeathsMoose Deaths to to

[Moose Death Rate]*[Moose][Moose Death Rate]*[Moose] ..

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Change the Change the EquationEquation property of the primitive property of the primitive Moose Death RateMoose Death Rate to to 0.100.10 ..3030

Change the Change the Flow RateFlow Rate property of the primitive property of the primitive Wolf BirthsWolf Births to to

[Wolf Birth Rate]*[Wolves][Wolf Birth Rate]*[Wolves] ..

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Change the Change the EquationEquation property of the primitive property of the primitive Wolf Birth RateWolf Birth Rate to to 0.20.2 ..3232

Change the Change the Flow RateFlow Rate property of the primitive property of the primitive Wolf DeathsWolf Deaths to to

[Wolf Death Rate]*[Wolves][Wolf Death Rate]*[Wolves] ..

3333

Change the Change the EquationEquation property of the primitive property of the primitive Wolf Death RateWolf Death Rate to to 0.120.12 ..

That's it! Let's check to make sure we get the same resultsThat's it! Let's check to make sure we get the same results

as before.as before.

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Run the model. Here are sample results:Run the model. Here are sample results:

Now it's time to make the wolf and moose populationsNow it's time to make the wolf and moose populations

interact. In this model extension, wolves will chase andinteract. In this model extension, wolves will chase and

consume the moose. The more moose they catch, theconsume the moose. The more moose they catch, the

faster the wolves reproduce, and the faster the moosefaster the wolves reproduce, and the faster the moose

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population declines. We'll make the moose death-ratepopulation declines. We'll make the moose death-rate

dependent on the number of wolves, and the wolf birth-dependent on the number of wolves, and the wolf birth-

rate dependent on the number of moose.rate dependent on the number of moose.

Create a new Create a new LinkLink going from the primitive going from the primitive MooseMoose to the primitive to the primitive Wolf Birth RateWolf Birth Rate ..3636

Create a new Create a new LinkLink going from the primitive going from the primitive WolvesWolves to the primitive to the primitive

Moose Death RateMoose Death Rate ..

3737

The model diagram should now look something like this:The model diagram should now look something like this:3838

Change the Change the EquationEquation property of the primitive property of the primitive Wolf Birth RateWolf Birth Rate to to 0.001*[Moose]0.001*[Moose] ..3939

Change the Change the EquationEquation property of the primitive property of the primitive Moose Death RateMoose Death Rate to to

0.0008*[Wolves]0.0008*[Wolves] ..

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Run the model. Here are sample results:Run the model. Here are sample results:

That's getting interesting! Let's increase the length andThat's getting interesting! Let's increase the length and

accuracy of our simulation.accuracy of our simulation.

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Change the Change the Analysis AlgorithmAnalysis Algorithm property of the Time Settings to property of the Time Settings to RK4RK4 ..4242

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Change the Change the Simulation Time StepSimulation Time Step property of the Time Settings to property of the Time Settings to 0.50.5 ..4343

Change the Change the Simulation LengthSimulation Length property of the Time Settings to property of the Time Settings to 100100 ..4444

Run the model. Here are sample results:Run the model. Here are sample results:

Great! The oscillatory behavior we see is typical of someGreat! The oscillatory behavior we see is typical of some

predator-prey systems. The wolves kill many of thepredator-prey systems. The wolves kill many of the

moose, but then the wolves have nothing to eat. Thismoose, but then the wolves have nothing to eat. This

leads the wolf population to drop, allowing the mooseleads the wolf population to drop, allowing the moose

population to recovery. This repeats in an ongoing cycle. population to recovery. This repeats in an ongoing cycle.

We can also configure the display to use a scatter-plotWe can also configure the display to use a scatter-plot

instead of a time-series to show the phase-planeinstead of a time-series to show the phase-plane

oscillatory behavior clearly.oscillatory behavior clearly.

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Run the model. Here are sample results:Run the model. Here are sample results:

There are many parameters in this model you canThere are many parameters in this model you can

experiment with. This form of model what is known as theexperiment with. This form of model what is known as the

Lotka-Volterra ModelLotka-Volterra Model in the modeling community. in the modeling community.

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