# Child of Wolf Sheep Predation

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## WHAT IS IT?

This model explores the stability of predator-prey ecosystems. Such a system is called unstable if it tends to result in extinction for one or more species involved. In contrast, a system is stable if it tends to maintain itself over time, despite fluctuations in population sizes.

## HOW IT WORKS

There are two main variations to this model.

In the first variation, wolves and sheep wander randomly around the landscape, while the wolves look for sheep to prey on. Each step costs the wolves energy, and they must eat sheep in order to replenish their energy - when they run out of energy they die. To allow the population to continue, each wolf or sheep has a fixed probability of reproducing at each time step. This variation produces interesting population dynamics, but is ultimately unstable.

The second variation includes grass (green) in addition to wolves and sheep. The behavior of the wolves is identical to the first variation, however this time the sheep must eat grass in order to maintain their energy - when they run out of energy they die. Once grass is eaten it will only regrow after a fixed amount of time. This variation is more complex than the first, but it is generally stable.

The construction of this model is described in two papers by Wilensky & Reisman referenced below.

## HOW TO USE IT

- Set the GRASS? switch to TRUE to include grass in the model, or to FALSE to only include wolves (red) and sheep (white).
- Adjust the slider parameters (see below), or use the default settings.
- Press the SETUP button.
- Press the GO button to begin the simulation.
- Look at the monitors to see the current population sizes
- Look at the POPULATIONS plot to watch the populations fluctuate over time

Parameters: INITIAL-NUMBER-SHEEP: The initial size of sheep population INITIAL-NUMBER-WOLVES: The initial size of wolf population SHEEP-GAIN-FROM-FOOD: The amount of energy sheep get for every grass patch eaten WOLF-GAIN-FROM-FOOD: The amount of energy wolves get for every sheep eaten SHEEP-REPRODUCE: The probability of a sheep reproducing at each time step WOLF-REPRODUCE: The probability of a wolf reproducing at each time step GRASS?: Whether or not to include grass in the model GRASS-REGROWTH-TIME: How long it takes for grass to regrow once it is eaten SHOW-ENERGY?: Whether or not to show the energy of each animal as a number

Notes:

- one unit of energy is deducted for every step a wolf takes
- when grass is included, one unit of energy is deducted for every step a sheep takes

## THINGS TO NOTICE

When grass is not included, watch as the sheep and wolf populations fluctuate. Notice that increases and decreases in the sizes of each population are related. In what way are they related? What eventually happens?

Once grass is added, notice the green line added to the population plot representing fluctuations in the amount of grass. How do the sizes of the three populations appear to relate now? What is the explanation for this?

Why do you suppose that some variations of the model might be stable while others are not?

## THINGS TO TRY

Try adjusting the parameters under various settings. How sensitive is the stability of the model to the particular parameters?

Can you find any parameters that generate a stable ecosystem that includes only wolves and sheep?

Try setting GRASS? to TRUE, but setting INITIAL-NUMBER-WOLVES to 0. This gives a stable ecosystem with only sheep and grass. Why might this be stable while the variation with only sheep and wolves is not?

Notice that under stable settings, the populations tend to fluctuate at a predictable pace. Can you find any parameters that will speed this up or slow it down?

Try changing the reproduction rules -- for example, what would happen if reproduction depended on energy rather than being determined by a fixed probability?

## EXTENDING THE MODEL

There are a number ways to alter the model so that it will be stable with only wolves and sheep (no grass). Some will require new elements to be coded in or existing behaviors to be changed. Can you develop such a version?

## NETLOGO FEATURES

Note the use of breeds to model two different kinds of "turtles": wolves and sheep. Note the use of patches to model grass.

Note use of the ONE-OF agentset reporter to select a random sheep to be eaten by a wolf.

## RELATED MODELS

Look at Rabbits Grass Weeds for another model of interacting populations with different rules.

## CREDITS AND REFERENCES

Wilensky, U. & Reisman, K. (1999). Connected Science: Learning Biology through Constructing and Testing Computational Theories -- an Embodied Modeling Approach. International Journal of Complex Systems, M. 234, pp. 1 - 12. (This model is a slightly extended version of the model described in the paper.)

Wilensky, U. & Reisman, K. (2006). Thinking like a Wolf, a Sheep or a Firefly: Learning Biology through Constructing and Testing Computational Theories -- an Embodied Modeling Approach. Cognition & Instruction, 24(2), pp. 171-209. http://ccl.northwestern.edu/papers/wolfsheep.pdf

## Comments and Questions

globals [grass] ;; keep track of how much grass there is ;; Sheep and wolves are both breeds of turtle. breed [sheep a-sheep] ;; sheep is its own plural, so we use "a-sheep" as the singular. breed [wolves wolf] turtles-own [energy] ;; both wolves and sheep have energy patches-own [countdown] to setup clear-all ask patches [ set pcolor green ] ;; check GRASS? switch. ;; if it is true, then grass grows and the sheep eat it ;; if it false, then the sheep don't need to eat if grass? [ ask patches [ set countdown random grass-regrowth-time ;; initialize grass grow clocks randomly set pcolor one-of [green brown] ] ] set-default-shape sheep "sheep" create-sheep initial-number-sheep ;; create the sheep, then initialize their variables [ set color white set size 1.5 ;; easier to see set label-color blue - 2 set energy random (2 * sheep-gain-from-food) setxy random-xcor random-ycor ] set-default-shape wolves "wolf" create-wolves initial-number-wolves ;; create the wolves, then initialize their variables [ set color black set size 2 ;; easier to see set energy random (2 * wolf-gain-from-food) setxy random-xcor random-ycor ] display-labels set grass count patches with [pcolor = green] reset-ticks end to go if not any? turtles [ stop ] ask sheep [ move if grass? [ set energy energy - 1 ;; deduct energy for sheep only if grass? switch is on eat-grass ] death reproduce-sheep ] ask wolves [ move set energy energy - 1 ;; wolves lose energy as they move catch-sheep death reproduce-wolves ] if grass? [ ask patches [ grow-grass ] ] set grass count patches with [pcolor = green] tick display-labels end to move ;; turtle procedure rt random 50 lt random 50 fd 1 end to eat-grass ;; sheep procedure ;; sheep eat grass, turn the patch brown if pcolor = green [ set pcolor brown set energy energy + sheep-gain-from-food ;; sheep gain energy by eating ] end to reproduce-sheep ;; sheep procedure if random-float 100 < sheep-reproduce [ ;; throw "dice" to see if you will reproduce set energy (energy / 2) ;; divide energy between parent and offspring hatch 1 [ rt random-float 360 fd 1 ] ;; hatch an offspring and move it forward 1 step ] end to reproduce-wolves ;; wolf procedure if random-float 100 < wolf-reproduce [ ;; throw "dice" to see if you will reproduce set energy (energy / 2) ;; divide energy between parent and offspring hatch 1 [ rt random-float 360 fd 1 ] ;; hatch an offspring and move it forward 1 step ] end to catch-sheep ;; wolf procedure let prey one-of sheep-here ;; grab a random sheep if prey != nobody ;; did we get one? if so, [ ask prey [ die ] ;; kill it set energy energy + wolf-gain-from-food ] ;; get energy from eating end to death ;; turtle procedure ;; when energy dips below zero, die if energy < 0 [ die ] end to grow-grass ;; patch procedure ;; countdown on brown patches: if reach 0, grow some grass if pcolor = brown [ ifelse countdown <= 0 [ set pcolor green set countdown grass-regrowth-time ] [ set countdown countdown - 1 ] ] end to display-labels ask turtles [ set label "" ] if show-energy? [ ask wolves [ set label round energy ] if grass? [ ask sheep [ set label round energy ] ] ] end

There is only one version of this model, created almost 10 years ago by J Bizzle.

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**Parent:** Wolf Sheep Predation

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