# Wolf Sheep Predation (docked)

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## WHAT IS IT?

This model explores the relationship between two different models of predator-prey ecosystems: an agent-based model and a aggregate model. Each of the models can be run separately, or docked side-by-side for comparison.

In the agent model, 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.

The aggregate model is a System Dynamics model of the relationship between populations our wolves and sheep. It is based on a version of the famous Lotka-Volterra model of interactions between two species in an ecosystem.

## HOW TO USE IT

- Adjust the slider parameters (see below), or use the default settings.
- Press the SETUP-COMPARISON button.
- Press the COMPARE button to begin the simulation.
- View the POPULATIONS and AGENT-POPULATIONS plots to watch the populations fluctuate over time

Parameters shared between agent and aggregate models:

- INITIAL-NUMBER-SHEEP: The initial size of sheep population
- INITIAL-NUMBER-WOLVES: The initial size of wolf population
- SHEEP-REPRODUCE: The probability of a sheep reproducing at each time step

Parameters for agent model:

- SHEEP-MAX-INITIAL-ENERGY: At setup time, sheep are given an energy between 1 and this value
- WOLF-GAIN-FROM-FOOD: The amount of energy wolves get for every sheep eaten
- WOLF-REPRODUCE: The probability of a wolf reproducing at each time step

Parameters for aggregate model:

- WOLVES-DEATH-RATE: The rate at which wolves die.
- PREDATION-RATE: The rate at which wolves eat sheep.
- PREDATOR-EFFICIENCY: The efficiency of the wolves in extracting energy to reproduce from the prey they eat.

## THINGS TO NOTICE

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?

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?

## 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 the System Dynamics Modeler to create the aggregate model.

## RELATED MODELS

Look at the Wolf Sheep Predation model for an example of an agent model which can produce a stable model of predator-prey ecosystems.

## CREDITS AND REFERENCES

- Lotka, A.J. (1956) Elements of Mathematical Biology. New York: Dover.
- 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. (in press). Thinking like a Wolf, a Sheep or a Firefly: Learning Biology through Constructing and Testing Computational Theories -- an Embodied Modeling Approach. Cognition & Instruction.

## HOW TO CITE

If you mention this model in a publication, we ask that you include these citations for the model itself and for the NetLogo software:

- Wilensky, U. (2005). NetLogo Wolf Sheep Predation (docked) model. http://ccl.northwestern.edu/netlogo/models/WolfSheepPredation(docked). Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.
- Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 2005 Uri Wilensky.

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

## Comments and Questions

;; 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 to setup clear-all ask patches [ set pcolor green ] 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 1 + random sheep-max-initial-energy 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 1.5 ;; easier to see set energy random (2 * wolf-gain-from-food) setxy random-xcor random-ycor ] display-labels reset-ticks end to go if not any? turtles [ stop ] ask sheep [ move death reproduce-sheep ] ask wolves [ move set energy energy - 1 ;; wolves lose energy as they move catch-sheep death reproduce-wolves ] end to move ;; turtle procedure rt random 50 lt random 50 fd 1 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 display-labels ask turtles [ set label "" ] if show-energy? [ ask wolves [ set label round energy ] ] end to setup-aggregate set-current-plot "populations" clear-plot ;; call procedure generated by aggregate modeler system-dynamics-setup system-dynamics-do-plot end to step-aggregate ;; each agent tick is DT=1 repeat ( 1 / dt ) [ system-dynamics-go ] end to compare go step-aggregate set-current-plot "populations" system-dynamics-do-plot update-plots display-labels end ; Copyright 2005 Uri Wilensky. ; See Info tab for full copyright and license.

There are 10 versions of this model.

## Attached files

File | Type | Description | Last updated | |
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Wolf Sheep Predation (docked).png | preview | Preview for 'Wolf Sheep Predation (docked)' | about 6 years ago, by Uri Wilensky | Download |

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