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Wolf Sheep Predation Refuge

by Daniel Torrao, Hugo Mendes, Jonathan Marques, Maria Anjo, Melania Falcon & Ruben Cunha (Submitted: 05/28/2008 )

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WHAT IS IT?

This model explores the stability of predator-prey ecosystems in the presence of a refuge area for preys. 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, predators (wolves) and prey (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. _______________________________________________________________________________________
Refuge Version:
A third variable was added to the model. The presence of a user-defined refuge makes it possible to study the stability of the predator-prey ecosystem in the presence of an area where predators are not allowed. This area can be modified in size.
Sheep can move randomly throughout the world. The wolves also move randomly, but are not allowed inside the refuge area.

HOW TO USE IT

1. Set the GRASS? switch to TRUE to include grass in the model, or to FALSE to only include wolves (red) and sheep (white).
2. Adjust the slider parameters (see below), or use the default settings.
3. Press the SETUP button.
4. Press the GO button to begin the simulation.
5. Look at the monitors to see the current population sizes
6. 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
REFUGE-SIZE: Relative size of the refuge area.

Notes:
- for refuge to work, the location of origin must be in the center of the world
- 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?
_______________________________________________________________________________________
Refuge Version:

Varying the size of the refuge, it is visible that this size affects the relationship dynamics between predators and prey, altering there survival. What do you notice when refuge is increased or decreased?

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?
_______________________________________________________________________________________
Refuge Version:

Try studying the model variation several times for each refuge size, with and without grass. What do you see?

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?
_______________________________________________________________________________________
Refuge Version:

Try creating a model in which the refuge can be used even without the location of origin being in the center of the world. You can also try creating a refuge with a different format (e.g. a square in the center) or a partial refuge, in which predators can enter at precise moments or situations. Is this possible?

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. (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.

To refer to this model in academic publications, please use: Wilensky, U. (1997). NetLogo Wolf Sheep Predation model. http://ccl.northwestern.edu/netlogo/models/WolfSheepPredation. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

In other publications, please use: Copyright 1997 Uri Wilensky. All rights reserved. See http://ccl.northwestern.edu/netlogo/models/WolfSheepPredation for terms of use.
_______________________________________________________________________________________
Refuge Version:

Daniel Torrão, Hugo Mendes, Jonathan Marques, Maria Anjo, Melania Falcón & Ruben Cunha (2008). Dinâmica Populacional (Supervisor: Prof. Dr. José M. N. Azevedo). Departamento de Biologia. Universidade dos Açores.

VERSION

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