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Wolf Sheep Predator-Mediated Coexistence

by Teresa S. Alexandre, Vanessa Costa & Rúben Rego (Submitted: 01/03/2017)

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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.

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<b>Predator-mediated coexistence model:</b>
This model explores the predator-mediated coexistence, which occurs when selective predation favours the coexistence of prey species that might otherwise exclude one another, contributing to an increase of the number of species in a community as long as the preferred prey species is the competitively dominant.

## 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.

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<b>Predator-mediated coexistence model:</b>
There are two types of prey: sheep and goats. The competition between them can be changed in the interface.
Wolves look around searching for sheep and goats to eat. Wolves eat both sheep and goats, but they will prefer to eat a sheep if they notice the presence of one in a patch near them (this preference can also be changed in the interface).

## 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

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

_____________________________________________________________________________________

<b>Predator-mediated coexistence model:</b>

Parameters:
INITIAL-NUMBER-GOATS: The initial size of goats population.
GOAT-GAIN-FROM-FOOD: The amount of energy goats get for every grass patch eaten.
WOLF-GOAT-PREFERENCE: Preference that a wolf shows for a goat.
GOAT-REPRODUCE: The probability of a goat reproducing at each time step.

## 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?

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<b>Predator-mediated coexistence model:</b>
Notice that when there's no wolves in the ecosystem, the dynamics between populations of goats and sheep will change. How so ? Why does that happen ?

## 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?

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<b>Predator-mediated coexistence model:</b>
Try to change the wolf-goat-preference in the interface. How does that afect the populations ?

Try to change the competitive domince between goats and sheep by playing with the 'sheep-gain-from-fodd' or'sheep-reproduce' and the 'goat-gain-from-food' or 'goat-reproduce'. How does that affect the populations ?

Take wolfs out of the equations changing the 'initial-number-wolves' to 0. What will happen ?

## 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?

Can you modify the model so the sheep will flock?

Can you modify the model so that wolf actively chase sheep?

## 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

Townsend, C. R., Begon, M. & Harper, J. L. (2008). Essentials of Ecology. Third Edition. Blackwell Publishing, 522 pp.

## HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

* 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.

Please cite the NetLogo software as:

* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 1997 Uri Wilensky.

![CC BY-NC-SA 3.0](http://ccl.northwestern.edu/images/creativecommons/byncsa.png)

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

This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML). The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.

This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2000.

<!-- 1997 2000 -->

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<b>Predator-mediated coexistence model:</b>

Copyright 2016. Teresa Sofia Alexandre, Vanessa Costa e Rúben Rego.

![CC BY-NC-SA 3.0](http://ccl.northwestern.edu/images/creativecommons/byncsa.png)

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