Turtles and Fish

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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, the "sheep-wolves" version, 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. In this variation, we model the grass as "infinite" so that sheep always have enough to eat, and we don't explicitly model the eating or growing of grass. As such, sheep don't either gain or lose energy by eating or moving. This variation produces interesting population dynamics, but is ultimately unstable. This variation of the model is particularly well-suited to interacting species in a rich nutrient environment, such as two strains of bacteria in a petri dish (Gause, 1934).

The second variation, the "sheep-wolves-grass" version explictly models 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. It is a closer match to the classic Lotka Volterra population oscillation models. The classic LV models though assume the populations can take on real values, but in small populations these models underestimate extinctions and agent-based models such as the ones here, provide more realistic results. (See Wilensky & Rand, 2015; chapter 4).

The construction of this model is described in two papers by Wilensky & Reisman (1998; 2006) referenced below.

## HOW TO USE IT

1. Set the model-version chooser to "sheep-wolves-grass" to include grass eating and growth in the model, or to "sheep-wolves" to only include wolves (black) 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:

MODEL-VERSION: Whether we model sheep wolves and grass or just sheep and wolves

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 (Note this is not used in the sheep-wolves model version)

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-REGROWTH-TIME: How long it takes for grass to regrow once it is eaten (Note this is not used in the sheep-wolves model version)

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 running the sheep-wolves-grass model version, one unit of energy is deducted for every step a sheep takes

There are three monitors to show the populations of the wolves, sheep and grass and a populations plot to display the population values over time.

If there are no wolves left and too many sheep, the model run stops.

## THINGS TO NOTICE

When running the sheep-wolves model variation, 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?

In the sheep-wolves-grass model variation, 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 in the sheep-wolves model variation?

Try running the sheep-wolves-grass model variation, 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?

## 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?

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

Can you modify the model so the sheep will flock?

Can you modify the model so that wolves 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

Wilensky, U. & Reisman, K. (1998). Connected Science: Learning Biology through Constructing and Testing Computational Theories -- an Embodied Modeling Approach. International Journal of Complex Systems, M. 234, pp. 1 - 12. (The Wolf-Sheep-Predation 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 .

Wilensky, U., & Rand, W. (2015). An introduction to agent-based modeling: Modeling natural, social and engineered complex systems with NetLogo. Cambridge, MA: MIT Press.

Lotka, A. J. (1925). Elements of physical biology. New York: Dover.

Volterra, V. (1926, October 16). Fluctuations in the abundance of a species considered mathematically. Nature, 118, 558–560.

Gause, G. F. (1934). The struggle for existence. Baltimore: Williams & Wilkins.

## 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.

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

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.

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globals [ max-Fishes ]  ; don't let Fishes population grow too large
; Fishes and wolves are both breeds of turtle.
breed [ Fishes Fish ]  ; Fishes is its own plural, so we use "a-Fishes" as the singular.
breed [ Wolves Wolf ]
turtles-own [ energy ]       ; both wolves and Fishes have energy
patches-own [ countdown ]

to setup
  clear-all
  ifelse netlogo-web? [set max-Fishes 10000] [set max-Fishes 30000]

  ; Check model-version switch
  ; if we're not modeling grass, then the Fishes don't need to eat to survive
  ; otherwise the grass's state of growth and growing logic need to be set up
  ifelse model-version = "Fishes-Turtles-grass" [
    ask patches [
      set pcolor one-of [ 52 105 ]
      ifelse pcolor = 52
        [ set countdown grass-regrowth-time ]
      [ set countdown random grass-regrowth-time ] ; initialize grass regrowth clocks randomly for 105 patches
    ]
  ]
  [
    ask patches [ set pcolor Blue ]
  ]

  create-Fishes initial-number-Fishes  ; create the Fishes, then initialize their variables
  [
    set shape  "Fish"
    set color 45
    set size 2  ; easier to see
    set label-color blue - 2
    set energy random (2 * Fishes-gain-from-food)
    setxy random-xcor random-ycor
  ]

  create-wolves initial-number-Turtles  ; create the wolves, then initialize their variables
  [
    set shape "Turtle"
    set color 72
    set size 3  ; easier to see
    set energy random (2 * Turtles-gain-from-food)
    setxy random-xcor random-ycor
  ]
  display-labels
  reset-ticks
end 

to go
  ; stop the simulation of no wolves or Fishes
  if not any? turtles [ stop ]
  ; stop the model if there are no wolves and the number of Fishes gets very large
  if not any? Turtles and count Fishes > max-Fishes [ user-message "The Fish have inherited the earth" stop ]
  ask Fishes [
    move
    if model-version = "Fishes-Turtles-grass" [ ; in this version, Fishes eat grass, grass grows and it costs Fishes energy to move
      set energy energy - 1  ; deduct energy for Fishes only if running Fishes-wolf-grass model version
      eat-grass  ; Fishes eat grass only if running Fishes-wolf-grass model version
      death ; Fishes die from starvation only if running Fishes-wolf-grass model version
    ]
    reproduce-Fishes  ; Fishes reproduce at random rate governed by slider
  ]
  ask wolves [
    move
    set energy energy - 1  ; wolves lose energy as they move
    eat-Fishes ; wolves eat a Fishes on their patch
    death ; wolves die if our of energy
    reproduce-Turtles ; wolves reproduce at random rate governed by slider
  ]
  if model-version = "Fishes-Turtles-grass" [ ask patches [ grow-Grass ] ]
  ; set grass count patches with [pcolor = 52]
  tick
  display-labels
end 

to move  ; turtle procedure
  rt random 50
  lt random 50
  fd 1
end 

to eat-grass  ; Fishes procedure
  ; Fishes eat grass, turn the patch 105
  if pcolor = 52 [
    set pcolor 105
    set energy energy + Fishes-gain-from-food  ; Fishes gain energy by eating
  ]
end 

to reproduce-Fishes  ; Fishes procedure
  if random-float 100 < Fishes-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-Turtles  ; wolf procedure
  if random-float 100 < Turtles-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 eat-Fishes  ; wolf procedure
  let prey one-of Fishes-here                    ; grab a random Fishes
  if prey != nobody  [                          ; did we get one?  if so,
    ask prey [ die ]                            ; kill it, and...
    set energy energy + Turtles-gain-from-food     ; get energy from eating
  ]
end 

to death  ; turtle procedure (i.e. both wolf nd Fishes procedure)
  ; when energy dips below zero, die
  if energy < 0 [ die ]
end 

to grow-grass  ; patch procedure
  ; countdown on 105 patches: if reach 0, grow some grass
  if pcolor = 105 [
    ifelse countdown <= 0
      [ set pcolor 52
        set countdown grass-regrowth-time ]
      [ set countdown countdown - 1 ]
  ]
end 

to-report grass
  ifelse model-version = "Fishes-Turtles-grass" [
    report patches with [pcolor = 52]
  ]
  [ report 0 ]
end 

to display-labels
  ask turtles [ set label "" ]
  if show-energy? [
    ask Turtles [ set label round energy ]
    if model-version = "Fishes-Turtles-grass" [ ask Fishes [ set label round energy ] ]
  ]
end 


; Copyright 1997 Uri Wilensky.
; See Info tab for full copyright and license.

There is only one version of this model, created about 1 month ago by Carson Fischer.

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