contaminacion empresas

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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.


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.


  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


  • 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


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?


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?


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?


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.


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


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.


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


Copyright 1997 Uri Wilensky.


This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit 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

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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;; Sheep and wolves are both "breeds" of turtle.

breed [empresas empresa]  ;; plural y singular
breed [arboles arbol]

turtles-own [energía]       ;; ovejas y lobos, ambos tienen una variable "energía" 
patches-own [ crecimiento ]   ;;variable que el estado de la hierba 20=lista para comer; <20 = no lista

;;iniciar --> establecer el mundo del modelo....

to iniciar
  ask patches [ 
    set crecimiento random 21
    ifelse (crecimiento = 20) 
    [ set pcolor black ]
    [ set pcolor blue ]

  create-empresas num-inicial-empresas  ;; crear a las ovejas, y inicializar sus variables, incluyendo energía
    set color pink
    set shape "house"
    set size 3.5  ;; más fácil ver
    set energía random (2 * empresas-energía-de-arboles) + 10
    setxy random-xcor random-ycor
  create-arboles num-inicial-arboles  ;; crear a los lobos...
    set color green
    set shape "tree"
    set size 1.5  ;; más fácil ver
    set energía random (2 * arboles-energía-de-aire)
    setxy random-xcor random-ycor


to ir
  if not any? arboles [ stop ]
  ask empresas [
  ask arboles [
    ;set energía energía - 1  ;; wolves lose energy as they move
  ask patches [

;;acá todos los comportamientos

to mover  ;; se usa tanto los lobos como las ovejas
  rt random 50
  lt random 50
  fd 1
  set energía energía - 1

to comer-hierba ;; sheep procedure
  ;; cuando la oveja come hierba, cambia a marrón
  if pcolor = blue [
    set pcolor black
    set crecimiento 0
    set energía energía + empresas-energía-de-arboles  ;; sheep gain energy by eating

to reproducir-empresas  ;; sheep procedure
    if random 100 < probabilidad-repro-empresas [  ;;si el número aleatorio esté menos que la meta
      set energía (energía / 2)                ;; dividir energía con mi hijo/a
      hatch 1 [ set heading random-float 360 ]   ;; producir un niño con heading aleatorio

to reproducir-arboles  ;; wolf procedure
    if random 100 < probabilidad-repro-arboles [  ;;si el número aleatorio esté menos que la meta
      set energía (energía / 2)               ;; dividir energía con mi hijo/a
      hatch 1 [ set heading random-float 360  ]  ;;  producir un niño con heading aleatorio

to cazar-empresas  ;; wolf procedure
  let prey one-of empresas-here                    ;;elige una de las ovejas acá
  if prey != nobody                             ;; si logramos encontrar una
    [ ask prey [ die ]                          ;; cómela
      set energía energía + arboles-energía-de-aire ] ;; recibir energía

to quizás-morir  
  ;; si no tenemos energía, vamos a morir
  if energía < 0 [ die ]

to crecer-hierba
  if crecimiento < 20 [
    set crecimiento crecimiento + 1
  if crecimiento = 20 [
    set pcolor blue

There is only one version of this model, created about 6 years ago by perla yamilet garcia whitaker.

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