globals [ max-fish ] ; don't let fish population grow too large ; fish and sharks are both breeds of turtle. breed [ fish a-fish ] ; fish is its own plural, so we use "a-fish" as the singular. breed [ sharks shark ] turtles-own [ energy ] ; both sharks and fish have energy patches-own [ countdown ] to setup clear-all ifelse netlogo-web? [set max-fish 10000] [set max-fish 30000] ; Check model-version switch ; if we're not modeling water, then the fish don't need to eat to survive ; otherwise the water's state of growth and growing logic need to be set up ifelse model-version = "fish-sharks-water" [ ask patches [ set pcolor one-of [ blue brown ] ifelse pcolor = blue [ set countdown water-regrowth-time ] [ set countdown random water-regrowth-time ] ; initialize water regrowth clocks randomly for brown patches ] ] [ ask patches [ set pcolor blue ] ] create-fish initial-number-fish ; create the fish, then initialize their variables [ set shape "fish" set color white set size 1.5 ; easier to see set label-color blue - 2 set energy random (2 * fish-gain-from-food) setxy random-xcor random-ycor ] create-sharks initial-number-sharks ; create the sharks, then initialize their variables [ set shape "shark" set color black set size 2 ; easier to see set energy random (2 * shark-gain-from-food) setxy random-xcor random-ycor ] display-labels reset-ticks end to go ; stop the simulation of no sharks or fish if not any? turtles [ stop ] ; stop the model if there are no sharks and the number of fish gets very large if not any? sharks and count fish > max-fish [ user-message "The fish have inherited the earth" stop ] ask fish [ move if model-version = "fish-sharks-water" [ ; in this version, fish eat water, water grows and it costs fish energy to move set energy energy - 1 ; deduct energy for fish only if running fish-shark-water model version eat-water ; fish eat water only if running fish-shark-water model version death ; fish die from starvation only if running fish-shark-water model version ] reproduce-fish ; fish reproduce at random rate governed by slider ] ask sharks [ move set energy energy - 1 ; sharks lose energy as they move eat-fish ; sharks eat a fish on their patch death ; sharks die if our of energy reproduce-sharks ; sharks reproduce at random rate governed by slider ] if model-version = "fish-sharks-water" [ ask patches [ grow-water ] ] ; set water count patches with [pcolor = blue] tick display-labels end to move ; turtle procedure rt random 50 lt random 50 fd 1 end to eat-water ; fish procedure ; fish eat water, turn the patch brown if pcolor = blue [ set pcolor brown set energy energy + fish-gain-from-food ; fish gain energy by eating ] end to reproduce-fish ; fish procedure if random-float 100 < fish-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-sharks ; shark procedure if random-float 100 < shark-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-fish ; shark procedure let prey one-of fish-here ; grab a random fish if prey != nobody [ ; did we get one? if so, ask prey [ die ] ; kill it, and... set energy energy + shark-gain-from-food ; get energy from eating ] end to death ; turtle procedure (i.e. both shark nd fish procedure) ; when energy dips below zero, die if energy < 0 [ die ] end to grow-water ; patch procedure ; countdown on brown patches: if reach 0, grow some water if pcolor = brown [ ifelse countdown <= 0 [ set pcolor blue set countdown water-regrowth-time ] [ set countdown countdown - 1 ] ] end to-report water ifelse model-version = "fish-sharks-water" [ report patches with [pcolor = blue] ] [ report 0 ] end to display-labels ask turtles [ set label "" ] if show-energy? [ ask sharks [ set label round energy ] if model-version = "fish-sharks-water" [ ask fish [ set label round energy ] ] ] end ; Copyright 1997 Uri Wilensky. ; See Info tab for full copyright and license. @#$#@#$#@ GRAPHICS-WINDOW 355 10 873 529 -1 -1 10.0 1 14 1 1 1 0 1 1 1 -25 25 -25 25 1 1 1 ticks 30.0 SLIDER 5 60 179 93 initial-number-fish initial-number-fish 0 250 250.0 1 1 NIL HORIZONTAL SLIDER 5 196 179 229 fish-gain-from-food fish-gain-from-food 0.0 50.0 4.0 1.0 1 NIL HORIZONTAL SLIDER 5 231 179 264 fish-reproduce fish-reproduce 1.0 20.0 4.0 1.0 1 % HORIZONTAL SLIDER 185 60 350 93 initial-number-sharks initial-number-sharks 0 250 50.0 1 1 NIL HORIZONTAL SLIDER 183 195 375 228 shark-gain-from-food shark-gain-from-food 0.0 100.0 20.0 1.0 1 NIL HORIZONTAL SLIDER 183 231 348 264 shark-reproduce shark-reproduce 0.0 20.0 5.0 1.0 1 % HORIZONTAL SLIDER 40 100 252 133 water-regrowth-time water-regrowth-time 0 100 30.0 1 1 NIL HORIZONTAL BUTTON 40 140 109 173 setup setup NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 115 140 190 173 go go T 1 T OBSERVER NIL NIL NIL NIL 0 PLOT 10 360 350 530 populations time pop. 0.0 100.0 0.0 100.0 true true "" "" PENS "fish" 1.0 0 -612749 true "" "plot count fish" "sharks" 1.0 0 -16449023 true "" "plot count sharks" "water / 4" 1.0 0 -13345367 true "" "if model-version = \"fish-sharks-water\" [ plot count grass / 4 ]" MONITOR 41 308 106 353 fish count fish 3 1 11 MONITOR 115 308 182 353 sharks count sharks 3 1 11 MONITOR 191 308 253 353 water count water / 4 0 1 11 TEXTBOX 20 178 160 196 Sheep settings 11 0.0 0 TEXTBOX 198 176 311 194 Wolf settings 11 0.0 0 SWITCH 105 270 241 303 show-energy? show-energy? 0 1 -1000 CHOOSER 5 10 350 55 model-version model-version "fish-sharks" "fish-sharks-water" 1 @#$#@#$#@ ## 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. 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-7500403 true true 270 75 225 30 30 225 75 270 Polygon -7500403 true true 30 75 75 30 270 225 225 270 @#$#@#$#@ NetLogo 6.0.4 @#$#@#$#@ set model-version "sheep-wolves-grass" set show-energy? false setup repeat 75 [ go ] @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ default 0.0 -0.2 0 0.0 1.0 0.0 1 1.0 0.0 0.2 0 0.0 1.0 link direction true 0 Line -7500403 true 150 150 90 180 Line -7500403 true 150 150 210 180 @#$#@#$#@ 1 @#$#@#$#@