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Background Information on Simulation Created for Lesson 5: Eat and Be Eaten: Prey as Predator,
Predator as Prey by Jennifer And ersen and Anne LaVigne
in col laborat ion wit h t he C reat ive Learning Exchange
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BackgroundInformationonSimulationCreatedforLesson5:EatandBeEaten:PreyasPredator,PredatorasPrey
Note:ThislessonbuildsonLesson4–WavesofChange:Predator‐PreyDynamicsintheOscillationcurriculumcreatedfortheComplexSystemsProject.Lessons3‐5worktogethertoshowhowapopulationinisolationcan
experiencegrowthordecline,butnotoscillation(Lesson3).Further,itisonlywhenconsideringapopulationinrelationtoawidersystemboundary,eitherinteractingwithanotherpopulation(Lesson4)and/orafoodsupply
(Lesson5),thatwehavethestructurenecessarytoproducecyclicbehavior.
Whilethescreenimages,role‐playingdescriptionandparametersettingspresentedinthisdocumentrefertotheC‐levelsimulation,muchoftheinformationisstillrelevanttotheA‐andB‐levelsimulations.
Contents Introduction................................................................................................................................................. 3
OverviewofModelBehavior ....................................................................................................................... 3
TheDefaultBehaviorPattern .................................................................................................................. 3
ExperimentFreely.................................................................................................................................... 4
PausingPeriodically ................................................................................................................................. 6
Real‐worldSituations............................................................................................................................... 7
ModelStructureandAssumptions .............................................................................................................. 9
LimitationsoftheModel ........................................................................................................................... 10
TalkingPoints–LinkingtheSimulationtoRealLife .................................................................................. 11
TheCauseoftheProblemisWithintheSystem........................................................................................ 12
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Introduction
Howdopredator‐preycyclesoccurinnature?Biologistsdonotalwaysagreeonwhatcausessuchcycles(andsomedisputethattheyevenexist).Wherecyclicbehaviorpatternshavebeenobserved,one
hypothesisisthattheenvironmentcreatesatightdependencybetweenpredatorandprey.Lesson4oftheOscillationcurriculumpresentsasimulationoftwopopulationsthatarelockedinsucharelationship.TheparametersforthissimulationhavebeeninspiredbythewolvesandmooseofIsle
Royale.
Anotherhypothesisfortheappearanceofpredator‐preycyclesisthata3‐levelrelationshipisatwork.Notonlyisapopulationofpreyanimalslimitedbytheirmainpredators,buttheirnumbersalsodeclineduetoreachingthelimitsoftheirfoodsupply.Theyare,inessence,squeezedfrombothtopand
bottominthefoodchain.
ThemodelofLesson4showsthatapreypopulationcanexhibitlogistic(S‐shaped)growth,smoothlyreachingthecarryingcapacityoftheirenvironment,whenthepredatorpopulationhasbeenremoved(throughhunting,disease,etc.).ThemodelinLesson5discussedinthisbackgrounddocumentaddsa
“biomass”componenttothemodelofLesson4,torepresentafoodsupplyforthepreyanimals.Theadditionofthisthirdlayerallowsstudentstoexperimentwithovershoot‐and‐collapsebehaviorwhenthepreypopulationisunrestrainedbypredators.Thepreypopulationcanoscillateduetointeraction
withthepredatorpopulation,andalsoduetointeractionwithitsownfoodsupply.Lesson5isarole‐playingsimulation.Studentsplaytheroleof“rookie”WildlifeManager;theiron‐the‐
jobtrainingistoinvestigatetheecosystemtheywillbemanagingbyexperimentingwiththissimulation.Theyareallowedtoissuehuntinglicensesforpreyandtagsforpredatorremoval.Throughvarious
modesofinteractionwiththesimulator(“Experimentfreely,”“Pauseevery5years”and“Real‐worldscenarios”)theycanformulateastrategyformanagingthisoscillatorysystem.
OverviewofModelBehavior
TheDefaultBehaviorPattern
Todisplaythedefaultbehaviormodeofthesimulation,makesure“Experimentfreely”isgreenandclickthe“Run”buttonwithoutmakinganychangestothesliderbars(seeFigure1).Therearesevenpagesof
graphs.Clickthewhitetriangleinthelowerleftcornerofthegraphtopagethroughthem.Pages2–4and6–7arecomparativegraphs.Eachtimeyouclickthe“Run”buttontosimulatethemodel,thecomparativegraphswillshowthenewruninadifferentcolor.Clickthe“Reset”buttontoclearthe
graphsandresettheparametervaluestotheirdefaultsettings.
Pleasenotethatwhenin“Experimentfreely”mode,itispossibletochangethesliderswhilethesimulationisrunning.Anotheralternativeistoclickthe“Pause”buttontopausethesimulationatanytime,inordertomakechangestotheslidersorsimplytoevaluatewhatishappening.
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Figure1:Thedefaultbehaviorofthemodel.
TheInstructionslinktellsstudents“thereisnoguarantee”thatthenumberofhuntinglicensestheyissuewillresultinsuccessfulkills.(Thereasonisthatthedensityofthepreyanimalshasaneffecton
huntersuccessjustasitdoesinreallife.)StudentsmayalsonoticethatPage5ofthegraphshows“Huntersdesiredlevelofhunting”tobe1500animalsperyear(afterthey’verunthesimulationatleastonce).Thesecluesgiveanindicationofastartingpointforexperimentingwithhuntinglevels.
Takentogether,theIntroductionmaterialandthegraphsexplainthesituationtherookieWildlife
Managersarebeingaskedtoaddress.Theareaundertheirmanagementhasnotbeenopentohuntinginthepast.Thepopulationsofpreyandpredatorsfluctuateovertime,yetthepreyanimalsaretypicallyhealthy,withahighaveragelifespan,duetotheabundantbiomass.Thepeaksinthecyclestendto
irritatethehumanpopulationthatlivesaroundthewildernessmanagementarea.Residentsarescaredofpredatorsandfearfortheirownsafetyandthatoftheirpets.Farmerscannotaffordtoloselivestocktopredators.Ahighpreypopulationalsocausesproblemsbecausetheanimalstramplecrops,destroy
gardens,causeaccidentsontheroads,andsoon.Canhuntingbeusedtoimprovethesituation?
ExperimentFreely
Atypicalrunthatstudentsmighttryin“Experimentfreely”modeistosetthesliderfor“Numberofpreyanimalstobehuntedperyear”to1500fortheentirelengthofthesimulation.Thisisalogicalsetting,butitactuallydestabilizesthesystemslightlyanddoesnotconsistentlyprovidethehunterswiththeir
desiredlevelofhunting.Figure2showstheControlPanelwiththischangemade.
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Figure2:Thebehaviorcreatedbychangingthesliderforpreyhuntingto1500forthewholesimulation.
Toseethisruncomparedtothedefaultbehaviorrun,checkPages2,3and4ofthegraph.Youwillsee
thatthepredatorpopulationdipslowerandstayslowerthanthedefaultrunformuchofthesimulation,butalsoshowssteeperincreasesontheupswingofthecycles.Furthermore,itappearsthatthecyclespeakatprogressivelyhigherlevels,althoughnotbymuch.Thepreypopulationpeakslaterandhigherin
thisruncomparedtothedefaultrun;biomassisonlyslightlyaffectedbythechange.OnPages6and7,youwillseethattherearenochangesfromthedefaultrun–thepreypopulationstillenjoyshighnutritionandthesameaveragelifespan.
Page5ofthegraphshowswhythepolicyofalwayshunting1500preyanimalscannotbeconsidereda
completesuccess.Thisgraphshows“Preykilledbyhunters”and“Huntersdesiredlevelofhunting,”asseeninFigure3below.
Figure3:Huntingversusdesiredhuntingwhen1500licensesareissued.
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Ifthiswereareal‐lifesituation,hunterswouldlikelygiveaharshassessmentofthejobtheWildlifeManagerisdoing.Theymaynotrealizethatthepreypopulationoscillatesovertime,andthatduring
thelowcyclesoftheoscillation,thepopulationdensityislow,andthereforetheanimalsarehardertofindandkill.Infact,huntersmayeventhinkthatmismanagementoftheherdisthecauseofthepoorhunting!Itwouldbeeasyforthemtosurmisethatifthemanagementjobwas“doneright”thenthey
wouldalwaysgettheirtrophyanimal.
PausingPeriodically
ArealWildlifeManagerwillnotsimplysetacertainlevelofhuntingandthenneverreevaluatethesituationovera50‐yeartimespan.The“Pauseevery5years”modeaddsalayerofrealism.Itrepresentsaplanningcyclewherebyamanagerormanagementteamreflectsonresultsachievedanddecideshow
besttomoveforward.Inreallife,suchplanningisoftenupdatedbetweentheextensivereviewseveryfiveyears.Inthecaseofwildlifemanagement,however,wecanreasonablyassumethatthereisatleastafewyears’delaybetweenreviewsbecauseittakestimetodothefieldworknecessarytoevaluatethe
sizeandhealthofwildpopulations.
Itisimportanttonotethatstudentsmayormaynotoperatethesimulationwithaparticulargoalinmindforthepreypopulation.Forexample,theymaymovetheslidersupordownwhenthesimulationpausesjustto“seewhathappens.”Thisislikelytoresultinoscillationsthatare“wild”andperhapseven
thedemiseofthepredatorpopulation.Withoutpredators,evenahighlevelofhuntingforpreywillnotpreventthepopulationfromovershootingthecapacityofthebiomasstosustainthem.StudentsshouldbeencouragedtocheckPages6and7ofthegraphtounderstandthehealthofthepreypopulation.
Huntersdonotwanttohuntsmall,weakanimals!
Anexamplerunusing“Pauseevery5years”modeisshowninFigure4.
Figure4:Anexampleofusing"Pauseevery5years"mode.
Thesimulationendedwithapreypopulationthatwasstilloscillating,buttheupsanddownsseemedmoredrawnoutattheendofthe50yearsthanatthebeginning.Thestrategyusedwastovarythe
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numberofpredatortagsissuedtokeeppredatorsrelativelylow,andnotallowhuntingofpreyforthefirst15yearstobuildupthepopulation.Atthattime,thepopulationwasconsideredlargeenoughto
allowpreylicensestobesetto2000peryearfortherestofthesimulation.ThehuntinggraphisshowninFigure5.
Figure5:WouldthisWildlifeManagerbeconsideredskillfulintheeyesofhunters?
Thefirst15yearsprobablywouldhavebeentoughforthisWildlifeManager!Thispersonhadagoalofbuildingupthepreypopulationandstuckwithit.Eventhoughhuntingcouldbeconsideredgoodforthe
restofthesimulation(preywerehealthyandkepttheirhighaveragelifespan),studentsmayhaveopinionsastohowlikelyitwouldhavebeenforthispersontobefiredhadthisbeenreallife.
Students’resultswillvarywidely.Itisimportantforthemtothinkthroughastrategyandhowtheywillexecuteit.Successshouldbemeasuredonnotonlyhowsatisfiedhunterslikelyare,butalsohow
healthytherestoftheecosystemisallowedtobe.
Real‐worldSituations
Settingastrategyandmakingadjustmentsalongthewayisgoodmanagementpractice.Itbecomes
moredifficultwhenvariousgroupsofpeoplewanttohavetheirsayinhowyou’redoingyourjob.The“Real‐worldsituations”modeismeanttotestresolveandshowthatcomplexsystemsaretoughtomanage.Thebombardmentofinformationandpressurethatcomesfrom“outside”canservetomuddy
thewatersforamanageronthe“inside”ofthesystem.Inreallife,thisisacontributingfactortoamisunderstandingofobserveddynamicbehavior.Forinstance,inarealsystemthatoscillates,itcanbeperceivedthatthebuffetingeffectsofoutsideeventsandperturbationsareactuallywhatcausethe
oscillation.What’sreallyhappening,however,isthatthesystemoscillatesbecauseofitsstructure.
Figure6showstheresultsofanot‐very‐successfulrunusing“Real‐worldsituations”mode.Themanagerstartedconservativelywithlowlevelsofhuntingforbothpopulations.Asmessageskeptappearingto
indicatehunterfrustration,thispersondidincreasepreyhuntingsignificantly.However,whendiseaseanddroughthitthearea,huntingwasloweredagain.Theslowrecoveryofthepreyanimalsgavethe
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managerafalsesenseofsecurityaboutthepredatorpopulation.Whenthepredatorpopulationincreaseddramatically,themanagertriedtocompensatebyissuingmorepredatortags.Thedamage
wasalreadydone;preynumbersdroppedduetothelargepredatorpopulationandthemanagerhadtoenduremessagesthatindicatedanangryresidentpopulationwascomplainingaboutthepredators.
Figure6:Using“Real‐worldsituations”modewillgenerateinterestingresults!
Figure7andFigure8showhoweventhoughhuntingwashighforsomeofthetime,hunterswerenotalwaysshootinghealthy,robustanimals.Infact,wecouldeveninferthathunterswouldhavebeenfrustratedwiththehuntingopportunitiesformostofthesimulation.Offeringdoublethenumberof
licensesinamaddashtocontrolthepopulationgrowthortomakeupforpastpoorhuntingisnotindicativeofaskillfulmanager.Evenworse,thesimulationendedwithapredatorpopulationthatwastoolargeforresidentsandfarmerstofeelcomfortable.
Figure7:Theexplosionofpreymeantthatanimalscouldnotfindenoughtoeat.
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Figure8:Huntingcouldnotkeeppacewiththegrowthofthepreypopulation.
Students’resultswillvarywidelywhenusingthismodeofthesimulation,justaswithusing“Pauseevery5years.”Theimportantlearningcomesfrombeingabletoarticulatewhatstrategy,ifany,theywere
followingandif/whyitbrokedownatanypointalongtheway.
ModelStructureandAssumptions
Themodelstructure1ispresentedinFigure9.Thisscreenisaccessedviathescreentitled“ExploretheModel:ModelasHypothesis.”Click“TourtheModelStructure”andusethespacebartotogglethroughthepresentationofthestructure.
Noticethattherearenooutsideinfluencesthatdrivethepredator‐preycycles.Thegreenvariablesare
parametersthataresetontheControlPanelofthesimulation.Theremainingvariablesaredefinedinternally,basedonrelationshipsindicatedbytheredarrows.Thevariable“Preyconsumptionofnewgrowth”iscoloredorangetoindicatethatitisrepeatedintwoplacestoavoidstretchingalinkacross
thediagram.Clickonthelinktitled“TourtheLoops”(locatedunder“TourtheModelStructure”)toreadmoreaboutthefeedbackloopsembeddedinthemodelstructure.
1Themodelpresentedinthislinkisactuallyasimplifiedversionofthemodelthestudentssimulate.Toexaminethecompletemodelstructure,pleasedownloadtheSTELLAfilefromtheCreativeLearningExchangewebsite.
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Figure9:Themodelstructureshowninthe"TourtheModelStructure”link.
LimitationsoftheModel
Lessons3–5areamini‐seriesoflessonsonpopulationdynamics.ThemodelintroducedinLesson3can
producealogisticgrowthpattern(onepopulationinisolationthatbumpsagainstthenaturallimitsofitsenvironment),butcannotbeusedtorepresentcyclicpopulationdynamics.Itsimplylacksthestructure(twopopulationsinabalancingfeedbackloop)necessarytoproduceoscillation.Themodelpresentedin
Lesson4doeshavethenecessarystructuretoexplainasimplehypothesisofpredator‐preycycles,butstillhaslimitationsbecausethefoodsupplyofthepreypopulationisnotrepresented.Intheabsenceofpredators,preyincreasetoacarryingcapacityandarenotabletoovershootit.
InLesson5,amorecomplicatedviewofpredator‐preycyclesisuncovered.Apreypopulationisshown
toexistinabalancingfeedbackrelationshipwiththebiomassaswellaswithpredators.Thismeansthatinisolation,withouttheinfluenceofpredators,apreypopulationcouldstillexhibitanoscillatory
behaviorpattern.Thisislikelytomanifestitselfinextremesituations,suchaswhenpredatorsaresuddenlyremovedduetohumaninterventioninthesystem,andpreyareallowedtogrowunchecked.Overshoot,collapseandarecoverymarkedbyoscillationareaplausibleresult.
Thismodelalsohaslimitations.Inareasheavilymanagedbyhumans,theremaybeacompleteabsence
ofallpredatorsapartfromhunters.Inthiscase,thehuntersarethemain“predator”population,andasimilaroscillatorybehaviorpatterncanappear,suchasthatshownintheDebriefsectionofthesimulation(BehaviorPatterns:Decisionsvs.Policies;clickthelink“Areal‐lifeexample”).Thismodelis
notintendedtorepresentsuchasituation,althoughsimilaritiesanddifferencescanbediscussedintheclassroom.
OtherlimitationsarethesameasthoseforLesson4.Predatorsgenerallyhavemorethanonetypeofpreyavailabletohunt,eveninsituationswherecyclesoccurwithaparticulartypeofprey.Conversely,
preyanimalsoftenexperiencepressurefromseveraltypesofpredators,notonlyone.Manyfactorsaffectbirthanddeathratesofbothpredatorsandprey,includingdisease,drought,introductionof
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invasivespecies,wildlifemanagementpolicies,huntingbyhumans,andsoon.Themodelpresentedinthislessonisanoversimplificationofanyrealpredator‐preysystem,butisaneffectiverepresentationof
a3‐levelgeneral hypothesisofpredator‐preycycles.
TalkingPoints–LinkingtheSimulationtoRealLife
Someusefulquestionsfordiscussionwithstudentsincludethefollowing:
• WhatotherrolesfromreallifemightlookliketheroleofWildlifeManager,whereprogressmustbemadetowardmultiple,oftenconflictinggoals?Anexampleintheareaofnaturalresourcescouldbe“damoperator”(allocatingwateramongcompetinguses),butother
examplesabound.Mayors/urbanplannersmustbalancegrowthanddevelopmentwithretainingthecharacterofanarea(historicbuildings,openspace,etc.);schooladministratorsmustmeetstate‐mandatedstandardsforteachingandrespondtonationaltrends,butthereare
alsomanylocalandregionaldifferencesthatcouldmakethejobdifficult.Leadersofcorporationsmustbalancethedrivetoreleasenewandinnovativeproductswithsafetyconcernsofbothworkersandcustomers.Politicalcampaigns,eitherlocalornational,could
provideplentyofmaterialforsuchadiscussionaswell.• Themodelshowsthatcreatinga“huntingpolicy”(settingagoalforthesizeoftheprey
population,forexample,andmanipulatinghuntinglevelstoachievethatgoal)andstickingtoit
despitepressurefromvariousgroupscanbeverytricky.Inreality,wildlifemanagersprobablydoabitofboth,regardlessofwhethertheyaremanagingasystemthatshowspredominatelyoscillatingbehaviororsomeotherbehaviorpattern.Itisreasonabletoassumethattheydo
havegoalsforthenaturalresourcestheymanage,butthattheymust,attimes,bowtopressureaswell.Studentscanbepromptedtodiscusssuchtradeoffsoraskedtoresearchreal‐life
examples(Yellowstone,Kaibab,IsleRoyale).Itisnotnecessarytofocusonoscillatingsystems.• Isthereactuallya“balanceofnature”thatwouldoccurnaturallyifhumansdidnotinterfere?If
so,whatwouldthatbalancelooklike?Inmodelssuchastheoneinthislesson,“dynamic
equilibrium”(alsocalledsteady‐state)occurswhenallthelevelsinthemodelareunchanging(theinflowsmatchtheoutflows).Consideringthethreelevelsfeaturedinthislesson,howlikelyissuchasituation?Whatfactorscouldpreventthatfromhappening,or,whatwouldpushthem
outofsteady‐stateiftheyeverwouldbeinit?Also,studentsshouldbepromptedtothinknotonlyof“events”thatmight“jigglethesystem,”butalsoofimportantlevelsthataren’teveninthemodel(thepyramidonthe“Real‐lifeWildlifeManagement”screencouldhelphere).
• Takingtheideasofthepyramidevenfurther,howlikelyisitthatpredator‐preycycleswouldoccurinanareathathasmanydifferenttypesofpreyforaparticularspeciesofpredator,ormanypopulationsofbothtypesofanimals?Inotherwords,arepredator‐preycyclesmorelikely
tooccurwhenthepopulationsaresomewhatisolatedgeographicallyorduetotheharshnatureoftheenvironment,orinareaswithabundantlifeandmanyopportunitiestomigrate?
• Whenhumansattempttomanageapopulationofwildanimals,whataresomefactorsover
whichtheycanhopetoexercisecontrol?Thismodelfeaturesthenumberofanimalsthatcanbehuntedasonefactorthathumanscan“control,”butstudentsmayalsohavenoticedthatthe
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fullhuntingquotaisnotalwaysattained.Basedonrunningthesimulationmodelandlearningaboutitsstructure,whatfactorscanpeoplerealisticallymeasureandinfluence?Whatfactors,in
turn,influencethebalancingfeedbackloopsthatcanproduceoscillatorybehavior?• Whywouldpopulationcyclesbeconsideredproblematic?Whatkindofpopulationdynamic
wouldhuntersliketosee(growth,steady‐state,decline,cycles)formooseordeer?Whatabout
non‐huntingoutdoorenthusiasts?Farmers?Theinsuranceindustry?• Ifyouhadtomakeanassumptionaboutthegeneralhealthoftheindividualanimalsintheprey
population,wouldyouthinkthattheanimalsaremosthealthywhenthepopulationisgrowing
rapidly,isclosetoitsnaturalcarryingcapacity,orexperiencingapopulationcrash?Whatwouldbeyourgoalinmanagingapopulationofpreyanimals(anidealbehavior‐over‐timetrajectory)?Wouldyouliketoseeournaturalareasincludepopulationsofpredatorsaswellasprey?
TheCauseoftheProblemisWithintheSystem
TheoverallgoaloftheOscillationcurriculumistoteachaprincipleofcomplexsystems:Thecauseofthe
problemiswithinthesystem.Socioeconomicsystemsthatoscillateareoftennotrecognizedasoscillatingduetotheirintrinsicstructure.Explanationsoftenpointtooutsideinfluencesthatarethemselvesoscillating,ortoaparticularcombinationofoutsidefactorsbelievedtodrivetheoscillation.
Yetweknowthataphysicalsystemsuchasaspring(presentedinLesson1)oscillatesbecauseitismadetodoso.Itdoesnotoscillatebecauseahandorotherforcecontinuallypushesitinanup‐and‐downorback‐and‐forthmotion.Aspringgetssetintomotionwithapushorapull,anditoscillatesduetoits
ownstructure.
Predator‐preysystemsarewell‐knownreal‐lifeexamplesofbiologicalsystemsthatcanoscillate.Thecyclescanbeexplainedviatheinternalstructureoftherelationshipsoftheparticularecosystem.
Understandingsuchsystemsisthefirststepindetermininghowtoinfluencethem,ifneedbe,tochangethebehaviorpattern.Becausethecauseofasystem’sbehaviorisduetoitsstructure,changingthebehaviorpatternisaccomplishedthroughchangingthestructure(ratherthaneliminatinganoutside
influence).Inthecaseofnaturalsystems,therewillalwaysbeoutsideinfluencesthatdisrupthumanmanagementofsuchsystems(drought,disease,fire,etc.).Applyingamanagementpolicythatacceptsthepresenceofandworkstodampentheoscillations(ifthatisthedesiredoutcome)isanexampleof
changingstructuretochangetheresultantbehavior.Ifthefirststepofunderstandingstructureisnevertaken,itisunlikelythateffortstoproducechangewillmovebeyondplacingblameonoutsideforcesthat“cause”theproblem.
Remaininglessonsinthisseriesillustratetheseideasusingoscillatingsystemsinhumanhealth(Burnout
cycles)andeconomics(Commoditycycles).