background information on simulation created for lesson 5...

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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

©2012CreativeLearningExchange•BackgroundInformationforPredator/Prey/BiomassSimulationPage2of12

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


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.


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.


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.


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


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


managerafalsesenseofsecurityaboutthepredatorpopulation.Whenthepredatorpopulationincreaseddramatically,themanagertriedtocompensatebyissuingmorepredatortags.Thedamage

wasalreadydone;preynumbersdroppedduetothelargepredatorpopulationandthemanagerhadtoenduremessagesthatindicatedanangryresidentpopulationwascomplainingaboutthepredators.

Figure6:Using“Real‐worldsituations”modewillgenerateinterestingresults!

Figure7andFigure8showhoweventhoughhuntingwashighforsomeofthetime,hunterswerenotalwaysshootinghealthy,robustanimals.Infact,wecouldeveninferthathunterswouldhavebeenfrustratedwiththehuntingopportunitiesformostofthesimulation.Offeringdoublethenumberof

licensesinamaddashtocontrolthepopulationgrowthortomakeupforpastpoorhuntingisnotindicativeofaskillfulmanager.Evenworse,thesimulationendedwithapredatorpopulationthatwastoolargeforresidentsandfarmerstofeelcomfortable.

Figure7:Theexplosionofpreymeantthatanimalscouldnotfindenoughtoeat.


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.


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


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


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).

background information on simulation created for lesson 5...

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