2015_Simulating sustainability: a resources perspective

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Simulating sustainability: a resources perspective

William Gracea a Australian Urban Design Research Centre, University of Western Australia, Perth, Australia Published online: 04 Jun 2015.

To cite this article: William Grace (2015): Simulating sustainability: a resources perspective, Journal of Natural Resources Policy Research, DOI: 10.1080/19390459.2015.1050202

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JournalofNaturalResourcesPolicyResearch,2015 http://dx.doi.org/10.1080/19390459.2015.1050202

Simulatingsustainability:aresourcesperspective

WilliamGrace*

AustralianUrbanDesignResearchCentre,UniversityofWesternAustralia,Perth,Australia

Aglobalpopulation–economy–resourcemodelexploresthefutureimpactofdeclining resourceavailabilityontheworldeconomy.Themodeltracksthelikelyfutureconsumptionofrenewableresources,fossilfuelsandnon-renewablematerialsandthe economicimpactofavailability.Scarcitywilllikelybecomeevidentduringthelatter partofthiscenturyandconstraineconomicproduction,reducingincomepercapita, livingstandardsandultimatelypopulation.Policyinterventionsinvolvingarapid transitionfromfossilfuelstorenewableenergy,reducedresourceintensityandmaterialsrecyclingarenecessarytocorrectthistrajectoryandfacilitateongoingimprovementsinglobalaveragelivingstandards.

Keywords: sustainability;population;resources;scarcity;limits;systems

1.Introduction

Inorderforpeopleeverywheretoattainandretainareasonablequalityoflife(i.e.,to achieveenduringhumanwellbeing),humansocietymustlivewithinthelimitsimposed bythebio-physicalworld.Thisistheessentialmessageconveyedinitiallybythefindings ofSystemDynamicsresearchintheearly1970s(e.g.,WorldDynamicsandLimitsto Growth)andnumerousresearcherssince.

UsingthetechniqueofSystemDynamics,theWorldDynamicsandLimitstoGrowth modelsestablishacausalstructurelinkinglivingstandards(thebasicconstituentof wellbeing)toproductionandconsumptionofrenewableandnon-renewableresources andpollutionabsorptioncapacity.Thesemodelsoperateattheglobalscale.However, effectivemanagementofproductionandconsumptioncannotoccur(presently)atthat scale.Thenear-termsystembehaviorattheglobalscalewill ‘emerge’ frominteractionsat smallerscales – nations,regionsandcities.Howevernocountrycanbe ‘sustainable’ in isolationandsoanymodelthatoperatesatthatscalemustreflectthekeyexogenous variablesarisingfromtheglobalscaleresourceflows.

Theworkdescribedhereusesarelativelysimplepopulation–economy–resource modeltoexplorethetrajectoryoftheworldsystemandtheimplicationsforenduring humanwellbeing.ThepurposeofthemodelisnottoprovideanalternativetotheLimits toGrowthWorld3modelbutrathertoestablishasimplifiedversionthatusesreadily availablemetricsforwhichdataisavailableatnationalandregionalscales.Thesame modelarchitecturecanthenbeusedasabasisforsmallerscaleversionsofthemodel which,whilebeingreflectiveoftheglobaldynamics,facilitatesexplorationofhighlevel policyoptionswithrespecttoresourceuseatthatscale.

*Email: bill.grace@uwa.edu.au

2.Aglobalsustainabilitymodel

JayW.Forrester ’slandmarkwork, WorldDynamics (Forrester, 1971),wasthepredecessorof better-knownglobalmodelsthatfollowed.Forrester’sWorld2model,whichusedtheSystem DynamicstechniqueintheDYNAMOprogramminglanguage,linkedpopulation,natural resourcesuse,capitalinvestment,foodandpollution.Themodelhighlightedthepotential limitstopopulationgrowtharisingfromcrowding,foodsupply,pollutionandnatural resources. 1 Anumberofotherglobalmodelshavebeenproducedsince,asdocumentedby severalauthors(Castro&Jacovkis, 2015;Meadows,Richardson,&Bruckmann, 1982).

IncludedintheseisthefamousLimitstoGrowthstudy(Meadows,Meadows, Randers,&Behrens, 1972)whichbuiltonForrester ’sworkin WorldDynamics viathe World3modelusingtheSTELLAsoftware.KeyvariablesintheWorld3modelincluded worldpopulation,industrialization,pollution,foodproductionandresourcedepletion. Themodelexploredvariousscenariosforthefutureoftheworldsystem.Severalofthe scenariossaw ‘overshootandcollapse’ oftheglobalsystemduringthetwenty-first century,whileothersresultedina ‘stabilizedworld’.Thestudywasupdatedinitiallyin 1992(Meadows,Meadows,&Randers, 1992)withtheWorld3–91modelandmore recently(Meadows,Meadows,&Randers, 2004)withafurtheriterationofthemodel, World3–03.Theessentialconclusionofthelateststudy,nowadecadeold,isthat humanityisdangerouslyinastateofovershoot.

Scenario1oftheWorld3–03modelisthereferencepointfortheotherscenarios presentedinLimitstoGrowth:The30YearUpdate.Thisscenarioproducesovershootand collapseintheworldsystemaround2025duetoa ‘non-renewableresourcescrisis’.In Scenario2themodelassumeshigherstocksofnon-renewableresourceswhichdelaysthe onsetofpopulationcollapsetoaround2050,althoughlivingstandardsbegintodecline around2025,asinScenario1.ThecollapseinScenario2istriggeredbypollution.

ThemodelIpresenthereishighlysimplifiedincomparisontotheWorld3–03model.It doesnotcontainmanyofthesectors(i.e.,sub-models)inWorld3–03,includingthe disaggregationoftheeconomyintoindustrialandagriculturalsectors.Furthermore,it onlyaccountsforcarbonpollution,whileWorld3–03includespersistentpollutionfrom industryandagriculture.Thesesimplificationsallowthemodeltofocusontheinfluenceof resourceconstraintsonaggregateglobaloutput.Thusitseekstocapturetheessential resourcecrisisreflectedinScenarios1and2ofWorld3–03butusingmoreaccessibledata.

Oneadvantageofthissimplifiedmodelisthatitusesmetricsthatcaneasilybe calibratedagainstreadilyavailabledata,whichfacilitatesaquasi-quantitativeanalysisof systemtrajectory.Themodelhasbeenconstructedtoprojectthecurrenttrajectoryof population,economicproductionandassociatedresourceuseintothefuture.Bydefinition therefore,itdoesnotreflectanychangesthatmayoccurtotheunderlyingrelationshipsin thefuture,whetherduetoscarcityorpolicy.

Ahighlevelcausalloopdiagram2 forthemodelissetoutin Figure1.Causalloop diagramsindicatetheinfluenceovertimeofinteractingvariablesonsystembehavior,and arethebuildingblocksofastockandflowmodel.

Themodel,whichissimulatedintheVensimsoftware,exploresthe350-yearperiod of1960–2310usinga1-yeartimestepandEuler ’sMethodfornumericalintegration.

Rapidgrowthineconomicproductionhasfacilitatedthemassiveincreaseinglobal populationoverhumanhistory(LoopR1),particularlysincetheriseofagriculturesome 10,000yearsago.Howevereconomicproductionisnotlinkedpurelytopopulationgrowth. GrossDomesticProduct(GDP)percapitagrowth(themaininfluenceonbasicliving standards)alsoreinforcespopulationgrowth(LoopR2),andhasbeengrowinginboth

Figure1.Causalloopdiagramofglobalsustainabilitymodel. Keystocksareshowninboxeswithinflowandoutflowratesasarrows.Arrowpolarityispositive unlessnotedasnegative. ‘R’ and ‘B’ representtheoverallpolarityofaloopaseitherreinforcingor balancing.

Figure2.(a)WorldPopulation;(b)WorldGDP.

developedanddevelopingnationsforcenturies.Morerecently,however,theriseinliving standardsindevelopingnationshasledtoreducedbirthrates(theso-calleddemographic transition) – LoopB1.

Economicproduction,inturn,dependsontheuseofnaturalresources(LoopB2), someofwhicharerenewable(e.g.,foodandfiber)andsomeofwhicharenon-renewable (e.g.,metalsandfossilfuels).Ofcoursethehumanpopulationalsoreliesmoredirectlyon naturalresourcesforsurvival(e.g.,productivesoilsandcleanwater) – LoopB3.

Amongthefiveloopsin Figure1,R1andR2havebeendominanttodate,as suggestedbythesimilaritiesbetweenthetrajectoriesofglobalpopulation(Figure2a) (UnitedNations, 2004)andglobalgrossdomesticproduct(Figure2b)(GroningenGrowth andDevelopmentCentre, 2010).

Akeyquestionforthefutureiswhetherglobalpopulationandlivingstandardscanbe stabilizedatlevelsthatdeliverenduringwell-beinggivenavailableflowsofnaturalresources.

2.1Theeconomy

TheeconomyismodeledhereinlinewithRobertSolow’sgrowthmodel(Solow, 1956)as developedbyMichaelRadzicki(2004).Specifically,theeconomy’soutputorGDPis determinedbytheCobbDouglasproductionfunction.

whereGDP=GlobalGrossDomesticProduct(ameasureofeconomicoutput)

K=stockofcapitalintheworldeconomy

L=stockofeffectivelaborintheworldeconomy

β =outputelasticityofcapital

RadzickihasshownthattheSolowmodelcanonlyexplainallofKaldor ’sso-called stylizedfacts3 (Kaldor, 1957)if(asSolowposited)itincludestechnicalprogress.In Radzicki ’smodel,technologyismodeledasastockthatactsasamultiplieronlabor, representingproductivityimprovementsduetotechnologicaldevelopmentintheworld economy.

TheSolowgrowthmodelwithtechnologicalprogressdescribeswellthehistorical exponentialgrowthintheworldeconomy.However,nothinglimitsgrowthinthismodel andsoitcontinuestoproduceGDPgrowthovertime(evenwithzeropopulationgrowth) aslongastherearestocksoflaborandcapital.TheversionoftheSolowmodelpresented hereincludesfactorsthatfacilitateproductionreachingadynamicstability.Thisis achievedthroughbalancingloopsthatconstrainsavings,andhenceinvestment,when GDPpercapitareachesathresholdvalue.ThethresholdoccurswhenGDPpercapita reachestheglobalaverageofaround$7000perpersonperyearcomparedtothepresent figureofaround$6000(constant2000US$).Exceedingthisthresholdultimatelyreduces Investmentto$0ataround$35,000perpersonperyearwhichisabout40%higherthan thatoftheOrganizationforEconomicCooperationandDevelopment(OECD)countries presently(World_Bank, 2013).

Themodelisfurthermodifiedtoaccountfornaturalresources.Specifically,the economicsectorisunaffecteduntilResourceAvailability(theratioofavailableresource flows4 todemandforresources)fallsbelow1.Furthermore,whenResourceAvailability fallstozero,Savings/InvestmentandTechnologygrowthalsofalltozero.Thecausalloop diagramoftheeconomyisshownin Figure3.

Figure3.Causalloopdiagramoftheeconomysector.

2.2Populationandlivingstandards

Asdescribedbefore,themodelassumesthatlivingstandardshaveacausal relationshiptopopulationgrowth( Figure1 ).Howeverathigherlevelsofliving standards,thedemographictransitionistriggeredandtherateofpopulationgrowth reduces,ultimatelytozero.TheUnitedNationsHumanDevelopmentIndex(HDI)is usedasaproxyforlivingstandards.ThecurrentglobalaverageHDIisaround0.68 (UnitedNationsDevelo pmentProgram[UNDP], 2012 ).Inthemodel,Iassume populationgrowthbecomeszeroatanHDIofaround0.90,whichisslightlyhigher thantheexistingindexforveryhighHDIcountries.Ialsoassumethatpopulation growthbeginstoslowwhennaturalresourcestocksfalltoaround40%oftheir initialvalue.

Thecausalloopdiagramforpopulationandlivingstandardsisshownin Figure4, whichexpandsthestructureshownin Figure1 toincorporateloopsforbothGDPand GDPpercapita.ThedemographictransitionbalancestheGDPloop(asdepictedin Figure1),butreinforcestheGDPpercapitaloop.Accordinglythedemographictransition loopisdepictedasbothreinforcingandbalancing,aspopulationchangeshaveopposite effectsonGDP(positivecausation)andGDPpercapita(negativecausation).

Figure4.Causalloopdiagramofthepopulationandlivingstandardssector.

2.3Naturalresources

Naturalresourcesarerepresentedinthemodelthroughthreesubsectors:fossilfuels(asa specificsubsetofnon-renewableresources);renewableresources;andothernon-renewablematerials.

2.3.1Fossilfuels

Economicactivityacrosstheglobeisdrivenbyenergy,whichremainslargelyderived fromthecombustionoffossilfuels – afinitenaturalresource.Themodelassumesthat demandforfossilfuelsisafunctionofthedemandforenergyacrosstheeconomy,taking intoaccountthefractionprovidedfromnuclearenergyandrenewableresourcessuchas solarenergy,windenergy,biomass,andsoon.Thecurrentfractionfromthesesourcesis around19%ofglobalenergyuse(InternationalEnergyAgency, 2009).Non-energyuseof

fossilfuels(e.g.,fertilizer,plastics)hasbeensimplymodeledataround30%ofthatused forenergypurposes,whichistheaveragesplitsince1980.Thecausalloopdiagramfor thefossilfuelssectorisshownin Figure5

2.3.2Renewableresources

RenewableresourcesarethosedefinedbyTheGlobalFootprintNetwork(GFN)andused inthecalculationoftheEcologicalFootprint(GFN, 2012).EcologicalFootprintrepresentstheconsumptionrateofrenewableresources,specifically:cropland,grazingland, forestland,fishinggrounds,andbuilt-upland.Thedemandforforestlandalsoincludes thatsufficienttosequestercarbonafteraccountingfortheoceans’ sequestrationcapacity (referredtohereafterasthecarbonfootprint).

DistinctfromEcologicalFootprint,Biocapacityisameasureoftheregenerationrate ofrenewableresources.BothBiocapacityandEcologicalFootprintareexpressedinunits calledglobalhectares(gha)peryear,where1gharepresentstheproductivecapacityof 1haoflandatworldaverageproductivity.Forexample,datafrom2010indicateaglobal Biocapacityof11.6×109 gha/yr.

Finally,theEcologicalFootprintRatioistheratioofEcologicalFootprintto Biocapacity;hence,itisameasureofresourceexploitationrelativetoregeneration. Statedanotherway,EcologicalFootprintisadepletionflow,whereasBiocapacityisa regenerationflow.ThesetwoflowsmodifyastockthatIhavereferredtoasEcological Capacity.Inturn,EcologicalCapacitydeterminestheabilityofecosystemstoprovide servicestosocietyfromrenewableresources.

ConventionalanalysestypicallyassumethatBiocapacityisaconstant,thatis,the regenerativecapacityofecosystemsisunaffectedbythestockofEcologicalCapacity.My model,incontrast,(optionally)allowsBiocapacitytoreduceasthestockofEcological Capacitydeclines,ultimatelytozeroifthestockisdepletedentirely.

Thetotalecologicalfootprinthasbeendisa ggregatedintocomponentsofrenewable resourcesandthecarbonfootprint(derivedherefromenergydemandandfossilfuel use).Thecarbonfootprintisconvertedtoaresourceconsumption(ingha/yr)by calculatingtheamountofproductivelandandseaarearequiredtosequestercarbon dioxideemissions.

ThecausalloopdiagramfortheEcologicalFootprintRatioisshownin Figure6

Figure5.Causalloopdiagramofthefossilfuelssector.

2.3.3Othernon-renewablematerials

Othernon-renewablematerialsaredefinedhereasmetaloresandthemineralsusedin industryandconstruction.Theseresourcesarefiniteandstocksarebeingconsumedatarate determinedbyeconomicdemand.Manymetalorescantheoreticallyberecycledcontinuously,althoughinpracticethemyriadwaysmetalsareincorporatedinproductslimitsthe potentialopportunity(UnitedNationsEnvironmentProgramme, 2011).Constructionand industrialmineralsaremainly ‘down-cycled’ ratherthanrecycled(e.g.,re-useofwaste concreteasaggregate).Forsimplicity,allnon-renewableresourcesareassumedheretobe recyclable,albeitwitha10%lossineachcycle.Aservicelifeof25yearsisassumed.The causalloopdiagramforothernon-renewablematerialsisshownin Figure7

3.Modelcalibration

Themodelwascalibratedforaninitialperiod(i.e.,1960through2010)byselecting initialstocklevelsandconst antsfromhistoricalrecords( Table1 ).Causalrelation-

Figure7.Causalloopdiagramoftheothernon-renewablematerialssub-sector.

Figure6.Causalloopdiagramoftherenewableresourcessub-sector.

Table1.Datasources.

DatausedinmodelSourceReference

GDPandInvestmentWorlddatabank(World_Bank, 2013)

PopulationWorlddatabank(World_Bank, 2013)

HumandevelopmentindexUnitedNations(UNDP, 2012)

Ecologicalfootprintand Biocapacity

Energyandfossilfuels

Globalfootprintnetwork (Ewingetal., 2010)

Worlddatabank (World_Bank, 2013)

Non-renewablematerialsSustainableEuropeResearchInstitute (SERI) (SERI, 2013) 8 W.Grace

shipsandgraphicalfunctionshavebeenconstructedsuchthatthesimulatedresults matchtherealdataascloselyaspossibleforthisperiod(graphsincludedin Appendix1 ).

4.Initialmodelrun

Scenario1 (Infiniteresources)

Themodelwasinitiallyrunfortheyears1960to2310assumingunlimited resources(byselectingveryhighinitialstockvaluesforecologicalcapacity,fossil fuelsandothernon-renewablematerials).Thisrunrepresentsafutureinwhichinfinite resourcesallowforcontinuouseconomicgrowthandimprovementinlivingstandards, unhinderedbyscarcity.Thepurposeofthisscenarioistoapproximatetheannualflow ofresourcesrequiredtoachievethisoutcome,asapointofreferenceforfurther scenarios.Thisscenario,ifitwerepossible,representsa ‘smoothlanding’ forhumanity (Figures8a–8d).

4.1Population,GDPandlivingstandards

Continuedeconomicgrowthimproveslivingstandards,whichenablesthedemographic transitionthatslowsandthenhaltspopulationgrowth.Globallivingstandards(HDI)and GDPpercapitaachievelevelssimilartothoseofcurrentlyhighincomecountries(over 0.9andUS$25,000respectively)atapopulationofaround11billionpeople(Figure8a). TheresultingglobalGDPisaround3.75x1014 constantUS$2000,aboutninetimesthe currentvalue.

4.2Energyandfossilvs.non-fossilfuels

Scenario1assumesnon-fossil-fuelenergyconsumptionremainsatthecurrentvalue ofaround19%,andmaterialsrecyclingremainsatlowlevels(10%).Becausea majorityofenergydemandremainsderiv edfromfossilfuels,fossilfueldemand followsasimilarpathtooverallenergydemand( Figure8b ).Energydemand stabilizesataround35millionkilotonnes oilequivalentperannum,overthree timesthecurrentrate.

Figure8.(a)Simulatedpopulation,GDPpercapita&livingstandards –Scenario1(RHSandLHSrefertorighthandandlefthandscalerespectively);(b) Simulatedenergydemandandfossilfueldemand –

Scenario1;(c)Simulatedecologicalfootprint –

Scenario1;(d)Simulatedconsumptionofothernon-renewable materials –Scenario1.

4.3Ecologicalfootprint

Inthemodel,theecologicalfootprintcontainstwoparts:arenewableresourcesfootprint (fromconsumptionofcropland,grazingland,forestland,fishinggrounds,andbuilt-up land)andacarbonfootprint(fromconsumptionoffossil-fuels). Figure8c depictsthese footprintsunderthe ‘no-limits’ simulation(Scenario1).The2007renewableresource footprintof8.4billionglobalhectaresperyeargrowsquitemodestlyto12ghaperyearin 2310.Howeverthecarbonfootprintgrowsrapidlyfrom8billionghaperyearin2007to around40billionghaperyearin2310.Thecombinedecologicalfootprintof50billion globalhectaresperyearisoverthreetimesthe2007valueandrepresentsanecological footprintratioofover4.

4.4Othernon-renewablematerials

Asidentifiedinthefigurein Appendix1 panelg,theconsumptionofmetaloresand industrial/constructionmaterialshasbeenrecentlygrowingatagreaterratethanrenewableresourcesorevenfossilfuels. Figure9 showstheglobalconsumption5 ofthese materialsandtheshareofconsumptionbytheUSAandChinasince1980(SERI, 2013).

Globalconsumptionisbeingdrivensign ificantlybygrowthintheChineseeconomyandassociateddemandformaterials.Whenthisrelationshipistranslatedintothe modelandprojectedforward,globalconsumptiongrowsbymorethanninetimes comparedwithconsumptionin2010( Figure8d ).Thismayinfactbeaconservative figurebecausethegraphica lfunctioncontrollingmaterialsuseperunitofGDPhas beensettoplateau.

5.Introducingnaturalresourcelimits

Next,themodelismodifiedtosetlimitsforeachoftheresourcesofinterest,inturn: renewableresources,fossilfuelsandothernon-renewablematerials.

Figure9.Actualglobalconsumptionofothernon-renewablematerials,1980–2009.

5.1Renewableresources

Themodelstructuredescribedin Figure6 wasinvokedbyassuminganinitialvalueofthe stockthatrepresentsEcologicalCapacity.Whileconceptuallywecanenvisionastockof globalhectaresfromwhichrenewableresourcesflow,thereisnophysicalstockthatcan bedirectlymeasured.AccordinglytheGlobalFootprintNetwork(GFN, 2012)doesnot reportthestocklevel,onlytheflowstoandfromthisstock.Forthepurposesofmodeling, however,itisnecessarytoestimatetheinitiallevelofstockintheyear1960.

Scenario2a (LimitedstockofEcologicalCapacity)

Forthissimulation,IassumeaninitialEcosystemCapacityof3680billionglobal hectaresin1960,equivalenttoabout500yearsofthe1980netdepletionrate(7.36bn gha/year).6 ThisrunalsoassumesthatBiocapacityisconstant(11.6bngha/yr),thatis, unaffectedbythestatusofthestock.Latersimulationsvarytheseassumptions.Allother resourcesremainunlimited.

Figure10a showsthestatusofEcologicalCapacity(specificallytheratioofthe resourcestockinagivenyeartoitsinitialstock)andtheavailabilityofrenewable resources(specificallytheratioofavailableresourcestothedemandforthoseresources). TheimpositionofanupperlimitonEcologicalCapacityresultsinrapiddepletionof EcologicalCapacityaftertheecologicalfootprintexceedsunity,thatis,around1980.This declineultimatelyleadstorenewableresourcescarcityaroundtheendofthetwenty-first century.Asisevidentfrom Figure10a,themodelassumesrenewable-resourceavailability beginstofallshortofdemand(i.e.,itsratiodipsbelow1.0forthefirsttime)when EcologicalCapacityisreducedtohalfofitsinitialvalue.

Thisscarcityofrenewableresourcesactsasabrakeoneconomicproduction,impactingadverselyonGDPpercapitaandhencelivingstandards.Aslivingstandardsdrop,and resourcesdiminish,populationgrowthplateaus,andthenreducesrapidly(Figure10b)to around600millionattheendofthesimulationperiod. Figure10b isdirectlycomparable to Figure8a

Becausetheregenerationofrenewableresourcesisconstantinthisscenario,ecologicalcapacitybeginstorecoveraround2150(Figure10a)aspopulationdeclines.However thisrecoveryisnotsufficienttostopthedeclineofGDPandpopulation.7 Thisscenario representsanovershootandcollapsesituation.

Scenario2b (DoubletheinitialstockofEcologicalCapacity)

Totestthemodel’ssensitivitytoassumptionsaboutEcologicalCapacitythisscenario doublestheinitialstocklevelto1000yearsofthe1980netdepletionrate.Doublingthe EcologicalCapacitydelaystheonsetofthethresholdsnotedabovebutdoesnotchange thesystem’sessentialbehavior(Figure11).

Scenario2c (HalftheinitialstockofEcologicalCapacity)

Ofcourseitisequallypossiblethattheinitialstockislessthanthearbitraryvalue assumedinScenario2a.HalvingtheinitialEcologicalCapacityto250yearsofthe1980 netdepletionratebringsforwardthepeaksin Figure11 byaround50yearsto2085 (graphnotshown).

Scenario2d (DegradingBiocapacity)

Thenextrunofthemodelinvokesthereinforcingloopshownin Figure6,which modifiesBiocapacity(theregenerationrateofrenewableresources)inaccordancewith thestocklevelofEcosystemCapacity.Aconvexgraphicalfunctioncontrolsthis

Figure10.(a)Simulatedrenewableresourcesavailability –Scenario2a;(b)Simulatedpopulation,GDPpercapita&livingstandards –Scenario2a.

Figure11.Simulatedpopulation,GDP/candlivingstandards – Scenario2b.

feedback,reducingBiocapacitytozerowhenEcosystemCapacityreaches10%ofits initialvalue(whichisreturnedtotheScenario2avalueforthisrun).

Resultsfromthismodificationofthemodel(Figure12a)initiallyfollowthepathsin Figure10a.Butinsteadofrecovering,EcologicalCapacityiscompletelydepleted, resultinginavailabilityofrenewableresourcesfallingtozerointhemiddleofthe twenty-secondcentury.

Theimplicationsofthisscenarioforpopulation,GDPpercapita,andlivingstandards aredepictedin Figure12b.Thepathissimilarto Figure10b initially,butpopulationfalls towardszeroasrenewableresourcesarecompletelydepleted.Thus,Scenario2dalso representsanovershootandcollapsesituation.

5.2Fossilfuels

Inthenextroundofsimulations,therenewableresourcelimitisremovedbutalimiton thestockoffossilfuelsisintroduced.Thelimitassumedforfossilfuelsisbasedon MaggioandCacciola(2012),inwhichhistoricaldataonoil(crudeandnaturalgas liquids),naturalgas,andcoalproductionarecombinedwiththreepossiblescenariosto estimatetheglobalquantityofresources(i.e.,ultimaterealizableresource=cumulative productionplusremainingreservesplusundiscoveredresources).Theirvaluesforultimateresources,basedonacomprehensiveliteraturesurvey,areshownin Table2

Theuppervaluesin Table2 represent177%,234%and125%,respectively,ofthe provenreservesofoil,gasandcoalreportedinBP’s ‘StatisticalReviewofWorldEnergy’ publishedinmid-2014.Theseuppervaluesareadoptedforthepurposesofthisstudy, afterbeingconvertedtokilotonnesofoilequivalent(ktoe)andtotaled.

Scenario3 (Limitedfossilfuels)

Theultimaterealizablefossil-fuelresourceisincorporatedinthemodelastheinitial totalstock,reducedbythefractionusedbythecommencementofthemodelin1960 (approximately10%fromthehistoricalproductiondata),leaving1.38×109 ktoeasthe initialvalueoftheFossilFuelstock.Thisquantityrepresentsabout110yearsofproductionat2012rates(12.6×106 ktoe/year;see Appendix1 panelh).

Theresultsofthisrunaresummarizedin Figures13a and 13b. Figure13a showsthe statusofthefossil-fuelstock(stockvalue/initialvalue)andtheavailabilityoffossilfuels

Figure12.(a)Simulatedrenewableresourcesavailability –Scenario2d;(b)Simulatedpopulation,GDPpercapita&livingstandards –Scenario2d.

Table2.Fossilfuels – ultimaterealizableresources.

RangeUnitsUppervalue(ktoe)

Oil&naturalgasliquids2250–3000Gigabarrels(GB)

409,200,000

Naturalgas 9500–15,400Trillioncubicfeet(Tcf) 362,208,000 Coal 550–750Gigatonnesofoilequivalent(Gtoe)750,000,000

Total 1,521,408,000

Source:MaggioandCacciola(2012).

(theratioofavailableresourcestothedemandforthoseresources).Theavailabilityof fossilfuelsbecomesconstrainedaround2035andtheresourceisexhaustedbytheendof thetwenty-firstcentury.Asinpreviousmodelruns,thisresourcescarcityhasadramatic effectontheeconomy,leadingtoovershootandcollapse(Figure13b).Doublingthe initialstockoffossilfuelsdelaystheonsetofthepeaksin Figure13b byaround40years (graphnotshown).

5.3Othernon-renewablematerials

Asimilarapproachwastakentomodelingtheimpactofinitialavailabilityofothernonrenewablematerials,specificallymetaloresandindustry/constructionmaterials.After removingthefossilfuellimit,acapwasplacedonthetotalquantityofothernonrenewablematerialsavailabletotheeconomy.Unlikefossilfuels,someofthesematerials arenotfully-consumedandremainavailableforrecyclingandreuse,althoughthe viabilityofdoingsovariesfrommaterialtomaterial.

Inthe30-yearupdateoftheLimitstoGrowthstudy(Meadowsetal., 2004,p.105),an estimateforthelifeexpectancyofvariousmetalsisquotedassuminganannualproductiongrowthrateof2%peryearfrom1999.Theselifeexpectancyfiguresrangefrom 530yearsfornickelto1070yearsforaluminum.Noguidanceisavailable,though,for totalglobalstocksofindustryandconstructionmaterials.

Scenario4 (Limitedstockofothernon-renewablematerials)

Itisassumed(conservatively)thattheinitialstockofallothernon-renewablematerials(in1960)isequivalentto1000yearsofproductionat1980rates.Itisfurtherassumed that25%ofthesematerialshadalreadybeenexploitedby1960,leaving75%availablefor firsteconomicuse.Ofthematerialsalreadyexploited,itisassumedthat60%were ‘inuse’,20% ‘lost’,and20% ‘recovered’ andavailableforrecyclingin1960.Forsimplicity therecyclingrateissetto10%forthisinitialsimulation.

Figure14 depictsthechangingstatusofothernon-renewablematerialsstocks throughoutthissimulation.Itindicatesarapidriseinthequantityofmaterialslost,due torapiddepletionofavailablematerialsandalowrecoveryrate.

Therapidconsumptionofothernon-renewablematerials(acontinuationofthe historicaltrendobservedin Appendix1 panelg)leadstoaparticularlysharp reductioninavailability(theratioofavailablematerialstodemandforthosematerials)asstocksbecomedepletedaftermid-century( Figure15a ).Availabilityislimited ultimatelybyrecoveredratherthanvirginmaterials.Theresultingsystembehavioris similartopreviouscases,involvingovershootandeventualcollapse( Figure15b ). Furthermore,doublingtheinitialstockof othernon-renewablematerialsdelaysthe

Figure13.(a)Simulatedfossilfuelandstock –Scenario3;(b)Simulatedpopulation,GDPpercapita&livingstandards –Scenario3.

onsetofpeakconditions(asobservedin Figure15b )by30 – 40years(graphnot shown).

6.Discussionofresults

LikeallSystemDynamicsstudies,thetimingandexactnumericvaluesarethecombined effectsofinitialconditions,positedcausalrelationships,andinparticular,theequations andgraphicalfunctionsthatregulatethem.Therefore,thetimingandvaluespredictedby thesimulationsarenottobetakenasaccurate.Howeverthebasicbehaviorofthesystem ispredictablefromourunderstandingofthedynamicsofgrowth-limitedsystems,thatis, thatdepletingresourcesatafasterratethantheirregenerationorsubstitutionmust eventuallyleadtotheirexhaustion,givingrisetoovershootanddeclineorcollapse. Giventhatthemodelshowsreasonablecalibrationwithactualdatafromthepast 50years,thenear-termresultsarelikelytobeclosertorealitythanthoseforlaterperiods ofthemodel.

Theseresults,whentakentogether,suggestpeakssomewhatlaterthanthosesuggested byScenario1ofWorld3–03(thereferencecaseofLimitstoGrowth – The30Year Update).Morespecifically,myresultssuggestGDPpercapitaandlivingstandardsmay peakasfollows(Table3),notingthatthemodelpresentedhereismoresimplistic,and initialstockvaluesmoreconservative.

Itisworthstressingagainthattheresultspresentedhereshouldnotbeconsideredas ‘predictions’.Norshouldtheybeconsideredmoreaccurateinmagnitudeortimingthan theWorld3–03Scenario1,notingthateventheauthorsofthatwork ‘donotbelieveit representsthemostlikelyrealworldoutcome’ (Meadowsetal., 2004,p.171).Rather,the intentisonlytoshowthatthissimplifiedmodelproducessimilartrajectories,yetwas easiertoparameterize.

Theessentialbehaviorofthesystemiscontrolledbytheratesofresourceconsumptionandregenerationorrecycling,andthevariablesthataffecttheserates.Thekey variableaffectingtheoverallconsumptionofresourcesinthemodelistheratioof resourcedemandtoGDP(hereafterreferredtoasresourceintensity).

Formostofthecalibrationperiodofthemodel(1960–2010)realworlddatashows thatworldwideresourceintensityhasbeendeclining.Muchofthisdeclinecanbe attributedtogrowthoftheservicesector.Bythemid-1990s,servicesaccountedfor almosttwo-thirdsofworldGDP(Figure16),upfromabouthalfinthe1980s (Soubbotina, 2000,p.50).Asdevelopingcountriesbecomewealthier,theproportionof

Figure14.Simulatedstocksofothernon-renewablematerials – Scenario4.

Figure15.(a)Simulatedothernon-renewablematerialsavailabilityandstock –Scenario4;(b)Simulatedpopulation,GDPpercapita&livingstandards

Scenario4.

Table3.PeakGDPpercapitaandlivingstandardsundervariousscenarios.

LimitAssumed[RelevantScenario]TimingofPeak[RelevantFigure]

StockofOthernon-renewablematerials [Scenario4]

Towardstheendofthetwenty-firstcentury [Figure15b]

StockofFossilfuels[Scenario3]Secondhalfofthetwenty-firstcentury [Figure13b]

FlowofBiocapacity[Scenario2d]Firsthalfofthetwenty-secondcentury [Figure12b]

Figure16.Sectorialstructureofworldeconomiesin1995. Source:Soubbotina(2000).

materialsandenergyperunitofoutputdeclinessignificantlyaseconomicproduction shiftsawayfromindustryandagriculturetowardsservices.China,forexample,has achieveda65%declineinenergyintensitybetween1970and2000(Soubbotina, 2000).

DataonGDPandtheglobalEcologicalFootprintfrom1961–2007supportthe hypothesisthatreductionsinresourceintensityaremainlyattributabletochangesin thestructureoftheworldeconomy. Figure17 illustratesthepercentageoftotal EcologicalFootprintattributabletodifferentresource-usecategoriesoverthisperiod. Thecontributionofcroplandandgrazinghasreducedmarkedlyandhasbeenreplaced bycarbon(aproxyforfossil-fuel-basedenergyconsumption).By2007,carboncontributesmorethan50%tothetotalEcologicalFootprint. 8 Ifcarbonisdeductedfromthe footprintmeasurement,thesubsequentEcologicalFootprintRatioreducestowellbelow 1(depletionislessthanrenewal),andisincreasingatamuchslowerratethanifthe carbonfootprintisincluded.Thispointisoftenneglectedinmediapresentationsofthe EcologicalFootprint.

Althoughtheeconomicintensityofrenewableresourceusehasbeensteadilydeclining(Figure18),thereseemstohavebeensomechangesintherelationshipbetweenGDP andnon-renewableresourcessincetheyear2000.First,therehasbeenasharpupturnin theresourceintensityofothernon-renewablematerials(i.e.,excludingfossilfuels). Second,energyintensityseemstohavestabilized,ratherthancontinuingitsrecent

decline.Finally,thecarbonfootprintintensityhasreturnedto1990levelsafteragradual declinesincearound1980.

Theshapesoftheseintensitycurvesarethebasisofthemodel’sassumedrelationships betweenresourceuseandGDP.Thus,asthelattergrowsexponentially,resourceuseis increasedaccordingly.

Inthesimulationsdescribedearlier,consumptionofresourcesisconstrainedonlyby availability,thatis,whetherornottherearesufficientresourcestomatchdemandatany pointintime.Asshownin Figures10a, 12a and 13a,suchresourceconstraintstakeeffect wellafterdepletionoftheresourcestocksbegin.Althoughtheassociatedbalancingloop eventuallytakeseffect – toreduceGDPand,thus,resourcedemand – itistoolateto avoidovershootanddecline.Thisresultchallengestheconventionalwisdomthatmarket economicswillhelpavoiddepletion,thatis,thatscarcitywillinduceapricesignalthat incentivizestechnologyimprovementsthatinturnleadtoreductionsinresourceuseor substitution.Acknowledgingthatmysimplifiedmodeldoesnotallowpricesignalsto

Figure17.Make-upoftheecologicalfootprint1961–2007.

Figure18.Naturalresourceintensity1960–2010.

directlyaffectresourcedemand,itsresultssuggestthattherapidonsetofeconomic scarcitywillprecludeourabilitytoavoidovershoot.AsSterman(2012)putsit:

Evenwithsignificantpotentialfornewtechnicalsolutions,aprosperousandsustainable futurecanonlybebuiltifgrowthofbothpopulationandmaterialthroughputceasevoluntarily,beforegrowthisstoppedinvoluntarilybyscarcityorenvironmentaldegradation.(p.50)

7.Introducingvoluntarymeasures

TheLimitstoGrowth – the30YearUpdate (Meadowsetal., 2004)includesscenariosthat avoidcollapse(Scenario6,8,9and10)throughtheadoptionofvariouspolicymeasures. Otherauthorshaveproducedsimilarcredibleoutcomesfromglobalmodels.Developers oftheHumanandNatureDynamics(HANDY)model(Motesharrei,Rivas,&Kalnay, 2014)foundthat:

collapsecanbeavoidedandpopulationcanreachequilibriumifthepercapitarateof depletionofnatureisreducedtoasustainablelevel,andifresourcesaredistributedina reasonablyequitablefashion.(p.101)

Toinvestigatethevoluntarypolicymeasuresnecessarytoavoidovershootanddeclineor collapse,Iexpandthemodeltoincorporatefurtherbalancingloops(i.e.,endogenous behavior).Modificationsarespecificallyappliedtothefossilfuelsandothernon-renewablematerialssub-sectorsonly.Nochangesaremadetotherenewableresourcessector, althoughthissub-sectorisaffectedindirectlybythecarbonfootprintofenergy.

7.1Fossilfuels

Anadditionalbalancingloopisaddedtothemodelwhichincreasestherenewableenergy fractionasfossilfuelstocksaredepleted(see Figure19).

Figure19.Causalloopdiagramofthemodifiedfossilfuelssub-sector.

7.2Othernon-renewablematerials

Additionalbalancingloopsareaddedtotheothernon-renewablematerialssub-sector. Thesebalancingloopsaretriggeredbythedeclineofothernon-renewablematerials stocks.Inresponsetothisdecline,theycauseagradualreductioninoveralldemandfor thesematerials,andagradualincreaseinthefractionofmaterialsrecoveredandreused.

Themodifiedcausalloopdiagramisdepictedin Figure20

Scenario5 (Voluntarymitigationmeasures)

Thestrengthsoftheadditionalbalancingloopsin Figures19 and 20 arevaried iterativelyuntiltheyoffsettheovershootbehaviorandreinstatethe ‘smoothlanding’ evidentintheno-limitsscenario.Thissmoothlandingisultimatelyachievedthrough additionofthefollowingpolicies.

Withrespecttofossilfuels:

● Increasingthefractionofrenewableenergyrapidlyfromthepresentlevelto1by thetimefossilfuelstocksdepleteto25%oftheirinitialvalue.

Withrespecttoothernon-renewablematerials:

● Reducingdemandforothernon-renewablematerialsby75%(perunitofGDP)as theirstocksdecline;andsimultaneouslyincreasingthefractionofmaterialsrecoveredfrom10–70%asstocksdecline.

Theapplicationofthesemodificationsreturnsthesystembehaviortosomethingcloseto the ‘smoothlanding’ oftheno-limitsscenario,asshownin Figure21a.Inthisscenario, livingstandardsreachthesamehighvaluesastheno-limitsscenariobutGDPpercapitais slightlylowerandpopulationstabilizesatlessthan9billion,comparedto11billion previously.Thischangedbehaviorisduetoreductionsinresourceintensitytriggeredby thevoluntarymeasures.Theresourceintensitywithrespecttofossilfuelsandcarbon footprintisdepictedin Figures21b and 21c

Figure20.Causalloopdiagramofthemodifiedothernon-renewablematerialssub-sector.

Scenario5;(b)Simulatedfossilfuelsintensity –

Figure21.(a)Simulatedpopulation,GDPpercapita&livingstandards –

Scenario5.

Scenario5;(d)Ecologicalfootprintintensity

Scenario5;(c)Simulatedother non-renewablematerialsintensity –

ThismodificationalsoreturnstheEcologicalFootprintRatiotounityastheCarbon Footprintreducestozero(Figure21d).Notethatthe ‘voluntarymeasures’ simulationdid notincludeanydirectreductionintherenewableresourceintensity(itisindirectly reducedbyreducingfossilfueluse).Thisresultthereforeimpliesthatcurrentpatterns ofrenewableresourceintensitymaybesustainableifthecarboncomponentcanbe eliminatedthroughatransitiontorenewableenergy.However,thereisanimportant caveatonthisconclusionwhichisdiscussedbelow.

Closerinspectionof Figure21a (Scenario5)suggeststhat,towardstheendofthe simulationperiod,GDPpercapitaisdropping,andlivingstandards(whicharemodeled asadirectfunctionofGDPpercapita)areonthevergeofdecline.Extendingthe timeframeofthemodelrevealsthatequilibriumhasnotinfactbeenachieved;overshoot hasbeenmerelydelayed,andoccursthereafter.Thereasonsforthisbehaviorareclear fromconsiderationof Figure20,whichdepictstheothernon-renewablematerials’ causal structure.

Thetotalstockofothernon-renewablematerialsatanytimeisthesumof:virgin materials,materials-in-use,materialsrecovered,andmaterialslost.Asvirginmaterialsare usedforthefirsttime,theyareconvertedtomaterials-in-useaccordingtotherateof demand.Thetimetheyresideinthatstockdependsonthelifeofthematerials,orrather thelifeoftheproductsthatembodythematerials.Clearlythisvariessignificantly,froma verylongperiod(e.g.,concreteintransportinfrastructure)toaveryshorttime(e.g., materialsinconsumergoods).Attheendoftheirlifetheyareeitherrecoveredor discarded.Itisimpossibletorecover100%ofmaterialsbecausetheyareboundtogether inproductsthatmaketheirseparationverydifficultinmanysituations(UNEP, 2011).In thecaseofsomemetals,veryhighrecoveryratesareatleasttheoreticallypossible. However,evenifitisassumedthat90%ofthematerialsinusecanberecovered,the balanceislosttotheeconomy.

Becausethelawsofthermodynamicspreclude100%recovery,theactofreducing demandandincreasingtherecyclingfractiononlydelaytheinevitable,albeitconsiderably.Eventually,stocksofviablyobtainablevirginmaterialswillbedepletedcompletely.Accordingly,inthelongtermtheconsumptionofmaterialsmustequaltheir recoveryorrecyclingrate.Becausesomeproportionwillbelostthrougheachcycle, theavailabilityofmaterialsmustdiminishovertimewithconsequencesforeconomic useofthosematerials.

Inthelongterm,theproportionofmaterialsthatarelostmustbesubstitutedwith renewablematerials,ifthesameeconomicdemandistobemet.Ifwefurtherassumethat therecoveryrateitselfwilllikelydiminishinthelongterm,asmaterialsgothrough multiplecyclesofrecoveryandrecycling,thissubstitutiontowardsrenewablematerials willneedtoincreaseovertime.TheimpactofthisontheEcologicalFootprintmustbe consideredinanymodelingoffutureeconomicuseofothernon-renewablematerials.

8.Policyresponse

Thevoluntarymeasuresoutlinedabove,withrespecttofossilfuelsandothernon-renewablematerials,onlyachieveglobalstabilityifallofthefollowingconditionsapply:

● Continuingimprovementsinlivingstandardsinthedevelopingworlddeliverthe demographictransition(andtherebyconstrainnetglobalresourceconsumption);

● Fossilfueluseforenergyiscompletelyeliminated;

● 70%ofothernon-renewablematerialsareultimatelyrecoveredandrecycled;

● Demandforothernon-renewablematerialsisultimatelyreducedby75%;and

● Allmeasuresoccursimultaneouslyandwithoutdelay.

Absenttheseconditions,themodelproducesovershootandcollapsebehaviorduringthe simulationperiod.Althougheasytoconfigureinamathematicalmodel,theimplementationoftheseorsimilarpoliciesatanywherenearthescaleandtimeframerequired, appearspresentlyinfeasible.Althoughsomeactionisbeingtakenwithrespecttogreenhousegasemissionsandrecoveryorrecyclingofmaterials,thescaleoftheseactionsdoes notreflecttheurgencyofthetask.Almostnoactionisbeingtakenonreducingthe economicdemandforothernon-renewablematerials,anditishighlyquestionable whetheritisevenpossibletoreducedemandperunitofGDPforsuchmaterialsby 75%,letaloneinthetimeframeidentified.

Thereispresentlylittlefocusontheproblemssetoutinthisarticleattheinternational ornationallevel.AlthoughtheUnitedNationsEnvironmentProgram’sInternational ResourcePanel9 recentlyproducedareportonde-couplingresourceusefromeconomic growth,10 eventhisdocumentistentativeaboutrecommendingnationalpolicies. Recommendationsrelatetoleadership,institutionalframeworks(changingthemindsets ofdecision-makers),andtheadoptionofpricesignals.Eventhisagendahasvirtuallyno momentuminnationalpoliticsinthecountriesthatmattermost.Thereisnoreferenceto theworkofthispanel,forexample,onthewebsitesoftheUSEnvironmentalProtection Agency,NaturalResourcesCanada,ortheUKDepartmentforEnvironmentFood& RuralAffairs.Policiesintheseandmostcountriesremainfocusedonwastemanagement andrecycling,ratherthantheeconomy-widetransformationsneeded.

Policychangewillonlyfollowmuchgreaterpublicawarenessoftheissuesand translationofthisawarenessintopoliticalaction.Acceleratingthisprocessisimperative ifwearetoavoidthepresentstateofglobalovershootprogressingtoseriousdeclineor collapse.UrgencyhasonlygrowninthenearlyhalfacenturysincetheoriginalLimitsto Growthstudy(Meadowsetal., 1972)cametothissameconclusion.

9.Furtherwork

Themodelpresentedhereaveragesglobalstocksandflows.Accordingly,itdoesnot accountforthelargedisparitiesbetweendevelopedanddevelopingnations’ resource demandandaccesstoresources.Thenextphaseofthestudywillseektoexplore interactionsbetweenthe ‘haves’ and ‘have-nots’ duetoresourcedistributionacross nations.FurtherphasesofmodelingwillbebasedonOECDGDPgroupings,nations, andcities.Developmentofthesemodelswillneedtoaddressavarietyofcomplexities relatedtotheimportandexportelementsoflocaleconomies.Accommodatingthese complexitieswillnecessarilyinvolveanumberofassumptions,theresultsofwhichcan onlyrealisticallybetestedthroughsensitivityanalysis.Accordingly,themodelswill(like themodelpresentedhere)include ‘sliders’ thatfacilitatesuchsensitivitytesting.

Anopensourceonlineversionofthismodelisavailableat https://forio.com/simulate/ williamrgrace/sustainable-world tofacilitateexplorationofthesystemdynamicsand policyoptions.Futuremodelswillsimilarlybemadeavailableonline.

Disclosurestatement

Nopotentialconflictofinterestwasreportedbytheauthor.

Notes

1.Asthenameimplies,therewasalsoaWorld1model,developedearlierbyForresteratthe behestoftheClubofRometohelpinvestigate ‘thepredicamentofmankind’ .

2.AnexplanationofcausalloopdiagramsisincludedinAppendix2andfurtherexplanationis availableat http://www.public.asu.edu/~kirkwood/sysdyn/SDIntro/ch-1.pdf.

3.Kaldor ’ssix ‘stylizedfacts’ areempiricalobservationsrelatedtoeconomicgrowththatappear toapplytotheeconomictrendsinmanydifferentindustrializedcountries.

4.Resourceflows(andhenceconsumptionofresources)areconstrainedasthestockofresources isdiminished.

5.InfactSERIreportsthesefiguresas ‘usedextraction’ whichapproximatesconsumption.

6.500yearsisanarbitraryfigurechosentoreflectthepossibilitythatconsiderableecological reservesmayremainevenaftertheecologicalfootprintexceeds1,beginninginthe1980s.

7.GDPpercapitaandlivingstandardsbegintorisearound2250butonlybecausedeclining populationreducesmorequicklythandecliningGDP.

8.Notingthatthecarbonfootprintistheamountofproductivelandandseaarearequiredto sequestercarbondioxideemissions.Therequiredquantityoflandandseaisthe ‘resource’ in thiscase.

9. http://new.unep.org/resourcepanel/

10.Itisnotphysicallypossibletocompletelydecoupleeconomicproductionandresourceuse. Thethrustofthereportisreallyaboutreducingtheeconomicintensityofresourceuse.

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Appendix1.Simulatedvsobserveddataforcausalrelationshipsandgraphical functionsassumedinthemodel 28 W.Grace

Appendix2.Causalloopdiagrams

Allsystemswithfeedbackaremadeupofcombinationsofso-calledreinforcingandbalancing loops.Thesecanbecharacterizedbycausalloopdiagrams.Inthefollowing,thearrowsindicatethe directionofcausality,forexample,chickenscomefromeggs.Thepolarityindicatesthatthe causationispositive.

Morechickensleadtomoreeggs,whichleadtomore chickens andsoon.

Thisisareinforcingloopandleadstoexponentialchicken populationgrowth(intheabsenceofotherinfluences)

Howevernothinggrowsforever,soinrealsystemstherearefactorsthatlimitgrowthordecline.We couldassume,forexample,thatchickensliveinanareainhabitedbyfoxes.

Themorechickenstherearethemorefoxestherewillbe (positivepolarity).Howeverthemorefoxestherearethe fewerchickenstherewillbe(negativepolarity).

Thisisabalancingloopbecauseitcounteractsthegrowthof chickenandfoxnumbers.Ifthisloopoperatedinisolation fromthefirstloop,chickennumberswouldfalltozero.

Whenthetwoloopsoperateintandem,wehavebothreinforcingandbalancingloopsinfluencing thenumberofchickensovertime,onethatcausesgrowthandonethatcausesdecline.

Theresultingbehaviorofthesystemovertimedependson:

● thenumberofeggshatchedperchickenperyear;and

● thenumberofchickensconsumedperfoxperyear.

Dependingontheseparametervalues,thenumberofchickensmay:

● growexponentially;

● stabilizeatanequilibriumlevel;or

● growexponentiallyinitiallyandthen collapsetozero.

Alloftheseoutcomesarepossible,demonstratingthatcomplexbehaviorcanresultfromasimple systemstructure.