how to use system dynamics to build a model · clearly a lot is missing from this model. we know...
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ModelBuilding
HowtouseSystemDynamicstobuildamodel
Illustratedbybuildingasimplechurchgrowthmodel
JohnHaywardUniversityofGlamorgan
WalesUK
ChurchGrowthModellingwww.churchmodel.org.uk
Whenwestartmodelbuildingitisnormaltothinkofthecentralelementinthemodel.
Inthecaseofchurchgrowththeobviousplacetostartisthechurch.Thisisourfirstelement.
Thisimmediatelyaskstwoquestions:
1. Whatdowemeanbychurch?Allthosewhobelieve?Allthosewhoattendaservice?Allwhoaremembers?AllwhoarepartofsomewiderChristiancommunity?Visibleorinvisiblechurch?
2. Whicheveroneoftheseischosen,thenhowisitmeasured?E.g.ifitisthosewhoattendaservicethenwhichservices,andhowregularly?
Wedon’tneedtospecifyfornowwhichoftheseconceptsofchurchwearethinkingof,unlessitbecomesneededforthemodel.Howevergoodmodellingwillalwaysnotethesequestionsasitproceeds.
ModelBuilding UsesStella9.1.3
StockAccumulation
Theelementaboveiscalledastockaccumulation,orstockforshort.Itrepresentsthechurch.
Itcapturesthetypeofelementwhichaccumulatesovertime.Agoodexamplesisabankbalance,ifmoneyisdepositeditstaysthereandatthesamevalue,unlessmoreisadded(perhapsthroughinterest),orsomeiswithdrawn.I.e.whatistheretodaywillstillbetheretomorrow,unlessthereissomeactiontochangeit.Itisnotthereandgoneinaninstant.
Forachurchof50peopleitwillremainachurchof50peopleweekafterweekunlesspeoplejoin,leaveordie.Thusastockisasuitableelementforachurch,whethermembershiporaverageattendance.
Astockcanbephotographed.Ifyoutakeasnapshotataparticulartimeyoucanseeitsvaluewithoutanyambiguity.Justthinkofachurchphotowithallthepeopleinrows.Thishelpsjustifychurchasastock.
StockAccumulation
Astockcanalsobepicturedasabathtubthatcontainsafixedamountofwateratanytime.
Itwillnotchangeunlessthetapisturnedonortheplugispulled.Itiseasytopictureitwithalevelofwaterinside.Howeverunlikeabaththereisnoautomaticlimittoitfillingtothebrimandoverflowing!
Hypothesis
Wenowsetourfirsthypothesis:10newpeoplecometochurcheachyear.
Ahypothesisisastatementofwhatwebelieveisthecauseofthebehaviourwesee.Insystemdynamicsitiscalledadynamicalhypothesisbecauseitisbelievedtobetheexplanationofhowsomequantitychangesovertime.
Wehaveseenachurchgrow–thuswehavehypothesisedthatitiscausedbyafixednumberofpeoplejoiningeachyear.Thespecificnumberof10isjustsowecanpicturetheconsequencesandisnotreallypartofthehypothesis.
Ourdynamichypothesisis:Aconstantnumberofpeoplejoinchurcheachyear.
Flow“peryear”
Thehypothesisinthiscaseisrepresentedbytheelement“cometochurch”whichiscalledaflow.
Aflowisalsocalledarateandisdifferentfromastockinthatitmeasureswhathappensoveraperiodoftime,notwhatisthereinaninstant.Thusourflowhasavalueof“peopleperyear”,unlikethestockwhichisjust“people”.
Thereare50peopleinthestock,and10peopleperyearjoining.
Aflowislikeatapwithwatergushingintothestock.Aflowcannotbephotographed,ifwediditwouldbeablur,becauseitismoving.Theflowcanonlybemeasuredwithreferencetoatimeperiod.Sowecansay10peoplejoinayear,or2.5everyquarter,onaverage.Butwecannotsayhowmanyjointhisinstant.
Wenowhaveamodelwecansimulate.With50peopleinthechurchand10peoplejoiningayearwhatistheshapeofthegraph?
Tomakeiteasieraskhowmanypeopleyouexpectinchurchafter10years.
Simulation
After10yearsthereare150.TheOriginal50andthe10X10whohavejoinedover10years.
Thegraphisastraightline,theresultofconstantgrowth.
Producingaresultlikethisiscalledasimulation
Simulation
Justtoproveitlookatthetableandseethatchurchisincreasingby10eachyear,50,60,70etc.
Thismodelissimpleenoughyoucouldworkoutitsconsequenceswithoutasimulation.
WhatisMissing?
Clearlyalotismissingfromthismodel.Weknowthisforatleasttworeasons
1. Weknowchurchesdonotincreaseindefinitely.I.e.,thereareobservationalreasonsforbelievingthatmoremustbeaddedtothemodel.Ourcurrentmodelcannotreproducewhatwesee.
2. Theoreticallyweknowthereareprocessesmissing.Weknowpeopleleavechurch,indeedbecauseofourknowledgeofpeopleweknowthattheydie.Thusourmodel,regardlessofitsbehaviour,doesnotrepresentwhatweknow.
Howeverweareconstructingourmodelonestepatatime.Thisisdonesothatwecanseetheconsequenceofeveryhypothesiswemake.
Wevalidateamodelthroughbothobservationoftheworldandourknowledgeofhowthetheworldworks.
Hypothesis:PeopleLeave
Foroursecondhypothesiswewillclaimthatpeopleleavethechurch,aswellasjoin.Thisisrepresentedbytheflowgoingoutofthestock.Aflowgoingoutofastockisliketheplugonabath,itletswaterout.
Thereamanyreasonspeopleleaveachurch:movehome,changechurches,giveupthefaith.Thereasonsforchangingachurchcanbebrokendownmoreaswell.
Tokeepthingssimplewewillnotmodelthesereasonsindetail.Itisunlikelythereisenoughdatatobeabletomakeaprecisemodelofthesereasons.
Biggerthechurch–>morepeopleleave
Insteadwewillclaimthatthebiggerthechurchthemorepeopleleave.
Thisisareasonableclaimasleavingisanormallyapersonaldecision,soifeachpersonactsindependentlythenonaverageapersonstaysinchurchafixedperiodoftime.Thusthemorepeoplethemorewillleave.
Thisiscalledacausallinkandisrepresentedbythecurvedarrowfrom“church”to“leavechurch”.Thisarrowiscalledaconnector.
Thisprocessisusedwithpercentages.Generallythelossesfromachurcharearound5%ayear(excludingdeaths).
Biggerthechurch–>morepeopleleave–>lesspeopleinchurchBalancingloop
Causalloop
Wenowhavewhatiscalledacausalloop,asthebiggerthechurch,thenthemorepeopleleave,thuslesspeopleinthechurch.
Thisiscalledabalancingloopastheeffectonthechurchnumbersistheoppositeofwhatwestartedwith.Itwillcausethechurchnumberstoreachastablevalue.
Converter
Assume10%leavethechurcheachyear.Thisiscontainedinthecircle“percentagewholeavethechurcheachyear”.Thecircleiscalledaconverteranditisconnectedtotheflowoutbyaconnector.
10%isabithigherthantheusualmeasuredvalues,butshouldillustratetheprinciple.
InflowStock Connectors
Outflow
Converter
Stocks,flows,convertersandconnectorstheelementsofasystemdynamicsmodel
Whathappensnext?
Eachyear10peoplejoin,but10%leave.
Whatdoyouthinkhappens?
Thechurchgrows,butthegrowthgetsslower.Why?
Becauseasthechurchgetsbiggermorepeopleleave.Inyear1,5peopleleft.Byyear9thechurchisbiggerso8peopleleft.
Runthesimulationonto30yearsandthechurchstopsgrowingasthenumberofpeopleleavingequals10,thesameasthenumberjoining.Thebalancingloophas“balancedthechurch”.
WhatisMissing?
Wellthereisstillmuchmissing.Thisiswhereitpaystoquestioneverything.
Letusstartbyasking“wheretopeoplegowhentheyleavechurch?”
Thusaddanewstockofallthepeoplewhohaveleftchurch.
Thisisnotimportantenoughtobeahypothesis,butitmaybeusedinalaterone.Thesepeopleareimportant,somemaycomebacktochurchoneday.
Next–howdopeoplecometochurch?
Thistimewewillconstructanewhypothesis‐peopleinthechurchbringnewpeople.
Thereisplentyofevidencethatthishappens,althoughfiguresarehardertocomeby!
Ofcoursethechurchmembersmaynotphysicallybringthem,theymayhavejusttoldafriendaboutthechurch.
Hypothesis:Peoplearebroughttochurchbychurchmembers
Thinkthroughthehypothesis
Themorepeoplethereareinchurchthenthemorepeoplearebroughttochurch.
Forexampleifeachpersonbroughtonenewpersoninayearthenthechurchdoubles.Soachurchof50adds50,butachurchof100adds100.
Thusthereisaconnectorfrom“Church”to“bringtochurch”
Morepeopleinchurch–>morecomearebrought–>morepeopleinchurchReinforcingloop
Wehaveanothercausalloop.
Themorepeopleinchurchthemorepeoplearebroughttochurchsothemorepeoplethereareinchurch–indeedthefasterchurchincreases.Thisisareinforcingloop.
Wheredopeoplecomefrom?
Thenextquestionistoask–wheredopeoplecomefrom?
TheWorld!
Tobemoreprecisefromthethepoolofallthepeopleoutsidethechurch.
Tobeevenmoreprecisethechurchcomesfromthepoolofpeoplewhohaveneverbeentochurch.Thisexcludesthosewhohaveleftthechurch.Theycouldcomeback–butthatassumptionhasnotbeenmadeatthispoint.
Howlikelyisitthattheachurchpersoncontactssomeonewhohasneverbeentochurch?
Iftheymakecontactwithpeopleoutsidethechurchasmuchasthoseinside,onadaytodaybasisinworkandleisure,thencontactdependsonthefractionofthepopulationoutsidechurch.Thisis“chanceofcontactinganoutsider”.
Saythereis1000peopleinthecommunityand200belongtothechurch.Sothereare800outsidethechurch.Thenthechanceofachurchpersoncontactinganoutsiderits800/1000whichis4outof5contactsarewithnonchurchpeople.
Youmayalreadybethinkingthisisaboldassumption.Churchpeoplespendfarmoretimewithchurchpeoplethantheydowiththeworld.Sothisnumbershouldbesmaller.
ButasChristiansinteractwithpeoplewhoarenotfriends,especiallypeopleatwork,itmaynotbeaslowasyouthink.
Fornowwewillleaveitasconstructed.Butthemodellingprocesshasmadeusaskthequestion.
NextwewillassumethatthereisafixednumberofpeopleanindividualChristiancouldbringtochurcheachyear.
Thisisanaveragenumberassomemaybringmorethanothers
SowecanworkouthowmanypeopleeachChristiandoesbringtochurchbytakinghowmanytheycouldbringifalltheircontactswerewiththoseoutsidethechurchandmultiplyingbythechancethepersonisanoutsider.
Thisalsoinfluenceshowmanyarebroughttochurch.
WhoBringsThem?
Thebestthingaboutsystemdynamicsisthatitkeepsmakingyouaskquestions!
Youmaybeasking“surelynoteverypersoninchurchbringsanotherin”.Noteverypersoninchurcheventellsthoseoutsideaboutthechurch,orGod,orJesus.Somechurchpeoplearemoreopenintheirfaiththanothers.
Hypothesis:NotallChristiansspreadthefaith
Thewordshavebeenchangedto“spreadthefaith”asbringingpeopletochurchinvolvesanumberofmechanisms.
SowearegoingtosplitthechurchintotwotypesofChristians.
TwotypesofChristians
Thosewhorecruit,andthosewhodon’t.
Thustwostocks
Thisisjustifiedonthegroundsthatthosewhorecruitaremorelikelytobehighlycommitted.
Sotheonlyflowto“leftchurch”isfromthenon‐recruitingChristians.
Hypothesis:Onlynon‐recruitingChristiansleavechurch
Thisisjustifiedonthegroundsthatthebestrecruitersarenewpeopleastheyaremorelikelytohaveanextensivenetworkoffriendsoutsidechurch.Alsohavingjustjoined,perhapsbeenconverted,theyhaveafreshenthusiasmforthefaith.
Afterawhiletheylosetheirnetworkoffriendsoutsidechurchastheybecomemoreintegratedintochurchlife.Perhapstheirenthusiasmlosesitsedgeafterawhile.
SothereisaflowfromrecruitingChristianstonon‐recruitingones.
Hypothesis:RecruitingChristiansstopdoingsoafterawhile
ThemorerecruitingChristianstherearethemorewillgiveuprecruitment.Aproportionalprocesses–sotheconnecterisplacedfromrecruitingChristianstostoprecruiting.
Thisalsodependsofthetimespentasarecruiter.
WhatHappens?
Thisistoohardtoreasonthroughordoarithmetic.Nowasimulationisessential.
Thegrowthofthechurchfirstincreasesfasterandthenitstartstoslow.
Whydoesitslowdown?
ChurchgrowthisslowingdownbecausethenumberofrecruitingChristiansisdeclining,theyarenolongerconvertingenoughpeople.Doesthegrowthreachalimit?
Infactchurchnumbersreachesapeakthenstartstodecline.Thechurchcannotmakerecruitersfastenoughtosustainitself,downto0by40years.Churchbecomesinactive,thendeclines.
Tostabiliseandavoidextinctionthepoolofpeopleoutsidethechurchneedstobereplenished.Thishappensbecausethosewholeavethechurcheventuallybecomeopentorejoiningandtherearenewpeopleborninthecommunity.
Thechurchmayalsokeepsomeofitsownchurchchildren,butthechurchalsohasdeaths.
Andsothemodellinggoeson–buthopefullyyoucanseethepotentialofusingsystemdynamicstobuildasimulationmodelofchurchgrowth.
FurtherInformation
JohnHaywardUniversityofGlamorgan
WalesUK
ChurchGrowthModellingwww.church‐growth‐modelling.org.uk
ThesoftwareStellaismadebyISEESystemswww.iseesystems.com