How to use System Dynamics to build a model · Clearly a lot is missing from this model. We know...

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