Seth Bullok
InformatisResearhInstitute,Sho olofComputerStudies,University ofLeeds
sethss.leeds.a.uk
Abstrat
Asimpleomputerprogramdatingfromthersthalf
ofthe nineteenth enturyis presentedas the earliest
knownexample ofan evolutionarysimulationmodel.
The mo del is desrib ed in detail and its status as
anevolutionary simulation mo del isdisussed. Three
broad issues raised by the mo del are presented and
their signiane formo dern evolutionary simulation
mo delling is explored: rst, the utility of attending
totheharaterofasystem'sentiredynamis rather
thanfo usingontheequilibri umstatesthatitadmits
of;seond,theworthofadoptinganevolutionaryp
er-sp etive onadaptivesystems b eyondthoseaddressed
by evolutionary biologial researh;third, thep
oten-tialforthenon-linearharaterofomplexdynamial
systems to b e explored through an individua l-ba sed
simulation mo dellingapproah.
Withthewar-timeandp ost-wardevelopmentofthe
rstmo dernomputers ameasurge of researh into
omputationaltheory. Seminal work by
mathemati-ianssuh asMCullo handPitts(1943)onthelogi
ofneuraliruitry,Turing(1952)ondiusion-reation
mo dels of morphogenesis, Walter (1963) and Ashby
(1956)onyb ernetis,vonNeumannandBurks(1966)
onautomatatheoryandself-repliation,andlater
Hol-land(1975)ontheformalprop ertiesofadaptation,
in-volvedtheappliationoflogi,mathematis,rob otis,
andontroltheorytoessentiallybiologialproblems.
The ab ove-ited piees of researh are now
reog-nised as the intelletual preursors to the eld that
hasometob eknownasartiiallife. Although,more
proximally,artiiallifeanb eonsideredtob ethe
o-spring ofartiial intelligene (see Bro oks,1991, and
Steels,1994,foraountsofartiiallife'srelationship
to artiial intelligene), it is b eoming inreasingly
apparentthat thework published under the artiial
liferubri(e.g.,mo delsofmorphogenesis,ellular
au-tomatamo dels,b ehaviourbased rob otis, the
simula-tion of adaptive b ehaviour, et.) hasinherited muh
ofitsmetho d,andsomewouldsaymadness,either
di-However, it will b e laimed here that a
partiu-lar kind of artiial life, the evolutionary simulation
model,originatedfarearlierthaneventherstofthese
seminal works. Coinidentally, the rst evolutionary
simulationmo delholdsmanylessonsthatarep ertinent
to day. Afterintro duingthemo delanddisussingits
statusasanevolutionarysimulationmo del,aseriesof
issues raisedby themo delwillb e presentedandtheir
impliationsformo dernartiiallifeexplored.
The Ninth Bridgewater Treatise
In 1837, twenty-two years b efore the publiation of
Darwin's On the Origin of Speies, and over a
en-turyb eforetheadventoftherstmo dernomputer,a
pieeofsp eulativeworkwaspublishedasanuninvited
NinthBridgewaterTreatise.Theprevious eightworks
in theseries had b een sp onsored bythe willof
Fran-is Henry Egerton, Earl of Bridgewater, and a
mem-b er oftheEnglishlergy. Thewill'sinstrutions were
to make money availableto ommission and publish
an enylop edia of natural theology onerning \the
Power,Wisdom,and Go o dness ofGo d,as manifested
intheCreation"(Bro k, 1966;Robson,1990).
Theninthpubliationinthisseriesisnoteworthyin
that, unlike typialworks of natural theology, it
nei-ther soughtto draw attentionto miraulousstates of
aairsdeemedunlikelytohaveomeab outbyhane,
andthusthoughttob etheworkofadivinehand(e.g.,
thelength oftheterrestrial day,whihseems
mirau-louslysuitedtothehabitsofmanandotheranimals),
nor did it seek to reonile sienti ndings with a
literal reading of the Old Testament (e.g., disputing
evidene that suggested an alarminglyanient earth,
aountingfortheexisteneofdinosaurb ones,or
pro-motingevidenefortheo urrene ofthegreat o o d,
et.). In ontrast to these ap ologeti eorts, the
au-thor of theninth Bridgewatertreatise pro dued what
is,tomyknowledge,therstinstaneofan
and analytialengine (the rst automatialulating
devies,andthuspreursorstothemo dernomputer).
Indeed,in1837hewasoneofp erhapsahandfulof
si-entistsapableofarryingoutresearhinvolving
auto-matedomputationalmo delling. Hismo delstands as
ausefully simple ase study, and an elegant example
oftheusetowhihomputersareb eingputinmo dern
artiiallife.
Theaimofthispap erwillnotb etodrawattention
to Babbage's mo del as an example of a partiularly
presient piee of work,antiipatingmuh ofmo dern
evolutionary simulation mo delling. Rather, this
an-tique evolutionary simulationmo del will b e revived,
notonlytoidentifysimilaritiesb etween Vitorian
si-eneandurrentartiiallife,butinordertohighlight
imp ortantasp etsoftheontemp orarypratieof
evo-lutionarysimulationmo delling. Inpursuingthisaim,
IamwellawareoftherisksofWhiggismin
interpret-inghistorialmaterial(seeHyman,1990,fordisussion
of Whiggismin thestudy of Babbage and his work).
Althoughamo dernp ersp etiveonthepastis
unavoid-able,thefatthatthispap erdo esnotprimarilyseekto
re-evaluateBabbage's workbut to re-analysemo dern
evolutionarysimulationmo dellingworkinthelightof
Babbage'smo delensures that theriskof mis-treating
Babbage'swork isslim.
The First EvolutionarySimulation
Model
Babbage's (1837) mo del (see also Babbage, 1864,
Chapter XXIX\Mirales" fora ratherwhimsial
a-ountofthemo del'sdevelopment)wassituatedwithin
what was then a ontroversial debate. It addressed
the dispute b etween atastrophists and
uniformitari-ans. Primafaiethis debate was internal to geology,
sine it onerned thegeologialreord's p otential to
showevideneofdivineintervention(prinipallyinthe
formofsupp ortfortheOldTestamentaountsofthe
Creationand theDeluge). Catastrophists argued for
aninterventionistinterpretationofgeologialevidene,
takingdisontinuitiesinthereord tob e indiatorsof
the o urrene of mirales (violations of laws of
na-ture). Inontrast, uniformitariansinsistedthat in
or-dertoarryoutsientienquiry,theentiregeologial
reord mustb e assumedto b e theresult of
unhang-ingpro esses. Allowingarolefordivinemirales,the
uniformitarianslaimed, would render omp eting
ex-planationsequallyvalid. No theoryould b e laimed
tob emoreparsimoniousoroherentthanaomp eting
theorythat invokedneessarilyinexpliable exogenous
inuenesinitsaountofthephenomenaatissue.
Geological Time
Geological Record
Computational Output
Computational Time
Figure 1: Babbage's (1836) evolutionary simulation
mo delrepresented theempiriallyobservedhistory of
geologialhangeasevidenedbythegeologialreord
(upper panel) as the output of aomputing mahine
following a program (lower panel). A suitably
pro-grammedomputingmahineouldgeneratesequenes
ofoutputthatexhibiteddisontinuitieswithout
requir-ingexternalinuene. Henedisontinuitiesinthe
a-tual geologial reord did not require \atastrophi"
divineintervention,butouldb etheresultof
\gradu-alist"pro esses.
thingofadeathblowwithLyell's(1830)publiationof
hisPriniplesofGeology,thepubliationofthe
Bridge-watertreatisesandworkslike themevidenes itsslow
demise. Onlysubsequenttotheoupdegr^aeprovided
by Darwin's work on evolution did natural theology
textsnallyeasetob epublished (Bro k,1966).
Babbage'sresp onsetotheatastrophistp ositionwas
to onstrut what an now b e reognised as a
ordingto somelaw(e.g.,theintegers, inorder,from
0 onwards), but then at some pre-dened p oint(e.g,
100,000) b egin to output a series of numb ers
aord-ing to somedierent law (e.g.,theintegers, inorder,
from200,000onwards). Althoughtheoutput ofsuha
diereneengine(ananalogueofthegeologialreord)
wouldfeatureadisontinuity(inourexamplethejump
from 100,000 to 200,000), the underlying proess
re-sp onsibleforthisoutputwouldhaveremainedonstant
(i.e.,thegenerallaw,orprogram,thatthemahinewas
ob eying would not have hanged). The disontinuity
would have b een theresult of thenaturallyunfolding
mehanial(andomputational)pro ess. Noexternal
tinkering analogous to the assumed intervention of a
providentialdeitywouldhavetakenplae.
Babbage thus tried to show that what might
ap-p ear to b edisontinuitieswerenotneessarily the
re-sult of meddling, but ould b e the natural result of
unhanging pro esses. Indoingthis heultivated the
image of Go d as a programmer, engineer, or
indus-trialist, apable of setting a pro ess in motion that
would aomplish His intentions without Him
inter-vening rep eatedly. InVitorian Britain,thenotionof
Go d as draughtsman of an `automati'universe, one
that would run unassisted,withoutindividualats of
reation,destrution,et.,provedattrative. This
on-eption was subsequently reiterated by several other
naturalphilosophers (e.g.,Darwin, Lyell, and
Cham-b ers)whoarguedthatitimplied\agranderviewofthe
Creator|Onewhoop eratedbygenerallaws"(Young,
1985,p.148).
Forthepurp osesofthispap er,whatisofinterestare
notthetheologialimpliationsofBabbage'swork,nor
the eet it had on the atastrophist/uniformitarian
debate, but the manner inwhih Babbage mobilised
hisomputationalresourestoattakatheoretialp
o-sition. Babbage's omputational system was a
sim-ple analogue of a natural system (the geology of the
planet) implementedmehanially. Babbage did not
seek to apture the omplexityof real geology inhis
system. Indeedtheanalogyb etweenthedierene
en-gine'sprogramandgeologialpro essesisarudeone.
However,theformalresemblaneb etweenthe
omput-ingmahineand thegeologialpro ess issuÆient to
enable a p ointab out the lattersystem's dynamisto
b emade.Babbage'somputingmahineisthuslearly
b eingemployedas amodel.
Evolutionary SimulationModels
WhatgroundsdowehaveforlaimingthatBabbage's
mo del is an example of an evolutionary simulation
resoures, et., would indiate that, even if it ould
b e alled asimulationmo del,Babbage's programmed
alulator should notb e awarded thestatus of
evolu-tionary simulationmo del. However,theadjetive
evo-lutionaryisb eingusedherenottoinvokethenotionof
biologialevolutionaryhange, but to draw attention
to thefat thatBabbage's mo delwasimplementedas
adynami,unfolding,pro ess. Forthemoment,afew
briefobservations will serve to give aavourof what
isintendedbythephrase 1
.
First,thefatthatBabbage'smo delisanunfolding
omputationalpro esssetsitapartfromworkinwhih
mo dels ofdynamihange are onstruted as
mathe-matial pro ofs and are thus not evolutionary
simula-tions. For example,Malthus' (1798)workon p
opula-tion dynamis,in whih he demonstrated that p
opu-lation growth would outstrip that of agriulture, was
onstruted usingpap erandp enil.
However,itisnotmerelytheomputationalnature
ofBabbage'smo delthatensuresitsstatusasan
evolu-tionarysimulationmo del. Hisrelianeontheongoing
dynamib ehaviourofhisomputationalmo del,rather
thanonanyendresultitmightpro due,distinguishes
itfrommo dellingworkwhih,althoughinvolving
om-putationalpro esses,uses omputersas to olsfor
solv-ingwhatwouldotherwiseprovetob eintratable
math-ematialproblems.Forexample,theuseofomputers
todisoverdigitsofpi,ortoiterativelysolvethe
dier-entialequationsthat mightompriseamo delof p
op-ulationdynamis,donotountas evolutionary
simu-lationmo dellingsinetheomputationalpro esses
in-volved are merely themeans of reahing apartiular
solution. Inontrast, thesubstantive elementof
Bab-bage'smo delistheevolutionaryasp etofthe
simula-tion(i.e.,themannerinwhihithangesovertime).In
thesenario thatBabbage onsiders,hissuitably
pro-grammeddierene engine will,in priniple, run
for-ever. Its alulationis notintendedto pro due some
endpro dut,butrathertheongoingalulationisitself
theobjetofinterest.
In thefollowingsetions partiularasp ets of
Bab-bage's mo del will b e expanded up on. First, the
im-pliations of onsidering the dynamib ehaviour of a
mo deltob e entral,ratherthanonentrating onthe
end-pro dutof somealulation,willb edisussed.
Dynamis and Stasis
Artiiallifeisp erhapsexlusivelyonernedwith
sys-tems that hange over time, and, furthermore, the
1
evolu-manner in whih suh systems hange over time .
Whether the system b e a ellular automaton
imple-mentingthe \gameof life",anautonomousrob ot
de-signed to navigate an extra-terrestrial terrain, or a
mo delof\omplexityattheedgeofhaos",itis
onsid-eredas atime-varyingsystemwithaertaindynami
harater. Itisthisharaterthatisofinteresttothe
artiiallifepratitioner. Will thedynamiharater
oftheellularautomatonadmitof\universal
omputa-tion"? Willthedynamiharateroftheautonomous
rob otresultinrobustwalkingb ehaviour? Willthe
dy-namiharater of the mo del exhibit \omplexity at
theedgeofhaos"?
We an ontrast this interest in dynami hange
with the approah taken by game-theoreti mo dels
(von Neumann & Morgenstern, 1944). Despite b
e-ingsimilarlyonernedwithsystemsthat hangeover
time (eonomies, individual eonomi agents,
eolo-gies, p opulations of reatures, individual reatures,
et.),game-theoreti aountsofadaptivephenomena
typiallyassumethatthesystemsunderonsideration
areat,or near,equilibria. Onethis assumptionisin
plae,thegametheoristisfaedwiththetaskofsp
e-ifyingamo delthat admitsofstable equilibriawitha
haraterthat mathesthatoftheobservedeonomi
orbiologialsystem.
For example, neo-lassial eonomi theory asserts
thatsinetheeonomiagent,homoeonomius,isan
ideal maximiser of exp eted utility, suh agents will
learamarketat theequilibriumprie. There isthus
nosenseinaskingwhatb ehaviourwouldresultfroma
systemomprisedof agentswhoannot maximise
ex-p eted utility. Suh asystemis farfromequilibrium,
andthusnotlikelytob efoundtoreet realeonomi
situationsinwhihmarketsareeitherat ornear
equi-libria. Sine, from this p ersp etive, eonomiagents
are assumed to b e optimalplayers, one merelyneeds
to identifythe equilibriumprie analytiallyin order
todesrib e theb ehaviourofthemarket,as thisisthe
priethatwillb esettledup on. Attentiontotheglobal
dynamisofthemo delis notneessary sine the
sys-temwillnotsp endtimefarfromequilibrium.
Whilsttheseassumptionsare,forthemostpart,
em-inently reasonable, there are senarios in whih the
onditions that real eonomi agents nd themselves
inresultintheirinabilitytondtheequilibriumprie,
e.g., sellers at an aution who are wary of the
exis-tene of artels amongst their fellow bidders. In
or-dertomo delthesesystems,approahesthattakeinto
aountariherpalletofdynamib ehaviour are
ne-2
Artiiallifeislearlynottheonlyeldonernedwith
dynamialsystems. Relatedelds suhasyb ernetis and
essary (see,e.g.,Binmore, 1987,1988,forritiques of
the traditional axiomati approah to game-theoreti
eonomimo delling).
A similar p ersp etive is evident within
game-theoreti aounts of evolutionary systems.
May-nardSmith(1982)identiesthisproblemattheoutset
ofhisb o ok, Evolutionand the Theory of Games,
\An obvious weakness of the game-theoreti
ap-proahtoevolutionisthatitplaesgreat
empha-sis on equilibrium states, whereas evolution is a
pro ess ofontinuous,oratleastp erio dihange.
Thesameritiismanb elevelledatthe
empha-sis on equilibria in p opulation genetis. It is of
ourse mathematiallyeasiertoanalyseequilibria
thantrajetories ofhange"(p. 8).
However,unlikeeonomists,evolutionarygame
the-orists have b etter grounds for pursuing aprogram of
whatFrank(1998)termsomparativestatis thanthis
app ealto theintratabilityofdynamimo dels.
Iden-tifying equilibria, and exploring their sensitivity to
mo delparameters inorderto makepreditions ab out
analogous real-world systems is a pro ess with some
hane of engagingwith empirial biologial
observa-tions,sine,giventhat thenaturalsystems aroundus
are likelyto b e at or near equilibrium,we have some
haneofolletingappropriatedata. Thelikeliho o dof
obtainingtheobservationsneessarytodeideb etween
omp eting theories invokingtrajetories of hange is
muhsmaller.
One areainwhihsuh dataare routinelyolleted
isintheonstrution ofphylogenetihistories by
sys-tematiians|thebiosienedesendentsofthe
geolo-giststhatBabbage'smo deladdressed. Forourpresent
purp oses,these historiesareimp ortantb eause
dier-ingevolutionarytheories oftenmake thesame
predi-tions onerning urrent states of aairs. This is b
e-ause it is present-day phenomena that the theories
attemptto aount for. However,omp etingtheories
may make diering preditions onerning the prior
states ofaairsthat haveledto theurrentsituation.
For instane, Ryan (1990) attempts to distinguish
b etweentheoriesthatomp etetoaountforthe
har-ater of sensory systems and signallingb ehaviour
ex-tant inthe natural world by onstruting a
phyloge-neti tree for several sp eies of frog. From this
hy-p othetial historyof sp eiation eventsRyanattempts
to disount ertain theories whose preditions do not
maththehistorialaounthehasonstruted.
Evolutionarysimulationmo dellinganontributeto
thisstyleofhyp othesistestinginawayinwhihmo
d-elling metho dologies that exlusively attend to
pro-tempassedthrough b eforeitreahed thisequilibrium.
Suh aountsofthetrajetories followedbyevolving
p opulations priorto (p otentially)ahieving equilibria
mightb eusedtodistinguishb etweenomp eting
theo-ries.
This is not to say that data from simulationswill
simply augment data from phylogeneti
reonstru-tions, but that the impliationsof evolutionary
theo-riesfortheharaterofevolutionarytrajetoriesmight
b elariedthroughevolutionarysimulationmo delling.
The preditions resulting from suh a lariation
ouldthenb eomparedtoempirialdataintheusual
manner.
Althoughitisp erhapsreasonabletoexp etthe
nat-uralsystemsweseearoundustob eatstableequilibria
giventheevolutionarytimesalesinvolved,aswith
eo-nomisystems, there aresituations inwhihevolving
p opulations mayonsistently fail to reah equilibria,
orinwhihtheequilibriathatevolutionarysystemsdo
reaharemoreompliatedthanp ointattrators. For
example, Maynard Smith followsthe passage quoted
ab ove with apreditionthat yli attrators willb e
disovered to haraterise muh of the b ehaviour
ex-hibitedbyplayersinvolvedinasymmetrigames. This
predition has b een supp orted by the disovery of a
sp eies oflizardthat o urs inthree distintmorphs,
eahofwhihdominatesoneothermorph,andis
domi-natedbytheremainingmorph. Suhasystemis
analo-goustotheparlourgamesissors-pap er-stone,inwhih
playing one move onsistently willnever b e a lasting
strategysineanysuhstrategyan b edefeated
(Sin-ervo&Lively,1996;MaynardSmith,1996).
In addition, theorists are oming to realise that
manyinterestinggamesexhibitmultipleequilibria.
Un-fortunately,nakedgametheoryisunabletodetermine,
giventheexisteneofmorethanoneequilibriumstate,
whih equilibrium a p opulation will arrive at.
Ad-ditional riteria for deiding b etween equilibria(e.g.,
on grounds of parity, eÆieny, et.) have b een
of-fered(Harsanyi&Selten,1988),buttheseoftenapp ear
somewhatarbitrary. Thenaturalsolutiontothis
equi-libriumseletionproblemistoenquirewhihequilibria
arisefromwhih initialonditions(Binmore,Gale,&
Samuelson, 1995a; Binmore, Samuelson,& Vaughan,
1995b) | aquestion addressing the dynami
hara-terofthemo del.
Despiteaknowledgingthat the b ehaviourof
adap-tivesystems isinherentlydynami,andthatattention
tothesedynamismightenabletheoriststodistinguish
b etweenomp etingtheories,theoristsofteneshewthe
studyofdynamihange. Thisaountsfortheaent
ria ineonomis, or \exitp oints"in languagehange
(Lab ov, 1994), rather than the general dynami b
e-haviourofsuh mo dels. This isnotto saythat game
theory and other formal approahes annot tolerate
limitsetsof ahigherorderthanonstanttrajetories,
or have noonsideration of initialonditions or
tran-sientb ehaviours. However,suh mattersaretypially
regarded as sp eialases that require additional
ana-lytitehniquesiftheyaretob eaddressedatall(e.g.,
MaynardSmith,1982,devotesanapp endixtodealing
withylitrajetories).
In ontrast, evolutionary simulationmo delling will
prinipally onern itself with the harater of a
mo del'sevolutionarydynamisratherthansome\end
pro dut" of these dynamis, whether it b e within a
p opulationof learningeonomi agents,a p opulation
ofevolvingreatures,orap opulationsupp ortinga
de-velopingultureorlanguage. Fromthisinherently
dy-namip ersp etive, ylilimitsets andstart-up
tran-sients, drift and haos, are on an equal fo oting with
gametheory'sardinallimitset, thep ointattrator.
Subjet Matter
Perhaps the asp et of Babbage's mo del that most
learlydistinguishesitfrommo dernevolutionary
sim-ulationmo dellingis itssubjet matter. Severalissues
arerelatedtothis observation.
First,theovertly theologialonerns ofthedebate
Babbage engaged with are for the most part missing
from ontemp orary siene. Mo dern sientists now
rarely struggle against matters of faith or religion in
print (see Dawkins, 1998, however, for one
ontem-p orary example). Despite this, just as ertain
om-mentatorslaimthat Babbage'smo delinuened the
oneption ofGo dinthe19thentury (Young,1985),
some researhers have taken mo dern artiial life to
haveimpliationsfortherelationshipb etween religion
andsiene (Helmreih,1997).
Leaving religious mattersto one side, it isalso the
ase that whereas Babbage's system mo dels an
ab-stratgeologial pro ess,themajorityofurrentmo
d-elling work in this vein addresses biologial subjet
matter. It is probablethat in1836,Babbage and his
ontemp orarieswouldnothavereognisedadierene
b etween geology and biology, sine these elds and
manyothersunder theumbrellaofnaturalphilosophy
hadyettopartompanyandb egintosp eialise.
How-ever, nowthat we understandthat themehanismby
whih organismi evolution pro eeds (the dierential
transmissionof geneti material)is notpresent in
everbroaderlassoftopisand problems? 3
Some of the non-biologial disiplines that are b
e-ginning to adopt this approah have b een exploring
questions of hange for some onsiderable time. For
instane, b oth anthrop ologyand linguistis involve a
historial, diahronior developmentalelement. The
studyof languagehange, forinstane, predates
Dar-win's theoryofevolution; indeed Darwinmadeuse of
researh into thehistory andrelatedness oflanguages
informulatinghistheoryofnaturalseletion.
Inontrast,otherdisiplineshavetakenupthe
hal-lengeofunderstandingthedynamisoftheir
phenom-ena more reently. For example, eonomis (despite
thepromptingofVeblen,1898,attheturnofthe
en-tury)hasonlyreentlyb eguntoonsiderthepro esses
thatmightunderly theevolutionofeonomisystems
(.f.,theineptionoftheJournalofEvolutionary
Eo-nomisin1991,that buildsonthepioneering work of
JosephShump eter,e.g.,1934). Previouslysuh
mat-terswerethepreserve ofhistoriansofeonomis.
Inthemostextremeases,novelsientiprograms
mustb edevelop edinordertopursuetheimpliations
of an adaptive systems p ersp etive. Memetis, the
studyoftheevolutionofideas,isone exampleofsuh
aneonatalparadigm.
What links this rather disparate group of
disi-plinesistheironernwiththedynamisofadaptation.
These dynamisare often studied by mo dellers using
tehniques develop edsp eiallytodealwiththeir
in-diginous problems,with noreferene to evolution, or
even with expliit rejetion of evolutionary thinking.
However,inreasinglytheorists areomingtosee
par-allels b etween the dynamis underlying many
dier-entadaptivesystems(.f.,theproliferationofjournals,
meetingsand b o oktitles involvingEvolutionary as a
leading adjetive). Although, the systems that they
studydo notinvolveadaptationintheformof
ortho-dox organismievolution, nevertheless, the neessary
ingredientsfor adaptationanb e identied: omp
eti-tionforlimitedresoures andheritablevariation. For
eonomisystems, thelimitingresoure isutility,the
variationexists at the level ofeonomi strategy and
inheritaneo ursso iallythroughsomekindof
learn-ingmehanism. Forlinguistis,thelimitingresoureis
languageusers, thevariationexistsatthelevelof
lan-3
For example, Miller (1997) has reently app ealed to
thenotionofself-organizationinanattempttoresolvethe
apparent paradox presented by,on the onehand, the
dis-overyofHitler'sindolene,and,ontheother,theintensely
struturedorderoftheThirdReih. Millerquotesevidene
from artiial life simulations that suggest that omplex
ordermayarisefromsimplelo alinterations,ratherthan
through languagetransmission.
Evolutionary biologists enjoy an advantage over
evolutionary simulation mo dellers dealing with
non-biologialsystems inthat they p ossess adetailed
un-derstanding of the mehanisms underlying biologial
evolution. As yet, omparable understanding of
eo-nomi, linguisti, ultural, or psyhologial
adapta-tion is relatively laking. Non-biologial
adaptation-istshave madeprogressbyappropriatingmehanisms
frombiologialevolution. Forinstane,adaptive
meh-anisms have b een b orrowed and used metaphorially
(e.g., epidemiologial notions of ontagion used to
mo delthespreadofinnovations,Cavalli-Sforza&F
eld-man, 1981) or literally, (e.g., the onept of
om-p etitive exlusionunderlyingneuralDarwinism,
Edel-man, 1987) However, fundamental researh into the
uniqueharaterof these non-biologialadaptive
sys-temsshouldeventuallyreifyorreplaethese
plaehold-ers (e.g.,Gatherer,1998).
Theprosp et of multiplelevelsof adaptation
inter-ating with one another further ompliates the
pi-ture. Thelearningmehanismsinvokedbyeonomists,
linguistsandulturalanthrop ologistsarenotxed
en-tities,butarethemselvestheresultsofadaptive
evolu-tionarypro esses. Someeorthasb eenmadetomo del
the interation b etween learning and evolution (e.g.,
Hinton&Nowlan,1987)andtoapplytheinsightsthus
gained to non-biologial adaptationist researh
pro-grams(e.g.,Kirby&Hurford, 1997). But until
theo-retialapproahestoparallel,interatingadaptive
sys-tems(e.g.,Laland,Odling-Smee,&Feldman,inpress)
anb eshowntob esound,thesemo dellingenterprises
willb elessseure thantheirbiologialforeb ears.
Insummary,anyresearh paradigmthatstudiesthe
b ehaviour of systems of entities whih interat with
eah other andtheirenvironmentover timesuh that
they hangeinanadaptive fashionisamenabletothe
evolutionary simulation mo delling approah. While
Babbage's appliationof asimulationmo delto what
isnowonsideredtob eanon-biologialtopipresaged
mo dernsimulationsofnon-biologialadaptivesystems,
his mo delis laking ina sophistiated notionof
geo-logial adaptation. Indeed it is unlear whether
geo-logialsystemsanb elassedasadaptiveinthesense
desrib ed ab ove. It is apparent that mo dern
desen-dentsofBabbage'smo delaremoreonernedwiththe
details of how adaptation o urs in natural systems,
ratherthanmerelydemonstratingthatsome
The phenomenon at the heart of Babbage's mo del
| disontinuity | is emblemati of the onerns of
present-day researhers employingevolutionary
simu-lationmo dels. However,it is inits approah to
non-linearity that Babbage's mo del departs most
signi-antlyfrommo dernmo dels.
Thereisasup erialresemblaneb etweenthe
atas-trophist debate of the 19th entury andthe more
re-ent dispute over the theory of puntuated equilibria
intro dued by Eldridge and Gould (1973). Both
ar-gumentsrevolved aroundthesigniane ofwhat
ap-p ear to b e abrupt hanges at geologial time sales.
However,whileBabbage'sdisputeenteredonwhether
hangeouldb eexplainedbyoneontinuouslyop
erat-ing pro ess or mustinvolvetwodierent mehanisms
(therstb einggeologialpro esses,theseondDivine
intervention),Gould andEldridgetake painsto p oint
outthattheirtheorydo es notsup eredephylogeneti
gradualism,butaugmentsit. Theywishtoexplainthe
twoapparent mo desof ation evidened by the fossil
reord (longp erio dsofstasis, shortburstsofhange),
notby invokingtwopro esses, but byexplaining the
unevenness of evolutionary hange. In this resp et,
the theory that Eldridge and Gould supply attempts
to meet a mo dernhallenge: that of explaining
non-linearity,ratherthanmerelyaommo datingit.
WhereasBabbage'saimwasmerelytodemonstrate
that aertain kindofnon-linearitywaslogially p
os-sible in the absene of exogenous interferene, mo
d-ernresearhers areprobing questionsofhowandwhy
non-linearities arise from the homogeneous ation of
low-level entities, and what impliations these
non-linearities may have for the systems under
examina-tion. Inordertoahievethis,mo dernsimulationmo
d-elshavehadtomoveb eyondtheelegantbutsimplisti
formofBabbage's demonstration.
This inreased sophistiation stems, in part, from
theuseofanexplanatorystrategythatinvokesa
\on-strutive" relationship b etween at least two relevant
levelsof desription: alevel ofexpliitlymo delled
in-dividual atomi entities and a higher level of
aggre-gate phenomena. The notion that the p ossibly
om-plexandnon-linearb ehaviourofhigher-level
phenom-ena emerges fromtheationof lower-levelentities
al-lows that an understanding of the onstrutive
rela-tionship that links them may b e all that is required
toaountfor theb ehaviour attheaggregate levelof
desription. Forexample,asimulationmo deloftraÆ
dynamismayinvolve routines that dealwith the
in-dividualvehilesomprisingthetraÆwithoutatany
p ointexpliitlyinvokingthehigher-levelphenomenon
ofthesimulation,anunderstandingofhowthe
\emer-gent" phenomena derive fromtheatomientities an
b e ahieved.
It is imp ortantto expliatethedierenes b etween
this kind of explanatoryprojet and the task metby
Babbage's mo del. Babbage did notneed to mo del a
system of entities at some atomi geologial level of
abstration and then simulate the emergene of
dis-ontinuities inthe geologialreord sine his projet
was merely to demonstrate that a lass of
phenom-ena ouldexist intheabsene of anelementthat had
previously b een onsidered neessary | external
in-tervention. As suh nothinghinged onthemanner in
whihthenaturalphenomenaatuallydidarise. This
kind ofexplanation is apro of ofonept of thetyp e:
\it is ommonlythoughtthat M is needed to
gener-ateP,buthere isamo delinwhihM ismissing,but
somethingthat lo okslikeP is exhibited". One ofthe
hallenges formo dernevolutionarysimulationmo dels
is to move b eyond this kind of explanation, and
re-veal the onstrutive relationships that hold b etween
atomiandemergentlevelsofdesription(see,e.g.,Di
Paolo, Noble &Bullo k, this volume, forfurther
dis-ussion).
Babbage himself was not satised with merely
demonstrating through simulationmo dellingthat
ap-parent disontinuitiesould b e theresult of
unhang-ing mehanial pro esses. He also sp ent some time
developing theories with whih he sought to explain
howsp eiexamplesofgeologialdisontinuityould
have arisen as the result of physial geologial
pro-esses. One example of apparently rapid geologial
hange that hadgured prominentlyingeologial
de-batesine b eingdepitedonthefrontispieeofLyell's
PriniplesofGeology was theapp earene ofthe
Tem-pleofSeraphisontheedgeoftheBayofBaiaein
Poz-zuoli, Italy. The surfae of the 42-fo ot pillars of the
temple areharaterised bythree regimes. Thelower
p ortions of the pillars are smo oth, their entral p
or-tions have b een attaked by marine reatures, while
ab ove this regionthepillars areweathered but
other-wiseundamaged. Theseabrupthangesinthe
hara-terofthesurfaeofthepillarsweretakenbygeologists
tob eevidenethatthetemplehadb eenpartially
sub-mergedforaonsiderablep erio doftime.
For Lyell(1830), an explanation ould b e found in
the onsiderable seismi ativity whih, historially,
had haraterised the area. It was well known that
eruptions ouldover landinonsiderableamountsof
volanimaterialandthatearthquakesouldsuddenly
vol-whih thetemple sto o d into the sea. Thus the lower
p ortionwouldhaveb eenpreservedfromerosion,while
amiddlep ortionwouldhaveb eensubjetedtomarine
p erforations, and anupp er setion to the weathering
asso iatedwithwindandrain.
ReentworkbyDolan(1998)hasunoveredthe
im-pat that Babbage's own thoughts on the puzzle of
thepillarshadonthisdebate. Babbage,whilevisiting
the temple,noted an asp et of the pillars whih had
hitherto gone undeteted: a path of aliated stone
lo ated b etween the entral, p erforated, setion, and
thelower,smo oth,p ortion. Babbageinferredthatthis
aliation had b een aused, over onsiderable time,
by alium b earing spring waters whih had
gradu-ally o o ded the temple, as the land up on whih it
sto o dsanklowerandlower.Eventuallythissubsidene
aused the temple pillars to sink b elow sea-level and
resulted inthe marine erosion evident on the middle
p ortionoftheolumns.
Thus Babbage's explanation invoked gradual
pro-esses of umulative hange, rather than abrupt
episo desofdisontinuoushange,despitethefatthat
theevidenepresentedbythepillarsisthatofsharply
sep erated regimes. Babbage's aountof this gradual
hange relied on the notion that a entral, variable
soure ofheat, b elowtheearth's rust, aused
expan-sionandontrationofthelandmassesab oveit. This
expansion or ontration would lead to subsidene or
elevation of the land masses involved. Babbage
ex-ploited the p ower of his new alulating mahine in
attemptingtoprovehis theory,but notintheformof
asimulationmo del. Instead,heusedtheengineto
al-ulatetables ofvalues that represented theexpansion
of granite under various temp erature regimes. With
thesetables, Babbageouldestimatethetemp erature
hanges that would have b een neessary to ause the
eetsmanifestedbytheTempleofSeraphis.
Here, Babbage is using a omputer, and is
mov-ingb eyondagradualistaountthat merelytolerates
disontinuities (i.e., his Bridgewater Treatise) to one
that attemptes top explain them. However, his
en-gineisnotb eing employedas anevolutionary
simula-tionmo del,butasaprosthetialulatingdevie. The
omplex,rep etitive,omputationsinvolvedinpro
du-ing and ompilingthese tables of gures would
nor-mally have b een arried out by \omputers", p eople
employedtomake alulationsmanually. Inreplaing
this error-prone, slow and ostly manual alulation
withhismehanialrekoningdevie,Babbage
demon-strates theappliationofomputingp ower tosolving
problems that are otherwise intratable. This use of
at leastapproximating) theresults of what would b e
extremely taxing or tedious problems has b eome a
mainstayofmuhaademipratie.
In ontrast, evolutionary simulation mo dels of the
kinddisussed inthis pap eroer anew rolefor p
ow-erful omputers. Where Babbage employed his
ma-hinetoeither(i)demonstratethatsomenatural
phe-nomenon ould b e simulatedin the absene of an
el-ement that had previously b een deemed a neessary
pre-requisite,or(ii)p erformotherwiseintratable
al-ulations inorder to supp ort theorybuilding/testing,
mo dernsimulationmo dellersattempttomoveb eyond
theseusesinpursuinganexplanatorystrategyinwhih
simulations are used to diretly explore explanatory
theories prop osed aswaysofunderstandinghow
om-plex, aggregateb ehaviourmightarisefromthe
homo-geneous ationoflower-levelentities.
A suessful example of ompleting this
explana-tory task an b e found in Di Paolo's (2000) mo del
of the evolutionof o-ordinated ommuniation.
Us-inganindividual-basedevolutionarysimulationmo del
featuringap opulationofagentsdistributedovera
lat-tie and playing an ation-resp onse game, Di Paolo
showsthateveninsituationsforwhihgame-theoreti
onsiderations predit that o-ordination will b e
un-stable, o-ordination may arise and p ersist. At this
p oint the mo del has fullled the same explanatory
roleasthatofBabbage'sBridgewaterTreatise: an
ag-gregatephenomena(o-ordinatedommuniation)has
b een demonstratedin theabsene of anelement
pre-viouslydeemedneessary (i.e.,anappropriate
equilib-rium inthe underlying game). DiPaoloaountsfor
the presene and harater of this o-ordinated
om-muniationby rst drawing attention to the manner
inwhihthespatialstruture ofthemediumgivesrise
to lusters of individuals. Subsequent exploration
re-vealsthatindividualsintheenterofsuhlustersfae
a senario that diers signiantly from those at the
p eriphery. Analysis demonstrates that the strategi
asymmetryindued bythisspatialorganisationis
suf-ienttoenableo-ordinatedommuniationtop ersist
as astablestrategy.
Notiethatmerelyapp ealingtotheexisteneof
spa-tiallustering,andinvokingtheideathato-ordination
\emerges" fromthe interations of game-playersthat
existinaspatially-struturedmediumwouldb etofall
shortofsuhasuessful explanation.Suhanapp eal
wouldinfatb elosertotheap ologetiistuseof
\mira-les"asexplanationsforphenomenathatwould
other-wiseb einexpliable. Indeedonstruingemergent
omparison.
InsummaryBabbage'smo delusefullydemonstrates
asimpleexplanatorystrategywhihmo dern
evolution-ary simulation mo delling hop es to move b eyond. In
order to do so, evolutionary simulation mo dels must
domorethaninvokethenotionofemergene. The
re-lationship b etween atomi and aggregate phenomena
mustb eexpliatedsuessfully.
Conlusions
Inmanyresp ets Babbage's mo delseond-guesses
as-p ets of mo dern evolutionary simulation mo delling.
Hisuseofanongoingomputationalprogramtomo del
the dynamisof anatural system, his attention to a
debatethatwouldnowb eregarded asexternalto
evo-lutionarybiology,and his onentration on high-level
non-linearphenomenaandtheabilityoflow-level
pro-essestogiverisetothem,areallprominentfeaturesof
mo dernindividual-based simulationsof adaptive
sys-tems.
However, Babbage's mo del do es not address the
manner in whih exploring the dynamis of a
simu-lationanexpliatetheonstrutive relationshipsthat
aountforhigh-levelaggregatephenomenaintermsof
the b ehaviour of systems of low-level atomientities.
The mo del do es provide an example of a more
sim-ple explanatory strategy, that of demonstrating that
some high-level phenomenon survives the removal of
an element previously deemed to b e a neessary
pre-requisite for it. Moving b eyond this lass of
explana-tionhasb eenidentiedhereasanimp ortanthallenge
formo dernevolutionarysimulationmo delling.
Babbage'smo delmayresembleurrentartiiallife
inonenalresp etthatisp erhapsworthnoting. Up on
publiation of the Ninth Bridgewater Treatise, the
work was treated with some disdain. His
demonstra-tionof the p ower of automatiomputingwas
gener-allyregardedasimpressive. But althoughhismahine
was aremarkablefeat ofengineering itwas p ereived
tob e ato olill-suitedto thejobofnaturalphilosophy
and his mo delgained littleredibility as a result. It
wasgenerallyagreedtohaveoverstepp edsomeb
ound-ary. Inontrast,Dolan's(1998)reentworkhasshown
thatBabbage'sempirially-driventheoriesonthe
geo-logialpro esses resp onsiblefortheapp earene ofthe
TempleofSeraphiswerereadilytakenonb oardbythe
eminent uniformitartian geologists of the time. Like
Babbage's Bridgewater treatise, ontemp orary
evolu-tionary simulation mo dels may also b e \uninvited".
Perhaps thelessonsweanlearnfromBabbage'swork
Aknowledgments
ThankstoHenriettaWilsonandtwoanonymousreferees
forhelpful omments.
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