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System Growth


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Population Growth and Environment as a Self-organizing System


InternationalEcotechnologyResearch Centre, Cranji’eld University,Bedford,MK43OAL, UK (Received16November1998)

Overrecent yearsa newunderstandingofcomplex systems,and theirdynamicsand evolution hasemerged,and these have been shownto provideanewbasisfor modelsofthechanging patternsofpopulationand economic activities thatshapethelandscape.Inthispaperwe makeclear thenecessarily partial descriptionthatany particularmodelmust provide,and showthe importanceof amultidisciplinary,holisticunderstanding, linking any particular model to the co-evolutionofits environment.Inaddition,weshowhowevolutionaryprocesses link the microscopic level of molecules through successive scales of structure and organizationultimately to thebiosphere itself, toissues of climatic change,of biomesat the continental scale and atmosphericand oceanic circulationpatterns. Somevery recent results will be shown whichdemonstrate that the world climate hasalreadybeen modified considerably by human activities, particularly agriculture, underlining the vital need to understand better theon-goinginteractionbetween human activities and thebiosphere.

Models will be described which can link the co-evolution of thesemultiple scales of organization andchange, and which can be used to help to explore the consequences of differentpossible policies,and in thisway to provideinformationconcerningtheagendas, risksand issuestobe addressed in the21stCentury,as well aspointing to possible policies thatmaybe appropriate.Alreadymodels exist which can explorethedynamicsofurban development,thepatternsofland-use,and thepossibleenvironmentalimpactsof these in the contextof a still fastgrowing population.Such modelsprovideaframeworkwithin which questions such asthoseconcerningenergy consumption, transportation, social conditions can be explored and agendas and priorities set. Clearly, advances in information and telecommunications technologies present great opportunities for increasing accessi- bilitieswithoutnecessarily increasing mobilityorenergy consumption,and models which can helpinassessingtheirpotential impactondevelopmentand in their successfulimplementa- tionare ofgreatvalue.

Complex systemmodels can also be ofgreatuse inexploringthelongtermimplicationsof thepresent, increasing,reliance on marketsystemsand economicsignalsinthe allocation of resourcesandpatternsof investment.Inparticular, complexsystemsmodels canexplorethe effects of theprecise regulatory frameworkwithin which amarketoperates,and as a result maybe able tosuggest waysin whichlongterm,sustainabledevelopmentcan beachieved despitethepresentshorttermhorizonsof theplayersinmarketdynamics.Inaddition,of course, theycanilluminateand informactorsabout thelongerterm,andperhaps actually lengthenthe time horizon consideredbymarketparticipants.In short,theinsights arising fromcomplexsystemsmodelscould,hopefully, playaroleinexpandingtheunderstanding, theconceptualframework and the ethical basis of decisionmakinginthe 21stCentury.



Keywords." Complexsystems,Evolution, Urban self-organization,Integrated models, Decision support tools


Withthenewmilleniumapproaching,reflection on the human predicament and its possible future seems appropriate. The "enlightenment", and its expression in the industrial revolution gavepeople thehope ofabetter futureforall,where thequality of life would continually increase, for ever more people, underthe benign influence of scientificand technologicalprogress. It projectedthetriumph of rationality, and reason over the dark forces of superstition andignorance, andseemedto promise wealth and health for all. Today, however, un- certainties and doubts concerning our future are apparent everywhere. Our present way of life, heavily dependent on material and energy inputs, seems unsustainable over the long term, and naturally this gives rise to some vital questions.

Howcan theunsustainable desired lifestyles of the modern world be changedin order to make them sustainable? Should we change our desires, or change the means by which those desires are realized’?And, what issustainability anyway? Isit some maximal level ofproduction and consump- tioncorrespondingtothegreatest possible exploita- tionof"natural"resourcesin whatwouldlargelybe an"artificial" environment, ordoesit concern our capacity to adapt and change and "fit" within a relatively "natural"environment, andto developa diverseandvaried abundanceofactivities, spread- ing the "environmental load" of our activities broadly, and using our creativity and innovation to betterfit intonature?

The problems with which we are faced result from thesuccessofthetraditional scientific view of the worldas amechanicalsystem,whoseworkings could be completely understood, and therefore which could be ever-increasingly exploited. The traditional "engineering"approachtoaproblemor a constrainthas always been to specify exactlyits apparent "role" andcontext, andvieweverythingas

a "device" which turns inputs into outputs at acertain "cost". Progress then was made by pro- ducing a piece of technology, a mechanism or structure,whichcould"better" turn the inputs into outputsaccordingtothe established"cost/benefit"

criteria. But the very success and growth of these technological solutions changes the context in which they exist: both from the input side the raw materials and production structures that are required,and theoutputside, meaningtheimpacts onsociety andonthebiosphere.

The institutional structures of society, parti- cularlywith their presentheavyemphasison econ- omicvariables, andthe verygeneralmotivation of short termprofitmeanthat the failure to foresee the limits of technology, and the growth of environ- mental andsocial problemswas almost inevitable.

Thismyopiastemsfrom the traditionalphilosophy of science, rootedin Newtonianconcepts, thatsaw reductionism as the key to understanding. In this reductionist view, improving (according to local criteria) the "separate pieces" of something must make the wholeperform better.But,as weshallsee, wereallyinhabitaComplex Systemin whicheach part, and indeed different levels of structure and organizationarecoupled togetherandco-evolve,so that thepieces ofsomething cannot be considered separately from the whole. The new millenium is therefore a good time to recognize that we need to develop a new approach to the human situa- tion, one based on ourunderstandingofComplex Systems, and the limits to prediction and under- standingthat thisimplies. We needto seeourselves asinhabitinganested set ofco-evolved,hierarchical structures, linking through intermediate levels of organization,thebiospheretothe atomsandmole- cules ataparticularplace.Inreality, theclimate,the oceancurrents, thelandscapes, the settlement pat- terns, the cities and each individual are all linked, in acomplex web ofinteraction, some apparently stableand some evolving.Inthenewcenturywecan


hopetounderstandourpredicamentalittlebetter, definingouragendasatleast,andpossibly gaining somewisdom in our decisionmaking.


If we examinearegion, and consider the remains of populations and artefacts thatlitterthelandscape, then after dating and classifying them, an evolu- tionary tree of some kind emerges, possibly with discontinuities suggesting disaster and invasion, but nevertheless suggesting a changing "cast of characters"and ofbehaviours, overtime.

On the left, we have "reality". It is drawn as a

cloud,since wecansaylittleaboutitother than that it includes all detail ofeverything, everywhere, as wellasallperceptionsand allpointsof view. How- ever,ifwesimplylistwhatwe see then it includesa landscapewith peopleofmanykinds performinga varietyoftasks, businesses, factories, homes, vehi- cles, and also fossils, disused mines and factories, closed railways, buried cities and evidence of much that hasdisappeared.Byconstructingaseries of taxonomic rules concerning the differences and similarities of the objects, together with their dates, we can construct an "evolutionary tree", showing that species, behaviours, forms, or arte- factsemerged andevolvedovertime.

This is really subjective however, since the dif- ferences thatwechoosetorecognizereflectalready our particular vision ofwhat is "important" in a social and economicsystem.The rules of classifica- tion thatwe use areseldomexplicitly justifiedhow- ever, and often result from previous experience about such systems and what seems to matter in them. Are there socio-economic "types" and ifso, what are they? Do demographic characteristics reflect economic categories? Do firms ofthe same sectorandsizebehave similarly?What isasector?Is thereasmuch variation withinagroup asbetween groups?Whatevertheprecise argumentsadvanced, in order to "understand" a situation, and its possible outcomes, we do classify the system into components, and attempt to build mathematical

models that capturethe processes that are increas- ingordecreasingthese different components.

Atanyparticularmomenttherefore,weidentify the different objects or organisms that are pres- ent, and attempt to write down some "population dynamics" describing the increase and decrease of each type. We apply the traditional approach of physics, which is to identify the components of a system, and the interactions operating on these, both toandfrom the outsideworld andbetween the differentpopulationsof thesystem.Inecology,this will consist of birth and death processes, where populations give birthat anaverage rateifthere is enough food, and eateach other according to the average rates ofencounter, capture and digestion.

In economics, the macroscopic behaviour of the economy is assumed to result from the aggregate effects ofproducers attempting to maximize their profits, and of customers attempting to maximize their utility. This assumes that they know the outcome of what they have not yet tried and also that transactions, production, and consumption occur at averagerates, changing the GNP, unem- ploymentand other macroscopic indicators. These ideas areall basedonthe "mechanical paradigm" of Newtonianphysics,and assume that allindividuals, producers,andconsumersofagiven typearetaken tobe identical andequaltothe averagetype.Sucha model expressesthe behaviourorfunctioningofthe system at that time as a result of the causal rela- tionships that are present. This gives the illusion that we have a mechanical representation of the system which can be run on a computer, to give predictions.

However, as we see clearly from our broader picture of Fig. which shows the ’evolutionary tree",the predictionsthat suchamodelcangivecan only be correct for as long as the taxonomy oj the systemremainsunchanged.The mechanicalmodelof deterministic equations thatwe canconstructatany giventimehasnowayofproducing"new"typesof objects,newvariables,and sothe "predictions" that itgenerateswillonlybe true untilsomemoment,un- predictablewithinthemodel,when there is anadap- tationorinnovation,andnewbehaviouremerges.


Assumptions SystemBoundary

Classification Avrag=ng Stationarity

REALITY Time "’..

Equilibrium AllDetail Evolutionary


Dynamical System



and Policies Longer Term //ShortTermDescription i) EvolvingTaxonomy

/ i)Fixed








FIGURE Dataand classification of populations andarte- facts leadtothe picture ofanevolutionarytreeofsomekind.

Mathematical models have concentrated on the causal rela- tionsat agiventime.

In order to build mathematical models, we identifythe differentobjectsororganismsthat are presentataparticularmomentand attempttowrite down the mechanisms describing the increase and decrease of each type. We apply the traditional approach of physics, which is to identify the components of a system, and the interactions operating on these, both to and from the outside worldand between the differentpopulationsofthe system.Byconsideringthedemographic,economic andenvironmentalprocessesinplayat agiventime, a mathematical model can be produced which appears to offer deterministicpredictionsconcern- ing the future, assuming differentpossible policies orexogenousevents.

However, as we see clearly from our broader picture of the "evolutionary tree", the predictions thatsuchamodelcangivecanonlybe correct foras longasthequalitativestructure


the systemremains

unchanged. Developmentconcerns particularly the emergence of newspatial organization, new activ- ities and behaviours, and the structural changes thatthese leadto. The mechanicalmodel ofdeter- ministic equations that we can construct at any giventimehasnoway ofproducing"new"typesof objects,newvariables,and so the"predictions"that

it generateswill only be true until some moment, unpredictable within the model, when there is an adaptation or innovation, and new behaviour emerges.

In recent research newmodels have been devel- oped (Allen, 1992a,b; 1993; 1994a,b) which can generate a true structurally changing evolution, with new entities and activities appearing. How- ever, the relationship of these models to more conventional ones has not been made clear, and this is the aim of this first section. The conceptual framework ofFig. allows us to understand the relationship between different modelling techni- quesused toprovide decision support,in terms of the assumptions that underlie them. We compare the assumptions made by different approaches to policy exploration and planning, such as static optimization models, evaluations based on short termcost/benefits, and the difficulties involved in long term, complexsimulations.

Clearly,theevolutionarytreereflects thechang- ingstructure ofthe system,with differentvariables, over the long term, as different types of actors emerge,flourishandthendissappearorchange. In the short term, however, we can identify the dif- ferent objectsor actorsthat arepresent, and write down some "system dynamics equations" describ- ing the mutual interaction of the different actors present.Inotherwords,indescribingtheshort term we can apply the traditional approach ofphysics (Prigogine andStengers, 1987; Allen, 1988),which is to identify the components ofa system, and the interactions operatingon these, both to and from the outsideworld and betweenthe differentpopula- tions of the system. Inecology, this will consist of birthand death processes, wherepopulations give birth atanaveragerateifthereisenoughfood,and eat each other according to the average rates of encounter, capture and digestion.Ineconomics,the macroscopicbehaviourof theeconomyisassumed to result from the aggregate effects of producers attempting to maximize their profits, and of cus- tomersattemptingtomaximize theirutility. Sucha model expressesthe behaviour orfunctioningof the system, givenits structure, but does not "explain"


whythis structure is there. Inorder todo this, we must try to understand and "model" the evolu- tionarytreeof successive structures.

Let us consider carefully the assumptions that have tobemade in order to arrive atadescriptionin terms ofsystem dynamic equations. Such systems are characterized by dynamical equations of the type:



dt dy







where G, H, and Jare functions which have non- linear termsinthem, leadingtochangesinx, y andz which are not simply proportional to their size.

Also, thesefunctions are made up of terms which involve variables x, y and z and also parameters expressing the functional dependence on these.

These parameters reflect three fundamentally dif- ferent factors in theworkingof thesystem:

The values of external factors, which are not modelledasvariables inthe system.These reflect the "environment" of the system, and ofcourse may be dependent on spatial coordinates.

Temperature,climate, soils, world prices,interest rates arepossibleexamplesofsuchfactors.

The effectsofspatial arrangement, of juxtaposi- tion,of the entitiesunderlying the system. Often thesewillexpressnon-lineareffectsof densityfor example.

The valuescorrespondingtothe "performance"

ofthe entities underlying x, y orz, due to their internal characteristics like technology, level of knowledgeorparticular strategies.

Thesethreeentirelydifferentaspectshavenotbeen separated out in much of the previous work concerning non-linear systems, andthis has led to much confusion.Equationsof thetypeshown above display a rich spectrum ofpossible behaviours in differentregionsof bothparameter space andinitial

conditions.They range fromasimpleapproachtoa homogeneous steady state,characterizedbyapoint attractor, through thatof sustained oscillation ofa cyclicattractor,tothe wellknownchaoticbehaviour characteristicofastrangeattractor.Thesecaneither behomogeneous,but,much moreimportantly, they can involve spatial structure as well, and the phenomena ofself-organization canbe seen as the adaptiveresponseof asystemtochanging external conditions, even if it is viewed as having fixed attributes for its microscopic entities. In other words, we shall see that self-organization is a collective, spatial response to changingconditions ratherthananevolutionary responseonthepart of its constituentindividuals.

Inordertosee this letusfirstconsidertheassump- tions that are made in deriving system dynamics equation suchasin(1). Inthecomplex systemsthat underlie something like the "economy", there is a fundamental level which involves individuals and discrete events, like making a widget, buying a washing machine, driving to work, etc. However, instead ofattempting to "model" all these details, thesearetreated inanaverage way, and as has been shown elsewhere (Allen, 1990), in order to derive deterministic,mechanicalequationstodescribe the dynamics of a system, two assumptions are required:

events occurattheir average rate(Assumption1), all individuals ofagiven type,xsay, are identical and of averagetype (Assumption2).

The errors introducedby thefirstassumptioncan be corrected by using a deeper, probabilistic dy- namics,called the"MasterEquation"(Weidlichand Haag, 1983), which whileretaining Assumption 2 assumes that events of different probabilities can and dooccur. So,sequencesof events which corre- spondto successive runsofgoodorbad "luck" are included, with their relevant probabilities. As has been shown elsewhere (Allen, 1988) for systems with non-linear interactions between individuals, what thisdoes is todestroythe idea ofatrajectory, and gives to the system a collective adaptive capacity corresponding to the spontaneous spatial


reorganizationof its structure. Withoutgoingtothe mathematical rigour of the Master Equation, its effects can be imitated to some degree by simply adding"noise" tothe variables of thesystem,sothat the noisecan search out different spatial arrange- mentswhich may be stable under thenewconditions.

Inotherwords, self-organizationcanbeseen asthe adaptiveresponsetochangingexternalconditions, andmaybe greatly enhancedby addingnoise tothe deterministicequationsofsystem dynamics.

The fact is that unpredictable runs ofgood and bad luck, represented by "noise", can occur, and thismeansthat the precise trajectoryof the system does not exist in the future. Also, the fact of these deviations from the average rate of events means thatareal systemcan"tunnel"through apparently impassable potential barriers, the separatrices in state space,andcanswitch between attractor basins and explore the global space of the dynamical system in a way that the dynamical system would notitselfpredict.

Let us now make the distinction between self- organization andevolution. Here,it istheAssump-

tion 2 thatmatters, namelythat all individualsare identical and equal to the average type. The real

worldischaracterizedby systemin which there is in fact microscopicdiversity underlyingthe classifica- tion scheme of variables chosen at any particular time for thesystem model. The effects of this have been described elswhere(AllenandMcGlade, 1987;

Allen, 1988; 1990;1992a,b; 1994a,b)andsoweshall simply say that whenmicroscopic diversityis taken intoaccount,then itleadsto amathematical model of an evolutionary tree, where new behaviours emerge and an ecology of actors eventually fills anyresourcespace.Weshall not discuss these wider issues any further here.

We can summarize the different levels of model from deterministic equations to full evolutionary models asshown inFig. 2.

In reality,the interaction of thesystemwithinthe largeronewhich is its environment will leadto a co- evolutionary dialogue involving the wider situa- tion. This Co-evolution ofsystemand environment means that, inreality, the changes in the environ- mental parameters will partially be related to the adaptationsthatoccurwithinthe system.

Systemsmodels ingeneraldescribe theconnected behaviourofsub-systems.If thesearefew, andeach sub-system has a fixed internal structure, then a


1.Events theiraverage No"noise", "luck".

2.Nomicro-diversityamongindividuals,i.e. AllXidentical.


1.Parametersof extemal Environment Fixed/changing 2.Parametersnsitive "juxtaposition":spatial/network 3.Parametersreflecting "internalnature"ofelements/sub-systems.


The highest levelwillbe the BIOSPttERE.

The model is run under scenarios of either fixedorchanging Parameters1.

DETERMINISTICMODEL Assumptions and used.


Non-Linear Dynamics, Chaos, CellularAutomata PointAttractors, Cycles,chaos Variables only change


system change



OUTCOME Parameters fixed.

Individualswith fixed behaviour Spatial/networkStructure

change Collectiveadaptation of

Structure possible.

Variables only change

EVOLUTIONARYMODEL Neitherassumption used.


Selection operates individual diversity underneath

self-organizing spatia/network

Variables adapt and change both QUANTITATIVELYand Parameters fixed.

Individualswith fixed behaviour

FIGURE2 The hierarchy of modelling. Deterministic and self-organizing models assume that the underlyingsub-systems are

"fixed" in nature, whileanevolutionary modelattemptstodeal with possiblechangesatthat levelaswell.


Model of Internal







willbeatoms/molecule Their fixed"behaviour" that self-organizationunderlies all evolution.


systemsmodel can beacomplete representationof the behaviouroftheconnected parts.Agearbox,for example,canbemodelledsuccessfullyasan assem- blyofgears,providingthatnoneof the gear wheels gets stressed beyond breaking point. A complex system, however,isonewhere therearesomany sub- systems connected together, that some reduced, aggregate description is necessary. In this case the behaviour will be defined in terms ofaggregate

"variables", representing"average"typesand aver- ageevents. Obviously, all macroscopicsystemsare

"complex" systems, since theyare ultimately com- posed ofatoms andmolecules.However,if,asin the case of thegearbox,there existmacroscopiccompo- nentswhose internal structurecanbeassumedtobe fixedduringthe systemrun, then asimple systems model will correctly describe the courseof events, providingthat theintegrity ofthecomponentsisnot compromised. Clearly, for cases of breakage, a deeper description may be needed. For complex systems made up of microcomponents with fixed internalstructure,their interactions canleadto


organization. However, if the microcomponents have internalstructure, and if in addition this can changethrough time,thuschangingthe behaviour of the individualelements,then evolutioncantakeplace as the emergent macrostructure affects the local circumstances experiences by individuals, and this in turnleads toastructured adaptive responsewhich in turnchangesthe macrostructuregenerated.

Clearly, "dissipative structures", as discovered and investigated by the Brussels School (Nicolis and Prigogine, 1977; Prigogine andStengers, 1987;

Shieve and Allen, 1982) are all examples of self- organization, since the molecules underlying the chemical and biological reactions studied do not change their nature. Complex spatio-temporal organizationcan form insuch systems, as aresult of the non-linearities of the interaction processes, andsothey demonstrate theemergence of structure atahigherscale thanthatof the interacting entities.

In the case of the Brusselator, for example, the molecules interact over distances of 10


but the spiral waves and characteristicpatterns are of theorder of centimetres.

Complex systems modelling involving elements with internal structure that can change however, leads naturally to a hierarchy of linked levels of description. Stability, or at least metastability is achieved when the microstructures arecompatible with the macrostructures they both create and inhabit.

Inmany cases in addition to the Assumptions and 2 required to yield deterministic, dynamic equations, afurther assumption is introduced that the system is also supposed to have run itself to equilibrium, so that the correspondence between the real object and that model is made through equilibrium relations of balance betweenthe vari- ables. In neo-classical economics, much ofspatial geography, andmanymodelsoftransportationand land-use, the models that are used operationally today are still based on equilibrium assumptions.

Locations of jobs and residences, land values, traffic flows, etc. are all assumed to reach their equilibrium configurations "rapidiy", following some policy or planning action, with the more extreme practitioners even using the theory of

"rationalexpectations"to claim thatpeople"knew"

what the equilibrium wouldbe before it happened and socould and did prepare to move toit.

Such an approach, as well as being somewhat absurd, falls to take into account the possibil- ity ofany "run-away" processes where growthen- courages growth, decline leads to further decline andsoon,which can occurduringachange.Actions directly affect which evolutionary trajectory the system takes, anevolutionary trajectory that does not stop after any particular delay. Similarly, the equilibrium approach supposes that the situation observed in a region or market system expresses some maximized utility for the actors, where consumers and producers have minimized costs and maximized benefits. This approach assumes thatallthe actors knowwhatthey want, know how togetit,and ifobserved,aredoing whatthey would wish given the choices open tothem. Such ideas gave rise inrealityto apurely descriptive approach to problems, following, in a kind of post hoc calibration process, the changes that occurred.


It leads to a "laisser faire" strategy, unjustifiably restricting theoptions open to actors anddecision makerswithmultiple andcomplex agendas.

In fact,those wishingtouseequilibriummethods should accept the burden ofproof, since it is they who make the additional assumption.They should prove that the relaxation times of the processes involved inthesystemaretrulyshort withrespectto anytimeofinterest, and thereforethat theirassump- tion isjustified. In reality, in the main stream of economics, such evidence is never presented, but nevertheless, non-equilibrium methods have until recently in general simply been ignored. This is really because accademic disciplines are also the product of social phenomena, and the "positive feedback" processesof mutual citation and felicita- tion. "Lock in" is not just a phenomenon seen in technology change. Itrunsverydeeply through all self-organizing systems.

However, although dynamic modelstracetrajec- tories intime, theycannotanticipatethe qualitative changes that mayoccurwhen an evolutionary step takes place. At such a time, the taxonomy ofthe system changes, and therefore the mathematical model ofcausal relations ceases to be correct. It mightbegoodfor sometime,whilethetaxonomyis stable and nonew classesor types have appeared.

But, this will only be revealed when the model is shown to be incorrect, and in need of re-formula- tion. In Physics and Chemistry the predictive models which work so well rely on the fact that the individual elements that make up the system mustobeyfixedlaws which govern their behaviour.

The mechanisms arefixed,and the moleculesnever learn.

But, living systems cannotbe described by such deterministic laws. To see why, let us imagine a very simple human situation,forexample,of traffic movingalong a highwayor ofpedestrians milling around a shopping centre. Clearly, movements cannotbe predicted usingNewton’slaws of motion because acceleration, change of direction, braking and stopping occur at the whim ofeach driver or pedestrian. Newton’s laws, the laws ofphysics are obeyedatall timesbyeachpartof thesystem,but,

despite this, theyare notofhelpinpredictingwhat will happen because the decision to coast, turn, accelerate or brake lies with the human being.

Planets, billiardballs, andpoint particles arehelp- less slaves totheforce fields in whichthey move,but peoplearenot!Peoplecanswitchsourcesof energy on oroff andcanrespond, react,learnand change according to their individual experience and per- sonality. Theycan see the potentialusefulness for some modification in their timing, technique or tools,and they cantinkerand experiment perhaps to find ways toovercome aproblem,or a newway to achieve some desired result. This is where innovation comes from, and so, the diversity of the experiments performed or ideas tried out will reflect thediversityof thepeopleconcerned,andthe ability of these experiments to be translated into improved and new production and business will reflect the encouragement or discouragement experienced by innovative individuals, and the informationflows and scanning thatorganizations aredoingto gather andevaluate such initiatives.

Becauseof thisuncertaintyinthelonger term,we cannotknowwhat actionsarebestnow.Evenifan individual knows exactly what he would like to achieve, then because he cannot know with cer- tainty howeveryoneelsewillrespond,hecan never calculateexactlywhatthe outcome will be.Hemust make his decision, and see what happens, being readytotake correctiveactions,ifnecessary. Since, inbusiness,on the road and in theshoppingcentre we are allmaking these kinds ofdecisions, simul- taneously, all the time, it is not surprising that occasionally there are accidents, or that such sys- tems run ina"non-mechanical" way.Animportant point to remember here is ofcourse that human beings have evolved within such a system and therefore that the capacity to live with such per- manent uncertainty is quite natural to us. It may evenbe what characterizes the living. However, it also implies that much of what we do may be inexplicablein rational terms.

The "mechanical" approach is softened but not fundamentally changed by statistical models of decisionprocesseswhere theprobabilityofmaking


aparticular choice isproportionalto theexpected utility derived. This gives rise to probabilistic behaviour for individuals and deterministic be- haviour for sufficiently large populations. How- ever, this simple approach ignores the fact that decisions made by individuals are not really independentofeachother,andthat there isaneffect of the communication between individuals. Fash- ions, styles and risk minimizing strategies affect collective behaviourconsiderably,and mean that it cannot be derived as the sum of independent, individual responses.


As we have seen above, in deriving kinetic equa- tions in order to model the system that exists at a given time,ithas beennecessarytoderiveareduced description of reality. This is made in terms of typicalelements of thesystem,stereotypes,accord- ing to the classification scheme that we have decided to apply. Underneath the "model" there willalwaysbe thegreaterparticularityanddiversity ofreality.

Inthe mechanicalview, predictions canbemade by simply running the equations forward intime, and studying where they lead. Is there a unique

"attractor", into which all initial states eventually fall, or are there many possible final end points?

Does the system continue in a series of eternal cycles?Or,doesitdisplaychaoticbehaviour,asthe trajectorywraps itself arounda"strangeattractor"?

Despite the interest of these questions, we should remember they are only of any significance if the equations and the


mechanisms within them remain a good description of the system, and explanationcanbe obtained in terms of the internal functioningof thesystem. But, from thepicture of the evolutionarytree inFig. thatweknow really characterizescomplex systems,thetaxonomyof the system, the variables present and the mechanisms which linkthemactually changeovertime. Because ofthis,thedynamical systemthat we arerunningas a model of the system will only be a good

description for as long as there is noevolutionary change, and no new variables or mechanisms appear. In other words, the predictions of the dynamical system model will only be correct for aslongasthe model itself isacorrectdescriptionof the system,and this is only forsomeunpredictable lengthof time.

Figure offersus aconceptualframework within which we can understand technological evolution, and this has been described elsewhere (Allen, 1994a,b). Inorder to describeevolutionarychange, we must try to suppress Assumption 2 discussed aboveandputback the effects of innovators. Nelson and Winter(1982)have set outaseminalframework for economics in which internal variabilities and the differential survival of firmsareexplicitlytaken into accountasthey competeintheproductionofa particulargood.The evolution concerns returnson investment andtechniques ofproduction, and has been the basis for many later studies (Anderson

et al., 1988; Silverberg et al., 1988; Saviotti and Metcalfe, 1991). Clark and Juma (1987) have also set out the essential points concerning the differ- ence between the long and short term view of economic systems, and how this leads to anevolu- tionaryview.

Returning to the general conceptual framework ofFig. 1,weseethat in order forusto understand and modelasystemthat canchange itstaxonomy endogenously wemust "put back" what Assump-

tions and 2 took out in order to get to the deterministic description of non-linear dynamics.

Clearly,the future of anysystemwillbe due to two kinds of terms: changes brought about by the deterministic action of the typical behaviour of its average components, and structural qualitative changes brought about by the presence of non- average components and conditions within the system.

We reallyhaveadialogue between the"average dynamics"of thechosen description(aprocessthat results in what wemay call selection) and the ex- ploratory, unpredictable "non-average" perturba- tions around this that results from the inevitable occurrenceofnon-averageeventsand components,


a search or exploration process that generates information about the "pay offs" for other be- haviours. This leads to the new concept ofEvolu- tionaryDrive(AllenandMcGlade, 1987; Allen and Lesser, 1993).

Inordertoexplore thebehaviourofsystemswith endogenously generatedinnovations and selection wedefine a"possibilityspace",aspacerepresenting the range ofdifferent techniques and behaviours thatcould potentiallyarise (Fig. 3). Inpractice, of course, this isa multi-dimensional space of which we would only be able to anticipate a few ofthe principle dimensions. This "possibility space" will beexplored byindividualsand groups who explore the pay-offs ofnewbehaviour. In biology, genetic mechanism ensures that different possibilities are explored, and off-spring, off-spring of off-spring and so on, spread out over time from any pure condition.Inhumansystems the imperfections and subjectivityof existence mean thattechniques and behaviours areneverpassedonexactly, andthere- fore that exploration and innovation are always present as a result of the individuality and con- textual nature of experience. Physical constraints meanthat somebehaviours do betterthan others, andsoimitationandgrowth leadtothe increase of somebehavioursandthe decline ofothers.

Byconsidering dynamicequationsin which their is a "diffusion" outwards incharacter space from anybehaviourthatispresent,we cansee howsucha system would evolve. If therearetypesofbehaviour withhigher and lower pay-offs,then the diffusion

"up-hill"isgradually amplified,that "down-hill" is suppressed, andthe"average" forthewhole popu- lation moves higher up the slope. This is the mechanism by which adaptation takes place. This demonstratesthe vitalpart played by exploratory, non-average behaviour, and showed that, in the long term, evolution selects for populations with the abilitytolearn,rather than for populationswith optimal, butfixed, behaviour.

The self-organizing geographic models devel- oped previously (Allen and Allen & Sanglier 1977-1990) are a simple particular case of these general ideas. Instead of some "behaviour" space, whatwehave isreal, geographic space. Individuals ofany particular type, X, all differ from one an- otherby being located atdifferent pointsinspace.

By using distributions of choice and behaviour around an average, the microscopic diversity of individuals is taken into account, and this allows the "exploration"ofseeminglyunpopular,irrational and non-averagedecisions. Inthis way,changesin the "pay-offs"fornovelbehaviour can bedetected




FIGURE3 The effects of behavioural exploration in possibility spacearestructuralchange.


inthe system, andinnovations cantake off.Inthis case,it concerns "spatial"innovations, suchas the spontaneous emergence ofnewcentresofemploy- ment, or ofperipheral shopping centres, ofindus- trial satellitesandso on.Becauseofthepresenceof positive feedbackloops, there were many possible final states to whichthe systemcantend,depending on the precise position and timing of non-average events. Information can onlycomefromthepaths that wereactuallytaken, not fromthose thatwere not and because of this, patterns of change feed uponthemselves, andself-reinforcementofgrowth and decline are the result. Instead ofan objective rationality expressing genuine comparative advan- tages,the beliefsandthe structuresco-evolve(Allen and Lesser, 1991).

In this section we shall take the evolutionary modelsastage further andexaminethe mutualco- evolutionof differentpopulations. Instead of con- sidering theevolutionof techniques andbehaviours in a fixed landscape expressing higher/lower pay- offs,weshallallow forthefactthat the "pay-offs", theadaptivelandscapes,arereally generated by the interactionsofapopulation with theotherpopula- tions in the system. In the space of"possibilities"

closelysimilarbehavioursareconsidered tobemost incompetition witheach other, since they require similarresources, and must find asimilar niche in the system. However, we assume that in this par- ticular dimensionthereis some "distance" inchar- acterspace,somelevelofdissimilarity,atwhichtwo behavioursdonotcompete.

During the initial phase of an experiment in which we start offwith a single population in an

"empty"resourcespace,resources areplentiful, the centreof the distribution, the average type, grows better thanthe eccentrics at the edge. The popula- tionforms a sharp spike,withthe diffusing eccen- trics suppressed by their unsuccessful competition with the average type. However, any single beha- viour canonly growuntil itreachesthe limits setby itsinput requirements,orinthecaseofaneconomic activity, by the market limit for any particular product.After this,it isthe"eccentrics", the"error- makers" that grow more successfully than the

"average type", and the population identity be- comesunstable.The singlesharplyspikeddistribu- tionspreads, and splits into new populations that climb the evolutionary landscape that has been created,leading awayfrom the ancestraltype.The newpopulationsmove awayfromeach other,and growuntil in their turnthey reachthe limitsoftheir newnormality,whereupontheyalso splitinto new behaviours,graduallyfilling theresourcespectrum.

InFig.4 we seethe changing quatitativestructure ofthe system overtime, in some two-dimensional possibility space. In this way, instead of simply evolving towards thepeaksof a fixedevolutionary landscape, through their interactions populations reallycreatethelandscape uponwhichthey move, andby movingacross itchangeit. So thedifferent behaviours present grow, splitoff,andgraduallyfill the possibility spacewith an"ecology" ofactivities, each identity androlebeing formedby themutual interactionandidentitiesoftheothers. The limitof such a process would be given by the amount of energy that is available for useful work that can be accessed by the "technological" possibilities potentially open to the system. This means that evolutionary processes wouldexplore andreinforce mutuallyconsistenttechnologies and strategies that capture parts of the energy flows through the sys- tem and use them to build and maintain their necessaryinternal structure.Thelimitwould beset bytheamountof availableexergy.

Whilethe "error-making" and inventive capacity ofthe systemin our simulation is a constant frac- tionoftheactivity presentat any time, the system evolves indiscontinuous steps of instability, sepa- rated by periods oftaxonomic stability. In other words, there are times when the system structure can suppress the incipient instabilities caused by innovativeexplorationof itsinhabitants,andthere areothertimeswhenit cannotsuppress them, anda newpopulation emerges.

Although,competitionhelpsto"drive"theexplo- rationprocess, whatisobservedisthatasystemwith

"error-making" explorations of behaviourevolves towards structures which express synergetic com- plementarities. Inotherwords, evolutionalthough


FIGURE4 Inthiscasethelandscape explored bythe emergent behaviours isshaped bythem. Periods of stuctural stabilityare separated byperiods ofchange, dependingonwhether the systemcancontrol itsownerror-makingor not.


driven toexplorebyerror-making and competition, evolves cooperative structures.The synergy canbe expressed either through "self-symbiotic" terms, where theconsequences ofabehaviour in addition to consuming resources is favourable to itself, or through interactions involving pairs, triplets, and so on. This corresponds to the emergence of

"hypercycles" (Eigen andSchuster, 1979).

Several important points can now be made.

Firstly, a successful and sustainable evolutionary systemwillclearly beonein whichthere isfreedom for imagination and creativity to explore at the individuallevel, andto seekoutcomplementarities and loops of positive feedbackwhich willgenerate a stable community of actors. Secondly, the self- organization of oursystem leadstoahighly cooper- ativesystem,where thecompetition perindividual is low, but where loops of positive feedback and synergyarehigh.Inotherwords,the






populations, each seeking its own growth, leads toasystem whichismorecooperative than competitive.Thevision of amodern,freemarket economy leading to, and requiring a cut-throat society where selfish competitivity dominates, is shown tobefalse,atleast in thissimplecase.

Fromourexample, the discovery ofcooperativ- ities, andthe formation ofcommunities ofplayers with a sharedinterestin each others success is the outcome of the evolutionary process. The third important point, particularlyforscientists,isthatit wouldbe impossibletodiscernthe"correct"model equationsevenfor our simple20populationprob- lem,fromobservingthepopulation dynamicsofthe system. Because any single behaviour could be playingapositive, ornegative roleinaself,orpair ortriplet,etc.interaction,itwouldbeimpossibleto

"untangle" its interactions and write down its equations simplybynoting the population’sgrowth or decline. The system itself, through the error- making search processcanfindstable arrangements ofmultiple actors, andcan self-organizeabalance between theactorsinplay, and theinteractionsthat they bringwiththem, but this does not meanthat we candeducewhatthewebof interactionsreallyis.

This certainly poses problems for the rational

analysis of situations, since this must rely on an understanding oftheconsequences of thedifferent interactionsthatarebelieved tobe present. Itisalso truethatalthoughwewouldnotbe ableto "guess"

how to arrange the populations to form a stable community,evolution can findhowtodothis itself.

Itis theessence ofself-organization.

Clearly,if we cannotreally know how thecircles of influence are formed by looking at the data, theonlychoicewould betoask theactorsinvolved, inthecase of ahumansystem. Andthis in turnwould raise the question of whetherpeople really under- stand the roots of their own situation, and the influences of thefunctional, emotionalandhistor- ical links that build, maintain and cast down organizations and institutions. The loops of posi- tive feedback that build structure introduce a trulycollectiveaspecttoanyprofound understand- ing of their nature, and this will be beyond any simplerationalanalysis, usedin agoal-seeking local context.


Inthis section, theideas of"self-organization" are appliedtothedevelopment of cities,with a view to establishingthe basisforadecision support frame- work capable of exploring the longer term con- sequences ofdecisions, policies and oftechnology change. We hope from this to be able to build a model which, atleast,canpredictthesortofstruc- turethat may evolve underacertainscenario,with the accent on the qualitative features of that structure,rather thanonquantitative accuracy.

The first step in the operation is to choose the significant actors of the system, whose deci- sions, and the interplay of these, will cause the urban system to evolve. In agreement with much previouswork, particularly, forexample, thephil- osophyofaLowry-typemodel,wefirstincludethe basic sectorofemploymentforthe city,and,inpar- ticular, tworadicallydifferentcomponents ofthis;

the industrial base and the business and financial


employment. Then we consider the demand for goods and services, which will give rise to alocal manufacturing and maintenance sector, as well as to tertiary service employment, generated by the population of the city andby thebasic sectors.We shall suppose that there are two levels: frequently required, short-range services and more special- ized,rarerlong-rangeset.The residents ofthe city, dependingontheirtype ofemployment,will exhibit arange ofsocio-economicbehaviour, and for this we have supposedtwo populations corresponding essentiallyto "blue" and"white" collarworkers.

This is our"taxonomy"of thecity.Inreality,over long times these variables will change, as a "blue collar" worker ceases to "be" what he was, and

"whitecollar" worker splitsintodifferenttypes and classes, and new industries and activities appear.

Nevertheless,for the modelweshalldevelop, these categorieswillbeconsidered assufficiently stablein their locationalpreferences forthe timeperiod that we want to consider, that the categories remain coherent and meaningful during the simulation.

Having specified the variables,wenowneedto de- finethe mechanismsthatcausethechangesinvalue of thesevariables ineachzone. These mechanisms express the average effects of individual events or decisions which lead to the growth or decline of peopleorjobsof agiven typein azone,ortotheir in or outmigration. Inother words they capturethe effects of birth,death,and migration ofpeopleand ofjobs.

While birth and death rates are cultural and socialparameters reflectingthereligious,socialand economic circumstancesof individuals, thecreation or reduction ofjobs in a particularsector reflects in thelongertermtheprofitability of thatsector in thatzone. Iffor example, demand exceeds supply in the retail sector in a given zone, then the excess profits that are possible willlead to invest- mentand jobcreation. This will increasesupply and potentially reducethe excessprofits, butin sodoing it willhavechangedthe distributionof population as thenewjobs created lead to re-locations of the employees,and tothe transfer oftheirdemands for goods and services to the neighbourhood. This in

turn will change the pattern ofprofitabilityin the other sectors, andwillleadtothe furthercreation of jobs and ofpopulation. So, the linkages between people andjobs, and jobs and people through the spatial expression ofintermediateandfinaldemand will lead to a complex cascade ofchange and re- adjustmentasthecity grows.

Inordertomodelthe mechanismsgoverningthe location and re-location pattern, the investment pattern, we need to model notjust the behaviour that is observed in the data, but the underlying reasonsthatlie behind it.Inotherwords,we need to represent the locational criteria of the different types ofactor, and the changingopportunitiesthat they perceive around them, and from this to generateour"urban dynamic".Themodelisthere- forebasedonthe interaction mechanisms of these variables,which in essence requireaknowledge of thevalues andpreferences ofthe different typesof actorsrepresentedby the variables,and, of course, how these valuesconflictand reinforce eachother as the system evolves. In other words, the model is driven by the actions and behaviours that characterize actors who are fulfilling certain roles or tasks corresponding to theirjob requirements, and also to theircultural "identity" which dictates how they may wish to be viewed, and also their patternof finalconsumption.

Theprofessional rolesthat actorsadoptconcern the successful functioning of their activities, and these therefore reflect their beliefs concerning the

"functional requirements" ofjobs in the different sectors. So,heavy industrymustshipinlarge quan- tities ofraw materials, engage in energy and ma- terial intensive transformationprocesses,getridof wastes, andthenshipoutthefinishedproducts. Its activitieslead to a characteristic "value-added per squaremetre", which sets limitsonthe rents which stillallow profits, and addto thelocational criteria which apply. Similarly, office headquarters for financial institutions for example, need to be at centresof communication,inprestigious surround- ings, preferably where they can meet with other similarprofessionalsoverlunches,so astokeep up with the newsandwiththe latest trends. Obviously,


logisticconsiderationsplayavitalroleinthecom- mercialand retailing sectors, and the spatial organ- ization,or ratherself-organization ofsupplychains canbeseen asthe underlying dynamicof urbanand regional development. From the interdependent locational criteria that characterize the different urban actors, needingtobeneartheircustomers,or to cheapaccessible land,etc. ourmodelconsistsof equationswhichexpress theseas a set ofinteracting mechanisms.

The model is inspired by data coming from Brussels, and so comes much closer to really de- scribing reality. Theinteractionschemeisshownin Fig. 5.

There are five types of employers: industrial, financial, two levels oftertiary activity, and local industry. Each of these has its own locational criteria involving land and their infrastructural requirements, as well as differing types ofaccess to road, rail, canalorto aircommunication. They also have differing labour requirements both in terms ofthe numher ofjobs created per squaremetre and in the socio-economic group of employees.

Thus,heavy industry requires overwhelmingly blue collar labour, whereas the financial and business firmsof the centralbusiness districtemployalmost entirely white collar citizens. We have therefore chosen to distinguish between these two types of residents,and these togetherwith the five types of employers fromour’mechanics’ofsevenmutually interactingvariables.

This model has been reported elsewhere (Allen

etal., 1983)someyears ago, but recently, the whole system has been redeveloped for the PC environ- ment and the models are again a focus of interest (Fig. 6). We can include the various different transporation networks that traverse and link the different parts ofurban space. All the perceived

"distances" and decisions concerning residential location, shopping destinations, etc. can be made with respect to the perceived attractiveness of the different possible transport modes and routes available.Canthe qualitativeevolutionof Brussels be"generated" spontaneously byourmodel? Ifthis is possible, then itimplies that the model contains the "reasons" why the structure of Brussels has

Lowestlevel Heavy


..-- "!







\ industry

White-collar residents

High level tertiary

Economic _de_ m_an__d

Labour ----4,. demand Influence


FIGURE 5 The interaction scheme for adynamic, spatially self-organizingurban model.


t::IGURE6 ThescreenofourPCbased "Brussaville" modeldeveloped by T. Buchendorfer.

become what it has, and more importantly there- fore, whythis mightchangein the future. Itallows anexploration of thepossiblelimitstothestability of thisstructure, indicatingalternativefuture struc- tures that might evolve under different possible policies,investment decisionsandchangingscenar- iosof inand out migration.

Ourbasic setofurban mechanisms isrepresented byaset of non-linear differentialequationseach of which describesthe time evolution of the number of jobs or residents of a particular type at a given point. In ahomogeneous space one possible solu- tion ofthese equationswould be to have anequal distribution of all variables on all points. Such a non-city, although theoretically possible, corre- sponds to an unstable solution, and any fluctua- tionsbyactors around this solution will result ina higher pay-off, and this will drive the system to somestructural distributionofactors,withvarying amounts of concentration and decentralization.

There are two reasons behind the structure of the system: the first is due to the non-linear interaction mechanisms whichgiveriseto instabilitiesas men- tioned above. The second is due to the spatial heterogeneity of the terrain and of thetransporta- tionnetworks.

The road network takes into account three different qualities of road and thepublic transport networks considered are those of the train, bus, metroandtram.Each link of each networkdepends on the relative sensitivity ofan actorto these. We have therefore a dynamic land-use-transportation model which permits the multiple repercussions involved in the various decisions concerning land use or transportationto beexplored as the effects are propagated, damped or amplified around our interactivescheme.

Weseethatoururban systemevolves to a com- plex interlocked structure ofmutually dependent concentrations. We have two poles of heavy



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