An agent-based model of

exaptive processesMarco Villani1, Stefano Bonacini1, Davide Ferrari2, Roberto Serra1, David Lane1

1Department of Social, Cognitive and Quantitative Sciences, University of Modena and Reggio Emilia, Reggio Emilia, Italy2School of Statistics, University of Minnesota, Minneapolis, MN, USA

Correspondence:Marco Villani, Department of Social, Cognitive and Quantitative Sciences, University of Modena and Reggio Emilia, viaAllegri 9 Reggio Emilia, Reggio Emilia 42100, Italy.Tel: þ 39 0522 523553;Fax: þ 39 0522 522512;E-mail: marco.villani@unimore.it

AbstractA key problem in research on innovations is that of understanding their origins. In thispaper, we propose that radical innovations are created by a process of ’exaptation’, andwe introduce a dynamical model that describes how it may happen. In particular, ourmodel is focussed on the interplay between artefact innovation and attributions offunctionality. We propose that the explicit representation of artefacts and categories easesthe understanding of the exaptation phenomenon, seen in this context as a shift in termsof ‘leading attributions’ and allows the identification of the elements favouring theemergence of innovations.European Management Review (2007) 4, 141–151. doi:10.1057/palgrave.emr.1500085Keywords: innovation; agent-based model; exaptation; cognitive representation

Introduction

Amajor problem in research on innovations is the

understanding of creativity, that is, the origin ofinnovations. A common claim in the literature is that

innovations are recombinations of current capabilities, asSchumpeter claimed, and that search is local (see e.g.,March, 1991). This perspective treats creativity then asdiscovered in close proximity to current practice. Acontrary perspective is to consider creativity as suddenblind insight. In our opinion, the local recombination andsearch perspective fails to treat the many cases ofsignificant creativity that we observe, while the latterperspective yields little theoretical and conception gain.

The key point seems to us that those approaches lack anappropriate ontology. In particular, the recombination-centred perspective emphasises the role of artefacts, leavingthe agents (whether humans or human organisations) asecondary role of pure recombinators. It becomes, there-fore, possible to ignore the role of agents and to follow thepure technological trajectories of the artefacts. However,human agents – which are endowed with sophisticatedcognitive and communication capabilities – can create anduse artefacts in ways, which are not just obvious at all.Indeed, they are embedded in a web of relationships amongthemselves, with their organisations and with theirenvironment, which affect their ways of thinking and ofusing artefacts. Therefore, in our view, in order to

understand innovation it is much more appropriate to takeexplicitly into account the presence of both artefacts andagents, rather than trying to ‘project out’ of the descriptionone of these two terms.

The fact that agents (be they human beings or groups ororganisations) have an internal structure also affect theirbehaviours. Broadly speaking, interactions between parti-cular (groups of) agents often take the form of recurringpatterns that persist over time. Making (new) artefacts, forexample, or generating (new) forms of organisation in asociety, is a multi-faceted process that is based on recurrentsets of actions, in which a number of agents with differentroles are involved. In this process, new concepts andobjects are discovered and invented by simultaneouslysurveying the opportunities offered by the social andmaterial environment, and adapting the existing categor-isations of the agents. When looking for inventions (newstrategies, new products, or organisational innovations) thedifferent agents participating in this process can explore avariety of opportunities from one’s own perspective. But foran innovation to emerge, there must also be a degree ofconvergence among their perspectives so that the group asa whole aligns itself around the creation and use of theinvention.

In order to innovate, agents should share (or come toshare) a common system of beliefs, which enables them to

European Management Review (2007) 4, 141–151& 2007 EURAM Palgrave Macmillan Ltd. All rights reserved 1740-4754/07 $30.00

palgrave-journals.com/emr

interact and otherwise express themselves in ways that theymutually recognise (e.g., do things in compatible ways,identify and use similar resources, share technology, havesimilar norms, similar institutions). Key features of thissystem are the categories, the tools the individuals use toprocess such a kind of information (Selby and El Guindi,1976); in addition, a large body of literature in socialpsychology has emphasised the central role of categoricalthinking in social relationships (Macrae and Bodenhausen,2000; Markman and Gentner, 2001).

In this paper, we propose a model by which radicalinnovations are created by a process of ‘exaptation’ (Gouldand Verba, 1982; Ceruti, 1995; Gould, 2002), whichaccording to our hypotheses represents a key aspect ofinnovation processes. In particular, our model is focussedon the interplay between artefact innovation and thefunctionalities, which agents attribute to artefacts throughtheir categories. Our claim is that the explicit representa-tion of artefacts and categories eases the understanding ofthe exaptation phenomenon, seen in this context as a shiftin terms of ‘leading attributions’, and allows the identifica-tion of the elements favouring the emergence of exaptation.

Artefacts are key components of human organisationsand activities. Artefacts are entities forged by constituententities of an organisation that enhance that organisation’sfunctionality. One of their main properties of interest to usis their capability to convey information, although they maynot be explicitly designed for this purpose. In addition,there are artefacts specifically designed to store and carryinformation: books, radios, televisions, human languages,including the very special kind of artefact represented bycomputers, objects able to process information at a veryhigh abstraction level.

Since artefacts convey information, their explicit repre-sentation eases the understanding of the exaptationphenomenon, seen in this context as a shift in terms of‘leading attributions’. Actually, their introduction is im-portant in order to characterise the ontology necessary toidentify exaptation events. In the model presented here, wefocus on phenomena occurring at the micro-level (howindividuals collect information about the external world,categorise it, and combine existing categories in order tocreate new ones) and meso-level (the exchange of informa-tion among individuals). However, we do not explicitlyinclude the details concerning the macro-level events (theshared system of beliefs and the common physical andtechnological resources), that are left for further research.

In the first two sections, we will provide a detailedintroduction on the notion of exaptation. The third andfourth sections describe the model that we developed inorder to explore some aspects of exaptation and itsdynamics. Finally, we discuss the results of our firstsimulations.

ExaptationRecently, the concept of exaptation has been introduced toexplain the changes resulting from innovation processesand the rise of new technologies. Exaptation originatesfrom the domain of biology, where it appears for the firsttime in Gould and Verba (1982) who referred to speciesevolution as the mechanism complementary to Darwinian

adaptation. The following definition provided by Ceruti(1995) gives insight on the main idea of exaptation: ‘ytheprocesses whereby an organ, a part, a characteristic(behavioural, morphologic, biochemical) of an organism,which was originally developed for a certain task, isemployed for carrying out tasks that are completelydifferent from the original one’. The typical exampleprovided by Gould (2002) is represented by a line offeathered dinosaurs, arboreal or runners who developedthe capability to take advantage of feathers for flying,when originally they were intended for thermoregulationpurposes.

Furthermore, exaptation can provide a key to interpretthe serendipity that characterises the generation of newproducts. Exaptation emphasises that the functionalities forwhich a technology has been selected are only a subset ofthe consequences generated by its introduction. In manycases, the number of consequences generated by a newtechnology, a product, or a process can be incredibly largeand thus, its exaptive potential practically unbounded.Hence, exaptation is to be interpreted as a central ideaconnecting technological progress and emergence ofrecurrent patterns of interaction.

Mokyr (1998) defines the phenomenon of exaptationsaying that ‘it refers to cases in which an entity was selectedfor one trait, but eventually ended up carrying out a relatedbut different function’. Such a definition captures the ideathat exaptations are those characteristics of a certaintechnology that are co-opted by another origin or utilitybecause of their current role. Different from adaptations,which present functions for which they are selected, theexaptations generate effects that are not subject topressures from the current selections, but potentiallyrelevant later on.

A classical example of technical innovation illustratingboth adaptation and exaptation is the Compact Disk (CD).The CD was originally developed in 1960 in the PacificNorthwest National Laboratory in Richland, WA and it wasdesigned for a specific task: solve the problem of the soundquality deterioration of the classical vinyl records. Itsinventor, J.T. Russell, developed a system based on the ideaof using light to carry information, avoiding the usualcontact with mechanical parts of the recording device. TheCD-ROM was patented in 1970 as a digital-optic system forrecording and reproducing sound. Later, researchers usedthe technology of the CD-ROM for a different purpose:storage media for computer data. Although the latterrepresented a function not originally intended for theCD-ROM, it became very clear that it was indeed effective.As a result, during the 1970s, the Laboratory refinedthe CD-ROM technology commercialising a product thatcould be usefully employed for different purposesand improving some of its characteristics (increment ofmemory capacity, recording speed, recording and repro-duction sound quality).

Another important aspect of such a phenomenon isrepresented by what Gould defines as ‘exaptive pool’. Theexaptive pool represents the potential allowed for futureselection episodes (at all levels). There are two categories ofpotential: (i) intrinsic potential and (ii) real entities.

In order to understand intrinsic potential, the readershould recall the smallest and lightest among the US coins,

An agent-based model of exaptive processes Marco Villani et al.

142

the dime, which despite its very little purchasing value, isstill in use. An unforeseen consequence of its technicalcharacteristics is that the dime can be employed as anoccasional screwdriver. Hence, the dime is an adaptation ifconsidered as money and exaptation if considered as ascrewdriver. Note that, the potential for the additionalfunctionality as a screwdriver is an intrinsic characteristicof the dimensions and the shape of the coin and, thus,cannot be considered as disjoint or separated from it.

The second category of the exaptive pool includes realentities, matter or material things that became part of theitem under exam, due to various reasons. They are notcurrently associated with a particular use and at the sametime do not generate substantial damages, thus avoidingelimination by selection, a phenomenon called ‘neutralmutation’ in biology (Kimura, 1983). The members of thiscategory can be generated in various ways as structures thatpreviously were considered useful or as neutral character-istics introduced ‘in incognito’ with respect to the selectionprocess. A now classical example, quoted in Gould andLewontin (1979) can be found in architecture, wherespandrels (initially empty spaces between the vaults andarchs in churches) have been later used as a support forpaintings and mosaics: while their initial role was that ofstructural elements, spandrels thus became a key aestheticfeature.

The origin and peculiar features of exaptationIn order to complete a picture of the exaptation phenom-enon, we consider two questions. (i) What are the factorsthat lead to the birth of such a process? (ii) What are thetraits that distinguish exaptation from other processes?

In order to answer the first question, we can rememberthat in our description exaptation originates from theinterplay between the artefacts and the functionalities,which agents attribute to them through their categories:therefore, we have to describe what an artefact is, what acategory is and which kind of relations can they have.

In a very general way, we can describe an artefact as ahierarchical structure composed by subparts that areapproximately independent in the short term, but con-nected by a global behaviour in the long term (i.e., thenotion of decomposability, introduced by Simon (1996). Asa consequence, the subparts are selected and proliferate intime as a consequence of being only one among manyaspects of the whole artefact. While some such subparts canhave an important role with respect to the goal of the wholeartefact, others remain latent waiting future activation.

Agents evaluate artefacts using their categories, a categorybeing a tool the agents use in order to:

� focus the attention on a subset of the artefact character-istics;

� interpret the highlighted features;� give an evaluation of the artefact functionality, based

upon the highlighted features (‘I like’, ‘I hate’, ‘verygood’, and so on).

Based on the above observations, we can divide the possibleorigins of an exaptation into three groups:

(1) the case where a subpart is already providing a positivecontribution to the functionality for which the technol-ogy was selected; only in a later moment and afterchanging the context, the subpart becomes the maincomponent;

(2) the case where the subpart has no role in the overallperformance of the system;

(3) the case where the subpart provides a negativecontribution to the overall performance of the system.

An example of case (1) is represented by the phonographinvented by Edison in 1877. The innovative technology foramplifying and reproducing sound suggested the commer-cialisation of the invention as an office dictaphone. Onlysuch a dramatic change of the context led to the exaptationof the phonograph, later re-named as gramophone, andnowadays considered one of the most popular inventionsmade during the 19th century. Case (2) is well identifiablein the process of vitrification, originally developed toreduce environmental pollution (safe waste disposition andlimited radio-active waste), is now mainly exaptated forbiological dangerous processes such as elimination ofbiochemical weapons. Finally, case (3) can be exemplifiedby the innovation in plastic production during the SecondWorld War, based on sub-products deriving from oilrefinement (Dew et al., 2004).

Next, we begin to address the second question of whattraits distinguish exaptation from other processes. First,exaptation is not a simple side effect, that is, an unintended(and often undesirable) consequence of a particulartreatment. Although the apparent affinity between the twonotions, an exaptation is usually identifiable with respect tochange of context, whereas we cannot say the same for aside effect. Second, exaptations are not an alternativedescription of the Schumpeter’s process (Schumpeter,1934), usually understood as a creative combination ofexisting ideas belonging to different entrepreneurs.Although it is true that in economics, exaptation is mainlydue to entrepreneurs, it usually refers to the variation ofcontext that generates a change in the utility of thetechnology, not to a simple mixture of existing elements.

One could think that an exaptation is simply anunintended consequence of technology. However, thisstatement ignores the fact that the act of exaptatingrequires the intentional activation of a technology thatotherwise would remain latent; and it is actually theentrepreneur that makes possible such an activation.

Finally, the basic research often generates inventions thatare initially designed without an immediate and definedtarget, and thus at least in the first phase are not properlyadaptive. The process of exaptation points out that theprinciple of such research is non-adaptive in its nature.

The modelThere are in literature models that describe the feedbacksbetween artefact innovation and attributions of function-ality (e.g., see Ferrari et al., in press); nevertheless, thesemodels do not take into account explicitly the presence ofartefacts.

The aim of the EMIS system (Exaptation Model inInnovation Studies) is to highlight the factors that

An agent-based model of exaptive processes Marco Villani et al.

143

contribute to the occurrences of exaptation, by means ofthe explicit description of both artefacts and agents. EMIS isan agent-based model characterised by the presence of twokinds of social agents (A), producers and users. The agentshave only partial knowledge of the world, and eachproducer owns: (i) a set of categories (C), utilised tointerpret a certain set of artefacts and (ii) a set of weightsrepresenting the importance that a certain agent assigns toeach cognitive characteristics of an artefact (represented bymeans of the correspondent categories). The modelpostulates a continuous interaction between producersand users: the artefacts are transferred from the producersto the users and subsequent feedback messages are sentfrom the users to the producers. The aim of the model is toanalyse the effects of the ambiguities present in artefactsand categories on the exaptation phenomena. Obviously,this implementation is only a first step toward a morecomplete model of exaptation; in particular, we defer tofurther works the problem of the origins of the categories,as well as the representation of the interdependencies andcomplementarities among the features composing theagents’ categories.

AgentsThe agents Ai (iA{1,y, g}, gAN0) are the model mainactive units. They have limited system knowledge and aredistinguishable by means of their identifier ID. Their totalnumber g is not changing in time, and are grouped in twodifferent classes:

� producers (represented by means of the symbol Ap,where pA{1,y, l})

� users (represented by means of the symbol Au, whereuA{1,y, h})

Thus, the total number of agents is g¼ lþ h.Each agent owns a given number of categories, which can

be different for agents belonging to the two differentclasses. We denote the categories belonging to producersand users by Cp and Cu, respectively.1 The number ofcategories belonging to a given agent is constant at any timeperiod. Moreover, each agent is characterised by a weightvector (different for agents belonging to different classes,respectively Wp and Wu).

Note that in our representation, only the producers areable to build and modify the artefacts (one artefact for eachcategory owned by the producer). Conversely, only theusers can evaluate the artefacts.

CategoriesIn this work, we use the term ‘functional attribution’, orsimply ‘attribution’, referring to: ‘the functionality carriedout by the corresponding feature of the artefact I’mevaluating is useful/indifferent/damaging’ (or ‘I wish/don’t_care/don’t_wish to give to the artefact I’m buildingthis particular functionality’ if we are considering produ-cers). Thus, we say that the set of categories owned by andagent corresponds to his/her collection of attributions. Wedefine the knowledge space as the collection of all thepossible functionality attributions.

In this context, each category is a D-dimensional vector,whose elements Cx

(j) (indicated by the words ‘characteristic’,

or ‘feature’) are discrete random variables taking values{1, 0,�1} with the following probability distribution: t ifCx

(j) ¼ 1, (1�t�e) if Cx(j) ¼ 0, and e if Cx

(j) ¼�1, where t andeA[0, 1]. Further, we assume that the number of relevantcharacteristics (i.e., the characteristics corresponding tosymbols ‘1’ and ‘�1’) is only a fraction Z of the totalnumber of features. A category composed only by relevantcharacteristics implies not realistic agents attributingrelevance to each single cognitive detail.

The agents are also able to modify their categories: incase of categories trespassing such a threshold, not all therelevant features can be memorised (in the rest of the paperindicated by the symbol |1|). In order to simulate such amemory loss, the number of relevant features nC|1| iscomputed after each modification. If K¼ nC|1|�Z40, aremoval process eliminates each relevant feature withprobability

Pk ¼ K

nCj1j

recovering in such a way a more realistic situation.

WeightsEach agent owns a D-dimensional vector of weights, whoseelements, Wp

(i) and Wu(j) take values in the interval [0, 1].

Each element represents the importance that the agentassigns to the corresponding cognitive feature of itscategories. For example, we could appreciate a car becauseof several reasons: power, style, size, price, colour,maintenance costs, practicality, and so on; nevertheless,not all these characteristics have the same influence on ourfeeling. Namely, Wx

(i) (wA{u, p}) represents the weightthat the agent assigns to the ith cognitive feature of theD-dimensional cognitive space (colour is more importantthan maintenance costs, or class more than price, etc.). Inthe present version of the model, these vectors are builtduring the initialisation phase at t¼ 0 and are constant withrespect to time.

ArtefactsThe artefacts are ‘goods’, built by producers and utilised byusers. Each artefact artp

s is identified by an identificationvariable, IDs and corresponds to only one category (eachcategory belonging to a particular producer Idp). Theartefacts artp

s are characterised by an extremely simplerepresentation: they are D-dimensional vectors, whoseelements (again indicated by the words ‘characteristic’ or‘feature’) take values {0, 1}, where 1 indicates the presenceof a given characteristic (feature) and 0 its absence. In sucha representation, the producers can build new artefacts bymodifying their categories.

Despite this simple representation, the artefacts are suitablydefined for conveying information, and can be successfully‘interpreted’ by users; this fact allows the system to produceinteresting behaviours.

Artefact productionIn this section, we introduce one of the more delicateaspects of the model: the production artefacts. In thismodel, a producer tries to build an artefact as much aspossible similar to the prototype memorised in one of its

An agent-based model of exaptive processes Marco Villani et al.

144

categories, but despite his efforts it has to deal with errorsand physical/technical constraints. Typically, a producerprocesses already existing artefacts, and tries to add somedesirable characteristics to it. Namely, the producer selectsone of its categories, and attaches the tag 1 to the artefact incorrespondence to a 1 memorised for the chosen category.Similarly, the producer places a 0 tag in correspondence toa �1 tag, a 0 tag in the category meaning that the produceris not interested in changes in these positions and therefore,the already present values will not be altered (see Table 1for a simple example).

In particular, we wish to highlight that the artefactfeature can take only two values (0 and 1), whereas thecorresponding feature on the categories can take threevalues (1¼ ‘wish’, 0¼ ‘indifference’, �1¼ ‘not desired’).Therefore, the feature correspondence represented inTable 1 can be characterised as follows:

� if the values are identical, there is no change in artps

� if Cp(j) ¼ 1, then artp

s ¼ 1

� if Cp(j) ¼ 0, then artp

s is unchanged

� if Cp(j) ¼�1, then artp

s ¼ 0

If some additional restrictions were not imposed, thisprocess would lead to the ‘perfect’ artefact, where all thedesired characteristics are present at the maximum level(e.g., think of a unrealistic car, able to fly, navigate, interactwith human beings, produce and translate documentsand make excellent coffees). In order to take into accountthese constraints, we decided simply to bind the numberof characteristics present simultaneously in the sameartefact. If, after the producer processing, an artefact hasnumber 1’s exceeding the given threshold s, a stochasticremoval process eliminates a subset of the currentcharacteristics.

Such a removal process is slightly more complex than thecorresponding process acting on categories. For instance,

characteristics that are judged to be irrelevant to the agentpurposes should have a deletion probability higher thancharacteristics that are regarded as having higher impor-tance. Therefore, we can have three main situations:

� N1: the number of 1’s in artefact artps , corresponding to a

feature 1 in Cp(j)

� N2: the number of 1’s in artefact artps , corresponding to a

feature 0 in Cp(j)

� N3: the number of 1’s in artefact artps , corresponding to a

feature �1 in Cp(j)

In correspondence to these numbers, we have the followingthe removal probabilities:

� P1: probability that a 1 in artefact artps is eliminated, when

the feature Cp(j) is 1

� P2: probability that a 1 in artefact artps is eliminated, when

the feature Cp(j) is 0

� P3: probability that a 1 in artefact artps is eliminated, when

the feature Cp(j) is �1

The following relation holds for the above quantities:

ð1 � P1ÞN1 þ ð1 � P2ÞN2 þ ð1 � P3ÞN3 ¼ s

Note that in order to set the probabilities P1, P2 and P3, wehave to fixm: quotient between P1 and P3

l: quotient between P1 and P3

In particular, we wish to obtain P1oP2oP3, that is,

P1

P3¼ mo1 ) P1 ) mP3

P2

P3¼ lo1 ) P2 ¼ lP3

Therefore, we have

ð1 � mP3ÞN1 þ ð1 � lP3ÞN2 þ ð1 � P3ÞN3 ¼ sand obtain the elimination probabilities

P3¼ �ðs � N1 � N2 � N3ÞðmN1 þ lN2 þ N3Þ

; P1 ¼ mP3; P2 ¼ lP3

As a consequence, it is enough to act only on twoparameters (l and m).

Finally, we remark that since the final goal is to simulateexaptation phenomena, we can disregard an overly detaileddescription of production processes and costs.

FunctionalityIn EMIS, we define the ‘functionality of an artefact withrespect to a particular category’, as an index measuring thelevel of user’s satisfaction with the artefact. The indexappraises the satisfaction received from the artefact, whenthe user evaluates the corresponding category. Its max-imum value, denoted by Fmax, indicates that the artefact fitsperfectly in the requirements contained in the associatedcategory.

In order to evaluate an artefact, the agent must ‘interpret’it by means of one of its categories. Practically, the agentperforms a filtering operation on the artefact using theinvolved category, according to the scheme reported inTable 2.

Table 1 Artefact production/innovation

Considered vector Feature value

Artefact – Ap 1 0 1 0 1 0Category – Ap 1 1 0 0 �1 �1New artefact 1 1 1 0 0 0

The producers have to modify the already-existing artefacts. Anartefact is a string of ‘1’ (the feature is present) and ‘0’ (the featureis absent); the category is a string of ‘1’ (the agent monitors thecorresponding feature and considers in a positive way itspresence), ‘�1’ (the agent monitors the corresponding featureand considers in a negative way its presence) and ‘0’ (the agentdoes not monitor the corresponding feature). The new artefacthas started from an already existing one. Therefore, if theproducer desires a given characteristic (‘1’ tag on the corre-sponding category position) the new artefact has a ‘1’ on theinterested position; if the producer does not desire a givencharacteristic (‘�1’ tag on the corresponding category position)the new artefact has a ‘0’ on the interested position; if theproducer does not monitor the characteristic (‘0’ tag on thecorresponding category position) the new artefact maintains thevalue of the already existing artefact.

An agent-based model of exaptive processes Marco Villani et al.

145

The hypotheses of Table 2 are very simple:

� if Api ¼ 1 and Cu

(i) ¼ 1 (user’s desires and producer’srealisation coincide), then the comparison produces adesirable outcome (denoted by 1);

� if Api ¼ 1 and Cu

(i) ¼�1, (user’s desires and producer’srealisation do not coincide), then the comparison resultsin an undesirable outcome (denoted by �1);

� all the other cases correspond to a situation ofindifference.

Clearly, the dynamics generated by such a model shouldtend to produce the ‘correct’ positioning of 1’s in theartefact vector. In order to achieve this goal, we can definethe artefact functionality (with respect to a given category)simply as the scalar product between the comparison vectorart-C and the agent’s weight vector Wu. Note that the largestfunctionality value Fmax of an artefact with respect to agiven category is given by the scalar product between theweight vector and the category itself, where all the ‘�1’s areset to be ‘0’.

DynamicsThe most critical interactions for the outcome of the modeltake places between producers and users. Two distinct partscompose the interaction process: (i) when the user receivesand evaluates an artefact built by a producer; (ii) when theuser provides feedback evaluation to the producer aboutthe satisfaction level reached by the artefact (the artefactfunctionality).

First, we focus our attention to the delivery andsubsequent evaluation of an artefact. In order to evaluatethe artefact the user computes its functionality (alreadydescribed in the previous paragraphs); filters the artefactwith respect to all her/his categories and finally commu-nicates the best result to the producer. Moreover, the usercan deliver to the producer some additional information,which can result useful for the future artefact innovations.Specifically, the user can transmit to the producerparticular subsets of the two categories that give the highestfunctionality values. These subset are composed of

� Ijq(q¼ 1), Actual Information (AI). Features of theselected category that correspond to the art-C character-istics that highly contribute to the determination of the

functionality value (it does not matter if in positive ornegative direction).

� Ijq(q¼ 2), Desired Information (DI). Features of theselected category that potentially have the highestcontribution power (the Ijq features that highly con-tribute to the scalar product between the selectedcategory Cu as is and the weight vector).

These two different kinds of information allow the userto explicit her/his requests. In particular:

� AI represents the features of the current artefact that givepositive or negative contribution to the functionality.

� DI expresses what the agent likes or dislikes about theartefact (when it is filtered by means of the selectedcategory).

Sometimes, it is possible that the two subsets have a non-empty intersection: for example, it is possible that anartefact feature be important for a category, and at the sametime it gives a negative contribution to the functionality ofanother category. In other words, in the example we aresupposing that for AI we observe Cu

(i) ¼ 1, whereas for DI wehave Cu

(i) ¼�1, as a result of some other category. In such acase, we impose that either AI or DI is randomly left out ofthe transmission.

The producer uses the transmitted features in order tomodify the features Cp

(i) of the category employed to buildthe artefact. The new value of each characteristic iscomputed by means of the following formula:

v ¼ ðadþ bcÞdþ c

where a is the value of the feature Cp(i) of the Ap, b is the

value of the feature Cu(i) of the Au, d is the influence of Ap on

next feature value and c is the influence of Au on nextfeature value.

The feature will be

1 if vXo0 if jovoo�1 if vpj

where o is the lower bound for the upper interval and j isupper bound for the lower interval (Figure 1).

The goal of the above calculation is to transform thefeatures communicated to the producers by the user. All theremaining features are left unchanged, except the admit-tance of some random ‘noise’ obtained as: a 1 or a �1starting from a 0 tag, a 0 or a �1 starting from a 1 tag, and a1 or a 0 starting from a ‘�1’ tag. Finally, in order to limitthe number of relevant features, the new vector is filteredby the removal process described in the previous section,according to the given threshold s. The final vectorrepresents the new category that the producer employs tobuild the subsequent generations of the artefact.

EMIS and the study of exaptationIn the initial paragraph, we have defined exaptation as asudden emergent phenomenon in evolution dynamics.Where does exaptation appear in our model? Recall thatEMIS simulates exchanges of products (artefacts) betweenproducers and users, the users evaluating the artefacts by

Table 2 Computation of the comparison vector art-C

Considered vector Feature value

Artefact – Ap 1 0 1 0 1 0Category – Au 1 1 0 0 �1 �1Comparison art-C 1 0 0 0 �1 0

The users have to interpret the already-existing artefacts. Anartefact is a string of ‘1’ (the interested feature is present) and ‘0’(the interested feature is absent); The comparison vector art-Cmonitors the details of the users’ artefact evaluation: it has thepositive value ‘1’ when, in the corresponding position, bothartefact and category are ‘1’, and has the negative value ‘�1’when on the corresponding position the artefact is ‘1’, but thecategory is not a desired one. All the other combinations give nocontribution to the evaluation.

An agent-based model of exaptive processes Marco Villani et al.

146

means of their categories. In this context, an exaptation is acategory change in interpreting the artefact. For example,after hundreds of steps the category that was systematicallyreturning the best functionality is no longer the best one:the last innovation(s) has (have) increased the functionalityof another category that in such a way becomes the newreferring category for the selected artefact.

Recall that the producer supplies the user only with thebest functionality value among all the values computed usingall the categories it owns. The category that furnishes such abest value during one interaction is likely to have a largevalue also in the next interaction, and so forth. In a sense,such best category is, for the user, the ‘leading’ category forthis particular artefact. Sometimes, but quite unlikely,another category reaches a functionality value larger thanthat of the leading category. In a sense, this can be interpretedas a variation of the utilisation context of the artefact underexam; in this case, we are observing an exaptation event.

Model dynamics

InitialisationIn order to test the model, we perform some preliminarysimulations by avoiding unnecessary complications. There-fore, we reduce the number of the actors, maintaining onlyone producer and one user:

l ¼ 1; h ¼ 1; g ¼ 2

The knowledge space of the categories involved is D¼ 1000features. The user utilises five categories, which guaranteesufficient diversity, while the producer owns only onecategory, corresponding to the artefact that it is building.

The other parameters we have to fix in order to create theinitial categories are:

1. the threshold Z, limiting the number of |1|’s in Ci(j), is set

to be 100;2. the initial fraction of 1s in Ci

(j), is set to be 0.05;

3. the initial fraction of value �1s in Ci(j), is set to be 0.05.

The value of Z is relatively low with respect to the D valueand indicates that the space of all the possible character-istics of a category is very large with respect to the reallyimagined ones. Each feature of the initial artefact (at timet¼ 0) takes the value 1 with probability

Part ¼sD

where s is the threshold defining the maximum number of1’s that can be present on an artefact, and D being the totalnumber of features composing the knowledge space. Thus,initially we have a ‘raw’ artefact that is able contains a largeset of details. In order to correctly link each artefact to itsreferring category, this raw artefact is filtered following theschema proposed in Table 1, and in sequence trimmed byeliminating the accidental ‘1’ exceeding the threshold s, asduring the usual production processes.

The parameters m and l, which tune the presence of 1swithin the artefact during the final elimination process, arefixed to 0.01 and 0.05, respectively, while the upper bound s isset to 200. Please note that s4Z, that is, we are assuming that

� the producer can build artefacts with not explicitlydesirable characteristics;

� the artefacts can carry out more characteristics than theplanned ones;

� the typical user focuses its attention only within a subsetof the whole potentiality of the artefacts.

Therefore, it is actually possible that an artefact carries outa number of functions larger than the number offunctionalities for which it has been selected (exaptive poolof possibilities). In the last part of this paper, we will seethat in order to study the exaptation phenomenon it isenough to trace the path for a single artefact.

In the second phase of the interaction process, theproducer creates new categories (new knowledge). In orderto do so it enriches its knowledge using the feedbackmessages sent by the user. Particularly, we choose to give thesame relevance to both the agents, by setting the balancingweights d¼c¼ 0.5, and o¼ 1/3, j¼�1/3, in order toobtain three intervals of approximately equal length. Hence,we have that the producer averages the feature values of itscategory with the corresponding values provided by the user.

A typical runFigure 2 shows some of the main variables simulated byEMIS. Figure 2a shows the best functionality value of theartefact at a given time step, and its Fmax value. Note that atstep 207 the user changes the leading category (exaptation)and Fmax. In this case, it is observed that the upper limit forthe achievable satisfaction decreases, despite an increase inthe actual functionality

Figure 2b shows the distance among user’s categories andthe artefact actually built by the producer. In this context,the distance describes the semantic discrepancy betweenthe artefact and the category referred to that particularartefact. Table 3 is based on the two following principles:

� a distance between artefact and category occurs when theagent ‘desires’ a feature that is not currently present;

Figure 1 Modification schema of the Ap features.

An agent-based model of exaptive processes Marco Villani et al.

147

� a distance between artefact and category occurs when theagent ‘does not desire’ the present feature.

At each step the user analyses producer’s artefacts, whichare interpreted using her/his own categories and furnishesto the producer, the corresponding more elevated value offunctionality. At step 207 the functionality value of category2 outperforms the functionality value of category 4. In therest of the simulations, category 2 maintains its superiorityand we do not observe new other exaptation events(Figure 3).

Experimental resultsWe individuate three main factors that are able to favourthe emergence of exaptation phenomena:

1. communication among different agents;2. communication and production noise;3. evolution of the users’ categories.

In all the situations the user can utilise two differentmodalities of communication:

1. Symmetrical: both communicated categories provide thesame amount of information ‘actual’ and ‘desired’.

2. Asymmetrical: the category that better interprets theartefact provides ‘actual’ information, while the secondone provides ‘desired’ information.

This specification has been introduced to verify whether thepresence of communication symmetry/asymmetry canfavour the occurrence of exaptation phenomena. Recallthat the ‘actual’ information represents the objective user’sevaluation, whereas the ‘desired’ information expresseswhat the user wants. Therefore, symmetric communicationmeans that the user treats the categories without any bias,whereas asymmetric communication means that the usertransmits an objective report about the first category, andthen communicates some desires corresponding to asecond one.

CommunicationTypically, the user transmits to the producer a (small)subset of the features extracted from the two categories thatare returning the best functionality values. In thisparagraph, we analyse the behaviour of our model byvarying the number of transmitted features, or bandwidth(B). In particular, in this set of experiments the totalnumber of transmitted characteristics is set to be B¼ {20,40, 60, 80,100, 200}.

First, we observe that the number of exaptations foundby using the asymmetric modality is consistently largerthan the number of exaptations found by using thesymmetric modality. Moreover, larger values for thebandwidth correspond to a larger number of exaptationevents, in both short and long run (50 and 1000 time steps,respectively) (see Figure 4). In particular, we noticed that alarger bandwidth with asymmetric modality could favourthe presence of exaptations during the long run. Con-versely, if the number of transferred features is small, theexaptation events are rare.

These facts suggest that an unbiased communicationmodality is not able to favour a context change, whereas aqualitatively asymmetric communication modality couldeffectively support the success of categories that are notfavoured initially. In this case, in order to favourexaptations phenomena, it is helpful to transmit a largeamount of information, creating the potential for thediscovery of new and previously disregarded solutions.

The exaptations occur mostly during the short period,whereas they are rarely observed during the long period.

Figure 2 Interactions between user and producer. At each step the user returns to the producer the best evaluation of the artefact on the basis of its owncategories. (a) (left) Shows this variable and its maximum value (Fmax in the text), obtainable only in the case of null distance among artefact and category. At step207 exaptation occurs, as the user changes the referring category (thus leading to a change of Fmax) value changes. In this case, the maximum reachablesatisfaction decreases, although the actual functionality value increases. (b) (right) Shows the distance among the user categories and the artefact actually built bythe producer.

Table 3 Example of semantic distance calculation between artefact andcategory

Considered vector Features value

Artefact – Ap 1 0 1 0 1 0Category – Au 1 1 0 0 �1 �1Distance 0 1 0 0 1 0

An artefact and a category are not similar (a) when the agent‘desires’ a feature that is not currently present on the artefact, or(b) when the agent ‘does not desire’ a feature that is currentlypresent on the artefact. The total distance is the sum of thesedifferences in all the positions of the strings that describe,respectively, agents and categories.

An agent-based model of exaptive processes Marco Villani et al.

148

Actually, during the first interactions the producer caneasily modify her/his artefacts and contemporarily increasethe functionality values with respect to several differentcategories. However, when the artefact is highly specialised,the simultaneous satisfaction of several requirements ischallenging. Conversely, symmetric information and largebandwidth values can support best performances of themodel in terms of attainment of Fmax, allowing producer tosatisfy user’s requests.

NoiseA second study concerns the analysis of two types of noisethat can be possibly specified in the model:

� Communication noise. The value of the features commu-nicated by the user agents is changed with probability a(1 or �1 from a 0 tag, 0 or �1 from a 1 tag, and 1 or 0from a �1 tag).

� Production noise. The value of the characteristics of theartefact built by the producer is changed with probabilityb (0 from 1, and 1 from 0).

The communication noise does not affect the mainbehaviour of the model, although its presence makes itmore difficult to reach larger functionality values. Theproduction noise worsens such a tendency, but at the sametime increases the frequency of exaptation occurrences,both in the long period and in presence of low bandwidthcommunications. Some innovations, obtained because ofthis type of error, are able to foster a change of context forthe whole artefact.

LearningIn the study presented in this section, we allow the user tomodify her/his own categories (so far considered as fixed),through two different modalities:

1. The user can randomly create a new category, andsubstitute one of the already existing ones (excluding thecategory, giving the highest functionality). This repre-sents the knowledge the user can acquire by interactingin new environments not explicitly modelled,

Figure 3 Artefacts’ evaluation. The figure shows the evaluation the artefact received from the agent’s categories during the same simulation of Figure 2. Pleasenote that at step 207 the second category suddenly increases its value and becomes the referring category.

Figure 4 Effects of the communication modalities. The user can communicate to the producer the artefacts’ features that mostly influenced the artefacts’evaluation, and/or the artefacts’ features that potentially can influence the artefacts’ evaluation. By using symmetric communication, for the first two categoriesthe user transmits both the features that influenced the artefacts’ evaluation and the features that potentially can influence the artefacts’ evaluation. By usingasymmetric communication, the user transmits for the best category the features that influenced the artefacts’ evaluation, and for the second category thefeatures that potentially can influence the artefacts’ evaluation. Part (a) shows the percentage of simulations (over 10 runs) with at least one exaptation fordifferent quantities of features transmitted to the producer. The time interval of reference (from 50 to 1000 steps) is also shown. Part (b) shows the averagenumber of exaptations for each simulation over 10 runs.

An agent-based model of exaptive processes Marco Villani et al.

149

2. The user can modify a randomly selected category (allfive categories being involved) by introducing someinformation coming from the artefact. This modalityallows the user to learn and to actively participate indefining its own satisfaction, measured by means of thealready presented variable Fmax.

Both modalities are characterised by the updating rate f,expressing the probability that at each time step thecategory of the user is selected for a substitution (updat-ing). In addition, we remark that the second modality needsthe change probability Pch for each feature (in all our trialsPch ¼ 0.02), once a feature is chosen for merging with thecorresponding artefact characteristics. The merging algo-rithm is described in Table 4.

The random modality shows a small increase in thenumber of exaptation events, for both symmetric and

asymmetric communications. Such a phenomenon appearsto be relevant and it is evident also during the longersimulation runs. An higher updating rate f does notenhance this phenomenon. The second modality showsmore interesting features. We find a bigger exaptationfrequency that increases almost linearly with the growth ofthe adjournment rate f (see also Figure 5a); also the Fmax

level of satisfaction increases with the adjournment rate(Figure 5b). A real example of ‘learned’ exaptation could bethat of the SMSs (the Short Message Service), initiallyintroduced to send brief official messages from thetelephone company and subsequently became a new meanfor the communication of mass. In this case, the userssucceeded in understanding the communicative potentialityof this system overcoming limits of space by means ofcreation of a particular language, more ‘assembled’ andintuitive. As a result, the phone companies initiated amarket strategy based upon this new functionality.

ConclusionCommon claims in literature about innovation are thatnovelties are recombinations of current capabilities andthat their search is local, or that creativity is constituted bysudden blind insight. Both views are not satisfactory,because the first hypothesis is not able to describe radicalinnovation, whereas the second one provides little con-ceptual gain.

In this paper, we propose that radical innovations arecreated by a process of ‘exaptation’. We introduce an agent-based model designed to investigate the dynamics of someaspects of exaptation in a world populated by agents, whoseactivity is organised around production and utilisation ofartefacts. The model, EMIS not only explicitly includesagents and artefacts, but also encompasses agents’ sub-jective representation of the artefacts by means of cognitivecategories. In our model, the agents build (as producers)

Figure 5 Learning from the environment. Agents can modify their categories by learning from the environment: at each time step there is the probability f ofselecting a category for modification; in this case, a fraction Pch of the category’s features change their value. The user can communicate to the producer theartefacts’ features that mostly influenced the artefacts’ evaluation, and/or the artefacts’ features that potentially can heavily influence the artefacts’ evaluation. Byusing symmetric communication, for the first two categories the user transmits both the features that influenced the artefacts’ evaluation and the features thatpotentially can influence the artefacts’ evaluation. By using asymmetric communication, the user transmits for the best category the features that influenced theartefacts’ evaluation, and for the second category the features that potentially can influence the artefacts’ evaluation. Part (a) shows learning modality: thepercentage of simulations (over 10 runs) with atleast one exaptation, by varying the adjournment rate f. Part (b) shows the average for the same runs: the fractionof the satisfaction index Fmax reached by the artefact functionality, by varying the adjournment rate f, for both random and learning modality. The learning increasesthe exaptation event probability.

Table 4 Learning from the environment

Considered vector Features value

Artefact – Ap 1 0 1 0 1 0Category – Au 1 1 0 0 �1 �1New category 1 0 1 0 0 �1

Agents can modify their categories by learning from theenvironment: at each time step there is the probability f ofselecting a category for a modification; in this case, a fraction Pch

of the category’s features change their value. The table shows allthe possible combinations and the correspondent outcomes. Thegeneral schema is that the differences tend to decrease and thatthe category is plastic. Therefore: (a) if the artefact feature is ‘1’,the corresponding feature of the new category become ‘1’, unlessthe involved characteristic is ‘not desired’ (in this case, it reducesthe distance and becomes ‘0’); (b) if the artifact features is ‘0’, thecorresponding feature of the new category also becomes ‘0’,unless the involved characteristic is ‘not desired’ (in this case, itmaintains the old value).

An agent-based model of exaptive processes Marco Villani et al.

150

and interpret (as users) the artefacts using cognitivecategories.

One of the main features of EMIS is the description of theinformation exchange dynamics among agents. Two mainprocesses characterise such a dynamics: (i) interpretationand storage of information by each agent and (ii)circulation of information through the exchange ofartefacts. The first process takes place in the cognitivedomain of each agent. In particular, at any given time, eachagent owns a cognitive representation of a number of realobjects (artefacts) in terms of a set of cognitive features(categories). The second process involves the communica-tion among agents of a fraction of the information stored incategories. Eventually, the producers employ their sets ofcognitive categories to make artefacts that are in turnsubmitted to the users. The users evaluate the functionalityof such artefacts by means of their cognitive categories andnext send signals to producers about their ‘satisfaction’with such artefacts.

The agents in the model are able to attribute ‘function-alities’ to the artefacts in terms of categories; a givenattribution can generate a certain reward associated withthe artefact of reference. Thus, the type of representationproposed is suitable to take into account exaptation events,which are understood as shifts in terms of the ‘leadingattributions’ (attributions corresponding to highest reward)that the agents assign to the artefacts.

The model has been implemented in a computerenvironment. The main goal of the computer simulationsis to determine some of the factors playing a central role inthe information-exchange processes, with particular atten-tion to the study of exaptation. From our first simulations,we can conclude that some of the most important elementsfavouring the emergence of exaptation events are:

1. an asymmetrical communication, where evaluations anddesires are differently expressed for different categories;

2. a high number of cognitive features (characteristics)communicated among the agents

3. a high level of production noise;4. the plasticity of the users’ categories.

In conclusion, we can assert that the explicit representa-tion of artefacts and categories eases the understandingof the exaptation phenomenon, seen in this context as a

shift in terms of ‘leading attributions’, and allows theidentification of the elements favouring the emergence ofexaptation.

Note

1 A more correct notation would be Ck, p and Ck, u, withkA[1,y, s], s being different for producers and users. Never-theless, for reason of clarity, in the following we omit such anindex: simply, the reader should remember that both users andproducers possess more than one category (the producersowning one category for each artefact).

References

Ceruti, M., 1995, Evoluzione senza fondamenti. Laterza, Bari: collana

‘‘Il nocciolo’’.

Dew, N., S.D. Sarasvathy and S. Venkataraman, 2004, ‘‘The economic

implications of exaptation’’. Journal of Evolutionary Economics, 14(1):

69–84.

Ferrari, D., D. Read and S. van der Leeuw, 2008 (in press). The emergence of

new categories in artefact innovation’’. In D. Pumain, D. Lane and S. van der

Leeuw (eds.) Complexity perspectives on innovation and social change.

Berlin: Springer.

Gould, J.S., 2002, The structure of evolutionary theory. Cambridge, MA: The

Belknap Press of Harvard University Press.

Gould, S.J. and R.C. Lewontin, 1979, The spandrels of San Marco and the

Panglossian paradigm, Proceedings of the Royal Society of London, B. 205,

pp: 581–598.

Gould, S.J. and E. Verba, 1982, ‘‘Exaptation, a missing term in the science of

form’’. Paleobiology, 8(1): 4–15.

Kimura, M., 1983, The neutral theory of molecular evolution. Cambridge:

Cambridge University Press.

Macrae, N. and G. Bodenhausen, 2000, ‘‘Social cognition: Thinking

categorically about others’’. Annual Review of Psychology, 51: 93–120.

March, J.G., 1991, ‘‘Exploration and exploitation in organizational learning’’.

Organisation Science, 2(1): 77–87.

Markman, A.B. and D. Gentner, 2001, ‘‘Thinking’’. Annual Review of

Psychology, 52: 223–247.

Mokyr, J., 1998, ‘‘Induced technical innovation and medical history:

An evolutionary approach’’. Journal of Evolutionary Economics, 8(2):

119–137.

Schumpeter, J.A., 1934, The theory of economic development (1983 Edition,

John Elliott, ed.), New Brunswick, NH: Transaction Publishers.

Selby, H.A. and F. El Guindi, 1976, ‘‘Dialectics in zapotec thinking’’. In K. Basso

and H. A. Selby (eds.) Meaning in anthropology. Albuquerque, NM:

University of New Mexico Press, pp: 181–196.

Simon, H.A., 1996, ‘‘The architecture of complexity’’. In Sciences of the

artificial, 3rd edn., Cambridge: MIT Press.

An agent-based model of exaptive processes Marco Villani et al.

151