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 DOI: 10.1177/105971230000800103

2000 8: 27Adaptive BehaviorEzequiel A. Di PaoloCoupled Agents

Behavioral Coordination, Structural Congruence and Entrainment in a Simulation of Acoustically  

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Behavioral Coordination, Structural Congruence and Entrainmentin a Simulation of Acoustically Coupled Agents.

EZEQUIEL A. DI PAOLOUniversity of Sussex, Brighton BNI 9QH, U.K.

Social coordination is studied in a simulated model of autonomous embodied agents that interact

acoustically. Theoretical concepts concerning social behavior are presented from a systemic per-spective and their usefulness is evaluated in interpreting the results obtained. Two agents movingin an unstructured arena must locate each other, and remain within a short distance of one anoth-er for as long as possible using noisy continuous acoustic interaction. Evolved dynamical recurrentneural networks are used as the control architecture. Acoustic coupling poses nontrivial problemslike discriminating ’self’ from ’non-self’ and structuring production of signals in time so as to min-imize interference. Detailed observation of the most frequently evolved behavioral strategy showsthat interacting agents perform rhythmic signals leading to the coordination of movement.During coordination, signals become entrained in an anti-phase mode that resembles turn-taking.Perturbation techniques show that signalling behavior not only performs an external function,but it is also integrated into the movement of the producing agent, thus showing the difficulty ofseparating behavior into social and non-social classes. Structural congruence between agents is

shown by exploring internal dynamics as well as the response of single agents in the presence ofsignalling beacons that reproduce the signal patterns of the interacting agents. Lack of entrain-ment with the signals produced by the beacons shows the importance of transient periods ofmutual dynamic perturbation wherein agents achieve congruence.

Keywords: Social behavior, embodied autonomous agents, acoustic interaction, coordination,entrainment, structural congruence.

1 INTRODUCTION

In the late forties W Grey Walter wired a headlampinto the steering circuit of his Machina speculatrixthat would be turned on while the robot was per-forming its exploratory behavior and turned off whenthe robot’s photoelectric sensor detected a moderatelight, (Holland, 1996, Walter 1950, 1953). Since thenatural tendency of these ’turtles’ was to explore theirenvironment following a cycloidal path until theydetected a source of moderate light, and then movetoward it while keeping a certain distance (i.e., avoid-ing intense light), some fascinating dancing patternswere witnessed when two of them (Elmer and Elsie)were placed on the same floor with all the sources oflight switched off except for their own headlamps. Aturtle in the exploratory mode would have its head-lamp on until its sensors detected the light coming

from its partner. Then the headlamp would go off. Ifthe same thing happened to its partner both turtleswould begin a movement toward a source of light thatwould be extinguished at the next moment, and there-fore they would resume exploration, i.e., turning theirlights back on, and so on. The turtles would approachand stop intermittently toward each other’s flickeringheadlamps, until the light of one of them would movebeyond the range of the other one’s sensor and theywould ’lose interest’. This simple experiment, explain-able in terms of wires, light bulbs and mechanicalbodies, poses nontrivial questions about the nature ofsocial behavior. Are Elmer and Elsie acting socially?Would they be if they were endowed with a mecha-nism that would let them regain their interaction pat-tern once it was lost? When is a behavior social? What

exactly do we have in mind when we say that socialbehavior is fundamental for understanding the evolu-

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tion of intelligence? Many inheritors of Walter’s tradi-tion still find these questions pressing.

Our goal in this paper is to address some of theseissues theoretically, and to present a model partiallyinspired by Walter’s interacting turtles in which wecan explore the value of the theoretical concepts intro-duced. More specifically, we set out to explore, bymeans of simulations, some of the coherent behavioralpatterns that can arise from sustained interaction

between embodied autonomous systems through anacoustic medium. We will show that this coherencecan be explained in terms of the systemic concept ofstructural congruence, the attainment of which is to be

expected under a variety of circumstances.The choice of sound as a means of interaction in

our model is not incidental. Acoustic interactions are

conspicuous in nature, and some of their physical fea-tures, as well as those corresponding to auditory per-ception, make this ’channel’ a particularly interestingone from the point of view of adaptive behavior. Forinstance, organisms using sound as a means of achiev-ing behavioral coordination must face nontrivial

problems such as distinguishing their own productionfrom those of others and avoiding mutual interferenceof signals’ . Problems like these did not arise in the wayElmer and Elsie were coupled.

Our approach differs from some recent modelsaddressing the evolution of communication (DiPaolo,1998; MacLennan, 1994; Werner, 1991) in that ourinterest is focused more on behavioral issues ratherthan on evolutionary ones. In order to make positivecontributions to evolutionary questions these modelsmust assume too much in terms of how the interac-tions between individuals are structured to be usefulfor understanding purely behavioral questions. In

contrast, we will aim at making fewer assumptionsabout the nature of the interaction and the behavioral

building blocks that we incorporate into our agents.A related type of work using simulations explores

issues like the evolution of symbolic systems and lexi-con formation. These models often made very strongassumptions about what communication is and aboutthe requirements of individual competence regardingcategorization and ’naming’ of categories. We believethat a much lower level understanding of social behav-ior must be achieved from the perspective of embod-ied autonomous systems, before we may hope to

explain behaviors such as ’giving a name to a category’

or ’referring to an external object’. Thus our work willbe more related to work done using real robots insocial interaction, (Billard, 1997; Dautenhahn, 1995;Mataric, 1995 and others), the aim of which cansometimes be understood as double: to address ques-tions about the nature of social behavior (for instance,the relation between social skills and individual com-

petence) as well as to build socially intelligent robotsthat can coordinate their actions in the performanceof a complex task. We will restrict ourselves only tothe former aim. This is why we specifically addressmeans of interaction that can be found in nature, suchacoustic signals, their physical implications and theproblems they pose. Our concern, therefore, lies moreon the scientific side: we want to test the usefulness ofour methodology in understanding natural socialbehavior. Any knowledge or inspiration we mayobtain about engineering issues will be considered as aplus.

The following section discusses some issues regard-ing social behavior from the point of view of couplingbetween autonomous systems. In section 3 we identi-

fy some basic physical aspects of sound as a channel ofinteraction and in section 4 we present a natural

example of complex acoustic coupling. Section 5 dis-cusses the scope and methods used for building andstudying the model presented in section 6. The rest ofthe paper presents and discusses the results obtained.

2 A SYSTEMIC PERSPECTIVEON SOCIAL BEHAVIOR

A dynamical systems approach to the study of adap-tive behavior (Beer, 1995) can be taken as opposingany type of functional explanation and favoring onlypurely operational descriptions in terms of attractors,potential wells, and couplings between complex sys-tems, (see Faith 1997). This may be too narrow a

point of view. The purpose of an operational explana-tion is not necessarily to act as a replacement of afunctional one, but rather to act as a constraint to the

possible functional interpretations that we may needto provide for pragmatic purposes. For this reason, itis a worthwhile enterprise to try to identify such oper-ational constraints using dynamical systems theoryand other systemic concepts even if a completedynamical description cannot be given. This is whatwe intend to do very briefly in this section for some

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general issues related to social behavior.When we think about social behavior, the first

thing that comes to mind is some notion of coordi-nated activity between two or more autonomous enti-ties. In order to understand what we mean by this, wemust describe the meaning of autonomy, interactionand coordination.A possible definition of autonomy in non-function-

al terms is given by Varela (1979, p. 55). A system isautonomous if its organization has the property ofbeing operationally closed. This does not mean thatthe system does not interact with its external environ-ment. It means that its organization is constituted bya network of internal processes, and that the operationof this network is sufficient for those constitutingprocesses to be generated and sustained (constituted)without any of them being driven from outside thesystem. At the same time the identity of the system isdefined as long as it remains operationally closed,(Varela 1979, p.57).

What sort of relation can an autonomous systemhave with its environment in order to remain

autonomous? It is clear that as soon as this relation is

one where the closure of the internal organization ofthe system is disrupted from the outside, autonomywill be almost certainly JoSt2. Preservation of autono-my divides the space of possible interactions into

those that are allowed and those that are not, and this

space is obviously contingent on the present state ofthe system. Allowed interactions will be manifested as

perturbations to the system that do not break its oper-ational closure, and not as instructing the dynamicalpath that the system will follow. A process, wherebythe system interacting with its environment undergoesa succession of allowed perturbations of this kindwithout losing its autonomy, is called a process of

structural coupling, (Maturana & Varela, 1980)3.Structural coupling occurs between a system and

its medium, which may include other autonomous

systems, in which case we speak of an interaction.However, mere interaction between autonomous enti-ties does not seem to be enough to describe the result-ing behavior as social even if it happens to have anadaptive function. There is something lacking in twoanimals just bumping into each other while trying toescape from a predator to call that a social interaction.What we are looking for is a concept that will allow usto describe the complex patterns of social behavior

that we observe in humans and other species. This isthe idea of coordination4.

Coordination is a subtle concept. In one interpre-tation, it involves the fact that many organisms canhave a complex behavioral repertoire that allows what,for an observer, seems to be a simultaneous instantia-tion of different behaviors, (for instance, walking andtalking in humans). When two or more organisms areinteracting only a part of this behavioral space may beoccupied directly in the interactive activity. However,if we do observe a coherence between behaviors not

involved directly in the interaction, then we are in thepresence of coordination, (Maturana & Varela, 1980,

p. 27 - 28). Another, equally valid, interpretationwould not require that the different behavioral

domains, the one in which the interaction occurs andthe one in which coordination is elicited, be simulta-

neously instantiated, but coherence in the latter stillneeds to show dependency on the outcome of theinteractive activity in the former.

Coherence means an observable agreementbetween behaviors of different organisms, from simpleinstances of synchronized activity or other forms oftemporal consistency (such as the group response toan alarm call) to more complex cases, such as the pat-terns shown by members of a wolf pack when hunt-ing large prey, or the approaching behavior and main-tenance of the pair bond in monogamous species oftropical birds by means of antiphonal duetting (seesection 4). We may ask why should there be any rela-tion between the coordinated behavior (in the last

example, song synchronization and approaching) andthe interaction (singing), unless both organisms weresomehow congruent enough in structural terms sothat (a) the coordinated behavior is possible for bothof them, and (b) their structures are such that thecoordinated behavior is somehow related operational-ly to the fact that they are undergoing a specific pat-tern of interaction. See figure 1 where the state of thebehavioral domains of two organisms in interactions isshown through time. Coherence is depicted by con-gruence in the form of the diagrams which representthe individual domains of behaviors. Interaction is

shown as a single activity in which both organismengage (top). Coordination is shown as additionalcoherence which depends (operationally) on the exis-tence of interaction (bottom).

Each perturbation that an autonomous system

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Figure 1. Illustration of the concept of coordination.

undergoes during structural coupling may inducechanges in its structure, and some of these changesmay be plastic. Plastic changes occur when the struc-ture of a system undergoes an alteration from which itdoes not recover within the same time-scale withwhich the change happened but with a larger one.Clearly, some of these changes may be permanent.

As a special case of structural coupling, coordinat-ed interactions between organisms may also inducesuch changes. The process of mutual coordination is,at the same time, a process of mutual selection of

plastic changes in their respective structures, so thatnot only the ensuing behaviors result in a coherentpattern but also the corresponding structural changesmay show some degree of coherence. The resultingrelation between the structures of the coupled systemsis known as structural congruence, and it is to be found

particularly between organisms that engage in interac-tion repeatedly and recursively. Sustained patterns ofinteraction tend to become embodied in the partici-pants in the form of a history of structural changesduring each individual’s lifetime. As a result, subse-quent encounters may be affected either in ways thatfacilitate the reproduction of the pattern of interac-tion, or in ways that do not. If facilitation of futureencounters is the result of certain patterns of interac-

tion, it is clear that those patterns will tend to be con-served. For certain plastic systems, this process couldconstitute the basis of social affinity, (an example ispresented in section 4).

Of special interest is the case where structural con-

gruence is achieved between ’unevenly plastic’ organ-isms, as in the case of parent/offspring social interac-tion. If structural congruence is understood as the

meeting of two distinct, though not completely dis-similar, structures in some common ground, it is clearthat those interaction patterns that facilitate their own

reproduction by inducing structural changes will tendto produce what for an observer would look like adirected structural change in the more plastic organismtowards a structure that is congruent with the less

plastic organism. This phenomenon, and its opposi-tion (the structural ’rejection’ of patterns that maketheir own reproduction difficult), could be used as anoperational basis for explaining many instances ofsocial learning.We should stress that there is nothing magical

about coordination. Consider one of its possible man-ifestation in rhythmic forms of behavior: entrainmentor synchrony. There is a growing literature on syn-chronization of coupled oscillators in biology andchemistry (see Winfree, 1980; Kuramoto, 1984 for’classic’ introductions). The striking fact is that undera vast set of conditions synchronization is the expect-ed result. Additionally, coordination in rhythmicbehavior is not just manifested in phase-locking, butmore remarkably in tendencies to correct phase devia-tions. Kelso calls this phenomenon relative coordina-tion after von Holst, (Kelso, 1995). Entrained behav-ior may be difficult to maintain in the case where the

interacting systems are not identical. However, thesystems, under certain conditions, may manage to

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compensate for phase slippage. Such is the case of anadult and child walking together at the same speed inspite of differences in their individual ’natural’ speeds.Even if we were able to provide a fully operationaldescription, in many natural cases we would tend tointerpret this compensating coordination as if the sys-tems involved had an ’interest’ in maintaining certaintypes of interaction. Something that, from availabledescriptions, Walter did not find in the behavior ofElmer and Elsie.

3 ACOUSTIC COUPLING

The use of sound is conspicuous in the animal worldwhere it is associated with a variety of behaviors, par-ticularly, but not exclusively, with social behaviors.The following list describes some of the relevant phys-ical characteristics of interactions that rely on an audi-tory channel. In general, these features should betaken as givens whenever such interactions are pres-ent.

Finite locality and directionality. Sound intensitydecays with the square of the distance to the sourceand it does not linger after it has been produced. It isalso affected by other factors like wind direction andspeed as well as the acoustics and filtering characteris-tics of the environment. Perception of sound is there-fore a reliable measure of proximity at the moment ofperception. Due to this feature the most basic behav-iors relying on (voluntary and involuntary) produc-tion of sounds are related to localization functions

(detection of predator/prey or potential mates, etc.).Localizability. Binaural perception allows for spa-

tial discrimination of the sound source. The mecha-nisms involved are varied, but rely mainly on tempo-ral and intensity differences between the sound per-ceived in each ear. Differences in time of arrival of anacoustic signal can be used to pinpoint its source if theduration is short. For continuous tones, this mecha-

nism is only effective at low frequencies (less than1400 Hz in humans), since it relies on a discrimina-tion of the wave phase (see Kandel, Schwartz, &

Jessell, 1991; Rozenweig, 1954; King & Carlile,1995). For higher frequencies this informationbecomes ambiguous as more than one cycle may occurwithin the distance that separates the ears. Another

mechanism provides discrimination based on differ-ences of intensities between the sound perceived by

each ear. Here, the actual difference due to intensitydecay of the sound wave is not as important as theshadowing effects of the relative angular position ofthe head with respect to the source. For short wave-

lengths the head casts a considerable shadow in thetravelling sound waves. In this case, differences in

intensity are much more accentuated if the bodycomes between the source and one of the ears. In

humans this difference can reach up to 20 dB for a

continuous tone of 6000 Hz (Feddersen, Sandel, Teas,& Jeffress, 1957). This mechanism facilitates activediscrimination involving movement of the body aswas first observed by Venturi’s experiments in the1790’s (see Rozenweig, 1961)5.

Sound affects many individuals at the same time.Although sound production can be directed, in thegeneral case sound is broadcast within its local range,and can affect more that one individual organism.Acoustic signals necessarily influence the originatorunless specific mechanisms prevent this from happen-ing (e.g., synchronized sensory inhibition in bats dur-ing emission periods in echolocation). The role of thislatter feature must not be downplayed. A discrimina-tion between externally and internally generatedsound (when necessary) poses the nontrivial problemof distinguishing between ’self’ and ’non-sel£’

Sound is continuous. Another feature that should be

considered as a given in acoustic interactions is the

fact that sound signals are inherently continuous,although they can be made discrete by controlling thetime structure of their production. In combinationwith the above, this feature introduces the problem ofhow interactions are structured temporally and withrespect to the number of participants to avoid inter-ference between simultaneous productions. One toone interaction and turn-taking patterns require a cer-tain degree of behavioral coordination, which, in

some cases, may result from acoustic interaction itself,but they may also involve different sorts of physicalcoupling such as body movements, touch, direction ofgaze, etc. Purely gestural interactions, in contrast, maytake place with a certain degree of simultaneity.

So far, auditory interactions have not received theattention they deserve, especially from those in theadaptive behavior community engaged in the study ofsocial behavior. For instance, many studies concernedwith the evolution of communication (Di Paolo,1997; MacLennan & Burghardt, 1994; Werner &

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Dyer, 1991, and others) already assume discreteness,turn-taking or some other structured regulation ofparticipation as the basic substrate upon which com-municative behaviors evolve. However, to be fair,none of these models is aimed at addressing the con-tinuous/discrete transition or the problem of how par-ticipants structure a pattern of interaction in time.Another common assumption is the one-to-one

nature of interaction which, as we have seen, is not a

given in the physical properties of the sound channel.Some of these assumptions have been also criticizedby Saunders and Pollack (1996). They present a

model of communication over continuous channelswhere many emitters can affect at the same time a

given agent in varying degree depending on the corre-sponding distances. The physical features of their sig-nalling channels are inspired by acoustic interaction,however they explicitly exclude the effects of self-stim-ulation and its associated problems.

At this stage, our model does not intend to address

all these issues. For instance, we will address the issueof self-stimulation over a continuous channel, but wewill restrict ourselves to pairwise interactions which isin itself a severe limitation. The motive for this restric-

tion, apart from some technical difficulties, is the (rea-sonable but not entirely justified) suspicion that thiswill be a useful preliminary step for understandingmore complex models with many agents interactingsimultaneously.

4 AN EXAMPLE OF COORDINATIONTHROUGH ACOUSTIC INTERACTIONS

In order to illustrate the concepts introduced in the

preceding sections we will briefly describe a naturalcase of social coordination and structural congruencevia an acoustic channel~.

In many monogamous species of tropical birds,singing is not limited to the male but both male andfemale sing together, in some cases performingantiphonal duets, i.e., alternation of different note

patterns (Farabaugh, 1982)7. Antiphonal duetting hasbeen studied in a number of East African species, par-ticularly in certain shrikes (Laniarius) (Thorpe, 1972;Hooker & Hooker, 1969; Wickler & Seibt, 1979).One of these species, the bou-bou shrike (Laniariusaethiopicus) lives in dense forests and produces a flute-like sound. Duets are constituted by patterns of notes

so precisely alternated that they can be confused withthe performance of a single bird. Each bird has its ownpart and they are not interchangeable, although somerare records have been made of birds that completedtheir partner’s part when alone. Each pair has a varietyof different patterns, some of which are exclusivelytheir own. Performance of duets can serve both the

purpose of localization and demarcation of territorywithin the dense foliage as well as maintenance of thepair bond (Wickler, 1980; Wickler & Seibt, 1980).Hooker and Hooker (1969) observe that there is no

signal other than the production of the first note forthe duet to start, and that the tendency to respond canbe very strong sometimes forcing the interruption ofpreening or a response through a beakful of live food.They also report the lack of observation of periods of’practicing’ in young shrikes which suggests that theparticular features of the duetting pattern are acquiredthrough interaction within the pair.

Duetting thus serves as an example of a type ofacoustic interaction which not only requires a highdegree of coordination in itself but can also coordinateother behaviors, such as approaching. The fact thatspecific pairs of duetting birds develop a repertoirethat reflects their own particular history of interac-tions, and, partly as a consequence of this, they willpair for life, can be taken as evidence of the role ofacoustic coupling in the achievement of ontogeneticstructural congruence.

5 METHOD

The rest of the paper will describe a simulation modelwhich will help us explore some aspects of the con-cepts discussed above. Inspired by the example ofduetting birds we will introduce a simulation ofembodied agents that can interact through an acousticchannel. We mentioned that duetting in shrikes canelicit localization behavior in dense foliage. Based onthis observation we propose to study how mobileagents that cannot use visual clues can approach eachother by the exclusive use of acoustic interaction (i.e.,signal production and phonotactic behavior). As weexplained in section 3, there are some basic assump-tions in this type of coupling that have to be madefrom the start, such as continuity and locality of thesound channel.We will use continuous time recurrent neural net-

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works as the internal architecture of the agents sincewe want our agents to produce behaviors that are con-tinuous in time and this type of network has provenadequate for generating such behaviors. In the spirit ofreducing the initial set of assumptions we will notbuild the agents directly, although we will specify cer-tain parameters (such as body size) as constant and

given8. An evolutionary search algorithm will be usedto explore the space of possible structures.A word must be said about the use of a genetic

algorithm (GA) in the context of this work. Since weare not concerned with providing an evolutionary sce-nario wherein the behaviors under study are a plausi-ble outcome, we will restrict our application of evolu-tionary techniques purely to the task of searching acomplex design space. Therefore, we will not deriveany conclusions about the likelihood of evolutionaryhistories that may lead to such behaviors. Examples ofnatural organisms that interact through an acousticchannel are sufficiently abundant to provide evidencethat such cases are not evolutionarily implausible.Instead, plausibility restrictions are imposed on theconstraints that provide the context of the searchprocess both in the form of the physical laws fed intoour model, and in the form of performance evaluatorsfor viable structures and behaviors.

It is fair, then, to inquire about the reasons forusing a GA instead of other equally efficient searchtechniques. Given the number of successful cases

where this method has been applied in recent yearsboth in simulated agents and actual robots, and at theinterface between the two (see Beer & Gallagher,1992; Harvey, Husbands, Cliff, Thompson, & Jakobi,1997; Jakobi, 1997, and others), one reason for usinga GA may be attributed simply to its proven adequa-cy for similar search tasks.

The study of the resulting behaviors will followmore traditional techniques of observation and analy-sis of interaction patterns and internal dynamics. Wewill also use perturbation and disruption of normalmodes of behavior in order to try to understand howsuch behavior is integrated.

6 THE MODEL

6.1 Sound

Sound is modelled as an instantaneous, additive field

of single frequency with time-varying intensity whichdecreases with the square of the distance from the

source. At this stage we will explicitly ignore effects oftime-delays and differences in frequencies of soundproduction, (i.e., no Doppler effect, differential filter-ing, etc.). This coarseness of modelling will fit with

the mechanism for spatial discrimination allowed inthe model and described below.

6.2 Bodies

Each agent is modelled as a circular body of radiusRo = 4 with two diametrically opposed motors andtwo sound sensors symmetrically placed at 45 degreesto the motors (see figure 2). The position of the sen-sors was chosen in order to introduce a back/front

asymmetry (although which is which is not specified)because we want to be able to evaluate angular effects,and coordination of physical orientation. A soundorgan is located at the center of the body, and regu-lates the intensity of the sound produced by the agent.The motors can drive the agent backwards and for-wards in a 2-D unstructured and unlimited arena. Inthis simple model, we may think of the agents as arigid body, small in size and having a very small mass,so that the motor output is the tangential velocity atthe point of the body where the motor is located. Thetranslational movement of the whole agent is calculat-ed using the velocity of its center of mass (the vectori-al average of the motor velocities), and the rotationalmovement by calculating the angular speed (the dif-ference of the tangential velocities divided by the bodydiameter). There is no inertial resistance to eitherform of movement.

Agents move freely in the arena except when theycollide with each other. Collisions are modelled as

point elastic, i.e., no energy loss and no effect in the

angular velocity of the bodies. While undergoing acollision, an agent moves in a direction which may notbe the one specified by its motor output, but whichcorresponds to a displacement that conserves themomentum of the whole system. The bodies of both

agents are taken as identical so that the result of anelastic collision is the instantaneous ’exchange’ of thevelocity vectors at the center of mass. However, due tothe lack of inertia, agents recover control of theirmovement immediately after the collision. The bodycircumference is taken as frictionless so that the angu-

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Figure 2. Body of agents and paths of acoustic signals.

lar velocities do not change during collisions.9Since the task that the agents must perform

involves some sort of spatial discrimination this mustbe provided by the relative activity of the sensors.These are physically separated so that in general theiractivity will be influenced by different external inten-sities, however such a difference provides poor dis-crimination especially if background noise is added. Anatural

mechanism, as we mentioned in section 3, involvesthe attenuation of intensity as high-frequency sound isshadowed by the body. The degree of attenuation islinked to the angular position and movement of theagent except in the case of sound produced by itself.This ’self-shadowing’ mechanism is modelled as a lin-ear attenuation without refraction proportional to thedistance travelled by the signal within the body, Dfh.This distance is given by:

where Dfen is the distance between the source and thesensor, and D is the distance between the source andthe center of the body. If A z 1, there is a direct linebetween source and sensor, and so Dfh = 0, (for A =1 1the sensor, the center of the body and the externalsource form a right triangle). The maximum value ofDfh is given when the sensor is directly opposed to theexternal source (Dfh = 2 Ro). The attenuated signal iscalculated by first calculating the intensity of the sig-nal at the position of the sensor in the usual way (i.e.,

applying the inverse square law without attenuation)and then multiplying by an attenuating factor whichgoes linearly from 1 when Dsh = 0 to 0.1 1 when

Dsh = 2 Ro. The process is repeated for the other sen-sor.

The agent’s controller is composed of a network offour dynamic inter-neurons and an arrangement ofsensors and effectors each one controlled by one neu-ron. The inter-neuron network is fully connected(including self-connections). Additionally, each inter-neuron receives one incoming synapse from each sen-sory node (of which there are only one for each audi-tory sensor) and each effector node (one for eachmotor, one for signal production and two gain regula-tors as detailed below) receives one incoming synapsefrom each inter-neuron. There are no direct connec-tions between sensors and effectors. This kind of

dynamical neural networks can serve as an adequatebasis for a fully embodied operationally closed mech-anism, and so they are a good tool for studying adap-tive behavior in simple autonomous agents, as somesuccessful cases have shown (Beer & Gallagher, 1992;Beer, 1996, and others). This is especially so whentime constraints become an essential part of adapta-tion. Inter-neurons and effector neurons obey the fol-lowing law: ,

and sensory neurons obey:

where, using terms derived from an analogy with realneurons, yi represents the cell potential, tl the decayconstant, bt the bias, z, the firing frequency, wl} the

strength of synaptic connection from node i to node jand I, the degree of sensory perturbation on the sen-sory node (modelled here as an incoming current).

In some models, sensors can be directly regulatedby their participation in the network dynamics (i.e.,by incoming synapses). We chose not to model directsynapses from the inter-neuron network into the sen-

sory neurons and instead we added an effector that

directly regulates the sensory gain in a multiplicativeway. Such regulation allows the agent to have the pos-sibility of extra control on sensory activity. The gain of

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effectors can be regulated as well. In all cases present-ed here we have used only two regulating neurons, onefor the gain of both auditory sensors (in a symmetricway), and another one for the gain of the sound pro-duction organ. In each sensor a transduction stepoccurs which transforms external stimuli into a degreeof perturbation (incoming current). Analogously foreffectors, a transduction step transforms the neuronfiring frequency into motor output. These transduc-tion steps are simply modelled as linear scalings (i.e., amultiplication of the firing rate by a gain). In sensorsor effectors with regulated gain the activation of theregulating neuron defines in each time step the scalingvalue by transforming linearly its own firing rate

(between 0 and 1) into the gain value (see next sectionfor ranges).

In order to constrain the production of sound to arealistic behavior we allow neurons to ’burn up’ if thecell potential exceeds certain limits due to intensestimulation. In sensory neurons this may happen inthe presence of intense sounds. In real auditory sys-tems the destruction of hair cells occurs for mechani-cal reasons and not due to intense incoming currentsinto the nerve cells. This is the reason for stressing thatthe meaning of Ii in this model should be taken as thedegree of perturbation or stimulation to the sensorycell and not necessarily as a literal current. The result-ing neuronal structures can be seen as approachingnatural cases where viable behavioral trajectories arecharacterized by a certain equilibrium between theautonomy of the nervous system and the autonomy ofthe individual cells. This mechanism also providesadditional significance to the sort of interactions thatan autonomous agent may engage in. Evolved agentsshould be expected to ’take care’ regarding the inten-sity of their own sound production and/or use theirsensory gain regulation accordingly.

6.3 Genetic Algorithm

A form of rank based selection genetic algorithm wasused as a search technique with a fixed population of90 agents evolving for up to 1000 generations, (after afew hundred generations highly fit individuals

evolved). Each agent was selected an average of tentimes to play with a different agent in the populationwhich was introduced in the arena at a random timeafter the first one. This delay is introduced in order to

to avoid cases where agents undergo similar dynamicsin an artifactual way simply because they start theiroperation at the same instant and from similar initialconditions 10. The second agent was placed at a ran-dom distance no smaller that 50 units from the cur-rent position of the first agent. The initial state of theagents was reset at the start of each trial; the cell

potential of each neuron y, was set to a randomly cho-sen small value taken uniformly from the interval

[-0.1,0.1].Fitness values were averaged over all the trials.

Fitness was allocated in terms of how much the agentshave approached each other at the end of the run,(FA = 1 - Dpma/ D1nitlaJ, and what proportion of theinteraction time they have spent within a distance of4 body radii of each other (FD) Additionally, theweighted sum of these proportions was modulated bya mild exponential term that decreases with the inte-grated energy used. This was done in order to com-pensate for the lack of an adequate model of energyconsumption. Agents making excessive use of motorswere penalized very mildly. The individual fitness Ffor a given trial (usually lasting 200 time steps 11) canbe expressed as:

where ap 0.25 and aa = 0.75 are the weighting factorsfor the approaching and maintenance of proximitytasks respectively, ae = 0.005 scales the modulation ofthe exponential and VR and VL are the translationalspeed of the right and left motors respectively. A finalfactor affecting fitness is cell death (see above). If atthe end of the trial run an agent has burnt up one ofits sensory or effector neurons, its total fitness in thatrun is reduced to zero.

Numerical integration of the model was doneusing the Euler method. This is a second ordermethod and therefore not very accurate, however it isfast enough to study many evolutionary runs. Tocompensate for the lack of accuracy the integrationstep was chosen in such a way that similar results wereobtained by using an order four Runge-Kuttamethod 12 with a time step of half the minimum neu-ronal decay constant. The resulting integration stepsfor the Euler method used was 0.1 (compare withdecay constants below).

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All network parameters (weights, gains and biases)were encoded in a real-valued vector of fixed dimen-sion. Each component specified a parameter by avalue in the interval [0,1 ] , (later scaled linearly to theappropriate interval). Transduction gains were chosenfrom the interval [0.05,10], biases from [-3,3],weights from [-8,8] and decay constants from [0.4,2].An agent with N inter-neurons and NSE sensors/effec-tors would have a genome size of (N + NSE) (N + 2) +NSE. Symmetry between left and right was enforcedonly for biases and gains but not for weights, and assome of the gain parameters were directly regulated bythe agent the resulting genome size was less than theabove quantity.

After ranking the population according to fitnessthe next generation is built by making 2 copies ofeach individual in the top third of the current popu-lation and one copy of each individual in the middlethird. No crossover operator was used, and mutationconsisted in perturbing the genome vector G with

probability p= 0.005 in a random direction by addinga normalized vector p multiplied by a distance m cho-sen uniformly from the interval [0,1 ] : G - G + mp.

Uniform noise was added to all the transduction

steps affecting sensors and effectors, (range = 0.1,mean = 0 or 0.05 if the transduction implies a non-negative value). These values of noise are also scaledby the gain of the corresponding sensor/effector.

7 RESULTS

Highly fit agents evolved reliably after a few hundredgenerations. About 16 different evolutionary searcheswere run. In 11 of them we observed a same qualita-tive form of behavioral strategy with small quantita-tive variations. With less frequency other behavioralstrategies were also observed but were not studiedthoroughly. We found the most frequent strategy tobe interesting enough for a detailed examination. Thereported results correspond to a single instance of thisstrategy, but the same conclusions apply in all 11 1

instances where the same behaviors were observed.

7.1 Approaching behavior

Agents successfully approach each other when two ofthem are in the same arena (figure 3 shows an exam-ple of the trajectories performed by the agents, and

figure 4 shows the distance between them as a func-tion of time). The structure of the evolved neural net-work can be seen in figure 5. Only 2 active inter-neu-rons are ’used’ by the agents; the other two have a con-stant activation of 1 or 0 (not shown). Examination ofthe sensory activation shows that the signal perceivedby one agent at the moment when the other one is .placed in the arena is very faint in comparison withthe agent’s own signal production, and even in com-parison with noise levels. Agents engage in a mode ofsearch behavior that relies on the fact that self-shad-

owing is a mechanism that can be exploited activelyby movement with a strong angular component, (fig-ure 3). This helps to discriminate external soundssince perception of an agent’s own signal does notdepend on its orientation. (Notice also that agentsplace their sensors ’on the back’ with respect to thedirection of movement.) Sensors act as leaky integra-tors and connect differentially to the inter-neuronswith similar absolute weights (figure 5, values not

shown), which means that the basic strategy wouldseem to involve rotation while moving, integration ofsensed intensities, and evaluation of the differencebetween left and right sensors (i.e., subtraction of owncontribution to sensed sound). This is an efficient wayof discriminating faint external sources.

However, this is not entirely right. We observe that

Figure 3. Trajectories of approaching agents. The second agentis introduced in the arena at t 10.

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Figure 4. Distance between agents as a function of time corre-sponding to run shown in figure 3.

Figure 5. Neuronal structure. NO and N1 : active inter-neu-rons, MR and ML: motors right and left, SR and SL: sensorsright and left, SenG: sensory gain regulation, SIG amplitudeof emitted sound, SigG: regulation for sound effector.

self-stimulation is also integrated into the productionof movement, as is evident from the fact that if wereduce progressively the capacity to hear their ownproduction, the behavior of the agents degeneratesvery rapidly into a rotation on the spot. Perturbationcan be done by altering the degree of self-stimulationin absolute terms (multiplying the perceived intensityby a factor between 0 and 1) or by introducing delaysbetween the agent’s own sound production and per-ception. We can conclude that the agents are not

merely acting on external cues as was suggested in theprevious paragraph, but the ability to hear themselvesis also integrated into the rest of the behavior. Fromanother point of view, this is also evidence that a func-tional characterization of signalling behavior as purelyconveying information of position, or even of changesof position, is not possible, nor is it possible to decom-pose movement into active sensing and approaching.

Figure 6 shows the signal produced and the regu-lated value of the sensory gain for an agent on its own.Figure 7 shows the same for an agent in interactionwith another agent. Figures 8 and 9 show respectivelythe corresponding power spectra’3. As would be

expected from the fact that sensors can ’burn up’ dueto intense activation, when the agent is emitting anintense signal sensory gain is reduced. We alsoobserve that signalling behavior has a marked rhythmwhen agents are interacting. ~Xlhat is the origin of thisrhythm? It cannot rely entirely upon internal mecha-nisms since it does not appear when the agent is byitself (figures 6 and 8), although the corresponding

Figure 6. Emitted signal (full line) and sensory gain (dashedline) for an agent by itself.

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Figure 7. Emitted signal (full line) and sensory gain (dashedline) for an agent that is interacting.

Figure 8. Power spectrum for emitted signal of an agent byitself.

z

power spectrum indicates the presence of other fre-

quencies.From the analysis of frequency spectra, we con-

clude that rhythm in signalling behavior is directlylinked to angular behavior. We reach this conclusionby comparing for one of the agents the frequency ofits signal with the frequency of the variation in angu-lar orientation relative to the line connecting bothagents, and, finally with the frequency obtained from

Figure 9. Power spectrum for emitted signal of an agent thatis interacting.

the difference of sound intensity at the position of thesensors, (figure 10)’4. All three spectra show a sharppeak for the same value of frequency.

Additional evidence of a connection between sig-nalling and angular movement is obtained from theobservation that, if a source of sound is placed at afixed distance and angular position with respect to amoving agent (i.e., movement has no influence on

Figure 10. Power spectra for signal (solid line), agent orienta-tion relative to the other agent’s position (dotted line) and dif-ference of intensity at sensor position (dashed line).

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Figure 11. Trajectory for an agent with a constant sourceplaced at a fixed position relative to the agent. The source isrepresented by a small circle.

Figure 12. Signal emitted by the agent for constant source.Run corresponds to figure 11.

sensed intensities), all rhythm in signalling behaviordisappears. This is shown in figures 11 and 12.

The previous evidence seems to suggest that

rhythmic signals originate entirely as a consequence ofthe angular movement of the agents. However, wemust be cautious with this conclusion since, as wesaid above, movement is not independent of signalproduction. From the observations made, it could aswell be argued that angular movement depends onrhythmic signalling and that rhythm in signals origi-nates somehow within the dynamics of interaction.The first explanation seems more plausible but wehave not been able to rule out the second one so far.This difficulty in itself points to the fact that behavioris quite integrated and makes functional decomposi-tion difficult. It gets harder if we consider the globalpicture of both agents in interaction as will be shownnext.

7.2 Entrainment, Turn-taking andStructural Congruence

Since patterns of joint activity are relevant for under-standing the behavior of individual agents we nowturn to the analysis of these patterns in cases of pro-longed interactions. Figure 13 shows the signallingbehavior of two interacting agents after havingapproached one another. Figure 14 shows the corre-sponding power spectra. We observe that, for longperiods, signals are phase-locked at some value nearperfect anti-phase. Although agents are similar, theyare not identical, and their ’natural’ power spectra(i.e., when acting on their own) are indeed different.This suggests that the observed entrainment mustsomehow be related to the coupling between theagents. Figure 13 (see also figure 19) shows that thisentrainment can be lost momentarily only to be

regained later. This phenomenon is similar to what wehave called relative coordination: the tendency toactively correct for phase-randomizing factors such asfluctuations or differences in natural behaviors or

physical properties.The anti-phase locking of signals can be interpret-

ed as a basic form of turn-taking. Since agents have noother way of knowing of the presence of the other butthrough acoustic coupling an efficient way of doingthis is by alternating the production of signals and so

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Figure 13. Signalling behavior of interacting agents (a solidline is used for one agent and a dashed line for the other).

Figure 14. Power spectra for signalling behavior, (a solid lineis used for one agent and a dashed line for the other).

minimizing overlap.Movement during periods of coordination is also

highly organized (figure 15). Agents perform almostperfectly synchronized ’dancing’ patterns alternatingtheir positions on the inside and outside of a curvedtrajectory while varying their angle of orientation inan almost identical manner. Agents collide slightlywith each other on certain occasions, and this alsoseems to be an ordered phenomenon (compare thesmooth portions of trajectory on the top of figure 15

Figure 15. Motion of agents during period of coordination.Agents are shown at two time steps. Collisions occur at thebottom sections of the cycloidal trajectory.

where the agents are not in contact with the portionsat the bottom, collisions occur only in the latter).We propose that the highly ordered patterns

shown by agents both in their movement and sig-nalling behavior are evidence of the achievement ofdynamic structural congruence through acoustic cou-pling. Coordination is achieved jointly by the agentsonce they have undergone specific, mutually per-turbed, transients in their respective dynamics. Asmuch as coordination cannot be reduced to thebehavior of a single agent, the specific ordered pat-terns we observe during coordination cannot be

explained by the activity of individual agents if theyare indeed the consequence of the structural congru-ence attained between them. In principle this mayseem strange, after all coordination could be con-ceived as the individual adaptation to the behavior ofone’s partner instead of a co-adaptation.

In order to prove that coordination in these agentsdoes not originate from an individual capacity foradapting we will examine how agents behave in thepresence of beacons that produce sound signals. Weplace a beacon in the arena in a fixed position, andone agent at a random angle, orientation and distancefrom it. Beacons can produce a variety of signals. Inall cases agents approach the beacon successfully buttheir signalling behavior differs from the case of twointeracting agents. Figure 16 shows this signallingbehavior when the beacon produces a periodic signalwith a period chosen to be equal to the one shown by

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coordinating agents. If the agent had an individualcapacity to adapt its signalling behavior to the soundperceived we would expect it to show a similar sig-nalling behavior in the presence of the beacon. It doesnot happen. It can be argued that the frequency usedby the beacon is not exactly right. A long simulationin which we perform a slow ’frequency sweep’ in thebeacon’s signal for the whole range of frequencies ofinterest shows no difference in the signalling behaviorof the agent. The possibility still remains that the par-ticular distribution of frequencies may matter. In

order to test this we perform the following experi-ment. A normal simulation with agents in interactionwas run, and the signalling behavior of one of theagents during coordination was saved. The ’taped’ sig-nal was broadcast from the beacon to the other agentnow by itself. The result (see figure 17) shows thatphase locking does not occur and signals are not evenrhythmic.

Figure 16. Signalling behavior in presence of periodic beacon.

All this evidence shows how relevant is the pres-ence of a period of mutual induction of changes in thedynamics of each agent. Beacons are completely non-plastic, and therefore their ’behavior’ cannot be influ-enced by the approaching agent. The lack of a tran-sient period of mutual triggering of changes of stateresults in no structural congruence, and consequentlyin no entrainment.

So far we have looked only at external manifesta-tions of structural congruence. Figure 18 presents fur-

Figure 17. Signalling behavior in presence of imitative beacon.

ther evidence, this time from internal dynamics. Inthis figure we observe the embedded time-delayedplots for the activation of the same inter-neuron intwo agents under different circumstances. The two

plots at the bottom correspond to the agents acting ontheir own, i.e., no coupling. Here we observe againthat although their structures are similar (both neuralnetworks present the same architecture shown in fig-ure 5), they are not identical (parameter values differslightly) and, consequently, their dynamics have dif-ferent attractors. The top four plots show the samevariable for the interacting agents. The two plots atthe top are taken from a period of coordination. Wecan appreciate the striking similarity between the twoattractors as well as the difference between them andthe natural dynamics. The plots at the center of thefigure correspond to agents interacting but during aperiod when coordination has been lost. These plotsalso show an interesting qualitative difference withrespect to the other cases. Agents do not return totheir ’natural’ dynamics when coordination is lost butto a different, uncoordinated state from which it is

possible for coordination to be regained, and whichsuggests that the structure of each agent has changedas a consequence of interaction.

In each case we can calculate the time correlation

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Figure 18. Time-delayed attractor dynamics in the same inter-neuron for two agents (A1 and A2) in different situations. Theselected inter-neuron was chosen for clarity in the plots.

in neuron activation between the agents:where Cov( x, y) is the covariance between variables xand y, S(x) the standard deviation of x and Nazi is thevector composed by the time series of activation val-ues for the inter-neuron in agent i in the period ofinterest. In the case of coordination p = -0.8443 ,for the case of interaction but no coordination

p = -0.3750 , and for the non-interacting agents&dquo; sp = -0.0403. A strong anti-correlation between

coordinating agents is in accordance with their sig-nalling behavior.

The transition from a coordinated toward an un-coordinated state can be induced both by fluctuations(noise) or by an instability due to internal differencesin the respective dynamics. However, the transitionfrom an un-coordinated state into coordination can

only be understood in the presence of an organizingcoupling between the two systems since fluctuations

Figure 19. Achievement, loss and regaining of coordination.Distance, relative orientation, signals, and estimation of rela-tive signal phase as functions of time.

will tend, on average, towards the loss of entrainment.In figure 19 we can see how these transitions occurand how different variables are affected. The four

plots are taken from a simulation run with the agentsinteracting. The plot at the top shows the distancebetween the agents. Coordination periods are con-spicuous since they present a much smaller range ofvariation in distance. During these periods agents per-form the ordered patterns of movement shown in fig-ure 15. These regions are marked &dquo;b&dquo; and &dquo;d&dquo;. In con-

trast, periods of no coordination (regions &dquo;a&dquo;, &dquo;c&dquo; and

&dquo;e&dquo;) show greater variation in distance. The secondplot shows the relative angular orientation betweenthe agents which remains near zero degrees duringcoordination and is uncorrelated the rest of the time.The third plot shows signalling behavior, and the plotat the bottom shows a continuous estimation of therelative phase between signals, (the horizontal lines

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mark 180 and -180 degrees) 16- . During coordinationand even a bit before (compare the beginning ofregion &dquo;d&dquo; in the top two plots with the same area inthe other plots), signals are produced near the anti-phase region. The fact that this correlation is mani-fested before the attainment of minimum distance

suggests that signal coordination may come first, andcoordination of movement may be its consequence.This makes sense if we think that signals can begin tobe coordinated from a certain distance greater thanthe minimum.

8 DISCUSSION

Our basic model shows some interesting phenomenalike turn-taking and organized movement arisingfrom basic features of the physical nature of acousticcoupling between embodied agents. In interpretinghow these phenomena arise we have made use of the-oretical concepts concerning social behavior under asystemic, non-functional perspective as well as otherconcepts taken from the dynamics of coupled oscilla-tors. We think that much is to be gained from thisperspective and that we have barely started to exploreits potential.

In our model agents interact acoustically, andthrough this interaction they mutually coordinatetheir patterns of movement, and they structure theiracoustic coupling into a form of alternated produc-tion that resembles turn-taking. It is not inconceiv-

able that this result could have been different, (forinstance, fairly constant signalling behavior, totallydecoupled from movement and perception). Initiallywe may be surprised that agents organize their inter-actions in the way they do but we have seen that thereis nothing magical about this organization if we ana-lyze the process operationally.

However, providing a thorough operational expla-nation can be hard. Apart from the potential com-plexity of such an account, one of the main difficul-ties lies in the fact that many operational aspects ofthe system act concurrently, so it is not always possi-ble to speak in terms of causality, as we noticed

implicitly in the discussion on the origin of rhythm insignal patterns. Nevertheless, we can formulate a ten-tative operational route to understanding what goeson in our model. We start from the physical aspects ofsound production and perception as operational

assumptions. Embodied agents actively exploit self-shadowing as a localization mechanism by favoringcycloidal movement as a search strategy. Angularmovement introduces rhythm in perception which isalso manifested in signalling behavior. Rhythmicacoustic signallers become entrained through mutualperturbation for the same reasons other coupled oscil-lators do under a variety of circumstances, even in thepresence of fluctuations and individual differences.

Finally, coherent signalling behavior drives patterns ofmovement into an ordered state.

If the best we can do is to give an incomplete oper-ational account of what happens in an artificial worldone may justifialbly ask what is the scientific value ofour methodology. Although, as discussed in section 5,our model says nothing about the evolutionaryaspects of social coordination, we can consider some

implications of our analysis as to how certain evolu-tionary questions could be framed.

The study of social behavior and its relevance tothe evolution and development of human capabilitieshas often been approached from a purely functionalangle. We repeat that there is nothing wrong with thisbut that functional considerations should be ground-ed on what we know about the operation (at differentlevels) of the systems concerned. A functional expla-nation can be derived from the abbreviation of certainnomic relationships. But without a sufficient explo-ration of what those relationships might be, we runthe risk of missing alternative ways of building func-tional links as well as the risk of building functionallinks that disregard operational constraints. For

instance, the received wisdom has been in recent yearsthat social life is important for understanding the evo-lution of human intelligence because social life can bevery complex, and our ancestors needed to be goodpredictors of the outcomes of social interactions. Inthis theory there is a separation of social life and indi-vidual capabilities, and a functional bridge is builtbetween them. This distinction can serve its purpose,as long as it does not become reified into the opera-tion of the various systems involved. Because, at the

operational level, even in our simple model the artifi-ciality of this separation becomes evident. In particu-lar, we have found that the use of the same channel forself-stimulation and social interaction makes it diffi-cult to decompose the behaviors of an agent intosocial and non-social categories. This shows that there

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can be direct operational links between what we see aspurely social and what we see as purely individual.A related aspect that shows how the divide

between social and individual capabilities tends topermeate into unnecessary operational requirementsis the re-discovered fact that behaviors arising fromco-adaptation do not necessarily imply an individualcapability for performing similar tasks. We saw this inour model when we demonstrated that agents are

incapable of entering into coherent signalling behav-ior with beacons that produce ’artificial’ signals, butthey can do it with other agents. The successful per-formance of certain behaviors need not be within therealm of competence of the individual organism ifthese tasks are performed socially in a coordinatedfashion, a fact that should serve as a warning whenev-er we try to extrapolate operational features (how anorganism should work) from functional interpreta-tions of observed evidence (what it does) ~~.

To show the potential of our methodology we willfinish with a brief comment about how our modelcould be improved and what else could be studiedwith it. In section 2 we briefly touched upon someideas about how social forms of learning could beunderstood from a systemic perspective as a form ofdirected structural change due to the achievement ofstructural congruence between unevenly plasticorganisms. The feasibility of this hypothesis could beeasily tested by extending our model to include richerforms of plastic change, some of which become grad-ually ’solidified’ during the lifetime of an agent. Somecases of imitative learning could possibly be explainedin these terms. But the idea is more powerful still, asit could also explain other phenomena such as thebonding observed between duetting pairs in

Laniarius. Once some of the structural changesundergone because of mutual perturbation havebecome ’frozen’ in ways that favor following encoun-ters with the same individual(s), social affinity is theunsurprising outcome.

NOTES

1An interesting line of research dealing with acousticinteractions using robots is the modelling of thebehavior of female crickets in the presence of songsproduced by males, (see for instance Lund, Webb,& Hallam, 1997). So far this work has only been

focused on reproducing the behavior of females inresponding to songs (produced by real crickets), sothat self-stimulation did not constitute a problem.

2Consider the nervous system as a candidate opera-tionally closed system. If we want a dog to performa trick, and we imagine that this can be achieved byinserting electric currents in specific locations of itsbrain, in that case the dog’s nervous system willcease to act as operationally closed.

3The word "structural" originates in a distinctionbetween a system’s organization and its physicalcomposite realization or structure (if we are dealingwith a physical system). This is how we will use theterm in this paper; in particular, when speaking ofan organism’s or an agent’s structure we will bereferring to the set of components that constitutethe whole of its body including nervous system orcontroller. At each moment, the state of the systemis completely determined by a previous state and byits structure. As physical systems, interactions

between two autonomous entities occur betweentheir structures and not their organizations.However, the term would not be as clearly definedif we were dealing with non-physical systems thatwe presume autonomous (say, a financial market).

4Sometimes also called "orientation". However, wewill reserve this term to refer in our model to the

angular orientation of the agents.

5More specific mechanisms, such as the auditoryapparatus of the cricket, combine frequency dis-crimination with enhancement of intensity differ-ence by means of a particular set of delays and fil-ters, (Lund et al., 1997, and literature cited there-in).

6In humans such coordination is apparent. There ismuch evidence of coordination between speech andbody movements of both speaker and listener, bothin adults and infants (Condon & Sander, 1974;Condon, 1979; port, Tajima, & Cummins, 1998).However, a different example may help to put cer-tain distance from specific human behavior andavoid issues that, at this stage, we are not ready toaddress using the present methodology.

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7Duetting has also been observed in many monoga-mous primate species. See (Haimoff, 1986) for adescription of the evolutionary convergence ofmany aspects of duetting in primates of differenttaxa.

8An exploration of the influence of each of the manyparameters of our model is not our aim. We will

concentrate on analyzing some instances of viablebehaviors under the constraints we impose. Thesignificance for natural cases will be given by thevalidity of the choices we make.

9In the simulations reported here we have not usedtouch sensors that activate when the agents collide.The main reason for this is that we want to explorelong-term behavior, even after the agents have suc-cessfully approached one another. We have observedin simulations that the introduction of touch sen-sors can have as a consequence the termination of

(translational) movement in the agents after the firstcollision (i.e., agents find each other, collide andthen rotate on the spot in nearby positions).

10It must be remembered that after a few generationsa large proportion of the population would haveconverged to similar structures.

11This number is determined by the choice of otherparameters, such as motor gain and initial distanceof separation, in order to make the approaching taskpossible.

12 See (Press, Teukolsky, Vetterling, & Flannery, 1992)for a description of these methods.

13All power spectra in these and the following figuresare calculated by first normalizing the signal to avalue between 0 and 1, then subtracting its meanvalue and calculating the square of the absolutevalue of the Fast Fourier Transform.

14Since the signal produced by the agent reaches itsown sensors symmetrically, performing this differ-ence in the value of intensity will also provide infor-mation about the angular movement of the agentrelative to the external source.

15This last value is only illustrative of the different’natural’ behavior of the agents.

16This estimation is obtained by a continuous nor-malization of the signal and its derivative to theunit circle after filtering out the noise, and then cal-culating the phase difference as a function of time.This is shown in the range between -360 and 360

degrees to aid visualiztion, i.e., the horizontal linesindicate a same phase value.

17The so-called Machiavellian intelligence hypothesis,see (Humphrey, 1976), and the collections (Byrne& Whiten, 1988; Whitten & Byrne, 1997).

18A simple relevant example is provided in (Di Paolo,1997) where state-less machines in coordination can

produce specific sequences in the presence of a con-stant environmental stimulus.

ACKNOWLEDGEMENTS

Many thanks to Phil Husbands, Inman Harvey,John Stewart, Matt Quinn and three anonymousreviewers for helpful comments on this work. Theauthor is grateful to the Consejo de InvestigacionesCientificas y Técnicas de la República Argentina and anOverseas Research Student Award (CVCP).

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ABOUT THE AUTHOR

Ezequiel A. Di Paolo

Ezequiel Di Paolo has studied Physics at the Universidad de Buenos Aires, andNuclear Engineering at the Instituto Balseiro (CNEA-Cuyo) where he received hisMSc in 1994. From 1995 to 1998 he did his doctorate on the evolution and devel-

opment of social behavior under the supervision of Phil Husbands at the School ofCognitive and Computing Sciences, University of Sussex, where he is now workingas a lecturer in Evolutionary and Adaptive Systems. His current interests includemodelling adaptation to bodily disruptions such as inversion of the visual field, evo-lutionary models on the persistence of ecological patterns, and methodologicalaspects of individual-based computational modelling.

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