Dominance interactions, spatial dynamics and ... - Semantic Scholar

‘Animals and Animats’, conference SAB96, Hemelrijk, 1

Dominance interactions, spatial dynamics and emergent reciprocity in a virtual world. Charlotte K. Hemelrijk AI Lab, Department of Computer Science, University of Zürich, Winterthurerstr 190, CH-8057 Zürich, Switzerland, Fax 0041-1-363 00 35, Email: [email protected].

In: From Animals to Animats 4: Proceedings of the Fourth International Conference on Simulation of Adaptive behavior, Cambridge, MA: The MIT Press/Bradford Books (1996), p 545-552. Eds: P. Maes, M. Mataric, J-A Meyer, J. Pollack, S. W. Wilson.


Dominance interactions, spatial dynamics and emergent reciprocity in a virtual world. Charlotte K. Hemelrijk AI Lab, Department of Computer Science, University of Zürich, Winterthurerstr 190, CH-8057 Zürich, Switzerland, Fax 0041-1-363 00 35, Email: [email protected].

Abstract In many studies on social demeanour it is overlooked how complex social behaviour may result from simple self-reinforcing interactions between entities. In this paper an individualoriented computer model is used to study whether the spatial dynamics between artificial agents and their autocatalytic interactions may result in a rank-related differentiation of social-activity profiles and ‘repayment’ of social acts. The entities are completely identical at the start of the simulation and very simple: they lack a predefined tendency to reciprocate, but are gregarious and perform interactions in which winning is self-reinforcing. They perceive the others’ capacity to win either indirectly, by refering to former experiences with partners, or directly. In this artificial world entities can be ordered according to a dominance hierarchy and a social system with a spatial structure is formed. Furthermore, entities of different rank have their own behavioural profile and patterns of reciprocation emerge. These patterns are particularly apparent in loose groups and among the simplest entities (i.e. those that perceive rank directly). These epiphenomena may also contribute to reciprocation found in real animals such as primates.

1 Introduction In studies on social behaviour it is commonly assumed that individual complexity lies at the root of intricate social interaction patterns. In primates, for instance, social complexity is attributed to their high intelligence. It is argued by many that the cognitive capacities of primates are especially manifest in the way they regulate their relationships with group-members (Byrne & Whiten, 1988). An illustrative example is coalition formation, a phenomenon documented for many primate species. Coalitions occur when a third individual C aggressively intervenes in a dominance interaction between two opponents A and B (act 2 in figure 1). C is considered to ‘oppose’ the one she attacks (A in figure 2) and to

‘support’ the other (de Waal & Luttrell, 1988) - in this case B. When on a later occasion B ‘pays back’ by helping C in a fight, reciprocation of support is said to have occurred. Reciprocation of ‘support’ was measured in macaques and chimpanzees and thought to result from keeping records of acts given and received and a motivation to pay in return; as such, it was considered as an indication for the high intelligence of these species (de Waal & Luttrell, 1988). These authors claim that chimpanzees (but not macaques) also reciprocate ‘opposition’. De Waal & Luttrell see this as evidence for the higher intelligence of these apes (compared to macaques).

A

1

B

2 C Figure 1. Schematic representation of a triadical interaction: 1) fight between A and B, next 2) C attacks A. The behaviour by C is interpreted as‘opposition’ against A and ‘support’ for B.

The terms ‘support’ and ‘opposition’ presume that the animals take a specific social context into account, which requires subtle cognitive skills. Such an anthropomorphic approach is common usage in primatology, because complex mental abilities are more easily accepted for monkeys and apes than in any other taxon and are even the main source of interest for many primatologists. The problem, however, is that the terminology already implies an interpretation and that no effort is taken to consider more parsimonious alternatives. This contrasts strongly with the view adopted by studies in ‘New Artificial Intelligence’ and ‘Artificial Life’. These have demonstrated that behaviour which looks complex and sophisticated to an observer, can often be achieved without central control or global knowledge (such as keeping records) but instead comes about by simple mechanisms (e.g. Pfeifer & Verschure, 1995). The apparent complexity is then a result of the local interaction of an agent with its environment and with other agents.

‘Animals and Animats’, conference SAB96, Hemelrijk, 3 Along the same lines, Deneubourg and Goss (1989) have shown that apparently ‘clever decisions’ in ants may emerge from simple self-reinforcing interactions. Therefore, any study trying to explain the complexity of social behaviour, including those on primates, should at the same time ask what part of it must be coded explicitly into the capacities of individuals and what part is determined by the interactions between individuals (Hemelrijk, in press). To gauge the complexity generating effects of interindividual interactions, I investigate the ‘social organisation’ of a group of simple, artificial agents by means of an individual-oriented model. By analysing the patterns that emerge, I will supply alternative parsimonious explanations that may help to look at primate behaviour from a new perspective. I will focus on aggressive interactions, dominance, coalitions, and reciprocation, since these are considered pivotal in most primate social organisations. Whereas social hierarchies are conventionally considered to result from differences between individuals in (possibly inherited) qualities (Ellis, 1994), in the approach adopted here I study dominance ranks that arise by chance and self-reinforcement. This rationale is justified by experimental results from various animal species. These experiments have demonstrated that once an individual has won an interaction (and this may initially be due to chance), this success increases the likelihood of winning again (the so-called ‘winner’ effect, see Chase et al, 1994). Using an individual-oriented model formalism, Hogeweg (1988) has shown that the ‘winner’ effect and the spatial distribution of the engaging entities (so-called SKINNIES) influence each other mutually, resulting in a spatial configuration with dominants in the centre and subordinates at the periphery. This led me to suggest that also reciprocation might result as a side-effect of dominance rank and spatial configuration (Hemelrijk, in press) in the following way: Because higher ranking agents dwell more often in the centre, they will meet others more frequently and therefore also more that are involved in a fight. This leads them to ‘support’ others in fights more often than do low-ranking ones. In turn, each agent will encounter higher ranking entities more often than lower ranking ones. Consequently, entities will more often ‘support’ higher ranking agents. According to this scenario, agents ‘support’ more often those from whom they receive ‘support’ more frequently in return (but do not necessary return the exact frequency they received) and this is exactly the definition of reciprocation at a group level (see Methods for details). Note that in this way reciprocation comes about without the need to postulate a specific motivation or capacity to ‘pay back’. The aim of this paper is to investigate the interconnections suggested above by studying in a virtual world the behaviour of simple artificial creatures that have a tendency to group. To examine the need for cognition in more detail, two ways to perceive dominance of others, differing in their cognitive complexity, will be compared. In the most simple case, agents (called Perceivers) directly perceive the capacity of winning of those they encounter.

In the more sophisticated case, entities (the so-called Estimators) assess dominance of others by recalling their last experiences with partners. Furthermore, the effects of group structure will be studied by comparing social interaction patterns in groups that vary in size and cohesiveness.

2 Methods In this section I will outline how reciprocity is defined and measured and present a description of the model.

2.1 Operationalisation of reciprocity At a group level, reciprocity can be approached in two ways, namely according to a model based on acting by one and reacting by another individual (the ‘actor-reactor’ model) or on acting and receiving by the same individual (the ‘actor-receiver’ model). In most studies the ‘actorreactor’ model is tacitly assumed. It implies that actors direct relatively more acts to those reactors that perform relatively more acts to them in return compared to what these reactors give to other actors. For instance, individual A gives most to the animal that also directs more to A in return than to any other individual in the group. Drawbacks of this model are that complete reciprocation appears impossible for an odd group size and that it is very hard to protect oneself against deception (Hemelrijk, 1990a). For instance, to make sure that the most preferred partner gives more to ego than to others, ego has to trace how often this partner directs acts to all others. In general, individuals therefore have to keep track of all acts directed among all other individuals. To collect such global information is time-consuming and requires extensive cognitive abilities. Under the ‘actor-receiver’ model, however, these problems do not arise: here, individuals give relatively more often to those from whom they receive more frequently in return. In this case, the required knowledge is much more ‘local’, since agents must tune their acts to what they receive from others, but do not have to bother about interactions among others. In addition, complete reciprocation is possible in both even and odd group sizes (Hemelrijk, 1990a). To test for ‘actor-receiver’ reciprocation among all pairs of group-members, a specially devised statistic (τKr) has been developed (Hemelrijk, 1990ab). This statistic measures the correlation between the corresponding rows of two social interaction matrices and the method reckons with the statistical dependency due to recurrent observations on the same individual (Hubert, 1987). The τKr-value for the correlation between a matrix for ‘given’ acts and ‘received‘ acts is thus a measure for the degree of reciprocation within a group.

2.2 The Model The model is individual-oriented and event-driven (see Hogeweg & Hesper 1979; Hogeweg, 1988; Villa, 1992; Judson, 1994). The modelling environment (written in object-pascal, Borland Pascal 7.0) consists of three parts:

‘Animals and Animats’, conference SAB96, Hemelrijk, 4 * the ‘world’ (toroid) with its interacting agents, Select Random Partner

Others

* its visualisation, Yes

* special entities that collect and analyse data on what happens in the ‘world’ (cf. the ‘recorders’ and ‘reporters’ of Hogeweg, 1988). The ‘world’ consists of a regular lattice of 200 by 200 square cells. Each cell can be occupied by only one entity. Conform most primate studies on reciprocation, I will confine myself to small populations of 5-10 individuals. Agents are able to move in one of eight directions. They have an angle of vision of 120 degrees and their maximum perception distance (MaxView) is 50 cells. Agents group and perform dominance interactions according to the sets of rules that will be described below.

2.2.1 Grouping rules In the primatological literature, two opposing forces affecting group stucture are postulated: on the one hand animals are attracted to one another, because being in a group provides safety. On the other hand, aggregation implies competition for resources and this drives animals apart. The forces leading to aggregation and spacing are realized in the model by the following set of rules (cf. Hogeweg, 1988; figure 1): • If an agent sees another within a critical distance (parameter PersSpace), it performs a dominance interaction with that entity. In case several agents are within PersSpace, the interaction partner is chosen at random. If the agent wins the interaction, it moves towards its opponent, otherwise it moves away. • If nobody is in its PersSpace, but an agent perceives others within a distance of NearView (eight cells), it continues to move on in its original direction. • If an agent detects others outside NearView, but within its maximum range of vision (= MaxView), it moves towards them. • If an agent does not perceive any other agent within maxView, it searches for group members by making a turn over an angle (x) at random to the right or left (= SearchAngle).

No

Yes No

DOMINANCE INTERACTION

Move On OTHERS

Ego Wins

PERSSPACE?

Ego Loses

Flee From Opponent

NEARVIEW ?

Others

Move To Other

Goto Opponent

MAXVIEW ? No Yes

TURN (Search Angle At Random To Right Or Left)

Figure 1. Flow chart for the behavioural rules of the entities

2.2.2 Perception of dominance A number of hypotheses about how dominance rank is perceived by others are entertained by various authors (Hemelrijk, in press). The most simple one is that the others’ capacity to win is directly perceived from external cues, such as pheromones in social insects. In many species, however, dominance may not be recognised externally. The capacities of others may then be estimated on the basis of an individuals’ former encounters with a partner. Such a representation asks for more ‘cognition’ and was used in Hogeweg’s SKINNIES (1988). Agents endowed with direct and estimated rank perception will be called Perceivers and Estimators respectively. The effects of both types of dominance perception will be compared in this paper.

2.2.3 Dominance interactions. Interactions between agents with direct perception of dominance ranks (i.e. Perceivers) are modelled after Hogeweg & Hesper (1983) as follows: 1. Each entity has a variable DOM (representing the capacity to win a hierarchical interaction). 2. After meeting one another in their PersSpace, entities display and observe each others DOM. Subsequent winning and losing is determined as follows by chance and values of DOM:

 DOMi 1 > RND(0,1)  wi = DOMi + DOMj  else 0

(1)

where w i is the outcome of a dominance interaction initiated by agent i (1=winning, 0=losing). In other words, if the dominance ratio of the interacting agents is larger than a random number (drawn from a uniform distribution), then agent i wins, else it loses. 3. Updating of the dominance values is done by increasing the dominance value of the winner and decreasing that of the loser:


  DOMi DOMi : = DOMi +  w i −  *STPDOM DOMi + DOMj     DOMi DOMj : = DOMj −  wi −  *STPDOM DOMi + DOMj  

for agent i. Updating for agent j is obtained by replacing DOMi,. by DOMj,. . now on, the initiation of a dominance interaction (2) From will be called ‘attack’ for short.

The consequence of this system is that it behaves as a damped positive feedback: winning by the higher ranking agent reinforces their relative DOM-values only slightly, whereas winning by the lower ranking gives rise to a relatively large change in DOM. To keep DOM values positive, their minimum value was arbitrarily put at 0.01. STPDOM is a scaling factor and set at 0.5. 4. Winning includes chasing the opponent, who responds by fleeing in the opposite direction (under a small random angle). In the case of indirect rank perception, the Estimators have to recognise others individually and to remember their personal experience with each partner. Dominance interactions are defined similarly as in the SKINNIES of Hogeweg (1988):

2.2.4. Timing regime Since paralell simulations cannot be run on most computers, a timing regime regulating the sequence of the activations, has to be included. The type of timing regime influences the results of a simulation. A biologically plausible timing regime must be locally controlled, i.e. by other entities and not by a monitor (e.g. Goss & Deneubourg, 1988). In the timing regime used here, each entity draws a random waiting time from a uniform distribution. The entity with the shortest waiting time is activated first. The decay of waiting time is the same for each entity. However, if a dominance interaction occurs within NearView of an agent, the waiting time of this agent is reduced stronger.

2.3 Experimental setup and Data collection

Both Perceivers and Estimators aggregated readily. The values of various parameters were varied to assess their effect on group formation. Especially changes in PersSpace and SearchAngle appeared to influence the cohesiveness of groups. During the runs, this could easily be observed by just looking at the screen: agents either tended to stick together or repeatedly left and joined the main group. Cohesiveness was measured quantitatively as the mean and the variance of the distance between all entities. In Figure 2 the mean and variance of distance to others are plotted against each other for different values of PersSpace and SearchAngle. Two clusters can be distinguished: the 2. If it wins, it ‘displays’ its expectancy to win as its one with low mean and variance corresponds to a case of updated relative dominance rank (=Di) and the partner cohesive grouping, the other represents loose grouping displays in return (=Dj). That is: with frequent fissioning and fusion of individuals. Also, mean and variance fluctuate less over time for cohesive DOMi,i than for dispersed groups. Since primate groups vary Di = DOMi,i + DOMi,j considerably in cohesiveness, the two classes of groups will be included as a condition in the experimental design DOMj,j described next. Dj = DOMj,j + DOMj,i Per type of entity (Perceiver, Estimator) and grouping (Cohesive, Loose) five runs were done for each of three population sizes (N = 5, 8 and 10) giving a total of 60 experiments. After stabilization of the dominance ranks 3. Winning is decided as in (1), using D i and Dj (which typically occurred around 1000*N activations), instead of DOMi and DOMj. data were collected for the next 500*N activations. Every 10*N activations the distance between agents was 4. Updating of the experiences of each of both entities calculated. Dominance interactions were continuously is done similar to (2), but involves four monitored and the following features were recorded: 1) the representations: identity of the attacker and its opponent; 2) their updated  DOMi,i   *STPDOM DOM-values and 3) cases of triadic interactions that DOMi,i : = DOMi,i +  w i − DOMi,i + DOMi,j  resemble ‘support’ and ‘opposition’ (i.e. cases in which a  third entity happened to attack one of two agents that were   DOMi,i   DOM : = DOM − w − *STPDOM involved in a fight one timestep before). 1. If an entity meets another in its PersSpace, it first consults its memory to establish whether it might win or loose a potential dominance interaction with that partner. Hereto, it performs the same dominance interaction as described in (1) and (2), but now based on the mental impressions it has of its own dominance rank and that of the other. If it looses this ‘mental battle’, it moves away. If it wins, it initiates a ‘real’ fight. Thus, unlike the Perceivers, the Estimators ‘decide’ whether or not to attack.

i,j

i,j

 

i

DOMi,i + DOMi,j 

‘Animals and Animats’, conference SAB96, Hemelrijk, 6 120

100

PersSpace 2, SearchAngle 90°

80

dispersed

60

PersSpace 4, SearchAngle 45°

40

average of mean 20

cohesive

the correlations are completely due to the interplay between dominance interactions and the spatial structure. Because lower ranked entities are more often chased away, they are directed more towards the periphery of the group and hence have less often others in their PersSpace than higher ranking ones have. This reduces their opportunity to attack and ‘support’ others.

12 10

0 0

5

10

15

20

average of variance

8 6

Figure 2. Mean and variance of distance to others averaged over 5 entities with indirect rank perceivement. Arrows indicate the transition from the starting point. Lines connect subsequent points in time.

2.4 Data analysis To establish whether higher ranking entities indeed attacked and ‘supported’ others more often, Kendall rank correlations (Siegel, 1956) were performed between dominance rank and the frequency of attack and ‘support’. To investigate whether the strength of these associations depended on population size, group type and the type of entity, the correlation coefficients were subjected to a three way analysis of variance. The degree with which group members reciprocate is expressed by τKr-values derived from the Kr matrix correlation (Hemelrijk, 1990ab). To estimate the effects of type of entity, type of grouping, population size and type of behaviour (‘support’, attack, ‘opposition’) on the degree of reciprocation, τKr-values for these four categories were compared using a four way analysis of variance.

3 Results 3.1 The emergence of dominance hierarchies and correlations with rank. A dominance hierarchy, such as shown in figure 4, developed among initially completely identical entities in all runs. Dominance rank appeared to be significantly positively associated with the frequency of attack in 73% of the runs and with ‘support’ in 40% of the runs. These results ask for a different explanation for Estimators and Perceivers. When Estimators win, they increase their expectancy to win again and therefore initiate increasingly more dominance interactions. Consequently, the number of cases in which a display is directed toward an agent already involved in a conflict itself (i.e. ‘support’) rises also. Perceivers lack a memory and always attack any other entity they encounter in their persSpace. Therefore,

4 2 0

No. of Activations

Figure 4. Changes of dominance values over time for 5 Estimators. Stabilization is assumed after 5000 activations

Correlations between dominance and the frequencies of attack are stronger in cohesive than in loose groups (figure 5) and in small than in large groups (data not shown). This holds both for Perceivers and Estimators.

*

0.8 0.6 0.4 0.2 0 Coh Disp -0.2 Coh Disp rank.behavior τ -0.4 “support” “attack” -0.6 -0.8 Behaviour Figure 5. The strength of the correlations between rank and behaviour (‘support’ and ‘attack’) represented by their mean τ-values and their standard errors in 30 runs for cohesive groups (Coh) and groups in which agents were dispersed (Disp); the asterisk denotes a significant difference between categories.

Possibly dominance interactions are more equally distributed over group members in cohesive groups than in aggregations that undergo repeated fissioning and fusion. Similarly, in small groups the interaction

‘Animals and Animats’, conference SAB96, Hemelrijk, 7 distribution may be more homogeneous than in large groups. This may allow for a tighter ‘locking’ of the dominance hierarchy and consequently stronger correlations between rank and attack.

*

Statistically significant reciprocation of ‘support’, attack and ‘opposition’ was observed in respectively 53%, 55% and 18% of the runs. Reciprocity of ‘support’ and ‘attack’ occurred more in loose than in cohesive groups (figure 6) and in large than in small groups (data not shown). This is probably due to the fact that looser as well as larger groups show more persistent sub-grouping. This implies that individuals direct more acts to and receive more acts from members of their own sub-group than that of others, i.e. a coarse form of reciprocity.

0.1

Reciprocity ( 0

P E “support”

P E “attack”

P E “opposition”

Behaviour Figure 7. The correlations for the degree of reciprocation of ‘support’, ‘attack’ and ‘opposition’ for Perceivers (P) and Estimators (E) are represented by their mean τKr-values and their standard errors in 30 runs; asterisks denote significant differences between categories.

4 Discussion

0.5

*

0.3

*

0.2 0.1 Reciprocity (

Coh

0 -0.1

*

0.2

3.2 Reciprocity

) 0.4 τK r

0.4

) τKr 0.3

Coh Disp “support”

Coh Disp

Disp

“attack”

“opposition”

Behaviour Figure 6. The correlations for the degree of reciprocation of ‘support’, ‘attack’ and ‘opposition’ for cohesive (Coh) and loose (Disp) groupse are represented by their mean τKr-values and their standard errors in 30 runs; asterisks denote significant differences between categories.

Reciprocity of ‘attack’ and ‘opposition’, but not of ‘support’ was weaker in the Estimators than in Perceivers (figure 7). This is not surprising, because when Estimators loose from certain partners they are likely to refrain from starting a ‘real’ fight with the same opponents again, whereas Perceivers attack everybody else independently of former cases of winning or losing. Reciprocity in ‘support’ is of course not inhibited in Estimators in this way because it is not tied to loosing or winning and reciprocity of ‘support’ therefore does not differ between both types.

The model clearly has self-structuring properties. Small parameter changes bring about very different grouping structures. Low values for personal space imply less repulsion among entities and thus more cohesive grouping. A large searching angle has the same effect. The generated group structures in combination with selfreinforcing dominance interactions lead to the emergence of social patterns. These are of a similar complexity as described for real animals: the entities can be ordered in a dominance hierarchy, they behave differently depending on their rank, they take part in ongoing interactions in a way that would be called ‘support’ in primates and they even reciprocate ‘support’ and ‘opposition’. However, they are able to do this without any of the cognitive capacities that have been postulated for monkeys and apes (such as record keeping and a motivation to pay back). Moreover, these patterns appear to be stronger in the simpler Perceivers than in the more advanced Estimators. This contrasts with the idea of de Waal & Luttrell (1988) who stated that reciprocation of ‘opposition’ plus ‘support’ asks for more intelligence than that of ‘support’ alone. Interaction processes among these artificial entities may operate in primate groups as well and have similar consequences, but in other aspects these artificial entities of course do not reflect real primates at all. In real primates cognitive fundaments may still underly reciprocation, although evidence for this is scarse. The message of this study is that correlations for reciprocity should be controlled for effects of social-spatial structuring before cognitive mechanisms are inferred. An obvious possibility that comes to mind is to cancel out the influence of proximity. However, when this was done (by means of a partial Kr test, see Hemelrijk, 1990b), the outcomes of the model did not change in any significant way. Apparently, the social-spatial structuring is more complicated than just an effect of proximity. In all

‘Animals and Animats’, conference SAB96, Hemelrijk, 8 probability the involved nonlinear effects cannot be dealt with satisfactory by the usual statistical procedures. Alternatively, social-spatial reinforcement may be reduced by separating animals from the complete group. Using such an experimental setup (Hemelrijk, 1994), I indeed found indications that macaques ‘supported’ others more often after having received a beneficial act than not. Although this suggests that the animals have the potential to pay back, the experimental data appeared incompatible with observations collected on the complete group: in the isolated triads individuals ‘supported’ partners that they never ‘supported’ in the intact group. It is therefore unclear what such experiments may tell us about behaviour in a large social network (Hemelrijk, in press). Another contribution of this model to primate studies is that it directly explains how variation in the degree of reciprocation may come about. Such variation has been documented for a number of primate species, (Packer, 1977; Bercovitch, 1988; Hemelrijk & Luteijn, in prep). In line with the results of this study it can be attributed to differences in cohesiveness and group size. Enlarging group size in the virtual world affects social patterning in a similar way as decreasing cohesiveness: in both cases the increased reciprocity is probably due to incremental unevenness in the distribution of interactions. Field studies in primates have shown that cohesiveness and group size depend considerably on the size and degree of clumping of food sources (van Schaik, 1989). Models on ‘artificial apes’ of te Boekhorst and Hogeweg (1994ab) have even demonstrated that such effects may override originally assumed species-specific differences in group structure. Up till now I have created cohesive and loose groups by changing parameters that steer the aggregation of agents. In a future version I will extend the model by examining how food distribution affects the emergence of different group types and hence patterns of social interaction.

Acknowledgements I am grateful to Bernd Goetz and René Schaad for introducing me to object-oriented programming. I like to thank René te Boekhorst for improving former versions of this paper and Rolf Pfeifer for continuous support. This work is supported by the Swiss National Science Foundation, grant number 21-34119.92.

References Bercovitch, F. B. 1988. Coalitions, cooperation and reproductive tactics among adult baboons. Animal Behaviour 36: 1198-1209. Boekhorst, I. J. A. te & Hogeweg, P. 1994a. Effects of tree size on travelband formation in orangutans:data-analysis suggested by a model. In: Artificial life. R. A. Brooks and P. Maes, ed., pp. 119-129. Cambridge, Massachusetts: The MIT Press. Boekhorst, I. J. A. te & Hogeweg, P. 1994b. Selfstructuring in artificial 'CHIMPS' offers new

hypotheses for male grouping in chimpanzees. Behaviour 130:229-52. Byrne, R. W. and A. Whiten 1988. Machiavellian intelligence. Social expertise and the evolution of intellect in monkeys, apes, and humans. Oxford, Clarendon Press. Chase, I. D., Bartelomeo, C., Dugatkin, L. A. 1994. Aggressive interactions and inter-contest interval: how long do winners keep winning ? Anim. Behav. 48: 393-400. Deneubourg, J. L. and S. Goss 1989. Collective patterns and decision-making. Ethology, ecology and evolution 1: 295-311. Ellis, L., Ed. 1994. Reproductive and interpersonal aspects of dominance and status. Social stratification and socioeconomic inequality. Westport, Greenwood publishing group. Goss, S. and J. L. Deneubourg 1988. Autocatalysis as a source of synchronised rhytmical activity in social insects. Insectes Sociaux 35 (3): 310-315. Hemelrijk, C. K. 1990a. Models of, tests for, reciprocity, unidirectionality and other social interaction patterns at a group level. Anim. Behav. 39: 10131029. Hemelrijk, C. K. 1990b. A matrix partial correlation test used in investigations of reciprocity and other social interaction patterns at a group level. J. theor. Biol. 143: 405-420. Hemelrijk, C. K. 1994. Support for being groomed in long-tailed macaques, Macaca fascicularis. Animal Behaviour 48: 479-81. Hemelrijk, C. K. in press. Reciprocation in primates: from complex cognition to self-structuring. In: The great apes revisited. T. N. B. McGrew L. Marchant, ed. Hogeweg, P. 1988. MIRROR beyond MIRROR, Puddles of LIFE. Artificial life, SFI studies in the sciences of complexity. Redwood City, California, Adisson-Wesley Publishing Company. 297-316. Hogeweg, P. and B. Hesper 1979. Heterarchical, selfstructuring simulation systems: concepts and applications in biology. Methodologies in systems modelling and simulation. Amsterdam, North-Holland Publ. Co. 221-231. Hogeweg, P. and B. Hesper 1983. The ontogeny of interaction structure in bumble bee colonies: a MIRROR model. Behav. Ecol. Sociobiol. 12: 271-283. Hubert, L. J. 1987. Assignment methods in combinatorial data analysis. New York and Basel, Marcel Dekker, inc. Judson, O. P. 1994. The rise of the individual-based model in ecology. Trends in ecology and evolution 9: 9-14 Mantel, N. 1967. The detectiuon of disease clustering and a generalised regression approach. Cancer Res 27: 209-220. Packer, C. 1977. Reciprocal altruism. Nature 265: 441443.

‘Animals and Animats’, conference SAB96, Hemelrijk, 9 Pfeifer, R. and P. Verschure 1995. The challenge of autonomous agents: Pitfalls and how to avoid them. The artificial life route to artificial intelligence: building embodied, situated agents. Hillsdale, New Jersey, Lawrence Erlbaum associates. 237-263. Schaik, van C. P. 1989. The ecology of social relationships amongst female primates. In: Comparative socioecology, the behavioural ecology of humans and other mammals. V. Standen and G. R. A. Foley, ed., pp. 195-218. Oxford: Blackwell. Siegel, S. 1956. Nonparametric statistics for the behavioral sciences. New York, McGraw-Hill. Villa, F. 1992. New computer architectures as tools for ecological thought. Trends in ecology and evolution 7: 179-183. Waal, F. B. M. de and L. M. Luttrell 1988. Mechanisms of social reciprocity in three primate species: symmetrical relationship characteristics or cognition ? Ethology and Sociobiology 9: 101118.