Charlotte K. Hemelrijk

Models of, and tests for, reciprocity, unidirectionality and other social interaction patterns at a group level

Research on reciprocity is impaired by confusing definitions and often wrongly used statistical tests. Here, two models of the mechanism on which reciprocity may be based are discussed and an initial step towards a new fremework for its analysis is presented. A distinction is made between reciprocity and interchange. In the case of reciprocity, for one kind of act the same kind is received in return. In interchange, however, two different kinds of acts are bartered. Three types of reciprocity/interchange in social actions among all pairs of group-members are distinguished (‘qualitative’, ‘relative’ and ‘absolute’) on the basis of the precision of the reciprocity/interchange. Permutation procedures for association between matrices (such as the Mantel Z and two other newly derived tests) are used as a statistical test for detecting reciprocity/interchange. A rough comparison of the power of the two new tests is included. The tests can be applied to all kinds of group-living animals and to all sorts of social behaviour. The distinction between the three types of reciprocity/interchange and the matching statistical methods are also useful for defining and detecting other patterns in social interactions, like unidirectionality and associations between different kinds of social behaviour. The influence on social interactions of variables like dominance rank, age and sex can be analysed in the three forms by testing correlations between invented matrices which represent the influence of these variables (the so-called hypothesis matrices) and social interaction matrices. These methods are extended for two categories of individuals, thus allowing the investigation of, for example, reciprocity between males and females. The methods are illustrated with examples of coalition formation and grooming behaviour among captive chimpanzees, Pan troglodytes.

A matrix partial correlation test used in investigations of reciprocity and other social interaction patterns at group level

Reciprocity and other social interaction patterns can be studied at two levels, within pairs (i.e. at dyadic level) and among pairs (i.e. at group level). In this paper advantages of the latter approach are emphasized. However, an analysis at group level implies the correlation of interaction matrices and because such data are statistically dependent, the significance of a correlation has to be calculated in a special way. This is done by means of Mantels permutation procedure. In order to reckon with individual variation, Mantels permutation procedure is used in combination with the so-called Kr statistic, whereby correlations are calculated simultaneously for each separate row. With the aid of the Kr test, the correlation for interchange of grooming for the receipt of “support” in conflicts in baboons and vervet monkeys [data from Seyfarth (1976, Anim. Behav. 24 , 917–938, 1980, Anim. Behav. 28 , 798–813)] was reconfirmed. However, this result may have arisen as a by-product of correlations with other variables. Therefore, the partial form of the Kr test is derived and applied to Seyfarths data and it appears that the interchange of grooming for the receipt of “support” in conflicts, is indeed a spurious correlation in vervets but not in baboons. Direct tuning of grooming to the amount of received “support” seems therefore unlikely in case of the vervets but may exist in the baboons. Some further suggestions are given about the way in which reciprocity/interchange may emerge as a by-product of simple (behavioural) rules. In certain behaviours (like for instance “reconciliation”) missing values occur “conditionally”, i.e. when the preceding behaviour (a fight in case of “reconciliation”) was absent. The same Kr partial correlation test can be used in order to make efficient use of the existing data. This is illustrated with an example of a test for reciprocity of “tolerance” during food sharing among captive female chimpanzees.

Towards the integration of social dominance and spatial structure.

My aim was to show how individual-oriented (or artificial life) models may provide an integrative background for the development of theories about dominance by including effects of spatial structure. Dominance interactions are thought to serve two different, contrasting functions: acquisition of high rank and reduction of aggression. The model I present consists of a homogeneous virtual world inhabited by artificial agents whose actions are restricted to grouping and dominance interactions in which the effects of winning and losing are self-reinforcing. The two functions are implemented as strategies to initiate dominance interactions and the intensity of aggression and dominance perception (direct or memory based) are varied experimentally. Behaviour is studied by recording the same behavioural units as in real animals. Ranks appear to differentiate more clearly at high than at low intensity of aggression and also more in the case of direct than of memory-based rank perception. Strong differentiation of rank produces a cascade of unexpected effects that differ depending on which function is implemented: for instance, a decline in aggression, spatial centrality of dominants and a correlation between rank and aggression. Insight into the origination of these self-organized patterns leads to new hypotheses for the study of the social behaviour of real animals. Copyright 2000 The Association for the Study of Animal Behaviour.

The formation and maintenance of crayfish hierarchies: behavioral and self-structuring properties

Abstract Behavioral changes in fighting and the development of dominance relationships were analyzed in groups of juvenile crayfish (Astacus astacus) using quantitative behavioral techniques. When individuals were placed into an aquarium, the number of agonistic challenges, their mean duration, and maximum intensity reached were high initially but then decreased steadily as the hierarchy developed. In all groups, linear hierarchies emerged which became increasingly stable over time. Winning influenced subsequent fighting behavior on two distinct time scales. In the short term, recent winners became progressively less likely to retreat. Second, individuals occupying dominant positions for days became increasingly likely to escalate to higher intensities early in the encounter. Both effects biased the outcome of future interactions such that winning enhanced further success and losing decreased an individual’s subsequent chances for dominance.

An individual–orientated model of the emergence of despotic and egalitarian societies

Single behavioural differences between egalitarian and despotic animal societies are often assumed to reflect specific adaptations. However, in the present paper, I will show in an individual–orientated model, how many behavioural traits of egalitarian and despotic virtual societies arise as emergent characteristics. The artificial entities live in a homogeneous world and only aggregate, and upon meeting one another and may perform dominance interactions in which the effects of winning and losing are self–reinforcing. The behaviour of these entities is studied in a similar way to that of real animals. It will be shown that by varying the intensity of aggression only, one may switch from egalitarian to despotic virtual societies. Differences between the two types of society appear to correspond closely to those between despotic and egalitarian macaque species in the real world. In addition, artificial despotic societies show a clearer spatial centrality of dominants and, counter–intuitively, more rank overlap between the sexes than the egalitarian ones. Because of the correspondence with patterns in real animals, the model makes it worthwhile comparing despotic and egalitarian species for socio–spatial structure and rank overlap too. Furthermore, it presents us with parsimonious hypotheses which can be tested in real animals for patterns of aggression, spatial structure and the distribution of social positive and sexual behaviour.

Artificial fish schools: collective effects of school size, body size, and body form

Individual-based models of schooling in fish have demonstrated that, via processes of self-organization, artificial fish may school in the absence of a leader or external stimuli, using local information only. We study for the first time how body size and body form of artificial fish affect school formation in such a model. For a variety of group sizes we describe how school characteristics (i.e., group form, spread, density, polarization, turning rate, and speed) depend on body characteristics. Furthermore, we demonstrate that the nearest neighbor distance and turning rate of individuals are different for different regions in the group, although the agents are completely identical. Our approach shows the significance of both self-organization and embodiment in modeling of schools of artificial fish and, probably, in structuring schools of real fish.

Self-organized aerial displays of thousands of starlings: a model

Aerial displays of starlings (Sturnus vulgaris) at their communal roosts are complex: thousands of individuals form multiple flocks which are continually changing shape and density, while splitting and merging. To understand these complex displays both empirical data and models are needed. Whereas detailed empirical data were recently collected through video recordings and position measurements by stereo photography of flocks of thousands of starlings, there are as yet no models that generate these complex patterns. Numerous computer models in biology, however, suggest that patterns of single groups of moving animals may emerge by self-organisation from movement and local coordination (through attraction, alignment and avoidance of collision). In this paper, we investigated whether this approach can be extended to generate patterns resembling these aerial displays of starlings. We show in a model that to generate many of the patterns measured empirically in real starlings we have to extend the usual rules of local coordination with specifics of starling behaviour, mainly 1) their aerial locomotion, 2) a low and constant number of interaction-partners and 3) preferential movement above a roosting area. Our model can be used as a tool for the study of these displays, because it provides new integrative hypotheses about the mechanisms underlying these displays and of swarming patterns in biological systems in general.

Schools of fish and flocks of birds: their shape and internal structure by self-organization

Models of self-organization have proved useful in revealing what processes may underlie characteristics of swarms. In this study, we review model-based explanations for aspects of the shape and internal structure of groups of fish and of birds travelling undisturbed (without predator threat). Our models attribute specific collective traits to locomotory properties. Fish slow down to avoid collisions and swim at a constant depth, whereas birds fly at low variability of speed and lose altitude during turning. In both the models of fish and birds, the ‘bearing angle’ to the nearest neighbour emerges as a side-effect of the ‘blind angle’ behind individuals and when group size becomes larger, temporary subgroups may increase the complexity of group shape and internal structure. We discuss evidence for model-based predictions and provide a list of new predictions to be tested empirically.

Some causes of the variable shape of flocks of birds.

Flocks of birds are highly variable in shape in all contexts (while travelling, avoiding predation, wheeling above the roost). Particularly amazing in this respect are the aerial displays of huge flocks of starlings (Sturnus vulgaris) above the sleeping site at dawn. The causes of this variability are hardly known, however. Here we hypothesise that variability of shape increases when there are larger local differences in movement behaviour in the flock. We investigate this hypothesis with the help of a model of the self-organisation of travelling groups, called StarDisplay, since such a model has also increased our understanding of what causes the oblong shape of schools of fish. The flocking patterns in the model prove to resemble those of real birds, in particular of starlings and rock doves. As to shape, we measure the relative proportions of the flock in several ways, which either depend on the direction of movement or do not. We confirm that flock shape is usually more variable when local differences in movement in the flock are larger. This happens when a) flock size is larger, b) interacting partners are fewer, c) the flock turnings are stronger, and d) individuals roll into the turn. In contrast to our expectations, when variability of speed in the flock is higher, flock shape and the positions of members in the flock are more static. We explain this and indicate the adaptive value of low variability of speed and spatial restriction of interaction and develop testable hypotheses.

The construction of dominance order: comparing performance of five methods using an individual-based model

In studies of animal behaviour investigators correlate dominance with all kinds of behavioural variables, such as reproductive success and foraging success. Many methods are used to produce a dominance hierarchy from a matrix reflecting the frequency of winning dominance interactions. These different methods produce different hierarchies. However, it is difficult to decide which ranking method is best. In this paper, we offer a new procedure for this decision: we use an individual-based model, called DomWorld, as a test-environment. We choose this model, because it provides access to both the internal dominance values of artificial agents (which reflects their fighting power) and the matrix of winning and losing among them and, in addition, because its behavioural rules are biologically inspired and its group-level patterns resemble those of real primates. We compare statistically the dominance hierarchy based on the internal dominance values of the artificial agents with the dominance hierarchy produced by ranking individuals by (a) their total frequency of winning, (b) their average dominance index, (c) a refined dominance index, the Davids score, (d) the number of subordinates each individual has and (e) a ranking method based on maximizing the linear order of the hierarchy. Because dominance hierarchies may differ depending on group size, type of society, and the interval of study, we compare these ranking methods for these conditions. We study complete samples as well as samples randomly chosen to resemble the limitations of observing real animals. It appears that two methods of medium complexity (the average dominance index and Davids score) lead to hierarchical orders that come closest to the hierarchy based on internal dominance values of the agents. We advocate usage of the average dominance index, because of its computational simplicity.