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Bioscience Horizons Advance Access published online on March 3, 2009
Bioscience Horizons, doi:10.1093/biohorizons/hzp008
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© 2009 The Author(s)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

The application of social network theory to animal behaviour

Amelia Coleing*

University of Chester, Chester, UK

* Corresponding author: Blagdon Manor Farm, North Tamerton, Holsworthy EX22 6RL, UK. Tel: + 44 07884494989. Email: milli_uk{at}hotmail.com

Supervisor: Roger Davies, University of Chester, Chester, UK.


   Abstract
Top
 Abstract
The Application of Social...
 Materials and Methods
 Results
 Discussion
 References
 
Social network analysis (SNA) is a mathematical technique for analysing social relationships and the patterns and implications of these relationships (Wasserman S, Faust K (1994) Social Network Analysis: Methods and Applications. Cambridge: Cambridge University Press). It has only recently been discovered by behavioural biologists as a useful tool in the study of animal behaviour (Wey T, Blumstein DT, Shen W et al. (2008) Social network analysis of animal behaviour: a promising tool for the study of sociality. Anim Behav 75: 333–344). Video recording over a 2 month period was used to record the behaviour of the elephant group at Chester Zoo. SNA was applied in an investigation of the group structure and interactions of the group. Observations of individual and group behaviour were based upon 40 h of playback of the social interactions were recorded and analysed using AGNA (2003) and Pajek (2005) packages. The analysis showed that the many facets of individual behaviour could be understood in terms of social structure of the group. This study has demonstrated that SNA is a powerful approach to understanding group dynamics and is particularly applicable to the study of obligate social species. In conclusion, it is suggested that SNA is potentially a useful tool in the management of captive animal populations.

Key words: social networks, animal social behaviour


   The Application of Social Network Theory to Animal Behaviour
Top
 Abstract
 The Application of Social...
Materials and Methods
 Results
 Discussion
 References
 
There have been many methods devised to measure social complexity in studies of animal behaviour.1–4 These measures often reflect the social relationships between individuals indirectly; such as by group size or mating system, and usually assume homogeneity of effect on all individuals.5 Social network analysis (SNA) is a method that measures social relationships directly, providing a deeper understanding of complex sociality and group structure.5,6 Network theory can be used to analyse relationships among social entities (such as individuals or units) and the patterns and implications of these relationships.6 It provides formal descriptors for characterizing social groups and by providing quantitative measures of relationships, it allows testing of statistical models about relationships and structure.6

There have been previous studies of behaviour using SNA. It originated in mathematical graph theory7 and has been applied to many areas of human social behaviour. It has long been investigated in sociology,8, 9 anthropology,10, 11 social psychology12 and economics13,14 and related disciplines. Some current studies involving a social network approach include research into terrorist networks,15 traffic patterns,16 food webs17and neural networks.18 It has only recently been recognized by behavioural biologists as a potential technique in animal behaviour.5 There were some early studies applied to primates19 and more recently, there have been studies applying network theory to animal behaviour. Species such as fish,20 dolphins,21 sea lions22and recent studies on primates such as rhesus macaques23 and pigtail macaques24 have used this approach. SNA has potential value in the study of animal social behaviour5 and may even allow insights about evolution, the maintenance of sociality and the forces driving social organization.5,21 Network analysis has also been used to represent transmission events such as social learning, pathogens in epidemiological research and animal signals.5, 25 In addition, network analysis can be used to examine other aspects of animal behaviour such as kinship ties and the sharing of resources, such as food or territories.5

There are many facets to animal relationships that may be represented by SNA. For instance, it may be used to analyse social interactions, including those involving dominance hierarchies, agnostic exchanges or grooming. McCowan et al.23 used SNA to detect social instabilities in a group of captive rhesus macaques, including affiliational, aggressive and submissive behaviours. More complex components of group behaviour may be explored in SNA by combining matrices and network diagrams of different aspects of behaviour.

A social network is commonly represented visually by matrices and graphs known as network diagrams (Table 1 and Fig. 1).


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  		Table 1. Matrix containing values to represent the existence (presence or absence) of relationships between entities

 


Figure 1
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  		Figure 1. A network diagram (‘digraph’) representing the social relationships between the 10 members of the group. It consists of numbered nodes (‘vertices’) that represent social entities and ties (‘arcs’ or ‘edges’) that represent social relationships between vertices. Arcs in the network diagram may be weighted, directed or contain signs according to the relationship they represent. Vertex 3 shows an individual that bridges relationships between two subnetworks.

 
SNA may provide for the analysis of the social structure of an animal group at three different levels: individual, intermediate and group measures. At the level of the individual, measures may describe the individual's position in the network and the potential effect it has upon other group members.5 For example, the strength of an individual's relationship within the group can be measured by counting for the number of interactions an individual initiates or receives (their outdegree or indegree, respectively) and consequently, how well connected is that individual. Centrality provides a measure of the individual's structural importance to the group (Table 2).26,27 In theory, the more contacts that an animal has within the group then the more central it is, and therefore, the more influence it would have on those around it.5, 6, 28 Centrality, therefore, may also indicate how important an animal is as a point of social connection and transfer. The removal or death of an important individual, such as one occupying the position of a bridge position (Fig. 1), may cause the group to divide into two or more smaller subgroups.24, 29, 30


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  		Table 2. Glossary of terminology

 
Intermediate level measures may be used to identify the presence of subgroups and explore cliques in the network.5 Cliquishness describes the extent at which a network contains subgroups that exclude others from them socially.5, 28 At the group level, there are various measures that are used to explore aspects of overall network structure5 such as connectedness and cohesion, and these are generally used to compare different networks.

Defining the size of a given network may sometimes be difficult to achieve, particularly when studies are carried out in the species' natural habitat. For instance, decisions need to be made about which individuals to exclude from the network, and this affects decisions about network structure and the subsequent parameter estimates.5, 31 That being said, the majority of previous studies using SNA have investigated the social behaviour of wild-living animals, and so the problem of defining group dimensions is one that has been successfully overcome.20, 22 However, it is clearly the case that SNA is more easily applied in the study of confined groups of captive animals, whether in zoos, safari parks or aquaria. This study aims to explore the use of network analysis to investigate the group structure of Asian elephants (Elephas maximus) at the Chester Zoological Park, UK. Terms used throughout the paper are defined in Table 2.


   Materials and Methods
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 Abstract
 The Application of Social...
 Materials and Methods
Results
 Discussion
 References
 
Subjects
The study focused on 10 E. maximus housed at Chester Zoological Park. The group is composed of seven females and three males. Although many captive elephant groups tend to consist of few juveniles,32 this group has four.

The group consists of a mix of individuals; some of which are unrelated to any other individual and some have relatives within the group. Figure 2 illustrates the kinship relationships between members of this particular elephant group.


Figure 2
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  		Figure 2. The family tree showing the two sets of related elephants within the group. ThiHiWay is the grandmother. Upali is only related to Raman in the group.

 
Procedure
In order to use SNA techniques, it may be necessary to view the behaviour of all individuals simultaneously. For this purpose, a video camera is best used to record the interactions of the group. This has the advantage of giving the ability to record the behaviour of more than one individual at a time and then replay the video tape repeatedly for analysis of the timing and sequencing of events and social interactions, or the different individuals involved.33 I recorded from an observation hut placed one end of the elephant enclosure and so was out of sight of the animals at all times. In this study, the camera was focused on the largest number of subjects that could be fitted into camera view simultaneously and the camera microphone was be used to record orally any behaviour not in frame at the time.34 Forty hours of data were collected over many different days and weather conditions to ensure that a relatively complete catalogue of social interactions was collected.35

Data Recording
The footage collected during observations of the group was recorded via playback of the video tapes. An ethogram was used to classify and recognize behavioural categories involving all social interaction. These behavioural categories were chosen for the ethogram so as to highlight the more common social interactions, allowing the composition of the group to be described and simplified in network diagrams. The recording of different types of social interaction within the group (e.g. agonistic, play or other prosocial forms) allows for the eventual accumulation and recombination of sequences of social events to be explored using specialist software packages. In this study, use was made of AGNA36 and Pajek37 programs for the production of network diagrams.


   Results
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 Abstract
 The Application of Social...
 Materials and Methods
 Results
Discussion
 References
 
The social networks of some of the interactions are explored here, and some statistics and indices relating to network analysis used to explore basic properties of the group structure. The interactions explored include play, dominance, prosocial behaviour including affiliative body contact, greeting by body contact, close proximity and following networks.

Social Play Network
Figure 3 is a weighted digraph of the play relationships showing the frequency and direction of the play interaction. It shows the connectedness of play relationships of a subnetwork of five individuals. Unsurprisingly, this group consists primarily of the younger elephants, though both Sithami (the older juvenile female) and Upali (the adult male) also engage in social play with the youngsters Sundara, Tunga and Raman.


Figure 3
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  		Figure 3. A weighted digraph showing the structure of social play between the elephants at Chester Zoo. The figures (‘weights’) on the digraph indicate the frequency of the interactions between the members of the network.

 
A number of indices are available to characterize structural properties of the group, and some of these are shown for the social play network in Tables 3Go–5.


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  		Table 3. Descriptive statistics for the social play network

 


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  		Table 4. Matrix of geodesics for the social play network

 


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  		Table 5. Indices of the social play network

 
Tunga is a popular member of the play network, being linked with every other in this subgrouping, implying that he occupies a central position. The weights in Fig. 3 indicate that Tunga is the initiator of much play activity, shown by the high values associated with his outdegrees. Sukumar38 observed this in the natural behaviour of a male calf of Tunga's age. Using SNA, it would be possible to test for hypothetical change in the social structure of the group, for instance to examine changes to play in this group if Tunga were removed from it.

Centrality measures have been devised to compare the relative importance of individuals in a network.39 Table 3 contains the distribution of centrality measures within the group. According to this index, Tunga has a significantly central position in this particular network, though it is notable that Raman also has a relatively high index. The distribution of eccentricity in Table 3 shows that Tunga has the lowest value and therefore the shortest path length of the network. This indicates that he is well connected within the network of social play. The matrix of geodesics also reflects that Tunga is well connected within the subgroup and that Raman is well connected with the juveniles, but less so with the male, Upali. Sociometric status refers to the total number of interactions of the individual. Unsurprisingly, Tunga has the highest value, followed by Raman. Sundara and Upali have the lowest values, indicating a smaller number of interactions. Despite the fact that the youngsters form a rather tight-knit group in terms of social play, the group cohesion statistic is low (0.111 from a maximum of 1.0). However, this is because the adults of the group on the whole do not employ in social play. The density measure for the network is low (0.122 with maximum possible of 1), owing to the number of isolates in the network.

Dominance Network
The digraph shown in Fig. 4 is of dominance observed in the elephant group during this study. Arrows on the arcs show the direction of the interaction. For example, in this network diagram, Sheba is dominant over Maya and ThiHiWay. The weights on this network diagram indicate the frequency of instances of dominance that were observed during the study, but this could be recorded as the intensity of such interactions. The three most dominant females are Sheba, Maya and Jangoli. Notice that the dominance hierarchy in this group is neither linear nor transitive.40 Therefore, there is not one dominant individual as has been reported in wild herds of E. maximus and Loxodonta africana, with the matriarch being dominant over the entire herd.41, 42


Figure 4
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  		Figure 4. A weighted digraph showing dominance relationships between members of the elephant group at Chester Zoo.

 
Combining Networks to Analyse Higher Order Aspects of Social Structure
Social networks may be combined in order to investigate more complex aspects of behaviour than is possible using observations from a single category. This is made possible by the use of various operations using matrix arithmetic that enable different matrices to be combined by the processes of addition, multiplication or subtraction.43 For instance, if ‘Set A’ is the category ‘agonistic behaviour’ and ‘Set B’ representative of kin relationships, then the operation A – (A {cap} B) would show agonistic behaviour shown towards unrelated individuals (indicated by the shaded area).

To produce a digraph representing all body contact recorded between the group of elephants, the two matrices containing affiliative body contact and greeting were added together (Fig. 5). Elephants are very social individuals and use tactile communication,42 so it would be expected that there are high levels of body contact between individuals. Also, the fact that the group is captive and has restricted space may affect the levels of body contact between individuals. Affiliative body contact involved touching of another individual excluding greeting behaviour, such as standing with sides touching and comfort behaviour (rubbing the body against another). Greeting is an affiliative behaviour involving body contact including mouth checking (placing trunk in mouth of conspecifics), temporal checking (placing trunk on temporal gland of conspecifics), genital checking (placing trunk between rear legs of conspecifics) and trunk entwining (wrapping trunk around the trunk of conspecifics).44


Figure 5
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  		Figure 5. A combination of matrices involving body contact within the group. Infrequent cases have been excluded to clarify the digraph.

 
Regarding affiliative body contact, Maya is shown to be an ‘isolate’, that is an individual with zero indegrees and outdegrees. Upali also has few outdegrees. He is the bull, kept in a separate enclosure. Although he can contact the other individuals in the group, he cannot initiate contact unless the individual is already close to him (Table 6).


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  		Table 6. Distribution of sociometric status for the affiliative body contact network

 
The sociometric status of the network members (Table 6) shows that Raman has the greatest number of social interactions, followed by Tunga and Sithami. Of the adults, Sheba and Birma have the highest values.

Maya, Birma and Sheba are social isolates. Unsurprisingly, Tunga and Raman have high outdegrees to other members of the group. Betweenness centrality provides an index of the extent to which each vertex lies as a connecting point between other vertices, therefore indicating how important an individual is as a point of social connection and transfer. In the case of Fig. 5, this would enable a measure of the relative importance of Raman and Tunga in terms of their centrality to the entire body contact network. The measures are provided in Table 7. Table 7 shows that both Tunga and Raman are central to the body contact network. Raman has a higher value than Tunga, indicating that he is more influential. It is interesting, though logical to note that the two youngest members of the group are most influential to the group in terms of body contact. The youngsters of a group are likely to require more comfort behaviour in the form of body contact and are also more inquisitive, spending much of their time investigating their group members.


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  		Table 7. Distribution of betweenness centrality in the body contact network

 
Given that most social relationships between individuals in a network are based on a combination of both positive and negative interactions, then it would be useful to locate those individuals having the relationships that contain the greatest amount of prosocial behaviour. To do this for the data of this study, all prosocial matrices were combined to form a combined matrix of these positive encounters. The resulting network is displayed in Fig. 6. These matrices included affiliative body contact, greeting by body contact, close proximity and following networks. Social play was excluded owing to the lack of adult participation in this behaviour.


Figure 6
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  		Figure 6. A digraph based on a combination of all prosocial behaviour.

 
The descriptive statistics derived from the ‘prosocial network’ of Fig. 6 are given in Tables 8Go–10. There are a number of interesting features of this network. Firstly, a number of individuals receive much prosocial behaviour that they do not reciprocate. These are shown as a row of zeros in the geodesic matrix in Table 8. This applies to ThiHiWay, Upali and Jangoli. Maya is the social isolate of the group, whereas the central individuals connecting the group are the youngsters: Sithami, Tunga, Sundara and Raman. Jangoli's relationship with Sheba, Birma, ThiHiWay and Upali is based around her interactions with that central group. The youngsters are responsible for initiating the majority of prosocial behaviour, both with one another and with the adults. Of the adults, only Sheba and Birma engage in prosocial behaviour independently of the youngsters.


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  		Table 8. Geodesics for the combined prosocial behaviour category

 


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  		Table 9. Sociometric status of the group members regarding all prosocial behaviour

 


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  		Table 10. Two indices of centrality in the prosocial network

 
The sociometric status of group members is given in Table 9. This index, combined with the centrality measures in Table 10, suggests that Raman is at the heart of the prosocial behaviour that occurs in this group.

However, for closeness centrality, both Birma and Sheba have values that indicate cliquishness, at least among the adults.

The Existence of Subgroups in Social Structure
From a structural perspective, perhaps the most interesting area in which network analysis covers is in the statistical modelling of subgroups, such as cliques or social isolates. It is possible to use a variety of methods to identify subgroups and cliques within a network. A clique may be strictly defined by those subgroups whose only connection is to other members, known as ‘p-cliques’. For instance, Fig. 7 shows the p-cliques identified using Pajek.37


Figure 7
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  		Figure 7. Identification of cliques within the elephant social network, based on the combined body contact networks. The shading illustrates the levels of similarity between individuals and the existence of cliques within the networks.

 
Note that in Fig. 8, the levels of similarity are indicated for the vertices with the diagonal hatching (Upali, Jangoli and ThiHiWay, each having one indegree), white (Sheba, Birma and Maya, who are all isolates), horizontal hatching (Sithami, who uniquely has three indegrees) and grey (the youngsters Sundara, Raman and Tunga).


Figure 8
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  		Figure 8. Cliques identified on the basis of mutual body contact relationship.

 
The identification of cliques in the all prosocial network was carried out with Pajek37 using Ward's method of clustering,45 the result shown in Fig. 9. The existences of p-cliques are shown in Fig. 10. Owing to Tunga's connections with adults outside the central clique (vertices with a diagonal hatching in Fig. 10), he does not join with this particular clique. The members of the central clique have exclusive and reciprocated relationships with one another, which is the quintessential definition of a clique. The clustering shown in Fig. 9 suggests that Tunga lies in a transitional location between the other youngsters and adults. It is notable in Fig. 10 that in terms of initiating prosocial behaviour the adults are generally peripheral figures to the youngsters. Only Sheba and Birma show sociality that is not focused on the youngsters.


Figure 9
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  		Figure 9. Cluster analysis of prosocial behaviour cliques in the prosocial using Ward's method in the Pajek network analysis program.

 


Figure 10
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  		Figure 10. Identification of p-cliques in the prosocial network.

 
Two-step Relationships
Two-step relationships are where the relationship between two individuals influences the relationship between other individuals. In SNA, it is possible to assess two-step relationships using matrix algebra (for instance, using SPSS Syntax or MATLAB programs). A matrix provides information on all direct incidences where this behaviour is expressed over others. To find the two-step effects the first matrix is squared, which will calculate the effects on all relationships that are separated by two steps.

Table 11 shows the dominance matrix observed for the elephant group, containing the number of interactions observed between each member of the group. The matrix was converted to binary format using a threshold of ≥3 interactions and then squared. To calculate the effects of both direct and indirect dominance, the two matrices were then summed. The resulting digraph showing those individuals experiencing both direct and indirect dominance relationships is shown in Fig. 11. It is noticeable that dominance expressed in this way shows that there is no clear leadership in this group. The four adult females seem to be vying with one another for dominance, but no evidence exists that a leader is about to emerge from this group, judging by the ways in which they interact with one another.


Figure 11
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  		Figure 11. A network diagram indicating dominance relationships, including both direct and two-step influences.

 


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  		Table 11. Dominance matrix for the group of elephants at Chester Zoo

 
The most recent innovations of SNA have been in terms of testing hypotheses regarding network structures.46 For instance, it is possible to compare networks of the same group taken at two points in time, or to contrast the structural features of different networks, such as by using statistical measures. Within the same network, it is possible to compare the standing of individuals in the network using indices such as centrality, cohesion and density measures.


   Discussion
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 Materials and Methods
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 Discussion
References
 
Previously, the few studies that employ this method in animal social groups have focused on large groups.20, 22, 47 However, this method may be especially useful in the study and management of smaller, captive animal groups, such as among the primates, ungulates, meerkats and other obligate social species. The resulting social structure illustrated by the networks in this study allows factors affecting the group social structure to be highlighted. In this study, many inferences can be drawn from the social structures illustrated. In this particular group of elephants, there is no clear dominance hierarchy, and even when indirect dominance relationships (transitivity) are included, no such hierarchy was found. This may be due to the fact that this group consists of many unrelated individuals that have lived together for varying amounts of time. It may also suggest that the cows do not form a dominance hierarchy in captivity, perhaps lacking the ecological trigger points that set this off.48 The affiliative body contact network reflects that the greatest numbers of interactions are between related individuals of the group, which would be expected in an elephant herd.38 Tunga and Sithami are unrelated, but may have a high number of interactions because of the large amount of play in which they engage. It seems unusual that Sundara and Sithami, who are related, do not exhibit high levels of affiliative body contact even though they spend considerable time in close proximity. Tunga tends to follow Sithami and Upali, often just before he initiates play with those individuals. Maya is shown to be an isolate in the greeting network; she is an isolate in the affiliative body contact network, and in proximity network. Sheba was also an isolate in this network, owing to the fact that she tends to spend less time in close proximity or engaging in affiliative body contact with many individuals, other than Birma and Raman. This was also highlighted in the analysis of p-cliques within the group and in the two amalgamations to form the prosocial and body contact networks. The cliques were found to exist most strongly between the juveniles of the group, with Sheba, Birma and Maya as isolates. Raman tends to greet Upali, but not yet spend much time in close proximity or engage in much other affiliative body contact with him. This may be explained by his young age in that he exhibits interest in the male, but it not yet large enough to engage in the rough play with Upali as does Tunga. Much of the agonistic behaviour is directed by ThiHiWay towards Tunga. This may be due to the fact that Tunga frequently attempts to suckle from ThiHiWay, who is unrelated to him, and so these particular interactions could be interpreted as discipline.

Many current studies using SNA have concentrated upon wild social groups.20, 22, 47 The range of network indices and statistics allow hypotheses about group structure to be developed and tested.46 A range of statistics may be used to model the result of a change in social composition in managed populations, such as the removal of an individual or introducing a new member to a social group. It is possible to compare networks of the same group taken at two points in time, or to contrast the structural features of different networks, such as in the comparison of groups at different exhibits in various zoos. Within the same network, it is possible to compare the standing of individuals in the network using indices such as centrality, cohesion and density. Measures of centrality, for example indicate how important an animal is to the social structure. Identification of cliques can detect members of a network which may act as a bridge between two subnetworks and therefore important in maintaining the network as one group.

This method may be particularly useful for the study of captive animal groups with regards to animal management, for instance allowing greater welfare standards and breeding success within the group by enabling the assessment of compatibilities between individuals.48, 49, 50 A recent study by McCowan et al.23 used SNA measures to investigate social instabilities resulting in aggression-based morbidity in rhesus macaques, highlighting a use of this method to assess compatibility between captive individuals of a group. Studies that compare groups housed at different institutions may help to identify areas that encourage different aspects of social structure such as enclosure and group size,51 relatedness of individuals,48 length of time in the social group, weather conditions,52 visitor numbers53, 54 and feeding methods or resource distribution55 among other factors. It has been suggested48, 56 that optimum welfare and breeding success of captive elephant herds may ultimately be reached by creating herds of related individuals; but in the immediate future, experimentation with combinations of cows should ensure compatible herds can be developed to increase breeding success48, 50.

SNA can also provide insights into the nature of animal groups through the use of composite matrices from different aspects of social behaviour. In his discussion of this approach, Davies57 refers to the study of group ‘superstructure’. This involves combining many interconnected facets of social behaviour, such as was carried out in this study by amalgamating all the ‘prosocial’ categories. Davies argues that the analysis of group superstructure provides a more realistic comprehension of behaviour as it integrates many interlocking elements of social behaviour; some of which tend the group towards fusion and bonding, such as affiliation, cooperation, reciprocal grooming or the forming of allegiances, while others may tend the group towards fission, through agonistic behaviours between key members of the group, such as competition and rivalry, dominance or cliqueism. The emergence of novel matrices based on such composites sociomatrices may provide the basis of new insights and hypotheses about the underlying nature of social behaviour within the group.

The application of SNA might be in identifying individuals, cliques or subgroups within a network, whose positions within the group as a whole may be critical to its stability. For instance, some individuals act as a bridge between different subgroups, and their removal from the group by animal managers could have serious consequences for the social ‘glue’ that bonds the group as a whole. Knowledge of this kind not only facilitates a more effective level of animal management, but also creates a deeper understanding of interactions within the group so that large-scale manipulations, such as the attempt to reintroduce a group into their natural environment, may be more carefully planned.

A common criticism of SNA has been that it oversimplifies animal behaviour by providing only a ‘freeze frame’ of social interaction, whereas such behaviour should be treated as a series of dynamic events. However, this overlooks the fact that all data analytical methods are determined by the exact point at which the data were collected. Provided that the researcher does not regard SNA as representing some fixed, immutable nature of social behaviour, then an analysis of such networks can provide valuable information about the nature of social interaction within the group dynamic. For instance, this may be achieved by studying changes in the structural properties of the network over different periods of time, or under differing experimental manipulations.

To conclude, this study has highlighted the use of SNA and its wide range of possibilities for use in the analysis of animal social groups. It is clear from the results that there are a wide range of possibilities with SNA that are unavailable with other means of analysis of animal social behaviour. Using SNA, it has been possible to describe the basic nature of social relationships and matrix algebra was used to investigate combinations of interactions and more complex aspects of the social behaviour of the group. A range of network indices and statistics relating to network analysis have allowed individual and group characteristics to be investigated and compared. Its use in captive animal groups, as well as with large wild groups, may have great potential in furthering our understanding of the social lives of animals and in improving the management of captive groups.


   Acknowledgements
 
I thank Chester Zoological Park for the use of their facilities and the help of the staff.


   References
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 Abstract
 The Application of Social...
 Materials and Methods
 Results
 Discussion
 References
 

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