Measuring social structure: A comparison of eight dominance indices
Introduction
Since the landmark paper on peck order by Schjelderup-Ebbe (1935), dominance has been the subject of much theoretical debate, both as a concept (reviewed in Drews, 1993) and as a measurable individual attribute (e.g., Bekoff, 1977, Appleby, 1983, Boyd and Silk, 1983, Zumpe and Michael, 1986, de Vries, 1998, Tufto et al., 1998, Jameson et al., 1999, de Vries and Appleby, 2000). A variety of methods for analysing social structure have been proposed and compared (e.g., Appleby, 1983, Boyd and Silk, 1983, de Vries, 1998, de Vries and Appleby, 2000). It is now well understood that failure to meet underlying assumptions may limit the accuracy of a dominance estimate, particularly under conditions of non-linearity (e.g., de Vries, 1998, Jameson et al., 1999, de Vries and Appleby, 2000).
Despite the sophistication of theoretical models, it remains difficult to identify the best approach for measuring dominance in a group of social animals in which some type of hierarchy may or may not exist. Mathematically rigorous methods can prove cumbersome to apply, or inappropriate for straightforward tasks such as assessment of dominance in small groups, or over short time periods (e.g., Zumpe and Michael, 1986).
There may be considerable variation in social structure among groups that contain dominance hierarchies. These can be simple or complex, linear, near-linear or circular, and may contain reversals or intransitivities (Martin and Bateson, 1993). Hierarchies formed during group assembly tend to be linear or near-linear, while those formed as a consequence of dyadic interaction in the absence of other competitors tend to be non-linear and complex (Chase et al., 2002). In highly social animals, dominance may initially be determined by the outcome of a contest, but then subsequently maintained or modified through daily interactions such as displacements from feeding or resting areas, agonistic displays, or submissive behaviour (Crook and Butterfield, 1970, Kalinoski, 1975, Zumpe and Michael, 1986).
Differences in the way in which hierarchies are formed can affect estimates of social status. For example, Masure and Allee (1934) found that dominance relationships among pigeons developed after many agonistic interactions, while in fowl they were dependent upon the outcome of initial combat. In systems where multiple interactions per dyad are uncommon, it may only be possible to assign dominance on the basis of a single contest (e.g., Clutton-Brock et al., 1979). The choice of technique for measurement of social structure should ideally take such variation into account. Animals that live together in long-term social groups, in which dominant and subordinate animals interact on a daily basis, are likely to require a different method than that used for animals that test their dominance status less frequently.
In group-living animals, alpha status tends to be readily discernible and stable because many alpha males exhibit despotism, while the status of subordinates is often more difficult to define (Barlow and Ballin, 1976, Oliveira and Almada, 1996a). Non-linear relationships pose serious problems for statistical analysis involving between-group comparisons (Crook and Butterfield, 1970), so many researchers have chosen a method that will produce an essentially linear rank order. If there is incomplete but significant linearity in a dominance hierarchy, there may be more than one optimal solution, and deciding between these can be a somewhat arbitrary process (de Vries, 1998).
Some researchers have elected to chose two to three indices and correlate the results obtained. They then select either the simplest (e.g., Baker and Fox, 1978) or the most complex (e.g., Mateos and Carranza, 1996), of the methods that agree well, although there is some evidence that simple indices can be just as useful as more complex ones, especially for small groups in which all individuals interact (Barlow and Ballin, 1976). Other researchers have created a unique index by calculating average dominance status from the results of several dominance indices (Göransson et al., 1990). The critical assumption in this general approach is that indices that produce highly correlated dominance estimates will also yield similar results when social status is tested for its relationship to other aspects of behaviour.
In this paper, we take a first step in exploring the measurement of dominance from a practical standpoint. We review the properties of popular techniques, measure variation in the results obtained when these are each applied to the same real data set, and document patterns of index usage as a function of study organism and research group.
A review of the literature over the last 70 years yielded eight relatively simple indices. Seven of these have been quite popular, while the last, although little used in research on Animal Behaviour, has recently been recommended (Gammell et al., 2003). We used data from interactions observed among fowl, Gallus gallus, the system in which the concept of dominance was first developed (Schjelderup-Ebbe, 1935) to assess consistency in descriptions of social structure. First, we examined how well the indices correlated with one another. The dominance scores generated by each index were then compared with data on individual rates of crowing, using regression analyses. These reveal whether choice of method affects the proportion of variance accounted for, in an analysis of the relation between ‘rank’ and social behaviour.
In addition, we tabulated index use by research group and study organism from a total of 274 papers on social behaviour. The resulting summary reveals the possible influence of social and traditional factors on selection of a technique.
Section snippets
Subjects
We used 24 golden Sebright (Gallus gallus domesticus) bantam roosters and 27 hens. Domestic fowl are derived from the red junglefowl, G. g. gallus (Fumihito et al., 1994, Fumihito et al., 1996), and are still similar both genetically (Stevens, 1991, Siegel et al., 1992) and behaviourally to this subspecies (Collias and Joos, 1953, Collias, 1987, Andersson et al., 2001, Schütz and Jensen, 2001).
Observations were conducted on a series of eight social groups, each of which was housed sequentially
Comparison of dominance indices
The rankings produced by most of the indices were consistent (Table 1), although there was still sufficient variation to discern patterns of agreement between methods. Baker and Fox, Crook and Butterfield, Zumpe and Michael, David's Score and Peck Order ranked males identically. Rankings produced by Clutton-Brock et al. were closer to those produced by CAtt and FSI, than rankings by Baker and Fox, Crook and Butterfield, Zumpe and Michael, David's Score and Peck Order. CAtt and FSI ranked males
Discussion
Simple correlation of ranks suggested that all indices were in reasonable agreement (Table 1), but a closer examination revealed that they responded quite differently to variation in social structure. While strongly linear hierarchies generated similar results with all eight methods, the indices disagreed markedly when summarising data from groups that had weak linearity, intransitive triads or reversals (Table 2). Such groups were often characterised by a tendency for increased interaction
Acknowledgements
This study was carried in accordance with the Australian Code of Practice for the Care and Use of Animals for Scientific Purposes (NHMRC, 1997), and all procedures were approved under Macquarie University AEC protocol 99002. We thank W. McTegg and N. Lambert for bird care, R. Marshall for veterinary support and B. Stinson and H. Cooper for the Science Citation Index searches. We also thank A. Taylor for assistance with the statistical analysis, and A. Göth and P. Taylor for comments on this
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