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Visualizing Interaction and Sequential Data in Animal Behaviour: Theory and Application of Cluster-Analysis Methods

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The results of behavioural studies can be difficult to assimilate, often because such enormous quantities of data are involved, both as the studies are carried out and often in their final published form. This paper is concerned with data occurring in two-way tables which summarise, for example, the time each individual in a social group spends with every other individual, or the frequency with which every phrase in a bird's song follows every other one. We present some methods of cluster-analysis which help us to produce visual representations of such data. We describe how to build a single-link dendrogram (which is a way of representing a single-link cluster-analysis or SLCA) in Section 3 and a Maximum spanning-tree (MST) in Section 4. We also describe the properties of non-metric Multidimensional scaling (MDS) in Section 5, and B(2) cluster-analysis in section 6. Because methods of cluster-analysis often make fewer assumptions, we use them rather than factor analysis, principal-component analysis or canonical variate analysis. Section 8 compares the results of factor analyses with those of our cluster-analyses. The methods we describe are illustrated with reference to the times eleven free-living chimpanzees were seen together, analysed by SLCA in Section 3, MST in Section 4 and MDS in Section 5. Section 6 shows how B(2) analyses are used for the chimpanzee data, and Section 7 shows their application to data about sequences of phrases in a blackbird's song. In order to begin the cluster-analyses we present, our tables of raw data must be recast as tables of similarities. Section 2 introduces the art of constructing similarities, and Appendix I (1) shows how different kinds of similarity can be constructed from the same raw data. With reference to Appendix I (2b) and also to the data from BAERENDS et al. (1970) study of the incubation behaviour of herring gulls (Section 8), we emphasise that the act of constructing a particular kind of similarity commits one to a particular way of interpreting the data. Moreover, a method of constructing similarities can conceal differences of precision, Appendix I (3). Appendix I (2), examines the problems posed for cluster-analyses by asymmetric tables such as occur when elements precede other elements more often than vice versa, or when an individual in a social group grooms another for longer than vice versa. In Section 8, we illustrate how methods of cluster-analysis help us to interpret association data for 11 chimpanzees, and we examine the consistency of the chimpanzees' patterns of association through two consecutive 4-month periods. We then examine the association data of the whole community to which the 11 belong, and we use three consecutive analyses to show how the males in the community began to split into two sub-groups. We also compare he association data for three captive groups of rhesus monkeys; and we follow one group, comparing 12 consecutive monthly analyses to discover periods of change in that group's social organisation. We apply cluster-analyses to preceding-following tables from WIEPKEMA (1961) and BAERENDS et al. (1970), and we compare our interpretations of the original data with theirs. Finally, we show how cluster-analysis helps us to understand the songs of a blackbird, originally described by HALL-CRAGGS (1962). While we have emphasised the need to produce visual representations of our data, the need to evaluate them statistically remains, and Section 8-4 and Appendix II discuss the statistical methods for comparing dendrograms.

Affiliations: 1: Mathematical Institute, University of Kent, Canterbury; 2: Sub-Department of Animal Behaviour, University of Cambridge, Madingley, England


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