Dendrograms and hierarchical clustering
This protocol is extracted from research article:
Most sleep does not serve a vital function: Evidence from Drosophila melanogaster
Sci Adv, Feb 20, 2019; DOI: 10.1126/sciadv.aau9253

The dendrograms in Fig. 3D and fig. S2A are the result of a hierarchical clustering using the UPGMA (unweighted pair group method with arithmetic mean) method (61). During an interval of time, the proportion of time spent by an animal in a behavioral state can be formulated as an empirical discrete probability density function. In this context, the distance between each pair of animal was computed using the average of Bhattacharyya distances (62) over the entire dayEmbedded Image(8)Embedded Image(9)Embedded Image(10)where BDt is the Bhattacharyya distance at a time interval t; T is the set of all tested time intervals: T = {[0, 0.25), [0.25, 0.5), …, [23.75, 24)} hours; BCt is the Bhattacharyya coefficient at a time interval t; p and q are the observed distributions of behavior for two different individuals; and X is the set of discrete behaviors: X = {quiescent, micromovements, walking}.

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