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A primary challenge in understanding collective behavior is characterizingthe spatiotemporal dynamics of the group. We employ topological data analysisto explore the structure of honeybee aggregations that form duringtrophallaxis, which is the direct exchange of food among nestmates. From thepositions of individual bees, we build topological summaries called CROCKERmatrices to track the morphology of the group as a function of scale and time.Each column of a CROCKER matrix records the number of topological features,such as the number of components or holes, that exist in the data for a rangeof analysis scales at a given point in time. To detect important changes in themorphology of the group from this information, we first apply dimensionalityreduction techniques to these matrices and then use classic clustering andchange-point detection algorithms on the resulting scalar data. A test of thismethodology on synthetic data from an agent-based model of honeybees and theirtrophallaxis behavior shows two distinct phases: a dispersed phase that occursbefore food is introduced, followed by a food-exchange phase during whichaggregations form. We then move to laboratory data, successfully detecting thesame two phases across multiple experiments. Interestingly, our method revealsan additional phase change towards the end of the experiments, suggesting thepossibility of another dispersed phase that follows the food-exchange phase.

A Computational Topology-based Spatiotemporal Analysis Technique for Honeybee Aggregation