Connecting Empirical and Mathematical Approaches to Collective Behaviour

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Across scales, biological aggregates form striking patterns, display coordinated, cohesive motion, and function via principles of self-organization, yet complexity at the group level can obscure the underlying mechanisms. Determining how such group behaviour emerges and is sustained involves both direct observation of such groups, and mathematical models to test hypothetical behaviour regimes. ******My research program lies at this interface. I design and implement observational and experimental studies of collectives, from birds to humans. I develop algorithms to process and analyze these data, to summarize important statistical markers of interaction, and provide tests for comparison across species and condition. I develop, test, and simulate individual based differential-equation models to evaluate hypotheses of what individual interactions explain the observed group-level structure. By informing the construction and validation of these models via empirical data, I tie model predictions directly to the natural phenomena. I have used this empirical-theoretical approach to study large flocks of surf scoters in the field, to infer individual rules of interaction from reconstructed trajectories. Further analysis has revealed insights into the dynamics of order/disorder transitions, patterns of predation avoidance, and collective response to the environment.******I will extend my analytical methods to new datasets of collective motion. With a new collaborator in Sydney, Australia, I will analyze a collection of trajectory-based datasets of fish, both in the field and in the lab. These datasets include the collective defensive response to risk in damselfish in the Great Barrier Reef, the effects of inter-fish familiarity on collective behaviour of mosquitofish, and how behavioural parameters are shaped by speciation and environment within the family of Rainbowfish. The degree of control permitted by the laboratory data will allow for the development of an updated, stepwise modelling approach from individuals, to pairs, up to large collectives.******In the second main direction, I will study human collective behaviour via aural interactions. This research, based on pilot work already completed, uses an experimental system of humans clapping synchronously (groups of 2 to hundreds) to study what type of interactions allow synchronous clapping to arise, and how order parameters (group frequency, group synchrony) evolve after synchrony is achieved, via a coupled-oscillator modelling framework. This research extends work on human sensorimotor synchronization from the individual to the collective. Furthermore, effects such as group size, rhythmic initialization, and spatial information transfer will be studied.******These initiatives contribute to my overall research goal of measuring, and explaining pattern in organized collectives.