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Direction-Dependent Communication Mechanisms in Individual-Based Models of Collective Behaviour

  • Author / Creator
    Zmurchok, Cole MJ
  • In this thesis, we study direction-dependent communication mechanisms in individual-based models (IBMs) of collective behaviour. Previously, direction-dependent communication mechanism were incorporated into a non-local hyperbolic PDE model for collective behaviour. The PDE model exhibits numerous spatial patterns observed in nature by considering a variety of communication mechanisms. Like the PDE model, the IBM is formulated in terms of three social interaction forces: repulsion, alignment, and attraction, and the IBM includes information regarding conspecifics' direction of travel. We find that the IBM produces a variety of spatial patterns such as stationary groups, traveling groups, zigzagging aggregations, feathers, and ripple-like patterns, matching the rich behaviour of the PDE model. We also investigate the effect of incorporating density-dependent speed. We find that if individuals slow and speed in response to conspecifics, group splitting and group merging patterns arise. While the PDE model allows for the effect of direction-dependent communication mechanisms on collective behaviour to be seen at the population density level, the IBM model reveals how individuals move within these spatial patterns. To complete the study of direction-dependent communication mechanisms, 2-particle models are proposed as a framework for understanding how individuals respond to their neighbours. The foundation for this work is the anti-symmetric exclusion process that describes the movement of two particles on a infinite one-dimensional lattice when the particles exclude each other from space yet and have an anti-symmetric movement bias. We incorporate non-local repulsion and attraction interactions in the anti-symmetric exclusion process, and study this model by developing a master equation. Stochastic simulations reveal that non-local repulsion and attraction interactions result in group behaviour, with a finite mean separation distance. We also consider alignment interactions by considering the position and direction of travel of the particles, and develop a master equation for this process. Moving groups result from the inclusion of alignment interactions. We find that the 2-particle model framework reveals inter-individual behaviour that is characteristic of group patterns and provides a foundation for analytical work. Studying direction-dependent communication with these three perspectives (PDE, IBM, and 2-particle model) reinforces the important role that direction-dependent communication mechanisms have in producing the complex spatial patterns in nature.

  • Subjects / Keywords
  • Graduation date
    2014-11
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R39961
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Master's
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • de Vries, Gerda (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Lewis, Mark (Mathematical and Statistical Sciences)
    • Pass, Brendan (Mathematical and Statistical Sciences)
    • Bouchard, Vincent (Mathematical and Statistical Sciences)