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

Descriptions

Other title
Subject/Keyword
Individual-based model
Animal Communication
Pattern formation
Collective behaviour
Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Zmurchok, Cole MJ
Supervisor and department
de Vries, Gerda (Mathematical and Statistical Sciences)
Examining committee member and department
Pass, Brendan (Mathematical and Statistical Sciences)
Lewis, Mark (Mathematical and Statistical Sciences)
Bouchard, Vincent (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Applied Mathematics
Date accepted
2014-08-21T13:51:30Z
Graduation date
2014-11
Degree
Master of Science
Degree level
Master's
Abstract
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.
Language
English
DOI
doi:10.7939/R39961
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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File title: Direction-Dependent Communication Mechanisms in Individual-Based Models of Collective Behaviour
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