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Modeling collective motion in animal groups : from mathematical analysis to field data

University of British Columbia

Animals moving together cohesively is a commonly observed phenomenon in biology, with bird flocks and fish schools as familiar examples. Mathematical models have been developed in order to understand the mechanisms that lead to such coordinated motion. The Lagrangian framework of modeling, wherein individuals within the group are modeled as point particles with position and velocity, permits construction of inter-individual interactions via `social forces' of attraction, repulsion and alignment. Although such models have been studied extensively via numerical simulation, analytical conclusions have been difficult to obtain, owing to the large size of the associated system of differential equations. In this thesis, I contribute to the modeling of collective motion in two ways. First, I develop a simplified model of motion and, by focusing on simple, regular solutions, am able to connect group properties to individual characteristics in a concrete manner via derivations of existence and stability conditions for a number of solution types. I show that existence of particular solutions depends on the attraction-repulsion function, while stability depends on the derivative of this function. Second, to establish validity and motivate construction of specific models for collective motion, actual data is required. I describe work gathering and analyzing dynamic data on group motion of surf scoters, a type of diving duck. This data represents, to our knowledge, the largest animal group size (by almost an order of magnitude) for which the trajectory of each group member is reconstructed. By constructing spatial distributions of neighbour density and mean deviation, I show that frontal neighbour preference and angular deviation are important features in such groups. I show that the observed spatial distribution of neighbors can be obtained in a model incorporating a topological frontal interaction, and I find an optimal parameter set to match simulated data to empirical data.

Thesis/Dissertation

application/pdf

2009-08-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/11873

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/