Constraining Models of Collective Motion in Biological Systems

Abstract

Animals moving together as one is a commonly seen spectacle in both the sky, with flocks of birds, and in the oceans, with school of fish. Mathematical models have been developed over the last 50 years to gain a deeper understanding into how such coordination occurs or to recreate the behaviour digitally. There has been extensive numerical simulation and analysis done for these models but little comparison to actual data. This is due to the complexity of obtaining high quality data suitable for analysis. We were able take advantage of lightweight high definition cameras and drone technology to collect footage of collective behaviours. In this thesis we describe a computer vision algorithm we devised to detect and track individual sheep in the drone footage we collected. The algorithm emphasises the differences in the colours of the sheep and the grass background in order to locate the sheep. It then tracks the individuals throughout the video. In total the trajectories of 45 or more sheep were extracted from 14 videos ranging from 150 frames to 593 frames. In some of these videos the quadbike and farmers herding the sheep were also tracked. From these trajectories we were able to extract quantities such as average speed and global alignment which can then be used to compare to simulated data. We describe a number of models from the literature which aim to reproduce the types of behaviours we observed in our sheep flocks and some of these we expand on to make them include new features such as allowing agents speeds to change or allow agents to interact with a predator whist in an enclosed area. We go on to compare our observational data to two different types of these models. The first of these was a family of models which were able to replicate the emergent flocking behaviour seen in some of the observations. The second was a model able to simulate data to compare to our observations of “steady-state” flocking as well as being able to include the movement of the quadbike or farmer herding the animals. We will compare our observational data to simulated data using an approximate Bayesian computation rejection scheme to calculate an approximate joint posterior distribution for the parameters in each of the models. The parameters of these models were sampled from a Latin hypercube meaning we are able to cover the full parameter space efficiently.