Modelling and inference for the movement of interacting animals

As animal tracking data is becoming more readily available, statistically modelling the movement of animals is an increasingly utilised approach with which we can analyse their behaviours. Typically though, these models have been developed for the analysis of individual animals and so they fail to account for the social drivers of movement. In this thesis, we aim to build those social drivers into our movement models. Not only will doing so provide a more complete explanation for their behaviours, but it will also provide useful insight into their social structure in general.

Our solution is inspired by orderly social hierarchies - a simple, widely used construct that is easy to interpret whilst providing an in-depth view of social behaviours. The flexibility and level of insight gained from this approach is increased as we capture the dynamism of social behaviours through a continuous-time behavioural switching process. Alongside this framework, we define a multivariate diffusion process that can model the collective movement that results from such social interaction. We first develop our model in the simpler context of spatial homogeneity and explore Markov chain Monte Carlo inference methods with which we can estimate the model parameters in a Bayesian setting.

We then extend the above model to the spatially heterogeneous case, increasing the scope of its applications. We develop a novel model-fitting algorithm which allows us to circumvent a sizeable portion of the increased complexity and computational cost resulting from this extension. We are then able to explore additional customisation of our approach, such as building in a radius of interaction - a feature which can provide some further biological realism to the model.

The above models have been developed in continuous time to gain the resulting flexibility with regards to the temporal resolution and completeness of the data.