Deriving patterns from animal movement decisions: a comparison of approximation techniques and a continuous-time resource selection method

This thesis consists of two parts. First, I investigate the effect of using three partial differential equation (PDE) techniques on analysing some simple animal movement models. Results of examining a biased random walk show that an old approach from Patlak’s work in 1953 can give a very poor approximation even in this very simple case, while more recent methods correctly describe the movement process. By analysing central-place foraging models and movement in heterogeneous landscapes, I show that more recent PDE techniques can provide more accurate approximations of space use patterns when the kernel describing the movement is sufficiently smooth. However, for non-smooth movement kernels, all methods can result in quantitatively misleading approximations. This analysis provides an insight into the conditions under which the PDE methods might perform better.

Second, I present two continuous-time modelling frameworks for analysing animal movement depending on selection of resources over the whole landscape or in the surrounding area. The models are parameterised by a Markov chain Monte Carlo (MCMC) algorithm, allowing for movement decisions made at any time. Based on these frameworks, I generate simulations in various situations, including migration and foraging in patchy or rasterised landscapes. Analysis of simulated trajectories reveals that the inference algorithm can successfully capture the parameter values used in simulations in most cases. I also fit the migration model to spring migration data of some mule deer (Odocoileus hemionus). The results imply that migration might be explained by the trade-off between resources and travel distance. This work addresses some limitations of methods relying on discrete-time movement models and therefore provides an advanced tool for understanding movement driven by environmental factors.