Inferring spatial memory and spatiotemporal scaling from GPS data: comparing red deer Cervus elaphus movements with simulation models.

1. Increased inference regarding underlying behavioural mechanisms of animal movement can be achieved by comparing GPS data with statistical mechanical movement models such as random walk and Lévy walk with known underlying behaviour and statistical properties. 2. GPS data are typically collected with ≥ 1 h intervals not exactly tracking every mechanistic step along the movement path, so a statistical mechanical model approach rather than a mechanistic approach is appropriate. However, comparisons require a coherent framework involving both scaling and memory aspects of the underlying process. Thus, simulation models have recently been extended to include memory-guided returns to previously visited patches, that is, site fidelity. 3. We define four main classes of movement, differing in incorporation of memory and scaling (based on respective intervals of the statistical fractal dimension D and presence/absence of site fidelity). Using three statistical protocols to estimate D and site fidelity, we compare these main movement classes with patterns observed in GPS data from 52 females of red deer (Cervus elaphus). 4. The results show best compliance with a scale-free and memory-enhanced kind of space use; that is, a power law distribution of step lengths, a fractal distribution of the spatial scatter of fixes and site fidelity. 5. Our study thus demonstrates how inference regarding memory effects and a hierarchical pattern of space use can be derived from analysis of GPS data.