A new multi-scale measure for analysing animal movement data.

We present a new measure for analysing animal movement data, which we term a 'Multi-Scale Straightness Index' (MSSI). The measure is a generalisation of the 'Straightness Index', the ratio of the beeline distance between the start and end of a track to the total distance travelled. In our new measure, the Straightness Index is computed repeatedly for track segments at all possible temporal scales. The MSSI offers advantages over the standard Straightness Index, and other simple measures of track tortuosity (such as Sinuosity and Fractal Dimension), because it provides multiple characterisations of straightness, rather than just a single summary measure. Thus, comparisons can be made among different segments of trajectories and changes in behaviour can be inferred, both over time and at different temporal granularities. The measure also has an important advantage over several recent and increasingly popular methods for detecting behavioural changes in time-series locational data (e.g., state-space models and positional entropy methods), in that it is extremely simple to compute. Here, we demonstrate use of the MSSI on both synthetic and real animal-movement trajectories. We show how behavioural changes can be inferred within individual tracks and how behaviour varies across spatio-temporal scales. Our aim is to present a useful tool for researchers requiring a computationally simple but effective means of analysing the movement patterns of animals.