Indices of movement behaviour: conceptual background, effects of scale and location errors

A fundamental step in the emerging Movement Theory is the description of movement paths, and the identification of its proximate and ultimate drivers. The most common characteristic used to describe and analyze movement paths is its tortuosity, and a variety of tortuosity indices have been proposed in different theoretical or empirical contexts. Here we review conceptual differences between five movement indices and their bias due to locations errors, sample sizes and scale-dependency: Intensity of Habitat use (IU), Fractal D, MSD (Mean Squared Distance), Straightness (ST), and Sinuosity (SI). Intensity of Habitat use and ST are straightforward to compute, but ST is actually an unbiased estimator of oriented search and ballistic movements. Fractal D is less straightforward to compute and represents an index of propensity to cover the plane, whereas IU is the only completely empirical of the three. These three indices could be used to identify different phases of path, and their path tortuosity is a dimensionless feature of the path, depending mostly on path shape, not on the unit of measurement. This concept of tortuosity differs from a concept implied in the sinuosity of BENHAMOU (2004), where a specific random walk movement model is assumed, and diffusion distance is a function of path length and turning angles, requiring their inclusion in a measure of sinuosity. MSD should be used as a diagnostic tool of random walk paths rather than an index of tortuosity. Bias due to location errors, sample size and scale, differs between the indices, as well as the concept of tortuosity implied. These differences must be considered when choosing the most appropriate index.