Sampling rate and misidentification of Lévy and non-Lévy movement paths

Abstract

A large number of empirical studies have attributed Lévy search patterns to the foraging movements of animals. Typically, this is done by fitting a power-law distribution with an exponent of 1 < mu < or = 3 to the observed step lengths. Most studies record the animal's location at equally spaced time intervals, which are sometimes significantly longer than the natural time scale of the animal's movements. The collected data thus represent a subsample of the animal's movement. In this paper, the effect of subsampling on the observed properties of both Lévy and non-Lévy simulated movement paths is investigated. We find that the apparent properties of the observed movement path can be sensitive to the sampling rate even though Lévy search patterns are supposedly scale-independent. We demonstrate that, in certain contexts and dependent on the sampling rate used in observation, it is possible to misidentify a non-Lévy movement path as being a Lévy path. We also demonstrate that a Lévy movement path can be misidentified as a non-Lévy path, but this is dependent on the value of mu of the original simulated path, with the greatest uncertainty for mu = 2. We discuss the implications of these results in the context of studies of animal movements and foraging behavior.