A Langevin dynamics approach to the distribution of animal move lengths

Abstract

Movement is fundamental to the animal ecology, determining how, when, and where an individual interacts with the environment. The animal dynamics is usually inferred from trajectory data described as a combination of moves and turns, which are generally influenced by the vast range of complex stochastic stimuli received by the individual as it moves. Here we consider a statistical physics approach to study the probability distribution of animal move lengths based on stochastic dierential Langevin equations and the superstatistics formalism. We address the stochastic influence on the move lengths as a Wiener process. Two main cases are considered: one in which the statistical properties of the noise do not change along the animal’s path and another with heterogeneous noise statistics. The latter is treated in a compounding statistics framework and may be related to heterogeneous landscapes. We study Langevin dynamics processes with dierent types of nonlinearity in the deterministic component of movement and both linear and nonlinear multiplicative stochastic processes. The move length distributions derived here comprise the possibility of movement multiscales, diusive and superdiusive (Lévy-like) dynamics, and include most of the distributions currently considered in the literature of animal movement, as well as some new proposals.