A Langevin dynamics approach to the distribution of animal move lengths

Abstract

Movement is fundamental to the animals 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 differential 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 different 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, diffusive and superdiffusive (Lévy-like) dynamics, and include most of the distributions currently considered in the literature of animal movement, as well as some new proposals.

Revisiting Lévy flights on bounded domains: a Fock space approach

“…Indeed, we emphasize that while some methods are particularly associated with specific forms of jump length distributions p( ) (e.g., the discretization of the fractional Laplacian operator related to the Lévy jump length distribution [28]), the Fock space approach can be promptly applied to any p( ) inserted in equation (11). In particular, in recent years there has been a growing interest, in contexts as diverse as random lasers and random search foraging, related to less conventional forms of p( ), such as hyper-exponentials, attenuated power laws, or multiple-scale expressions [19,20,76].…”

Random diffusivity scenarios behind anomalous non-Gaussian diffusion

“…Its impact can be addressed through the superstatistical approach proposed by C. Beck and E. G. D. Cohen to extend statistical mechanics to complex heterogeneous environments. Superstatistics has been applied to run-and-tumble particles [13], animal movement [14][15][16], metapopulation extinction dynamics [17], time series analyses [18][19][20][21], and many other cases [22][23][24][25][26][27][28]. The superstatistics of fBm has been recently developed, providing theoretical support for various experimental ob-servations, such as, protein diffusion in bacteria [29,30], micro-particles in a bi-dimensional system with disordered distribution of pillars [31], and tracer diffusion in mucin hydrogels [32] (see Refs.…”

Mean first passage time and absorption probabilities of a Lévy flier on a finite interval: discrete space and continuous limit via Fock space approach

“…In practice, however, natural limitations often emerge in realistic contexts (e.g., the step length of a foraging animal cannot be infinite due to environmental and/or biological constraints), which can lead to large but finite second moment. In this sense, the terminology Lévy-like or limited superdiffusive behavior has been usually employed [85][86][87] to indicate that superdiffusive behavior occurs up to quite large spatial or temporal scales, before a crossover to the normal dynamics driven by the CLT takes place.…”