Open AccessA random walk description of individual animal movement accounting for periods of rest
Author(s) -
Paulo F. C. Tilles,
Sergei Petrovskii,
Paulo Laerte Natti
Publication year - 2016
Publication title -
royal society open science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 51
ISSN - 2054-5703
DOI - 10.1098/rsos.160566
Subject(s) - lévy flight , statistical physics , random walk , brownian motion , biological dispersal , mathematics , rest (music) , diffusion process , lévy process , first hitting time model , stochastic process , mean squared displacement , anomalous diffusion , brownian bridge , universality (dynamical systems) , continuous time random walk , cauchy distribution , fractional brownian motion , mathematical analysis , statistics , physics , computer science , innovation diffusion , population , knowledge management , demography , quantum mechanics , sociology , acoustics , molecular dynamics
Animals do not move all the time but alternate the period of actual movement (foraging) with periods of rest (e.g. eating or sleeping). Although the existence of rest times is widely acknowledged in the literature and has even become a focus of increased attention recently, the theoretical approaches to describe animal movement by calculating the dispersal kernel and/or the mean squared displacement (MSD) rarely take rests into account. In this study, we aim to bridge this gap. We consider a composite stochastic process where the periods of active dispersal or ‘bouts’ (described by a certain baseline probability density function (pdf) of animal dispersal) alternate with periods of immobility. For this process, we derive a general equation that determines the pdf of this composite movement. The equation is analysed in detail in two special but important cases such as the standard Brownian motion described by a Gaussian kernel and the Levy flight described by a Cauchy distribution. For the Brownian motion, we show that in the large-time asymptotics the effect of rests results in a rescaling of the diffusion coefficient. The movement occurs as a subdiffusive transition between the two diffusive asymptotics. Interestingly, the Levy flight case shows similar properties, which indicates a certain universality of our findings.