Please use this identifier to cite or link to this item:
Title: A random walk description of individual animal movement accounting for periods of rest
Authors: Tilles, Paulo F. C.
Petrovskii, Sergei V.
Natti, Paulo L.
First Published: 23-Nov-2016
Publisher: The Royal Society
Citation: Royal Society Open Science, 2016, 3: 160566
Abstract: 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.
DOI Link: 10.1098/rsos.160566
eISSN: 2054-5703
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © the authors, 2016. This is an open-access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Appears in Collections:Published Articles, Dept. of Mathematics

Files in This Item:
File Description SizeFormat 
160566.full.pdfPublished (publisher PDF)737.64 kBAdobe PDFView/Open

Items in LRA are protected by copyright, with all rights reserved, unless otherwise indicated.