A random walk description of individual animal movement accounting for periods of rest

Author(s)

Tilles, Paulo F. C. ; Petrovskii, Sergei V. ; Natti, Paulo L.

• Document type: Journal article
• Source: ROYAL SOCIETY OPEN SCIENCE; v. 3, n. 11 NOV 2016.
• Web of Science Citations: 3

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. (AU)

• FAPESP's process: 13/07476-0 - Random walk and mean-field models to estimate insect population density from trap counts
• Grantee: Paulo Fernando Coimbra Tilles
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor