A random acceleration model of individual animal movement allowing for diffusive, superdiffusive and superballistic regimes

Abstract

Patterns of individual animal movement attracted considerable attention over the last two decades. In particular, question as to whether animal movement is predominantly diffusive or superdiffusive has been a focus of discussion and controversy. We consider this problem using a theory of stochastic motion based on the Langevin equation with non-Wiener stochastic forcing that originates in animal’s response to environmental noise. We show that diffusive and superdiffusive types of motion are inherent parts of the same general movement process that arises as interplay between the force exerted by animals (essentially, by animal’s muscles) and the environmental drag. The movement is superballistic with the mean square displacement growing with time as at the beginning and eventually slowing down to the diffusive spread . We show that the duration of the superballistic and superdiffusive stages can be long depending on the properties of the environmental noise and the intensity of drag. Our findings demonstrate theoretically how the movement pattern that includes diffusive and superdiffusive/superballistic motion arises naturally as a result of the interplay between the dissipative properties of the environment and the animal’s biological traits such as the body mass, typical movement velocity and the typical duration of uninterrupted movement.

Movement patterns of the grey field slug (Deroceras reticulatum) in an arable field

“…An unambiguous identification of the movement pattern requires the movement data from multiple temporal scales as the pattern can be scale dependent, e.g. being superballistic at small scales but slowing down to diffusion at large temporal scales 59 , 60 . Such slowing down can happen due to different mechanisms, e.g.…”

“…Such slowing down can happen due to different mechanisms, e.g. as a behavioural response to meeting con-specifics 59 or due to the inherent effect of the environmental friction 60 . Here we hypothesize that slowing down of slug displacement (as observed in the case of the sparse release, see Fig.…”

Three-dimensional random walk models of individual animal movement and their application to trap counts modelling

“…They are easy to implement: it is rather straightforward to investigate movement paths using computer simulations based on RWs. More importantly, by considering individual movement as a stochastic process, it is often possible to obtain a general analytical description, in terms of the dispersal kernel and/or the statistical moments, as functions of time, and thus to reveal generic properties of different movement behaviours (Reynolds, 2010;Codling and Plank, 2011;James et al, 2011;McClintock et al, 2012;Tilles and Petrovskii, 2015;Tilles et al, 2017). While there has recently been considerable progress in understanding these issues, most theoretical studies on animal movement have been predominantly limited to 2D cases.…”

Apparent superballistic dynamics in one-dimensional random walks with biased detachment

“…IV C: Could duration-based selection of trajectories alter the conclusions drawn from MSD analysis? For example, when calculating the MSD TA (10) from experimental data it is common to include only those motors that remained bound to the track for a certain time [15][16][17], thereby ignoring those that detached. The selection of trajectories for MSD analysis is not always described, which makes it difficult for the interested reader to assess any bias that may manifest in the MSD.…”

“…To exceed α = 2, reaching the superballistic regime, it is generally thought an acceleration is required [9]. Examples include animal movement generated by muscle contraction [10] and particles optically trapped in air [11,12], subject to increasing temperatures [13], or subject to expanding media [14].…”