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

M.B Bonsall,S.V Petrovskii,D.A Ahmed,S Benhamou

doi:10.1016/j.jtbi.2021.110728

Abstract

Random walks (RWs) have proved to be a powerful modelling tool in ecology, particularly in the study of animal movement. An application of RW concerns trapping which is the predominant sampling method to date in insect ecology and agricultural pest management. A lot of research effort has been directed towards modelling ground-dwelling insects by simulating their movement in 2D, and computing pitfall trap counts, but comparatively very little for flying insects with 3D elevated traps. We introduce the mathematics behind 3D RWs and present key metrics such as the mean squared displacement (MSD) and path sinuosity, which are already well known in 2D. We develop the mathematical theory behind the 3D correlated random walk (CRW) which involves short-term directional persistence and the 3D Biased random walk (BRW) which introduces a long-term directional bias in the movement so that there is an overall preferred movement direction. In this study, we focus on the geometrical aspects of the 3D trap and thus consider three types of shape; a spheroidal trap, a cylindrical trap and a rectangular cuboidal trap. By simulating movement in 3D space, we investigated the effect of 3D trap shapes and sizes and of movement diffusion on trapping efficiency. We found that there is a non-linear dependence of trap counts on the trap surface area or volume, but the effect of volume appeared to be a simple consequence of changes in area. Nevertheless, there is a slight but clear hierarchy of trap shapes in terms of capture efficiency, with the spheroidal trap retaining more counts than a cylinder, followed by the cuboidal type for a given area. We also showed that there is no effect of short-term persistence when diffusion is kept constant, but trap counts significantly decrease with increasing diffusion. Our results provide a better understanding of the interplay between the movement pattern, trap geometry and impacts on trapping efficiency, which leads to improved trap count interpretations, and more broadly, has implications for spatial ecology and population dynamics.

Highlights

Modelling individual animal movement and navigation strategies using random walks has long been a successful tradition in movement ecology (Nathan et al, 2008)
We found that there is a non-linear dependence of trap counts on the trap surface area or volume, but the effect of volume appeared to be a simple consequence of changes in area
We showed that there is no effect of short-term persistence when diffusion is kept constant, but trap counts significantly decrease with increasing diffusion

Summary

Results

Random walks (RWs) are appropriate approaches for understanding species movement patterns as a stochastic or statistical description of dispersal 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 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). Simulation of trap counts using individual based models provides a robust and plausible alternative to analytical approaches

Conclusion

Introduction