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

JOURNAL OF THEORETICAL BIOLOGY

卷:524

Article

Ahmed, D. A.¹  Benhamou, S.²  Bonsall, M. B.³  Petrovskii, S., V^4,5 

[1] Gulf Univ Sci & Technol, Ctr Appl Math & Bioinfottnat CAMB, Dept Math & Nat Sci, POB 7207, Hawally 32093, Kuwait

[2] CNRS, Cogitamus Lab, Ctr Ecol Fonct & Evolut, Montpellier, France

[3] Univ Oxford, Dept Zool, Math Ecol Res Grp, Mansfield Rd, Oxford OX1 3SZ, England

[4] Univ Leicester, Sch Math & Actuarial Sci, Univ Rd, Leicester LE1 7RH, Leics, England

[5] Peoples Friendship Univ Russia RUDN Univ, 6 Miklukho Maklaya St, Moscow 117198, Russia

关键词: 3D random walks;    Simple random walk;    Correlated random walk;    Biased random walk;    Animal movement;    Trapping;    Optimal trap efficiency;   

DOI  :  10.1016/j.jtbi.2021.110728

来源: Elsevier

【 摘 要 】

Background: 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. Methods: 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. Results: 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. Conclusion: 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. (C) 2021 The Author(s). Published by Elsevier Ltd.

【 授权许可】

Free