How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement.
Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fashion when resources are abundant. We demonstrate that Einstein's original theory of collision-induced Brownian motion in physics provides a parsimonious, mechanistic explanation for these observations. Here, Brownian motion results from frequent encounters between organisms in dense environments. In density-controlled experiments, movement patterns of mussels shifted from Lévy towards Brownian motion with increasing density. When the analysis was restricted to moves not truncated by encounters, this shift did not occur. Using a theoretical argument, we explain that any movement pattern approximates Brownian motion at high-resource densities, provided that movement is interrupted upon encounters. Hence, the observed shift to Brownian motion does not indicate a density-dependent change in movement strategy but rather results from frequent collisions. Our results emphasize the need for a more mechanistic use of Brownian motion in ecology, highlighting that especially in rich environments, Brownian motion emerges from ecological interactions, rather than being a default movement pattern.
Spatial Ecology Department, Royal Netherlands Institute for Sea Research (NIOZ), , PO Box 140, 4400 AC Yerseke, The Netherlands, Theoretical Biology Group, University of Groningen, , Nijenborgh 7, 9747 AG Groningen, The Netherlands, Community and Conservation Ecology Group, Centre for Ecological and Evolutionary Studies, University of Groningen, , Nijenborgh 7, 9747 AG Groningen, The Netherlands, Institute of Integrative Biology, ETH Zürich, Universitaetstrasse 16, 8092 Zürich, Switzerland, Center for Advanced Studies of Blanes (CEAB-CSIC), , Accés Cala Sant Francesc, 14, 17300 Blanes, Girona, Spain, Department of Animal Ecology, Netherlands Institute of Ecology (NIOO-KNAW), , PO Box 50, 6700 AB Wageningen, The Netherlands, Project Group Movement Ecology, Netherlands Institute of Ecology (NIOO-KNAW), , PO Box 50, 6700 AB Wageningen, The Netherlands.
Monique
M
de Jager
Frederic
F
Bartumeus
Andrea
A
Kölzsch
Franz J
FJ
Weissing
Geerten M
GM
Hengeveld
Bart A
BA
Nolet
Peter M J
PM
Herman
Johan
J
van de Koppel
D000818:Animals; D001522:Behavior, Animal; D049872:Bivalvia / Q000502:physiology*; D017753:Ecosystem; D004777:Environment; D009068:Movement; D011156:Population Density; D011157:Population Dynamics
Brownian motion; Lévy walk; Mytilus edulis; animal movement; resource density; search efficiency