How superdiffusion gets arrested: ecological encounters explain shift from Lévy to Brownian movement

M. de Jager, F. Bartumeus, A. Kölzsch, F.J. Weissing, G.M. Hengeveld, B.A. Nolet, P.M.J. Herman, J. van de Koppel

Research output: Contribution to journalArticleAcademicpeer-review

41 Citations (Scopus)


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
Original languageEnglish
Article number20132605
Number of pages8
JournalProceedings of the Royal Society. B: Biological Sciences
Issue number1774
Publication statusPublished - 2014


  • power-law distributions
  • flight search patterns
  • environmental complexity
  • walks evolve
  • predators
  • dynamics
  • animals
  • mussels
  • success

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