title: The Lévy flight foraging hypothesis: forgetting about memory may lead to false verification of Brownian motion.
abstract: BACKGROUND
  The Lévy flight foraging hypothesis predicts a transition from scale-free Lévy walk (LW) to scale-specific Brownian motion (BM) as an animal moves from resource-poor towards resource-rich environment. However, the LW-BM continuum implies a premise of memory-less search, which contradicts the cognitive capacity of vertebrates.
  
  
  RESULTS
  We describe methods to test if apparent support for LW-BM transitions may rather be a statistical artifact from movement under varying intensity of site fidelity. A higher frequency of returns to previously visited patches (stronger site fidelity) may erroneously be interpreted as a switch from LW towards BM. Simulations of scale-free, memory-enhanced space use illustrate how the ratio between return events and scale-free exploratory movement translates to varying strength of site fidelity. An expanded analysis of GPS data of 18 female red deer, Cervus elaphus, strengthens previous empirical support of memory-enhanced and scale-free space use in a northern forest ecosystem.
  
  
  CONCLUSIONS
  A statistical mechanical model architecture that describes foraging under environment-dependent variation of site fidelity may allow for higher realism of optimal search models and movement ecology in general, in particular for vertebrates with high cognitive capacity.
authors.affiliation: Centre for Ecological and Evolutionary Synthesis, Department of Biosciences, University of Oslo, P.O. Box 1066, Blindern, Oslo, NO-0316 Norway.
authors.forename: Arild O
authors.initials: AO
authors.lastname: Gautestad
authors.affiliation: Centre for Ecological and Evolutionary Synthesis, Department of Biosciences, University of Oslo, P.O. Box 1066, Blindern, Oslo, NO-0316 Norway.
authors.forename: Atle
authors.initials: A
authors.lastname: Mysterud
keywords: Lévy flight foraging hypothesis; Memory-influenced movement; Optimal foraging; Scale-free space use; Site fidelity; Statistical mechanics of movement