The Lévy flight foraging hypothesis: forgetting about memory may lead to false verification of Brownian motion

Arild O Gautestad and Atle Mysterud in Movement Ecology

Arild O. Gautestad and Atle Mysterud



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.


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.


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.

Movement Ecology 2013, 1:9, Published: 14 October 2013

Tags: Movement Ecology;
Published Oct. 25, 2013 2:49 PM - Last modified Oct. 10, 2014 4:31 PM