Classification of anomalous diffusion in animal movement data using power spectral analysis

Ohad Vilk, Erez Aghion, Ran Nathan, Sivan Toledo, Ralf Metzler, Michael Assaf

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


The field of movement ecology has seen a rapid increase in high-resolution data in recent years, leading to the development of numerous statistical and numerical methods to analyse relocation trajectories. Data are often collected at the level of the individual and for long periods that may encompass a range of behaviours. Here, we use the power spectral density (PSD) to characterise the random movement patterns of a black-winged kite (Elanus caeruleus) and a white stork (Ciconia ciconia). The tracks are first segmented and clustered into different behaviours (movement modes), and for each mode we measure the PSD and the ageing properties of the process. For the foraging kite we find 1/f noise, previously reported in ecological systems mainly in the context of population dynamics, but not for movement data. We further suggest plausible models for each of the behavioural modes by comparing both the measured PSD exponents and the distribution of the single-trajectory PSD to known theoretical results and simulations.

Original languageEnglish
Article number334004
JournalJournal of Physics A: Mathematical and Theoretical
Issue number33
StatePublished - 19 Aug 2022
Externally publishedYes

Bibliographical note

Funding Information:
For fieldwork and technical assistance we thank Y Orchan, R Shaish, A Levi, S Rotics and M Kaatz. RN acknowledges support from JNF/KKL Grant 60-01-221-18 and DIP (DFG) Grant NA 846/1. RN also acknowledges support from The Minerva Foundation, the Minerva Center for Movement Ecology and the Adelina and Massimo Della Pergola Chair of Life Sciences. RM acknowledges the German Science Foundation (DFG) for support within grant ME 1535/12-1. OV and MA acknowledge support from the ISF Grant 531/20. MA also acknowledges Alexander von Humboldt Foundation for an experienced researcher fellowship.

Publisher Copyright:
© 2022 The Author(s). Published by IOP Publishing Ltd.


  • diffusion, anomalous diffusion
  • ecological movement data
  • power spectral analysis


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