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

Abstract

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.

11 pages, 5 figures

References in corpus (7)

• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Spectral content of a single non-Brownian trajectory
• First-passage and first-hitting times of Levy flights and Levy walks
• Classification of particle trajectories in living cells: machine learning versus statistical testing hypothesis for fractional anomalous diffusion
• Aging power spectrum of membrane protein transport and other subordinated random walks
• Self-organised criticality and 1/f noise in single-channel current of voltage-dependent anion channel
• $1/f^{\beta }$ noise for scale-invariant processes: How long you wait matters