Ergodicity breaking in area-restricted search of avian predators

TL;DR

This study reveals that avian predators exhibit ergodicity breaking in their movement patterns, with scale-specific behaviors and long waiting times, challenging traditional averaging methods in ecological analysis.

Contribution

The paper demonstrates ergodicity breaking in bird movement using high-resolution data and continuous-time random walk modeling, highlighting scale-dependent movement behaviors.

Findings

Subdiffusive movement behavior observed in avian predators.

Long power-law waiting times cause ergodicity breaking.

Local and large-scale movements are qualitatively different.

Abstract

Quantifying and comparing patterns of dynamical ecological systems require averaging over measurable quantities. For example, to infer variation in movement and behavior, metrics such as step length and velocity are averaged over large ensembles. Yet, in nonergodic systems such averaging is inconsistent; thus, identifying ergodicity breaking is essential in ecology. Using rich high-resolution movement datasets ($>\! 7 \times 10^7$ localizations) from 70 individuals and continuous-time random walk modeling, we find subdiffusive behavior and ergodicity breaking in the localized movement of three species of avian predators. Small-scale, within-patch movement was found to be qualitatively different, not inferrable and separated from large-scale inter-patch movement. Local search is characterized by long power-law-distributed waiting times with diverging mean, giving rise to ergodicity breaking in the form of considerable variability uniquely observed at this scale. This implies that wild animal movement is scale specific with no typical waiting time at the local scale.