Ergodicity Breaking in Area-Restricted Search of Avian Predators

Abstract

Quantifying and comparing patterns of dynamical ecological systems requires 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 data sets (greater than 7×10^{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 interpatch movement. Local search is characterized by long, power-law-distributed waiting times with a 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.