Phase transition and ergodicity breaking during avian foraging

In this talk we review two recent works dealing with the modeling of anomalous animal movement during foraging. 

In the first work we study ergodicity breaking in foraging of avian predators. Indeed, quantifying and comparing patterns of dynamical ecological systems requires averaging over measurable quantities. Yet, in nonergodic systems, such averaging is inconsistent; thus, identifying ergodicity breaking is essential in ecology. Using rich, high-resolution, movement data sets 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 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.

In the second work we study foraging of Egyptian fruit bats using a non-Markovian and nonstationary model of animal mobility, whichincorporates both exploration and memory in the form of preferential returns. Notably, a mean-field version of this model, first suggested by Song et al. [Nat. Phys. 6, 818 (2010)] was shown to well describe human movement data. Exact results for the probability of visiting a given number of sites are derived and a practical WKB approximation to treat the nonstationary problem is developed. Our results are shown to agree well with empirical movement data of the fruit bats when accounting for interindividual variation in the population. We also study the probability of visiting any site a given number of times and derive a mean-field equation. Our analysis yields a remarkable phase transition occurring at preferential returns which scale linearly with past visits. Following empirical evidence, we suggest that this phase transition reflects a trade-off between extensive and intensive foraging modes.