Active movement of foraging sea turtles generates anomalous looping
Animals inhabiting diverse environments by moving across different spatial scales, from insects to birds, marine predators, mammals and even humans, often display apparently random movement paths. Over the past decade, novel biologging technologies have recorded these patterns in increasing detail, generating a wealth of experimental data. A central challenge is to understand such complex patterns by constructing data-driven mathematical models. Many animal movements depart from Brownian motion, as described by correlated random walks, Lévy walks, or active particle dynamics. Yet, these movement models do not incorporate long-term non-Markovian memory extracted from experimental trajectories. Here, we construct a stochastic generalised Langevin equation from satellite tracking data for loggerhead sea turtles (Caretta caretta) foraging off the coast of West Africa. We find that these turtles exhibit active movement characterised by large-scale loops that are not explained by ocean currents or chirality. These loops maintain movement within a specific foraging region and, over intermediate timescales, generate superdiffusion similar to Lévy walks. We thus identify a loop-based form of active anomalous search related to foraging patterns observed across a wide range of animal species, which may inspire robotic search strategies and AI-based metaheuristic optimisation algorithms.