Spatially scale-invariant Lévy walk (power-law) patterns seem common among animals that move continually during searching. Scaling-laws also describe well the spontaneous patterns of waiting times of sit-and-wait ambush predators, which show random ‘burstiness’ that appears scale-invariant across a broad set of scales. The occurrence of these scaling laws has been attributed to stochastic decision-based queuing processes. Taken together these various studies suggest that stochastic decision-based queuing processes may apply more generally across taxa with divergent foraging strategies, ranging from highly mobile pursuit predators to the less mobile ambush predators. Here we provide support for this proposition by demonstrating that simple stochastic priority processes capture accurately the timings of dives made by little penguins (Eudyptula minor) in their natural habitat, whose use of space and time falls between that of sit-and-wait predators and Lévy walkers.