Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search

During their trajectories in still air, fruit flies (Drosophila melanogaster) explore their landscape using a series of straight flight paths punctuated by rapid 90 degrees body-saccades [1]. Some saccades are triggered by visual expansion associated with collision avoidance. Yet many saccades are not triggered by visual cues, but rather appear spontaneously. Our analysis reveals that the control of these visually independent saccades and the flight intervals between them constitute an optimal scale-free active searching strategy. Two characteristics of mathematical optimality that are apparent during free-flight in Drosophila are inter-saccade interval lengths distributed according to an inverse square law, which does not vary across landscape scale, and 90 degrees saccade angles, which increase the likelihood that territory will be revisited and thereby reduce the likelihood that near-by targets will be missed. We also show that searching is intermittent, such that active searching phases randomly alternate with relocation phases. Behaviorally, this intermittency is reflected in frequently occurring short, slow speed inter-saccade intervals randomly alternating with rarer, longer, faster inter-saccade intervals. Searching patterns that scale similarly across orders of magnitude of length (i.e., scale-free) have been revealed in animals as diverse as microzooplankton, bumblebees, albatrosses, and spider monkeys, but these do not appear to be optimised with respect to turning angle, whereas Drosophila free-flight search does. Also, intermittent searching patterns, such as those reported here for Drosophila, have been observed in foragers such as planktivorous fish and ground foraging birds. Our results with freely flying Drosophila may constitute the first reported example of searching behaviour that is both scale-free and intermittent.