Two modes in the velocity statistics in cautious walks of laboratory rodents

We have analyzed a large number of rodent tracks in open-field tests, in order to elucidate the statistics of their velocities. We found that the probability distribution of the absolute velocity of rodents can be approximated by a superposition of two Rayleigh distributions, with distinct characteristic velocities v 1 and v 2 with v 1 < v 2; this is in contrast to the single Rayleigh distribution for the velocity of a Brownian particle executing 2D random motion. We propose that the part of the distribution near the larger velocity, v 2, characterizes rodents’ progressions in space, while the part near v 1 describes other types of motion, such as lingering and body micromovements. We observed that the animals switched randomly between these two modes. While both velocities, v 1 and v 2, increase with age, their ratio, v 2 /v 1, also grows with age, implying an increased efficacy of switches between the two modes in older animals. Since the existence of the modes is observed both in preweaned, blind pups and in older animals, it cannot be ascribed to foraging, but instead reflects risk assessment and proactive inhibition. We called such motion “cautious walks”. Statistical analysis of the data further revealed a biphasic decline in the velocity auto-correlation function, with two characteristic times, τ s < τ l , where τ s characterizes the width of velocity peaks, and τ l is associated with the timing of the switches between progression and lingering. To describe the motion, we propose a stochastic model, which assumes the existence of two interfering processes: impulses to move that arrive at random times, and continuous deceleration. Its 2D Langevin-like equation has a damping coefficient that switches between two values, representing mode switching in rodents. Techniques developed here may be applicable for locomotion studies in a wide variety of contexts, as long as tracking data of sufficient resolution are available. ### Competing Interest Statement The authors have declared no competing interest.