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

We have analyzed a large number of rodent tracks in open field tests to elucidate the statistics of their velocities. We found that the probability distribution of the absolute velocity of individual rodents can be approximated by a superposition of two Rayleigh distributions, with distinct characteristic velocities, v₁ and v₂, with v₁2; this is in contrast to the single Rayleigh distribution for the speed of a Brownian particle executing 2D random motion. We propose that the part of the distribution near the larger speed, v₂, characterizes rodents' progressions in space, while the part near v₁ describes other types of motion, such as lingering and body micromovements. We observed that the animals switched randomly between these two modes. Since the existence of the modes is observed both in preweaned, blind pups and in older animals, it cannot be ascribed to foraging, but rather reflects risk assessment and proactive inhibition. We called such motion "cautious walks." Statistical analysis of the data further revealed a biphasic decline in the absolute velocity autocorrelation function, with two characteristic times, τ_s<τ_l, where τ_s characterizes the width of absolute 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 whose 2D Langevin-like equation has a damping coefficient that switches between two values, representing mode switching in rodent locomotion. A mechanistic analogy of rodent cautious walks is a Brownian particle that randomly switches its mass between a lighter weight and a heavier weight. 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.