Idzhilova, O. | Search bioRxiv

bioRxiv2025

Pros and cons of group averaging in studies of stochastic rodent locomotion

We analyze spontaneous walks of rodent pups in a novel environment. Individual speed distributions follow a two-component Rayleigh distribution, reflecting bimodal locomotion (progressions and lingering), while the ensemble-averaged distribution simplifies to a single exponential decay with a slower high-speed decay rate. This discrepancy arises from population heterogeneity in characteristic speeds. We propose a stochastic differential equation (SDE) for the averaged rodent, which in some cases can be derived by averaging the individual SDE. The SDEs reveal a striking mechanistic difference in the nature of individual and averaged motion: individual rodents exhibit viscous friction (deceleration proportional to speed), whereas the ensemble behaves as if subject to dry friction (constant deceleration). We propose an algorithm of creating a "reference" rodent, which retains the shape of individual distributions but utilizes averaged scale parameters. It can be a useful personalized comparison tool to extract the information on the locomotor modes, e.g. in biomedical contexts.

animal behavior and cognition↗

bioRxiv2024

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 v1 and v2 with v1 < v2; 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, 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. While both velocities, v1 and v2, increase with age, their ratio, v2/v1, 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,{tau} s < {tau}l, where{tau} s characterizes the width of velocity peaks, and{tau} 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.

biophysics↗