Reconstructing the Intrinsic Statistical Properties of Intermittent Locomotion Through Corrections for Boundary...

Area of Science:

• Movement Ecology
• Statistical Physics
• Animal Behavior

Background:

• Locomotion data is often collected in bounded environments, introducing geometric biases.
• These biases complicate the accurate inference of behavioral features from observations.
• A null model for intermittent movement is needed to understand these effects.

Purpose of the Study:

• To investigate how enclosure in bounded spaces affects statistical properties of random walks.
• To derive methods for compensating boundary effects in movement data.
• To reconstruct intrinsic step distributions from empirical observations in confined areas.

Main Methods:

• Statistical analysis of uncorrelated random walks within bounded geometries.
• Derivation of closed-form expressions for 1D and simple 2D geometries.
• Development of an implicit expression for arbitrary convex geometries.

Main Results:

• The steady-state stopping location and empirical step probability densities are altered by enclosure.
• A multiplicative transformation relates empirical to intrinsic step distributions.
• This transformation depends solely on the boundary geometry under no-go conditions.

Conclusions:

• Boundary geometry significantly impacts random walk statistics in confined spaces.
• A method is provided to correct for boundary effects in empirical movement data.
• Reconstruction of intrinsic movement patterns from bounded observations is feasible.