Determination of characteristic length scale in insect flight

Diffusion models are widely used to describe insect dispersal, but their validity depends on the time and length scales over which movement is observed. Motion can only be approximated as random at long length scales, in which the combined effects of many non-random processes become indistinguishable. In this study, simple random walk (SRW) and correlated random walk (CRW) simulations are compared to examine how directional persistence affects effective diffusion in five insect test-cases derived from literature. The transition from correlated motion toward effective diffusion was assessed using separate time-domain measures using the analytical and numerical time-dependent mean-squared-displacement (MSD) crossover and the time-dependent Kolmogorov–Smirnov distance, KSD ( t ) , between the CRW x -marginal displacement distribution and its asymptotic Gaussian form. The orientation-vector time series was then analyzed by examining how its variation was distributed across frequencies. Directional persistence increased low-frequency structure in the CRW orientation-vector power spectral density. An operational − 3 dB characteristic frequency was identified by comparing the CRW and SRW spectra and was converted into corresponding time and length scales. The choice of − 3 dB as the operational spectral threshold was supported by the close agreement of its mean characteristic time, 2.31 τ , with the numerical MSD crossover at 2.11 τ , the analytical MSD crossover at approximately 2 τ , and the earlier stage of Gaussian convergence at 2.13 τ using KSD ( t ) ≤ 0.1 . These results show that the transition toward effective diffusion is gradual and support the spectral cutoff as a characteristic estimate of the scale associated with this transition.