Are your data too coarse for speed estimation? Diffusion rates as an alternative measure of animal movement

Estimates of speed and distance traveled are routine in ecological research to provide a link between behavior and energetics. Conventional straight-line displacement (SLD) methods return severely and differentially biased estimates with no ability to evaluate the accuracy of the estimate. Recent methodological advances have improved our ability to estimate these parameters using continuous-time speed and distance (CTSD) estimation. However, even with CTSD estimation, many datasets are too coarse, or the location error is too great to reliably measure speed or distance traveled. To address these limitations, we investigated the relationship between CTSD-estimated mean speed and diffusion rate, where diffusion rate is defined as the variance in displacements per time interval. We calculated CTSD mean speed and diffusion rate estimates using telemetry data (i.e., trajectory data) from over 100 white-tailed deer and simulated telemetry data generated from a known movement model. We examined the relationship between the two measures in both datasets and the effect of sampling frequency on the effective sample size and the estimation of the two parameters. We found that mean speed and diffusion rate were strongly and nonlinearly correlated, with a 1% increase in diffusion rate predicting a 0.40% increase in mean speed (99% CI: 0.38-0.42%) for our focal species. Diffusion rate estimates remained substantially more accurate and precise than speed across sampling interval regimes, even when speed estimation was not possible. Our findings demonstrate that diffusion rate outperforms mean speed as a measure of movement activity under marginal data conditions. Diffusion rate is a reliable measure of movement activity and can link behavior to energetics across a wider range of datasets while maintaining accuracy even when data quality is low. By using speed and diffusion together, researchers can rely on more robust insights into space use across a range of ecological contexts.