Quantifying animal movement: Using a power-law to model the relationship between first passage time and scale

In a heterogenous environment, an animal will increase its search effort in areas where resources are abundant. This behavior can be detected in a path by a decrease in speed, an increase in tortuosity, or both. First passage time, the amount of time required for an animal to traverse a circle of a given radius, or buffer, is a common metric for quantifying spatial and temporal changes along a path. Historical methodology involving first passage time limits the utility of this metric. Here we instead follow the methodology put forth by Street et al. (2018) and use a power-law model to characterize the relationship between first passage time and the scale of the first passage time buffer radii. We then test the model’s applicability across multiple movement modes using simulated data and further explore its utility by applying it to a dataset of deer movement and the associated landscape data