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Table 1 Currently applied path characteristics. Different signals or parameters can be calculated either based on consecutive relocations within a trajectory (“stepwise”) or for multiple relocations such as identified path-segments (“across multiple steps”)

From: Path segmentation for beginners: an overview of current methods for detecting changes in animal movement patterns

Characteristic Description Type Calculation Reference
Displacement Increment of the X and Y values between two consecutive relocations, change in absolute spatial position primary stepwise [16, 34, 68]
Time lag Duration / increment in time between consecutive relocations (usually determined by sampling regime) primary stepwise [16, 34]
Turning angles / heading Relative and absolute turning angles between consecutive relocations, change in direction primary stepwise [16, 20, 37, 122]
Step length Euclidean distance between two consecutive relocations primary stepwise [16, 34]
Velocity / speed Distance traveled in a given time interval between two relocations; less sensitive to missing data than step length primary stepwise [16, 28, 34]
Persistence / turning velocity Transformations of speed and turning angle: persistence velocity represents the tendency and degree of a movement to persist in a certain direction. Turning velocity shows the tendency of a movement to turn in a perpendicular/opposite direction secondary stepwise [28, 35]
Net / mean squared displacement Squared displacement between the first and current relocation of the trajectory; applied to characterize diffusion behavior or migration patterns secondary stepwise [16, 20, 84]
First passage time Time required for crossing a predefined endpoint based on a circle (radius) around a starting relocation. Sums the times of all forward and backwards relocations within the radius; index of area-restricted search behavior secondary stepwise [31, 36, 123]
Residence time Extension of the first passage time accounting for returns of the animal in a given area. Sums the times of all relocations (backwards and forwards) of a trajectory within a given vicinity around a relocation. secondary stepwise [31]
Pseudo-Azimuth Recalculates the basic azimuth value at the midpoint between two consecutive steps to range within 0 and 360. Can be used as indicators for movements with same or parallel directions. primary stepwise [124]
Straightness index Ratio of Euclidean distance between the beginning and end of a trajectory and the total path length (sum of all step lengths) secondary across multiple steps [35, 123]
Sinuosity / Tortuosity Adaptions of the straightness index analyzing the probabilistic distributions of the changes in the turning angles and the beeline distance between the start and end points of the trajectory; index of path orientation secondary across multiple steps [38, 125]
Fractal dimension Measure of path tortuosity; non-Euclidean dimension of the trajectory varying between one (completely straight) and two (tortuous, completely spanning two-dimensional space); different implementations exist secondary across multiple steps [39, 126128]
Multi-scale straightness index Repeated calculation of the straightness index of a trajectory over a range of different temporal scales secondary across multiple steps [76]
Area interest index Repeated calculation of the straightness index for a limited size of a sliding window along the trajectory. With each repetition, the number of relocations within the trajectory is reduced secondary across multiple steps [76, 77]