Figure 1.

Schematic of potential movement time-series data: step length (net displacement between sequential locations) S; absolute direction Θ; and turning angle θ, defined to lie between (−π, π]—derived from time-indexed location data (x_t, y_t) typically collected from animal telemetry. In this paper, step-length time series S^N from multiple individuals are analysed in the context of socio-ecological and spatial information to understand properties of collective movement. Alternatively, the persistence and turning velocities at time t, defined as p_t = S_t cos(θ_t) and T_t = S_t sin(θ_t), respectively, could be studied with the methods of this paper.