Appendix A. Figures depicting the definition of turning angle between segments, criteria for a significant movement bout, segment distance versus turning angle, and a histogram of turning angles.
Our criterion of 800 m was determined from a plot of d against as locations with d < 800 m exhibited nearly uniform scatter for all . A negative correlation between d and , anticipated for a significant movement, was present for d 800 m (Fig. A4). Based on field observations we also rationalized that bison moving at least 800 m in 30 min would spend the majority of time sustaining travel rather than foraging. Our second criterion of 90° was chosen based on field observations of foraging and traveling bison. We decided that bison engaged in sustained travel (i.e., significant movement) would have a forward directional component (i.e., < 90°), similar to that with a correlated random walk (Turchin 1998), and that any movement with > 90° would be more representative of a foraging or searching trajectory.
|FIG. A1. The definition of segment distance (d) and turning angle between segments () for a bison vector (dark line with arrow). The turning angle between segments, , ranges between 0º≤≤180º.|
|FIG. A2. A bison travel vector consisting of two significant movements. By definition, for a significant movement the distance of each segment must be ≥800 m (i.e., d1 ≥ 800 m; d2 ≥ 800 m) and the turning angle must be ≤90º.|
|FIG. A3. A set of bison vectors that are representative of a foraging or searching trajectory for which the turning angle between segments has a value >90º and/or segment distances (d) are <800 m (i.e., d1< 800 m; d2< 800 m).|
|FIG. A4. A plot of segment distance (d) vs. turning angle () for consecutive bison GPS locations obtained <32 min apart.|
|FIG. A5. A histogram of turning angles for all of the GPS data before editing for significant movement based on distance and turning angle criteria.|
Turchin, P. 1998. Quantitative Analysis of Movement: measuring and modeling population redistribution in animals and plants. Sinauer Associates, Sunderland, Massachusetts, USA.