Ecological Archives A017-054-A1

Jason E. Bruggeman, Robert A. Garrott, P. J. White, Fred G. R. Watson, and Rick Wallen. 2007. Covariates affecting spatial variability in bison travel behavior in Yellowstone National Park. Ecological Applications 17:1411–1423.

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 alpha as locations with d < 800 m exhibited nearly uniform scatter for all alpha. A negative correlation between d and alpha, anticipated for a significant movement, was present for d geq 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., alpha < 90°), similar to that with a correlated random walk (Turchin 1998), and that any movement with alpha > 90° would be more representative of a foraging or searching trajectory.

   FIG. A1. The definition of segment distance (d) and turning angle between segments (alpha) for a bison vector (dark line with arrow). The turning angle between segments, alpha, ranges between 0º≤alpha≤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 (alpha) 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.

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