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First published online December 14, 2005
Journal of Experimental Biology 209, 128-140 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.01970

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Interpolation of animal tracking data in a fluid environment

Yann Tremblay^1,*, Scott A. Shaffer¹, Shannon L. Fowler¹, Carey E. Kuhn¹, Birgitte I. McDonald¹, Michael J. Weise¹, Charle-André Bost², Henri Weimerskirch², Daniel E. Crocker³, Michael E. Goebel⁴ and Daniel P. Costa¹

¹ University of California, Santa Cruz, Long Marine Laboratory, Center for Ocean Health, 100 Shaffer Road, Santa Cruz, CA 95060, USA
² Centre d'Etude Biologiques de Chizé, 79360 Villiers en Bois, France
³ Department of Biology, Sonoma State University, Rohnert Park, CA 94928, USA
⁴ NOAA, National Marine Fisheries, 8604 La Jolla Shores Drive, La Jolla, CA 92038, USA

View larger version (40K): [in a new window]   Fig. 1. Laysan albatross Argos track (A), and selected examples of linear (B) and Bézier (C) interpolation of this track (every 10 min). In B and C, the circled cross represents an Argos position that was removed to use as a reference position. The distance between this position and the corresponding interpolated location was calculated for each mathematical algorithm that we used (see Materials and methods). Note the possibility to visualize transit speed in interpolated tracks.

View larger version (33K): [in a new window]   Fig. 2. Selected example of a black-footed albatross track, illustrating some of the various versions of the track. In this example, the geolocation-like Argos track was interpolated using the Bézier algorithm with µ=0.3 (dashed line).

View larger version (28K): [in a new window]   Fig. 3. Occurrence of more accurate locations when using curvilinear algorithm compared with a linear interpolation method for each species, each curvilinear algorithm and each track (i.e. each individual). Dots (representing individuals/tracks) are alternately shown in black and grey for clarity. Dots to the right of the 50% line represent tracks in which the curvilinear method yields more accurate locations than the linear interpolation method.

View larger version (23K): [in a new window]   Fig. 4. Female northern elephant seal Argos tracks (A) and enlargement of a portion of a track (B), illustrating Runge's oscillation (overshoot) of the cubic spline (squares) interpolation (every 10 min) compared with the Bézier algorithm (circles).