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First published online March 2, 2007
Journal of Experimental Biology 210, 935-945 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02710

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Fractal landscape method: an alternative approach to measuring area-restricted searching behavior

Yann Tremblay^1,*, Antony J. Roberts² 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 Department of Mathematics and Computing, University of Southern Queensland, Toowoomba 4352, Australia

^* Author for correspondence (e-mail: tremblay{at}biology.ucsc.edu)

Accepted 8 January 2007

Quantifying spatial and temporal patterns of prey searching is of primary importance for understanding animals' critical habitat and foraging specialization. In patchy environments, animals forage by exhibiting movement patterns consisting of area-restricted searching (ARS) at various scales. Here, we present a new method, the fractal landscape method, which describes the peaks and valleys of fractal dimension along the animal path. We describe and test the method on simulated tracks, and quantify the effect of track inaccuracies. We show that the ARS zones correspond to the peaks from this fractal landscape and that the method is near error-free when analyzing high-resolution tracks, such as those obtained using the Global Positioning System (GPS). When we used tracks of lower resolution, such as those obtained with the Argos system, 9.6–16.3% of ARS were not identified, and 1–25% of the ARS were found erroneously. The later type of error can be partially flagged and corrected. In addition, track inaccuracies erroneously increased the measured ARS size by a factor of 1.2 to 2.2. Regardless, the majority of the times and locations were correctly flagged as being in or out of ARS (from 83.8 to 89.5% depending on track quality). The method provides a significant new tool for studies of animals' foraging behavior and habitat selection, because it provides a method to precisely quantify each ARS separately, which is not possible with existing methods.

Key words: fractal dimension, fractal landscape, elephant seal, albatross, foraging, prey-searching strategy, tracking, Argos, top predator, area-restricted search