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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 Tremblay1,*, 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


Figure 1
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  		Fig. 1. Example of a simulated track of an elephant seal. (A) A Global Positioning System (GPS)-like track containing two area-restricted searching (ARS) zones. (B) This shows the track after the introduction of spatial error and temporal sub-sampling, as obtained in real deployments using the Argos tracking technique. (C) The same track after the filtering and the interpolation process (see Materials and methods for details).

 

Figure 2
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  		Fig. 2. Test of the accuracy and the sensitivity to sub-sampling of the algorithm used to calculate fractal dimension. Tests were run on five datasets of known theoretical fractal dimensions. The thick line is a smoothed representation (moving average) of the thin line.

 

Figure 3
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  		Fig. 3. Graphic output of the fractal landscape analysis. (A) The fractal landscape: seven peaks in fractal dimension are distinguishable. (B) This illustrates the way the threshold for determining the peaks is determined. The blue line is a smoothing (moving average) of the calculated number of peaks over the threshold (gray line). (C) This shows the corresponding track, with the seven zones corresponding to the seven fractal peaks highlighted and numbered. The color of the circles delimiting the area-restricted search zones is scaled based on the area over the threshold of the corresponding fractal peak (green shade in A). This is considered as an index of searching intensity.

 

Figure 4
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  		Fig. 4. Performance of the fractal landscape method in the detection of area-restricted searching (ARS) in intact simulated tracks (Global Positioning System (GPS)-like tracks (A) and in corrected tracks (Argos-like tracks) (B). Open circles, albatross; blue triangles, elephant seal-like tracks.

 

Figure 5
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  		Fig. 5. Zoomed portion of a simulated track showing the circles in which the area-restricted searching (ARS) was constrained to stay within (gray circles, see Materials and methods for details) and the circles corresponding to the output of the fractal landscape method (yellow circles). The yellow circles are visually very close to the spatial extent of the simulated ARS.

 

Figure 6
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  		Fig. 6. Distribution of the sizes of the area-restricted searching (ARS) calculated by the fractal landscape method in albatross- (A) and elephant seal-like tracks (B). Kernel densities are shown instead of histograms for clarity. The blue, solid line is the distribution obtained with intact tracks [Global Positioning System (GPS)-like tracks] and the red, dotted line was obtained with corrected tracks (Argos-like tracks). The shift towards larger ARS is a consequence of the Argos spatial inaccuracies. A correction factor applied to these data improved results (black, broken line; see Results and discussion for details).

 

Figure 7
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  		Fig. 7. Example of the fractal landscape analysis output on a real track of Laysan albatross (Phoebastria immutabilis). The inset figure shows the entire track. The color of the area-restricted searched (ARS) zones corresponds to a searching-intensity index (see Materials and methods, and Fig. 3). The ARS with the highest intensities are spread along a west-east transect corresponding to a food-rich frontal zone (see Results and discussion). The broken perimeter corresponds to the area in which the small-scale searching (the ARS) occurred. It is proposed as a possible (but non-exclusive) method to extrapolate the second (larger) scale at which the individual operated (see Results and discussion for details).

 

Figure 8
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  		Fig. 8. Number of area-restricted searching (ARS) detected using the fractal landscape method using different segment lengths for the calculation of the fractal dimensions along the track.

 




© The Company of Biologists Ltd 2007