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Fractal scaling in bottlenose dolphin (Tursiops truncatus) echolocation: A case study

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  • Perisho, Shaun T.
  • Kelty-Stephen, Damian G.
  • Hajnal, Alen
  • Houser, Dorian
  • Kuczaj II, Stan A.

Abstract

Fractal scaling patterns, which entail a power-law relationship between magnitude of fluctuations in a variable and the scale at which the variable is measured, have been found in many aspects of human behavior. These findings have led to advances in behavioral models (e.g. providing empirical support for cascade-driven theories of cognition) and have had practical medical applications (e.g. providing new methods for early diagnosis of medical conditions). In the present paper, fractal analysis is used to investigate whether similar fractal scaling patterns exist in inter-click interval and peak–peak amplitude measurements of bottlenose dolphin click trains. Several echolocation recordings taken from two male bottlenose dolphins were analyzed using Detrended Fluctuation Analysis and Higuchi’s (1988) method for determination of fractal dimension. Both animals were found to exhibit fractal scaling patterns near what is consistent with persistent long range correlations. These findings suggest that recent advances in human cognition and medicine may have important parallel applications to echolocation as well.

Suggested Citation

  • Perisho, Shaun T. & Kelty-Stephen, Damian G. & Hajnal, Alen & Houser, Dorian & Kuczaj II, Stan A., 2016. "Fractal scaling in bottlenose dolphin (Tursiops truncatus) echolocation: A case study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 221-230.
    • Handle: RePEc:eee:phsmap:v:443:y:2016:i:c:p:221-230
    DOI: 10.1016/j.physa.2015.09.012
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    References listed on IDEAS

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    1. Schmitt, Francccois G. & Seuront, Laurent, 2001. "Multifractal random walk in copepod behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 375-396.
    2. Seuront, Laurent & Cribb, Nardi, 2011. "Fractal analysis reveals pernicious stress levels related to boat presence and type in the Indo–Pacific bottlenose dolphin, Tursiops aduncus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2333-2339.
    3. David W. Sims & Victoria A. Quayle, 1998. "Selective foraging behaviour of basking sharks on zooplankton in a small-scale front," Nature, Nature, vol. 393(6684), pages 460-464, June.
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