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First published online January 12, 2004
Journal of Experimental Biology 207, 697-708 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.00811

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Dynamical analysis reveals individuality of locomotion in goldfish

H. Neumeister^1,*, C. J. Cellucci², P. E. Rapp³, H. Korn⁴ and D. S. Faber¹

¹ Department of Neuroscience, Albert Einstein College of Medicine of Yeshiva University, 1410 Pelham Parkway South, Bronx, NY 10461, USA
² Department of Physics, Ursinus College, Collegeville, PA 19426, USA
³ Department of Pharmacology and Physiology, Drexel University College of Medicine, Philadelphia, PA 19102, USA
⁴ Institute Pasteur, 28 Rue du Dr Roux, Paris, Cedex 15, France

^* Author for correspondence (e-mail: hneumeis{at}aecom.yu.edu)

Accepted 24 November 2003

Goldfish swimming was analysed quantitatively to determine if it exhibits distinctive individual spatio-temporal patterns. Due to the inherent variability in fish locomotion, this hypothesis was tested using five nonlinear measures, complemented by mean velocity. A library was constructed of 75 trajectories, each of 5 min duration, acquired from five fish swimming in a constant and relatively homogeneous environment. Three nonlinear measures, the `characteristic fractal dimension' and `Richardson dimension', both quantifying the degree to which a trajectory departs from a straight line, and `relative dispersion', characterizing the variance as a function of the duration, have coefficients of variation less than 7%, in contrast to mean velocity (30%). A discriminant analysis, or classification system, based on all six measures revealed that trajectories are indeed highly individualistic, with the probability that any two trajectories generated from different fish are equivalent being less than 1%. That is, the combination of these measures allows a given trajectory to be assigned to its source with a high degree of confidence. The Richardson dimension and the `Hurst exponent', which quantifies persistence, were the most effective measures.

Key words: fish, behaviour, individuality, locomotion, velocity, nonlinear dynamics, complexity, discriminant analysis