Neumeister H, Cellucci C J, Rapp P E, Korn H, Faber D S
Department of Neuroscience, Albert Einstein College of Medicine of Yeshiva University, Bronx, NY 10461, USA.
J Exp Biol. 2004 Feb;207(Pt 4):697-708. doi: 10.1242/jeb.00811.
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.
对金鱼游动进行了定量分析，以确定其是否呈现出独特的个体时空模式。由于鱼类运动存在固有的变异性，因此使用五种非线性测量方法并辅以平均速度对这一假设进行了检验。构建了一个包含75条轨迹的库，每条轨迹时长5分钟，这些轨迹是从五条在恒定且相对均匀的环境中游泳的金鱼获取的。三种非线性测量方法，即“特征分形维数”和“理查森维数”（均用于量化轨迹偏离直线的程度）以及“相对离散度”（用于表征方差随持续时间的变化），其变异系数均小于7%，而平均速度的变异系数为30%。基于所有六种测量方法的判别分析或分类系统表明，轨迹确实具有高度的个体特异性，不同鱼类产生的任意两条轨迹相同的概率小于1%。也就是说，这些测量方法的组合能够高度自信地将给定轨迹与其来源进行匹配。理查森维数和量化持续性的“赫斯特指数”是最有效的测量方法。
