Fractal Distribution of an Oceanic Copepod Neocalanus cristatus in the Subarctic Pacific

Horizontal distribution of the copepod Neocalanus cristatus was shown to be fractal on the scale between tens of meters and over 100 km. The fractal dimensions ranged between 1.68–1.89, significantly higher than those of oceanic turbulence and phytoplankton distribution. 1. Introduction Heterogeneity in the horizontal distribution of zooplankton has been recognized for many years (e.g. Hardy, 1936). The phenomenon, however, has seldom been described precisely, although zooplankton patchiness is relevant to many aspects of biological oceanography. Recent studies reveal that copepod patches do not exhibit characteristic lengths (Mackas and Boyd, 1979; Tsuda et al., 1993) and that the patterns of copepod distribution are self-similar and independent of the scale of observation (Tsuda et al., 1993). These findings suggest that copepod distributions may be fractal. Mandelbrot (1967) introduced the concept of fractals for temporally or spatially irregular phenomena which show self-similarities over a wide range of scales. Many fractal objects have been found in nature (Mandelbrot, 1982), and the theory has been applied to some ecological studies (Morse et al. Therefore, plankton living in the medium should also have fractal facets. In fully developed turbulence, a given order of eddy generates smaller eddies by nonlinear interactions (Richardson, 1922). This recurring scheme produces a hierarchy of eddies in the sea. A hierarchical structure similar to the ambient flow was observed in the distribution of copepods (Tsuda et al., 1993). Spectral analysis has been used for examining irregular time series, and a relationship between fractal analysis and power spectrum analysis has been reported and some fractal measures provide a more stable estimation of dimension than that of power law index in spectral analysis when the number of data is limited (Higuchi, 1990). The goal of the present study is to test the hypothesis that the horizontal distribution of the oceanic copepod, Neocalanus cristatus, is fractal.