Power-law scaling in dimension-to-biomass relationship of fish schools

Hiro-Sato Niwa

doi:10.1016/j.jtbi.2005.01.022

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Power-law scaling in dimension-to-biomass relationship of fish schools

Hiro-Sato Niwa

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Abstract

Motivated by the finding that there is some biological universality in the relationship between school geometry and school biomass of various pelagic fishes in various conditions, I here establish a scaling law for school dimensions: the school diameter increases as a power-law function of school biomass. The power-law exponent is extracted through the data collapse, and is close to 3/5. This value of the exponent implies that the mean packing density decreases as the school biomass increases, and the packing structure displays a mass-fractal dimension of 5/3. By exploiting an analogy between school geometry and polymer chain statistics, I examine the behavioral algorithm governing the swollen conformation of large-sized schools of pelagics, and I explain the value of the exponent.

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Hiro-Sato Niwa. 2005-06-15. Power-law scaling in dimension-to-biomass relationship of fish schools. https://doi.org/10.1016/j.jtbi.2005.01.022

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