Scaling of size, shape and surface roughness in Antarctic krill swarms

Antarctic krill are obligate swarmers and the size and shape of the swarms they form can have a major influence on trophic interactions and biogeochemical fluxes. Parameterizing variability in size and shape is therefore a useful step toward understanding the operation of the Southern Ocean ecosystem. We analyse the relationships between the length L L⁠, thickness T T⁠, perimeter P P⁠, and area A A of 4650 vertical cross-sections of open-ocean krill swarms obtained within the Atlantic sector of the Southern Ocean in summer 2003. Our data show that these parameters are tightly interrelated. The thickness T T increases on average as L 0.67 L0.67 and has a log-normal distribution within each length class. The perimeter and area scale with L L and T T as P∼L 0.77 T P∼L0.77T and A∼L 0.86 T 0.48 A∼L0.86T0.48⁠. The swarm aspect ratio, T/L T/L⁠, decreases approximately as L −0.32 L-0.32⁠. The surface roughness (defined as P/A P/A⁠) has a weak dependence on swarm length and decreases approximately as T −0.46 T-0.46⁠, which can be explained only by the appearance of indentations and cavities in the swarm shape. Overall, our study finds that there are distinct limits to the size and shape of swarms that Antarctic krill appear to be capable of forming and we explore the potential explanatory factors contributing to these limitations.

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