A Laplacian characterization of phytoplankton shape

Abstract

Phytoplankton exhibit pronounced morphological diversity, impacting a range of processes. Because these impacts are challenging to quantify, however, phytoplankton are often approximated as spheres, and when effects of non-sphericity are studied it is usually experimentally or via geometrical approximations. New methods for quantifying phytoplankton size and shape generally, so all phytoplankton are analyzable by the same procedure, can complement advances in microscopic imagery and automated classification to study the influence of shape in phytoplankton. Here we apply to phytoplankton a technique for defining the size of arbitrary shapes based on the Laplacian—the operator that governs processes, such as nutrient uptake and fluid flow, where phytoplankton shape is expected to have the greatest effect. Deviations from values given by spherical approximation are a measure of phytoplankton shape and indicate the fitness increases for phytoplankton conferred by their non-spherical shapes. Comparison with surface-to-volume quotients suggests the Laplacian-based metric is insensitive to small-scale features which can increase surface area without affecting key processes, but is otherwise closely related to surface-area-to-volume, demonstrating this metric is a meaningful measure. While our analysis herein is limited to axisymmetric phytoplankton due to relative sparsity of 3D information about other phytoplankton shapes, the definition and method are directly generalizable to 3D shape data, which will in the near future be more readily available.

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Acknowledgements

It is a pleasure to thank Heidi Sosik, Lee Karp-Boss, and Emmanuel Boss for invaluable feedback. This research was primarily funded through National Science Foundation Awards EPS-1208732 and OCE-1315201. This study was also supported by National Science Foundation Graduate Research Fellowship Program (Grant No. 2388357).

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Correspondence to B. B. Cael.

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Cael, B.B., Strong, C. A Laplacian characterization of phytoplankton shape. J. Math. Biol. 76, 1327–1338 (2018). https://doi.org/10.1007/s00285-017-1176-8

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Keywords

  • Phytoplankton
  • Shape
  • Size
  • Laplace’s equation

Mathematics Subject Classification

  • 92B05
  • 35J05
  • 00A69