A Laplacian characterization of phytoplankton shape
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Author(s)
Strong, Courtenay
Barry, Brendan C.
Date Issued
September 2017
Journal
Journal of Mathematical Biology
Publisher
Springer Berlin Heidelberg
Citation
Cael, B. B., and Courtenay Strong. “A Laplacian Characterization of Phytoplankton Shape.” Journal of Mathematical Biology, vol. 76, no. 6, May 2018, pp. 1327–38.
Version
Author's final manuscript
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. Keywords: Phytoplankton, Shape, Size, Laplace’s equation
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00285-017-1176-8
