Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Parameter identification and sensitivity analysis for a phytoplankton competition model


Authors: Thomas Stojsavljevic, Gabriella Pinter, Istvan Lauko and Nicholas Myers
Journal: Quart. Appl. Math.
MSC (2010): Primary 35Q92, 35R30, 49K40
DOI: https://doi.org/10.1090/qam/1514
Published electronically: August 28, 2018
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Abstract: Phytoplankton live in a complex environment with two essential resources, light and nutrients, forming various gradients. Light supplied from above is never homogeneously distributed in a body of water due to refraction and absorption from biomass present in the ecosystem and other sources. Nutrients in turn are typically supplied from below mixed-up by diffusion from the benthic region. Here we present a model of two phytoplankton species competing in a deep freshwater lake for light and two nutrients, one of which is assumed to be preferred. The model is comprised of a system of non-
linear, non-local partial differential equations with appropriate boundary conditions. The parameter space of the model is analyzed for parameter identifiability - the ability for a parameter's true value to be recovered through optimization, and for global sensitivity - the influence a parameter has on model response. The results of these analyses are interpreted within their biological context.


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Additional Information

Thomas Stojsavljevic
Affiliation: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O.Box 413, Milwaukee, WI 53201-0413
Email: tgs@uwm.edu

Gabriella Pinter
Affiliation: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O.Box 413, Milwaukee, WI 53201-0413
Email: gapinter@uwm.edu

Istvan Lauko
Affiliation: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O.Box 413, Milwaukee, WI 53201-0413
Email: iglauko@uwm.edu

Nicholas Myers
Affiliation: Department of Mathematics, NC State University, P.O.Box 8205, Raleigh, NC 27695
Email: nmyers2@ncsu.edu

DOI: https://doi.org/10.1090/qam/1514
Received by editor(s): September 20, 2017
Published electronically: August 28, 2018
Additional Notes: This research was supported in part by the National Science Foundation, UBM-Institutional grant: DUE-1129056.
Article copyright: © Copyright 2018 Brown University

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