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Marine Ecology Progress Series

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MEPS 640:63-77 (2020)  -  DOI: https://doi.org/10.3354/meps13237

Empirically based minimalistic model for representing seasonal phytoplankton dynamics

Sofia H. Piltz1,2,3,*, Poul G. Hjorth2, Øystein Varpe4,5,6

1National Institute of Aquatic Resources, Technical University of Denmark, Kemitorvet, Bygning 202, 2800 Kongens Lyngby, Denmark
2Department of Applied Mathematics and Computer Science, Technical University of Denmark, Asmussens allé Bygning 303B, 2800 Kongens Lyngby, Denmark
3Department of Mathematics, University of Michigan, East Hall room 2074, 530 Church Street, Ann Arbor, Michigan 48109-1043, USA
4Department of Arctic Biology, University Centre in Svalbard, 9171 Longyearbyen, Norway
5Akvaplan-niva, Fram Centre, 9296 Tromsø, Norway
6Present address: Department of Biological Sciences, University of Bergen, 5020 Bergen, Norway
*Corresponding author:

ABSTRACT: Supported by chl a satellite data in the North Atlantic (and phytoplankton division rates computed from that data), the disturbance-recovery hypothesis for the initiation of phytoplankton blooms posits that the change in chl a concentration is proportional to the relative change in the phytoplankton division rate. We used this hypothesis, introduced by Behrenfeld, as a principal model assumption and constructed a non-autonomous ordinary differential equation model for seasonally varying chl a concentrations. Our quantitative comparison between model simulations and in situ measurements of chl a and primary production collected from a Swedish fjord was 2-fold: first, using approximate Bayesian computations, we found distributions of values for the 3 model parameters that best described the chl a data. Then, we validated our model by comparing the simulated (not fitted) division rate to the division rate determined from the data. Our minimalistic model was able to capture (1) the yearly trend in the chl a concentration, (2) the pattern of growth and decline in the phytoplankton division rate, and (3) the decreasing trend in the relative change of the division rate exhibited in the data for several individual years. Moreover, the modeling efficiency was positive (between 0.3 and 0.9 with an average of 0.63) for all 11 yr included in this study. We conclude that the change in chl a concentration being proportional to the relative change in the division rate is a possible explanation for the bloom dynamics in the Gullmar fjord. In addition, our work provides a simple and empirically based differential equation for representing yearly dynamics of primary production, e.g. for generating ecological hypotheses using models of other trophic levels.


KEY WORDS: Non-autonomous ordinary differential equations · Primary production · Chlorophyll a · Division rate · Gullmar fjord · Approximate Bayesian computation inference


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Cite this article as: Piltz SH, Hjorth PG, Varpe Ø (2020) Empirically based minimalistic model for representing seasonal phytoplankton dynamics. Mar Ecol Prog Ser 640:63-77. https://doi.org/10.3354/meps13237

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