Dynamics of the 'echo' effect in a phytoplankton system with nitrogen fixation

Khalid Boushaba, Mercedes Pascual

Research output: Contribution to journalArticlepeer-review


Consideration of nitrogen fixation adds a positive nonlinear feedback to plankton ecosystem models. We investigate the consequences of this feedback for secondary phytoplankton blooms and the response of phytoplankton dynamics to physical forcing. The dynamics of phytoplankton, Trichodesmium (the nitrogen fixer), and nutrients is modeled with a system of three differential equations. The model includes two types of nonlinear interactions: the competition of phytoplankton and Trichodesmium for light, and the positive feedback resulting from Trichodesmium recycling. A typical simulation of the model in time, with forcing by a varying mixed-layer depth, reveals a clear successional sequence including a secondary or 'echo' bloom of the phytoplankton. We explain this sequence of events through the stability analysis of three different steady states of the model. Our analysis shows the existence of a critical biological parameter, the ratio of normalized growth rates, determining the occurrence of 'echo' blooms and the specific sequence of events following a physical perturbation. The interplay of positive and negative feedbacks appears essential to the timing and the type of events following such a perturbation.

Original languageEnglish (US)
Pages (from-to)487-507
Number of pages21
JournalBulletin of Mathematical Biology
Issue number3
StatePublished - May 2005

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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