Stochastic modeling of phytoplankton allelopathy

Partha Sarathi Mandal, Linda J.S. Allen, Malay Banerjee

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

The study of dynamic interactions between two competing phytoplankton species in the presence of toxic substances is an active field of research due to the global increase of harmful phytoplankton blooms. Ordinary differential equation models for two competing phytoplankton species, when one or both the species liberate toxic substances, are unable to capture the oscillatory and highly variable growth of phytoplankton populations. The deterministic formulation never predicts the sudden localized extinction of certain species. These obstacles of mathematical modeling can be overcome if we include stochastic variability in our modeling approach. In this investigation, we construct stochastic models of allelopathic interactions between two competing phytoplankton species as a continuous time Markov chain model as well as an ItÔ stochastic differential equation model. Approximate extinction probabilities for both species are obtained analytically for the continuous time Markov chain model. Analytical estimates are validated with the help of numerical simulations.

Original languageEnglish
Pages (from-to)1583-1596
Number of pages14
JournalApplied Mathematical Modelling
Volume38
Issue number5-6
DOIs
StatePublished - 2014

Keywords

  • Allelopathy
  • Phytoplankton
  • Stochastic model

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