Dynamics of two phytoplankton populations under predation

Jean-Jacques Kengwoung-Keumo

doi:10.3934/mbe.2014.11.1319

Article Contents

2014, Volume 11, Issue 6: 1319-1336. Doi: 10.3934/mbe.2014.11.1319

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Dynamics of two phytoplankton populations under predation

Jean-Jacques Kengwoung-Keumo^1,

1.
Department of Mathematical Sciences, Cameron University, 2800 West Gore Boulevard, Lawton, OK 73505

Received: December 2013

Revised: May 2014

Published: September 2014

Abstract / Introduction Related Papers Cited by

Abstract

The aim of this paper is to investigate the manner in which predation and single-nutrient competition affect the dynamics of a non-toxic and a toxic phytoplankton species in a homogeneous environment (such as a chemostat). We allow for the possibility that both species serve as prey for an herbivorous zooplankton species. We assume that the toxic phytoplankton species produces toxins that affect only its own growth (autotoxicity). The autotoxicity assumption is ecologically explained by the fact that the toxin-producing phytoplankton is not mature enough to produce toxins that will affect the growth of its nontoxic competitor. We show that, in the absence of phytotoxic interactions and nutrient recycling, our model exhibits uniform persistence. The removal rates are distinct and we use general response functions. Finally, numerical simulations are carried out to show consistency with theoretical analysis. Our model has similarities with other food-chain models. As such, our results may be relevant to a wider spectrum of population models, not just those focused on plankton. Some open problems are discussed at the end of this paper.

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Mathematics Subject Classification: 91B74, 97M10, 62P12.

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