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JPR Advance Access published online on April 19, 2005
Journal of Plankton Research, doi:10.1093/plankt/fbi016
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© The Author 2005. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oupjournals.org
Received October 11, 2004
Accepted March 29, 2005

Article

Non-Linear Dynamics of a Pelagic Ecosystem Model with Multiple Predator and Prey Types

Georgina A. Gibson 1*, David L. Musgrave 2, and Sarah Hinckley 3

1 School of Fisheries and Ocean Science, University of Alaska Fairbanks, Fairbanks, AK 99775-7220, U.S.A.
2 Institute of Marine Science, University of Alaska Fairbanks, Fairbanks, AK 99775-7220, U.S.A.
3 NOAA, National Marine Fisheries Service, Alaska Fisheries Science Center, 7600 Sand Point Way, NE Seattle, WA 98115, U.S.A.

* To whom correspondence should be addressed.
Georgina A. Gibson, E-mail: george{at}ims.uaf.edu


  Abstract

Nutrient-Phytoplankton-Zooplankton model in which zooplankton grazed on a mixed prey field. Five alternative functional forms were implemented to describe zooplankton grazing, and the form for predation on mesozooplankton was prescribed by a product of a specific predation rate (h) and the mesozooplankton concentration raised to a power (q) which we varied between one and two. With all five grazing functions, Hopf bifurcations, where the form of the solution transitioned between steady equilibrium and periodic limit cycles, persisted across the q-h parameter space. Regardless of the values of h and q, with some forms of the grazing function we were unable to find steady equilibrium solutions that simultaneously comprised non-zero concentrations for all six model components. Extensions of Michaelis-Menten-based single resource grazing formulations to multiple resources resulted in periodic solutions for a large portion of the q-h space. Conversely, extensions of the sigmoidal grazing formulation to multiple resources resulted in steady solutions for a large portion of q-h parameter space. Our results demonstrate the consequences of the functional form of biological processes on the form of the model solutions. Both the steady/oscillatory nature of state variable concentrations and the likelihood of their elimination are important considerations for ecosystem modelling studies, particularly when attempting to model an ecosystem in which multiple phytoplankton and zooplankton components are thought to persist simultaneously for at least a portion of the seasonal cycle.


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