Abstract
We consider a closed Nutrient-Phytoplankton-Zooplankton (NPZ) model that allows for a delay in the nutrient recycling. A delay-dependent conservation law allows us to quantify the total biomass in the system. With this, we can investigate how a planktonic ecosystem is affected by the quantity of biomass it contains and by the properties of the delay distribution. The quantity of biomass and the length of the delay play a significant role in determining the existence of equilibrium solutions, since a sufficiently small amount of biomass or a long enough delay can lead to the extinction of a species. Furthermore, the quantity of biomass and length of delay are important since a small change in either can change the stability of an equilibrium solution. We explore these effects for a variety of delay distributions using both analytical and numerical techniques, and verify these results with simulations.
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Notes
In the case where the delay distribution extends infinitely into the past, the delay distribution must be approximated by a truncated version for simulation purposes.
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Acknowledgments
The authors gratefully acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada. M.K. also gratefully acknowledges financial support from the Ontario Graduate Scholarship Program.
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Kloosterman, M., Campbell, S.A. & Poulin, F.J. A closed NPZ model with delayed nutrient recycling. J. Math. Biol. 68, 815–850 (2014). https://doi.org/10.1007/s00285-013-0646-x
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DOI: https://doi.org/10.1007/s00285-013-0646-x