title: A closed NPZ model with delayed nutrient recycling.
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.
authors: Department of Applied Mathematics, University of Waterloo, Waterloo, ON,  N2L 3G1, Canada, mklooste@uwaterloo.ca.
authors: Matt
authors: M
authors: Kloosterman
authors: Sue Ann
authors: SA
authors: Campbell
authors: Francis J
authors: FJ
authors: Poulin
mesh_terms: D000818:Animals; D018533:Biomass; D003198:Computer Simulation; D017753:Ecosystem; D008954:Models, Biological; D010839:Phytoplankton / Q000378:metabolism*; D015048:Zooplankton / Q000378:metabolism*