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The study of planktonic ecosystems is important as they make up the bottomtrophic levels of aquatic food webs. We study a closedNutrient-Phytoplankton-Zooplankton (NPZ) model that includes size structure inthe juvenile zooplankton. The closed nature of the system allows theformulation of a conservation law of biomass that governs the system. The modelconsists of a system of nonlinear ordinary differential equation coupled to apartial differential equation. We are able to transform this system into asystem of delay differential equations where the delay is of threshold type andis state-dependent. The system of delay differential equations can be furthertransformed into one with fixed delay. Using the different forms of the modelwe perform a qualitative analysis of the solutions, which includes studyingexistence and uniqueness, positivity and boundedness, local and globalstability, and conditions for extinction. Key parameters that are explored arethe total biomass in the system and the maturity level at which the juvenilezooplankton reach maturity. Numerical simulations are also performed to verifyour analytical results.

An NPZ Model with State-Dependent Delay due to Size-Structure in Juvenile Zooplankton