Phytoplankton use light for photosynthesis, and the light fluxdecreases with depth. As a result of this simple light-dependence,reaction-advection-diffusion models describing the dynamics ofphytoplankton species contain an integral over depth. That is, models thatsimulate phytoplankton dynamics in relation to mixing processes generallyhave the form of an integro-partial differential equation (integro-PDE).Integro-PDEs are computationally more demanding than standard PDEs. Here,we outline a reliable and efficient technique for numerical simulation ofintegro-PDEs. The simulation technique is illustrated with several exampleson the population dynamics of sinking phytoplankton, a species group thatis most relevant in the context of the global carbon cycle. Our resultsconfirm recent findings that Sverdrup's critical-depth theory breaks downif turbulent mixing is reduced below a critical turbulence. We thereforeconclude that models that do not carefully consider the population dynamicsof phytoplankton in relation to the turbulence structure of the watercolumn may easily lead to erroneous predictions.

Model Development (acm I.6.5), LIFE AND MEDICAL SCIENCES (acm J.3), Ordinary Differential Equations (acm G.1.7), Partial Differential Equations (acm G.1.8)
Population dynamics (general) (msc 92D25), Method of lines (msc 65M20)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Huisman, J, & Sommeijer, B.P. (2002). Simulation techniques for the population dynamics of sinking phytoplankton in light-limited environments. Modelling, Analysis and Simulation [MAS]. CWI.