Population dynamics of sinking phytoplankton in light-limited environments: simulation techniques and critical parameters

Phytoplankton use light for photosynthesis, and the light flux decreases with depth. As a result of this simple light dependence, reaction-advection-diffusion models describing the dynamics of phytoplankton species contain an integral over depth. That is, models that simulate phytoplankton dynamics in relation to mixing processes generally have 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 of integro-PDEs. The simulation technique is illustrated by several examples on the population dynamics of sinking phytoplankton, using both single-species models and competition models with several phytoplankton species. Our results confirm recent findings that Sverdrupʹs critical-depth theory breaks down if turbulent mixing is reduced below a critical turbulence. In fact, our results show that suitable conditions for bloom development of sinking phytoplankton depend on a number of critical parameters, including a minimal depth of the thermocline, a maximal depth of the thermocline, a minimal turbulence, and a maximal turbulence. We therefore conclude that models that do not carefully consider the population dynamics of phytoplankton in relation to the turbulence structure of the water column may easily lead to erroneous predictions.