Catastrophic Transition in Vertical Distributions of Phytoplankton: Alternative Equilibria in a Water Column

Abstract

We showed a catastrophic transition between a surface maximum pattern and a subsurface maximum pattern of phytoplankton in a water column by a mathematical model considering the vertical distribution of phytoplankton and two resources, light and a limiting nutrient. In our model, we assumed that a water column consists of two layers: a complete mixing layer above a seasonal thermocline and an incomplete mixing layer below it. From numerical calculation of the model, we obtained that there are two stable vertical patterns of phytoplankton over a certain range of parameters of the model: a pattern having its maximum below the thermocline and another having its maximum above the thermocline. As other models having multiple stable equilibria, our model also exhibits a hysteresis effect and catastrophic transition when one of the parameters of the model changes continuously. These results indicate the possibility of the existence of alternative equilibria of vertical patterns of phytoplankton even if the trophic status and physical condition of the water column are similar. Moreover, the catastrophic transition between the steady states suggests one of the possible mechanisms of autumn algal blooms.