Patchiness and bistability in the comprehensive cyanobacterial model (CCM)

We analyzed spatiotemporal dynamics of cyanobacteria using a four-component mathematical model with nutrients, unicellular algae, colonial algae and herbivorous zooplankton. One of the astonishing abilities of cyanobacteria is the morphological change from the unicellular type to the colonial or filamentous type in response to grazing activities of zooplankton, the phenomenon known as phenotypic plasticity. Our model, referred to as comprehensive cyanobacterial model (CCM), includes the effects of phenotypic plasticity. Depending on parameter values, CCM exhibits not only bistability but also limit cycle oscillations without showing the paradox of enrichment, which has been a controversy among mathematical ecologists. Further, CCM is modified to reaction–advection–diffusion equations, the simulation results of which indicate that the ratio of the lateral diffusivity to the turbulent velocity significantly affects the appearance of patchiness patterns.