Vertical mixing and hysteresis in the competition of buoyant and non-buoyant plankton prey species in a shallow lake

• Vertical movement and mixing of different plankton species is modeled in a system of ordinary differential equations.
• Hysteresis is possible for a certain range of parameters.
• Introducing a grazing predator, the system exhibits different dynamics depending on the strength of mixing.
• A spatially extended model with horizontal dynamics shows additional dynamical possibilities if vertical mixing differs horizontally.

Some plankton species like cyanobacteria have an advantage in the competition for light in comparison to other species because of their buoyancy. This advantage can be diminished by vertical mixing in the surrounding water column. We introduce a non-spatial model, based on ordinary differential equations, which accounts for this effect. The main aim is to show that vertical mixing influences the outcome of competition between different species. Hysteresis is possible for a certain range of parameters. Introducing a grazing predator, the system exhibits different dynamics depending on the strength of mixing. In a diffusively coupled horizontal spatial model, local vertical mixing can also have a global effect on the biological system, for instance, destabilization of a locally stable solution, or the generation of new spatiotemporal behavior.